ACS Publications. Most Trusted. Most Cited. Most Read
Dynamic Control of Topological Charge of Vector Vortex in PCSELs with C6 Symmetry
More

OR SEARCH CITATIONS

My Activity
Publications

Figure 1Loading Img
Download Hi-Res ImageDownload to MS-PowerPointCite This:ACS Photonics 2023, 10, 12, 4112-4120
  • Open Access
Article

Dynamic Control of Topological Charge of Vector Vortex in PCSELs with C6 Symmetry
Click to copy article linkArticle link copied!

Open PDFSupporting Information (1)

ACS Photonics

Cite this: ACS Photonics 2023, 10, 12, 4112–4120
Click to copy citationCitation copied!
https://doi.org/10.1021/acsphotonics.3c00561
Published November 28, 2023

Copyright © 2023 The Authors. Published by American Chemical Society. This publication is licensed under

CC-BY 4.0 .

Abstract

Click to copy section linkSection link copied!
High Resolution Image
Download MS PowerPoint Slide

Vortex beams offer significant potential for various applications in fields such as communication, quantum computing, and particle manipulation. Typically, these beams are generated by using laser light that passes through a passive phase modulation component. In recent years, there has been an increasing emphasis on miniaturizing and integrating the vortex beam light source, aimed at expanding the range of applications. Our study contributes to this goal by presenting a novel method for directly generating vector vortex beams from photonic crystal surface emitting lasers while preserving C6 rotation symmetry. Our approach achieves topological charges of both +1 and −2, and we demonstrate the ability to dynamically switch between these orders by adjusting the injection conditions.

This publication is licensed under

CC-BY 4.0 .
  • cc licence
  • by licence
Copyright © 2023 The Authors. Published by American Chemical Society

Subjects

what are subjects

Keywords

what are keywords

Introduction

Click to copy section linkSection link copied!
Over the past three decades, significant fundamental studies on vortices have been carried out, and vortex beams have become one of the most important light sources today. A vortex beam (VB) is a type of light that possesses a helical phase front, which corresponds to the orbital angular momentum (OAM) of photons in quantum terms. (1−3) The OAM provides a new dimension of light and has promising applications in many fields. For instance, in optical communication, OAM multiplexing can be combined with traditional multiplexing methods to further increase channel capacity. (4−6) Moreover, the theoretically unlimited quantum number of OAM enables infinite bits to be encoded in a single code unit. (7) In the field of detection, the angular velocity of a rotating body can be obtained by irradiating it with vortex beams and measuring the frequency discrepancy of scattered light caused by the rotating Doppler effect. (8,9) Vortex beams can also transfer OAM to small particles through absorption, which causes the particles to rotate around the optical axis, making vortex beams useful as optical wrenches. (10) Furthermore, the hollow profile of the vortex beam in the transverse direction has led to the discovery of new applications. Optical tweezers, also known as beam-gradient traps, take advantage of the peculiar shape of vortex beams and can trap particles with a lower refractive index than the ambient in the dark core. (11−14) In contrast, optical tweezers that use a Gaussian beam trap particles with a higher refractive index.
In recent years, intensive attention has been focused on the vector vortex beam (VVB). The VVB is a particular class of VB and is characterized by its optical singular center surrounded with an azimuthally twisted polarization. The VVB can be viewed as the superposition of circularly polarized states (which carry spin angular momentum (SAM)) with different OAM values. The spin–orbit nonseparable structure is useful in both classical and quantum fields. Spin-to-orbital angular momentum transfer in nonlinear wave intermixing has been demonstrated with the assistance of the VVB, allowing the information transfer between different degree of freedom of photons. (15) In addition to investigating the entanglement of orbital angular momentum (OAM) and spin angular momentum (SAM) within each vortex vector beam (VVB), research has also explored the entanglement between VVBs, opening up possibilities for various quantum information. (16) On the other hand, the distinct focusing properties of VVBs have also been studied in recent years, leading to various applications. For example, the radially polarized beam can be focused into the so-called “needle beam”, which is known for its longitudinal polarization and extended depth of focus, making it useful in applications such as photolithography and microscopy. (17,18)
Due to the promising characteristics of VVBs, many methods have been proposed. The most straightforward method is spatially modulating the polarization of output beams; this is usually achieved with elements like q-plates, (19−21) spatial light modulators, (22,23) and electro-optic crystals. (24) Beside spatially modifying the polarization, VVBs can also be derived by proper design of laser cavity (25,26) or by superposition of two circularly polarized beams with different handedness and topological charges (TCs). (27−29) However, these methods suffer from issues like bulkiness in size, low damage threshold, or low efficiency, limiting their potential applications, such as in consumer electronics or photonic integrated circuits. In recent years, advancements in subwavelength structure technology have led to the emergence of metasurfaces as a new tool for generating vector vortex beams (VVBs). Metasurfaces are able to manipulate the phase and amplitude of light with small size and high efficiency, allowing for the creation of complex wavefronts that can generate VVBs. Compared to traditional methods, using metasurfaces to generate VVBs offers advantages such as higher efficiency and a smaller footprint. (30−39) In addition to metasurfaces, other techniques have also been investigated for generating VVBs. One such method involves the direct generation of VVBs from light sources, which has been achieved through the integration of metasurfaces and vertical-cavity surface-emitting lasers (VCSELs) by Fu et al. (40) Similarly, Cai et al. utilized an angular grating on a ring oscillator to extract light with OAM, resulting in a miniaturized architecture for generating VVBs that can fit within a single chip. (41) However, while metasurfaces and gratings can produce beams with specific OAM values, situations may arise in which it is necessary to adjust the OAM of the resulting beams. Therefore, relying solely on fixed OAM outputs may not always be practical.
Research in the field of photonic crystal (PC) structures has focused on exploring the topological nature of optical bound states in the continuum (BICs). These BICs have been identified as the vortex centers in the polarization direction of far-field radiation. (42,43) Experimental demonstrations have successfully showcased these features in photonic crystal slabs through optical or electrical pumping, and they are regarded as good candidates of VVB sources. (44−50) While VVBs show great promise, significant interest is put on the dynamic switching of the topological charge. Huang et al., in their research, (48) put forth a proposal involving the alteration of the imaginary part of the refractive index, effectively disrupting the symmetries of the structure through control of the optical pumping area. On a different front, Cai et al. delved into the realm of phase-change materials, employing them to enable local dynamic control of the transmission phase for both right-circularly polarized (RCP) and left-circularly polarized (LCP) metasurface components. (49) Additionally, Tian et al. harnessed the phase-change properties of perovskites to successfully switch exciting modes. In this study, we focus on PC structures that preserve C6 symmetry, as these structures exhibit more allowed topological charges (TCs). (50) We investigate the photonic band edge modes that are correlated with these TCs for our room temperature operated PCSELs with honeycomb and triangular lattices of the PC structures, respectively. After that, we explore the possibility of dynamic tuning of TCs. As the TCs are different among modes, the switching of TCs can be realized with lasing mode control. Specifically, we achieve mode switching by carefully regulating the junction temperature of the device through controlled injection conditions. It is noteworthy that all the previous TC switching investigations have been optically pumped, but in this study, we achieve dynamic switching within an electrically pumped semiconductor for the first time. This breakthrough represents a significant advancement in the field of PC structures and opens up new possibilities for practical applications in optoelectronic devices.

Methods

Click to copy section linkSection link copied!

Simple Derivation of Allowed Topological Charge in Different Symmetry Systems

As indicated in Figure 1, symmetry representations A and B are the Mulliken symbols, which stand for symmetric and antisymmetric polarization with respect to rotation around the principal rotation axis. In systems having a certain rotation symmetry R and without degenerate bands, the polarization vector at the transformed k point is equal to ±Rc(k), the transformed polarization vector at the k point multiplied with +1 or −1, as proven in ref (42). Figure 1 shows how the polarization of vector vortex beams of A and B representation twists around the vortex center. For example, in systems with C4 rotation symmetry, the polarization direction rotates ±90° as it goes from the right side (green arrow) to the upper side (red/blue arrow for A/B representation) of the vortex center. In the A representation, the vector could rotate 90 + 360n degrees, where n is the integer and 360n represents multiple 360° rotations of polarization vector. Therefore, the total twist number in a round trip around the vortex center, also known as the allowed TCs, may be 1 + 4n. In contrast, the polarization vector of B representation may rotate −90 + 360n degrees, resulting in allowed TCs of −1 + 4n. On the other hand, the possible charges in the C6 symmetry system are 1 + 6n or −2 + 6n, corresponding to A and B representations. Table 1 shows the allowed TCs for systems with different rotation symmetry. It is worth noting that the C3 symmetry system does not possess B symmetry representation because it cannot come back to the original vector after transformation of odd number times.
Table 1. Allowed Topological Charges for Systems with Different Rotation Symmetry
SymmetriesRepresentationAllowed charges
C2A1 + 2n
 B0 + 2n
C3A1 + 3n
C4A1 + 4n
 B–1 + 4n
C6A1 + 6n
 B–2 + 6n

Figure 1

Figure 1. Figure showing how the polarization vector twists around the vortex center in A and B representations.

High Resolution Image
Download MS PowerPoint Slide

Simulation Method of Polarization Vectors

The laser emissions of PCSELs with hexagonal and honeycomb lattices which preserve C6 symmetry were investigated in our study, allowing two of the lowest TCs of +1 and −2 (n = 0). We began with evaluating the TC of the first six photonic bands through analyzing the polarization vectors in the k space. Our calculation of polarization vectors assumes an infinite device size, which overlooks the impact of the field envelope. Additionally, we simplify the model by using the effective index of the transverse mode (the mode in the epitaxial direction) to substitute for the actual 3D PCSEL structure. By applying Bloch’s theorem, the electric field in a 2D photonic crystal at a resonance can be expressed in the Bloch form Ek(r, z) = eik·ruk(r, z), which is the product of a plane wave and a periodic function. k represents the in-plane wavevector, and r represents the in-plane position vector (bold font is used to represent vectors). The resonances above the light line can radiate to free space in the direction corresponding to their in-plane wavevectors, and the electric field at the far field is proportional to the integral of uk over the near field. In general, the periodic function uk can be expanded into the Fourier series. As the integration range becomes large enough, only the zeroth order term counts. Hence, the polarization vector c(k) = cx(k)x̂ + cy(k)ŷ can be obtained from the zeroth order term of the x- and y-components of uk. We use the plane-wave expansion method (PWEM) to solve the governed equation:
1εr(∇+ik)×(∇+ik)×uk=k02uk
where εr is dielectric constant of the simplified 2D structure. To prevent the convergence problem caused from truncation of the Fourier series, an effective tensor is used to smooth the dielectric function. (28) The orders of the Fourier series are taken from −11 to +11 in the calculation, which is large enough to get acceptable solutions. (51−53) In the C2T system (T refers to time reversal symmetry), cx and cy are proven to be in-phase, (42) this indicates linear polarization at far field. The BIC arises at the specific k-point where both cx and cy accidentally become zero, and the topology of this BIC can be deduced by examining the polarization’s twist number around that point. The evolution of the polarization direction in k space of the lowest six bands is presented in Figure S1 of Supporting Information.

Device Fabrication

PCSEL devices were fabricated according to our simulation targeting the lasing mode with TC values of +1 and −2. The lasing wavelength is at around 940 nm, aligning with the gain peak of the active layer. The schematic of our PCSEL structure is shown in Figure 2(a). The PCSELs were fabricated on the epitaxial wafer grown on the n-type GaAs substrate by metal organic chemical vapor deposition (MOCVD) in sequence of a graded index (GRIN) n-Al0.1–0.4Ga0.9–0.6As layer, a n-Al0.4Ga0.6As cladding layer, a n-GaAs separate confinement heterostructure (SCH) layer, an active region containing 3 pairs of InGaAs/GaAs multi quantum wells (MQWs), a p-GaAs SCH layer, a p-Al0.4Ga0.6As cladding layer, a GRIN p-Al0.4–0.1Ga0.6–0.9As layer, and a p+-GaAs contact layer. The PC structures of area 140 × 140 μm2 consisting of periodic air holes were fabricated in the top three layers through e-beam lithography and a dry etching process. The etching depth was approximately 250 nm. After the PC structure formed on the epitaxial wafer, a 250-nm-thick ITO cladding layer was deposited by the electron beam (E-gun) evaporator to serve as cladding layer and current conducting layer. (54) The p-type and n-type conducting metals were deposited on ITO and the back side of the substrate, respectively, to finish the device process. An aperture was preserved on the p-type metal for output. The top view of the optical microscope (OM) image of the actual device is shown in Figure 2(b). The diameters of the aperture, PC region, ITO cladding, and mesa are 120, 125, 210, and 260 μm, respectively. The top views of the PC lattices are shown in Figures 2(c) and 2(d), corresponding to hexagonal and honeycomb lattices. The honeycomb lattice is a special case of a hexagonal lattice with a two-hole basis. For each type of lattice, we design 3 different lattice constants for comparison. The designed lattice constants of the honeycomb lattice are 318.7, 320.7, and 322.7 nm, while they are 318, 319, and 320 nm for the hexagonal lattice. The filling factor, defined as the area ratio of the air hole, is 0.09 and 0.05 for the honeycomb and hexagonal lattices, respectively.

Figure 2

Figure 2. PCSEL structure and images of the device. (a) Schematic diagram of the designed PCSEL structure. The laser structure is mainly composed of an active layer, two SCH layers, two cladding layers, and a PC region. ITO layer is cladded on a PC for protection and current spreading purposes. (b) Top view of the OM image of the actual device. The diameters of the aperture, PC region, ITO cladding, and mesa are 120, 125, 210, and 260 μm, respectively. (c and d) Top-view SEM images of the PC structure with honeycomb (c) and hexagonal lattices (d). The black regions are etching holes that are expected to remain unfilled after ITO deposition.

High Resolution Image
Download MS PowerPoint Slide

Results and Discussion

Click to copy section linkSection link copied!
The L–I–V characteristics and lasing spectra of the PCSELs are depicted in Figure 3. The measurements were conducted in the pulse mode with a pulse duration of 1 μs and duty cycle of 0.1%. All the samples show similar I–V characteristics with a turn-on voltage of about 1.25 V and a serial resistance of about 2 ohms. The threshold currents of PCSELs with honeycomb lattices (Hon-PCSELs) and PCSELs with hexagonal lattices (Hex-PCSELs) are around 130 and 60 mA, respectively. The close threshold current of PCSELs with different lattice constants can be attributed to the relatively flat gain peak near these lasing wavelengths. The higher threshold current in Hon-PCSELs is attributed to the cancellation of in-plane feedback of the two-hole basis in the honeycomb lattice and larger radiation loss from the stronger first-order diffraction. Slope efficiencies range from 0.146 to 0.180 W/A in the honeycomb lattice and 0.125 to 0.130 W/A in the hexagonal lattice. The slope efficiencies of PCSELs with different lattice constants are thought to be similar because of the same filling factor of PC and thus the same components of optical loss. The deviation may come from the fabrication process and gain mode offset. The obvious higher slope efficiency in the honeycomb lattice is related to the larger radiation loss ratio. The lasing wavelengths are near the design at 940 nm and increase with respect to the lattice constant at a ratio of about 3.

Figure 3

Figure 3. L–I–V characteristics and spectra. (a, b) Measured L–I–V curves of Hon-PCSEL (a) and Hex-PCSEL (b) under pulsed electrical pumping. The different line styles stand for different PC lattice constants. (c and d) Measured emission spectra of Hon-PCSEL (c) and Hex-PCSEL (d). The different colors stand for different PC lattice constants. The maximum intensity has been normalized to the same value.

High Resolution Image
Download MS PowerPoint Slide
We have identified the lasing mode through comparison of the measured band diagram, lasing spectra, and calculated photonic band diagram, as shown in Figure 4. The band diagram can be measured by conducting angle-resolved electroluminescence (AREL) measurements of spectra below the lasing threshold. Here we scan along the Γ-M direction. The scattered points are the band calculated by the PWEM. The lasing modes in our devices are expected to exhibit TE polarization, which refers to the oscillation modes in which the electric field is predominantly parallel to the epitaxial layer. This judgment is attributed to the significant enhancement of the TE mode when subjected to in-plane compressive strain in InGaAs MQWs. Therefore, our discussion will focus on the TE modes due to their favorable response to the applied strain. At the frequency near Γ, there exist six modes for TE polarization, owing to the C6 symmetry. We define the modes from low to high frequency as A ∼ F modes. It is important to mention that the A/B mode described here should not be confused with the A/B representation above. In Hon-PCSELs with lattice constants of 318.7 and 320.7 nm (not shown in the figure), the lasing occurred near the E and F modes. In contrast, the lasing of Hon-PCSEL with lattice constant of 322.7 nm occurred near the A ∼ D modes.

Figure 4

Figure 4. AREL spectra below (left) and above (right) the lasing threshold of (a) Hon-PCSELs with a lattice constant of 318.7 nm, (b) Hon-PCSELs with a lattice constant of 322.7 nm, (c) Hex-PCSELs with a lattice constant of 318 nm, and (d) Hex-PCSELs with a lattice constant of 320 nm. The upper-right inset in (a) is the first Brillouin zone of the reciprocal lattice. The AREL measurements are conducted along the Γ-M direction. The Hon-PCSELs are measured with the pulse duration 1 μs and duty cycle 0.1%, while the Hex-PCSELs are additionally measured with a pulse duration 10 μs above the threshold. The scattered points are the TE and TM photonic bands calculated by the PWEM method. We define the modes with low to high frequencies as the A ∼ F modes.

High Resolution Image
Download MS PowerPoint Slide
On the other hand, in Hex-PCSELs, we found that a third peak appears as the pulse duration increases. The measurement results under 1 and 10 μs are both shown in Figures 4(c) and 4(d) for comparison. The lasing behavior is similar, with different lattice constants in the Hex-PCSEL. There are two peaks at the pulse duration of 1 μs, corresponding to the multipeaks shown in Figure 3(d). The top peak is near the E and F modes, while the second is near the C and D modes. Once the pulse duration is increased to 10 μs, a bottom peak lasing near the A and B modes appears. The comparison of the band diagram and lasing peak offers a rough identification on the lasing mode. In the next part, we will compare their polarization states and verify that the measurement results are consistent with the calculated results.
Figure 5(a) shows the far-field pattern (FFP) of Hon-PCSELs with a lattice constant of 318.7 nm. The pink arrows represent the polarization directions. The measured FFPs with a polarizer oriented along 0° and 90° are shown in the right panel of Figure 5(a). FFPs acquired with the polarizer set at different angles can be found in Figure S2 in the Supporting Information. It should be mentioned, in the case of VBs, that their distinctive feature is the twisting of the phase front, which necessitated an interference experiment for demonstration. (55) On the other hand, VVBs have their uniqueness in the twisting of polarization. In this case, the polarization information along the azimuthal angle offers more direct evidence to confirm the presence of VVBs. The FFPs measured with a polarizer show that the polarization twists two times along the azimuthal angle with the inverse direction of the polarizer, indicating the B representation with a TC of −2. We compare the measured results with the calculation and find it consistent with the TE F mode. The calculated magnitudes of the x- and y-components of the polarization vector (cx and cy) of the TE F mode are shown in Figure 5(b) and 5(c). The black nodal lines represent zero intensity of this component at the k points along the lines. BICs form when both cx and cy become zero. The laser emission around the intersection will form a vector vortex, and the order increases as the number of nodal lines crossing it increases. Figure 5(d) shows the orientation of the electric field, as indicated by its azimuthal angle (in radian) relative to the x-axis. Each 2π variation along the azimuthal angle results in one twist of polarization. The TE F mode shows a TC of −2 and is consistent with the experiment results in both the spectrum and polarization.

Figure 5

Figure 5. Far-field pattern and polarization direction of PCSELs with a honeycomb lattice. (a) Measured FFP of Hon-PCSEL with the lattice constant 318.7 nm. The pink arrows represent the polarization directions. The figures in the right panel depict the measured FFPs with the polarizer oriented along the pink arrows. The TC is identified to be −2. (b and c) The calculated magnitudes of the x- and y-components of the polarization vector of the TE F mode. The black lines represent zero intensity of this component. (d) Orientation of the electric field of the TE F mode at different k points. The orientation is indicated by its azimuthal angle (radian) relative to the x-axis. The TE F mode shows a TC of −2. (e–h) Measured FFP, calculated magnitude, and orientation of electric field for Hon-PCSEL with the lattice constant 322.7 nm. The TC is identified to be +1 and is consistent with the TE A mode in the calculation.

High Resolution Image
Download MS PowerPoint Slide
In contrast, Figure 5(e) shows the FFP of Hon-PCSELs with a lattice constant of 322.7 nm. In this case, the polarization twists only once and is in the same direction as the polarizer, indicating A representation with the TC of +1, which is consistent with the TE A mode in the calculation. Despite some simplifications, the simulation method accurately predicts the behavior of PCSELs and allows for rapid selection of the desired OAM order.
On the other hand, the Hex-PCSEL samples perform the same FFP and polarization with different lattice constants. However, they exhibit different FFP and polarization while the pulse duration is extended. Therefore, we conducted the analysis on different pulse conditions rather than on lattice constants. Figure 6(a) shows the measured emission spectra of Hex-PCSEL (lattice constant of 318 nm) versus different pulse duration conditions, where the repetition rate is fixed at 1 kHz. As the pulse duration increases from 1 to 10 μs, a third mode appears. The mode competition in Hex-PCSELs is believed to be caused by the smaller threshold gain difference, which is supported by the threshold gain simulations as shown in Figure S4 of the Supporting Information. As the pulse duration increases, the junction temperature in the semiconductor laser also rises, causing a red-shift in the gain peak. This shift leads to mode hopping from shorter to longer wavelengths. For further insights into the time-dependent thermal simulation and the associated mode and gain peak shifts, please refer to Figure S6. The information on the full-width at half-maximum (fwhm) of the lasing line width with respect to the pulse duration is shown in Figure 6(b) for reference. As we will clarify later, the two peaks correspond to the TE F and TE B modes. These two modes have different TCs, and switching between them allows for TC control.

Figure 6

Figure 6. (a) measured spectra of Hex-PCSEL with the lattice constant 318 nm under different pulse duration conditions, where the repetition rate is fixed to be 1 kHz. The numbers on the right-hand side represent the ratio of integrated power of the TE B mode relative to the TE F mode. (b) The fwhm of the two main peaks in (a). (c) Spectra measured with the heat plate temperatures 300 and 340 K. The pulse width is fixed to be 200 ns, and the current is ranging from 200 to 500 mA.

High Resolution Image
Download MS PowerPoint Slide
The power ratio between the two modes was found to be approximately 3.1 with a pulse duration of 10 μs. By extending the pulse duration further, the TE B mode can thoroughly dominate the output power. However, due to concerns about potential damage to the metal pad, the pulse duration is currently limited to 10 μs. This limitation can be addressed through the implementation of a suitable metal pad design, which poses no challenges to mature manufacturing technology. To demonstrate the total transition between the two modes, the temperature of the heat plate in contact with the n-metal pad was varied instead. In Figure 6(c), spectra are presented for heat plate temperatures of 300 and 340 K, with current levels ranging from 200 to 500 mA. To mitigate the self-heating effect in the junction, the pulse duration was reduced to 200 ns. The results show a high power ratio between the two modes at both temperatures, indicating that an injection current of 1 A and pulse duration above 15 μs could be enough to achieve a complete mode switching.
In Figures 7(a) and 7(e), we again present the FFPs measured without a polarizer (left panel) and with a polarizer (right panel) corresponding to pulse durations of 1 and 10 μs, respectively. For FFPs measured with other polarizer orientations, please refer to Figure S3 in the Supporting Information. Through the measurements, we observed that the TC was −2 in the 1 μs case but became +1 in the 10 μs case. The measured polarizations were consistent with the simulation results of the TE F and TE B modes, respectively. Remarkably, the modulation of orbital angular momentum (OAM) depended on the current injection condition without the need for any mechanical parts and exhibited a response time on the order of μs. Additionally, by adjusting the design of the photonic crystal geometry and the lasing band, we clearly demonstrated the ability to switch between other OAMs.

Figure 7

Figure 7. (a and e) Measured FFPs of Hex-PCSELs under 1 and 10 μs pulse duration conditions. The figures in the right panel depict the measured FFPs with the polarizer oriented along the pink arrows. The TC is −2 in the 1 μs case, while it becomes +1 in the 10 μs case. (b–e and f–h) Calculation results of the TE F mode and the TE B mode of Hex-PCSELs.

High Resolution Image
Download MS PowerPoint Slide
Moreover, we investigated the PCSEL with C2 symmetry by introducing perturbations on the hexagonal lattice. From the AREL measurement, the lasing peak is identified as the TE E or TE F mode. The measured charge of the resulting output beam is +1 and azimuthally polarized. The decreased charge is a result from the elimination of the double degeneracy of the nodal lines cx and cy at the Γ-point. The TC is invariant to changes in the lattice constant and injection conditions. Breaking the symmetry provides a method for generating a consistent TC. The details of applied perturbation and measurement results are presented in Figure S6.

Conclusion

Click to copy section linkSection link copied!
In conclusion, we have demonstrated the generation and manipulation of vector vortex beams with different TCs using our Hex-PCSELs and Hon-PCSELs, which is in good agreement with our simulation results. Through the experiments, we obtained an in-depth understanding of the generation and manipulation of vortex laser beams via electrically driven PCSELs. Hex-PCSELs exhibit a tendency for their modes to switch, whereas the modes in Hon-PCSELs are comparatively more stable. Our findings provide insights into the topological nature of photonic crystal structures and their potential applications in information processing and other fields that require the manipulation of light beams. Moreover, by fine-tuning the device structure or the driving current, we can manipulate the TCs of the beams, which opens up new possibilities for the development of more sophisticated optical communication systems and other applications. The results obtained from our experiments represent a significant advancement in the field of PCSELs and may pave the way for the development of smaller and more versatile devices.

Data Availability

Click to copy section linkSection link copied!

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Supporting Information

Click to copy section linkSection link copied!

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsphotonics.3c00561.

  • Additional polarization simulation results in k-space, FFP measured with a polarizer, and self-interference measurement results (PDF)

Terms & Conditions

Most electronic Supporting Information files are available without a subscription to ACS Web Editions. Such files may be downloaded by article for research use (if there is a public use license linked to the relevant article, that license may permit other uses). Permission may be obtained from ACS for other uses through requests via the RightsLink permission system: http://pubs.acs.org/page/copyright/permissions.html.

Author Information

Click to copy section linkSection link copied!
  • Corresponding Author
  • Authors
    • Chia-Jui Chang - Department of Photonics, College of Electrical and Computer Engineering, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan;  Orcidhttps://orcid.org/0000-0002-1897-4802
    • Yu-Wen Chen - Department of Photonics, College of Electrical and Computer Engineering, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan
    • Lih-Ren Chen - Department of Photonics, College of Electrical and Computer Engineering, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan;  Orcidhttps://orcid.org/0000-0002-4819-3337
    • Kuo-Bin Hong - Semiconductor Research Center, Hon Hai Research Institute, Taipei City 23678, Taiwan;  Orcidhttps://orcid.org/0000-0001-5027-6273
    • Jhih-Sheng Wu - Department of Photonics, College of Electrical and Computer Engineering, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan
    • Yao-Wei Huang - Department of Photonics, College of Electrical and Computer Engineering, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan;  Orcidhttps://orcid.org/0000-0001-8983-413X
  • Notes
    The authors declare no competing financial interest.

Acknowledgments

Click to copy section linkSection link copied!

This work was financially supported by Taiwan’s National Science and Technology Council under Contract Nos. MOST 110-2221-E-A49-058-MY3 and MOST 110-2622-8-A49-008-SB and partially supported by Hon Hai Research Institute. Y.-W.H. acknowledges support from the Ministry of Science and Technology in Taiwan (Grant No. 110-2112-M-A49-034-MY3) and support from the Ministry of Education in Taiwan under the Yushan Young Scholar Program.

References

Click to copy section linkSection link copied!

This article references 55 other publications.

  1. 1
    Allen, L.; Beijersbergen, M. W.; Spreeuw, R. J.; Woerdman, J. P. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. Phys. Rev. A 1992, 45 (11), 8185,  DOI: 10.1103/PhysRevA.45.8185
    Google Scholar
    1
    Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes
    Allen; Beijersbergen; Spreeuw; Woerdman
    Physical review. A, Atomic, molecular, and optical physics (1992), 45 (11), 8185-8189 ISSN:1050-2947.
    There is no expanded citation for this reference.
  2. 2
    He, H.; Friese, M. E.; Heckenberg, N. R.; Rubinsztein-Dunlop, H. Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity. Phys. Rev. Lett. 1995, 75 (5), 826,  DOI: 10.1103/PhysRevLett.75.826
    Google Scholar
    2
    Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity
    He, H.; Friese, M. E. J.; Heckenberg, N. R.; Rubinsztein-Dunlop, H.
    Physical Review Letters (1995), 75 (5), 826-9CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    Black or reflective particles can be trapped in the dark central min. of a doughnut laser beam produced using a high efficiency computer generated hologram. Such beams carry angular momentum due to the helical wave-front structure assocd. with the central phase singularity even when linearly polarized. Trapped absorptive particles spin due to absorption of this angular momentum transferred from the singularity beam. The direction of spin can be reversed by changing the sign of the singularity.
  3. 3
    Mair, A.; Vaziri, A.; Weihs, G.; Zeilinger, A. Entanglement of the orbital angular momentum states of photons. Nature 2001, 412 (6844), 313– 316,  DOI: 10.1038/35085529
    Google Scholar
    3
    Entanglement of the orbital angular momentum states of photons
    Mair A; Vaziri A; Weihs G; Zeilinger A
    Nature (2001), 412 (6844), 313-6 ISSN:0028-0836.
    Entangled quantum states are not separable, regardless of the spatial separation of their components. This is a manifestation of an aspect of quantum mechanics known as quantum non-locality. An important consequence of this is that the measurement of the state of one particle in a two-particle entangled state defines the state of the second particle instantaneously, whereas neither particle possesses its own well-defined state before the measurement. Experimental realizations of entanglement have hitherto been restricted to two-state quantum systems, involving, for example, the two orthogonal polarization states of photons. Here we demonstrate entanglement involving the spatial modes of the electromagnetic field carrying orbital angular momentum. As these modes can be used to define an infinitely dimensional discrete Hilbert space, this approach provides a practical route to entanglement that involves many orthogonal quantum states, rather than just two Multi-dimensional entangled states could be of considerable importance in the field of quantum information, enabling, for example, more efficient use of communication channels in quantum cryptography.
  4. 4
    Wang, J.; Yang, J. Y.; Fazal, I. M.; Ahmed, N.; Yan, Y.; Huang, H.; Willner, A. E. Terabit free-space data transmission employing orbital angular momentum multiplexing. Nat. Photonics 2012, 6 (7), 488– 496,  DOI: 10.1038/nphoton.2012.138
    Google Scholar
    4
    Terabit free-space data transmission employing orbital angular momentum multiplexing
    Wang, Jian; Yang, Jeng-Yuan; Fazal, Irfan M.; Ahmed, Nisar; Yan, Yan; Huang, Hao; Ren, Yongxiong; Yue, Yang; Dolinar, Samuel; Tur, Moshe; Willner, Alan E.
    Nature Photonics (2012), 6 (7), 488-496CODEN: NPAHBY; ISSN:1749-4885. (Nature Publishing Group)
    The recognition in the 1990s that light beams with a helical phase front have orbital angular momentum has benefited applications ranging from optical manipulation to quantum information processing. Recently, attention has been directed towards the opportunities for harnessing such beams in communications. Here, we demonstrate that four light beams with different values of orbital angular momentum and encoded with 42.8 × 4 Gbit s-1 quadrature amplitude modulation (16-QAM) signals can be multiplexed and demultiplexed, allowing a 1.37 Tbit s-1 aggregated rate and 25.6 bit s-1 Hz-1 spectral efficiency when combined with polarization multiplexing. Moreover, we show scalability in the spatial domain using two groups of concentric rings of eight polarization-multiplexed 20 × 4 Gbit s-1 16-QAM-carrying orbital angular momentum beams, achieving a capacity of 2.56 Tbit s-1 and spectral efficiency of 95.7 bit s-1 Hz-1. We also report data exchange between orbital angular momentum beams encoded with 100 Gbit s-1 differential quadrature phase-shift keying signals. These demonstrations suggest that orbital angular momentum could be a useful degree of freedom for increasing the capacity of free-space communications.
  5. 5
    Gibson, G.; Courtial, J.; Padgett, M. J.; Vasnetsov, M.; Pas’ko, V.; Barnett, S. M.; Franke-Arnold, S. Free-space information transfer using light beams carrying orbital angular momentum. Opt. Express 2004, 12 (22), 5448– 5456,  DOI: 10.1364/OPEX.12.005448
    Google Scholar
    5
    Free-space information transfer using light beams carrying orbital angular momentum
    Gibson Graham; Courtial Johannes; Padgett Miles; Vasnetsov Mikhail; Pas'ko Valeriy; Barnett Stephen; Franke-Arnold Sonja
    Optics express (2004), 12 (22), 5448-56 ISSN:.
    We demonstrate the transfer of information encoded as orbital angular momentum (OAM) states of a light beam. The transmitter and receiver units are based on spatial light modulators, which prepare or measure a laser beam in one of eight pure OAM states. We show that the information encoded in this way is resistant to eavesdropping in the sense that any attempt to sample the beam away from its axis will be subject to an angular restriction and a lateral offset, both of which result in inherent uncertainty in the measurement. This gives an experimental insight into the effects of aperturing and misalignment of the beam on the OAM measurement and demonstrates the uncertainty relationship for OAM.
  6. 6
    Wang, Y.; Zhang, J.; Ren, Y.; Cheng, L.; Zhu, B.; Zhao, Z. Demonstration of high-speed free-space optical communication using orbital angular momentum (OAM) modes. Opt. Commun. 2018, 426, 327– 332
    Google Scholar
    There is no corresponding record for this reference.
  7. 7
    Goyal, S. K.; Roux, F. S.; Forbes, A. Theoretical and experimental study of bit error rate performance of a spatially multiplexed free-space optical communication system using multiple orbital angular momentum modes. Opt. Express 2012, 20 (13), 1405– 1419
    Google Scholar
    There is no corresponding record for this reference.
  8. 8
    Lavery, M. P. J.; Speirits, F. C.; Barnett, S. M.; Padgett, M. J. Detection of a spinning object using light’s orbital angular momentum.. Science 2013, 341 (6145), 537– 540,  DOI: 10.1126/science.1239936
    Google Scholar
    8
    Detection of a Spinning Object Using Light's Orbital Angular Momentum
    Lavery, Martin P. J.; Speirits, Fiona C.; Barnett, Stephen M.; Padgett, Miles J.
    Science (Washington, DC, United States) (2013), 341 (6145), 537-540CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
    The linear Doppler shift is widely used to infer the velocity of approaching objects, but this shift does not detect rotation. By analyzing the orbital angular momentum of the light scattered from a spinning object, we obsd. a frequency shift proportional to product of the rotation frequency of the object and the orbital angular momentum of the light. This rotational frequency shift was still present when the angular momentum vector was parallel to the observation direction. The multiplicative enhancement of the frequency shift may have applications for the remote detection of rotating bodies in both terrestrial and astronomical settings.
  9. 9
    Qiu, S.; Liu, T.; Li, Z.; Wang, C.; Ren, Y.; Shao, Q.; Xing, C. Influence of lateral misalignment on the optical rotational Doppler effect. Appl. Opt. 2019, 58 (10), 2650,  DOI: 10.1364/AO.58.002650
    Google Scholar
    9
    Influence of lateral misalignment on the optical rotational Doppler effect
    Qiu Song; Liu Tong; Li Zhimeng; Wang Chen; Ren Yuan; Shao Qiongling; Xing Chaoyang
    Applied optics (2019), 58 (10), 2650-2655 ISSN:.
    The discovery of the optical rotational Doppler effect associated with orbital angular momentum of light paves a new way to detect the rotational speed of spinning objects. In this paper, we investigate the influence of lateral misalignment, i.e., the distance between the beam axis of a probe light and the rotation axis of a spinning object, on the rotational Doppler effect. First, we analyze the mechanism of the rotational Doppler effect of optical vortices based on the linear Doppler effect. Specifically, we consider the general case where the center of the optical vortex does not coincide with the rotation axis, and deduce the generalized formula of rotational Doppler shift based on a local scattering model. It is found that the bandwidth of the rotational Doppler signal depends proportionally on the amount of lateral misalignment, whereas the value of rotational Doppler shift remains constant. A proof-of-concept experiment is performed, and the measured results agree well with theoretical predictions. These findings may be useful for practical application of the optical rotational Doppler effect in remote sensing and metrology.
  10. 10
    Schmiegelow, C. T.; Schulz, J.; Kaufmann, H.; Ruster, T.; Poschinger, U. G.; Schmidt-Kaler, F. Transfer of optical orbital angular momentum to a bound electron. Nat. Commun. 2016, 7 (1), 129,  DOI: 10.1038/ncomms12998
    Google Scholar
    There is no corresponding record for this reference.
  11. 11
    Grier, D. G. A revolution in optical manipulation. Nature 2003, 424 (6950), 810,  DOI: 10.1038/nature01935
    Google Scholar
    11
    A revolution in optical manipulation
    Grier, David G.
    Nature (London, United Kingdom) (2003), 424 (6950), 810-816CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
    A review. Optical tweezers use the forces exerted by a strongly focused beam of light to trap and move objects ranging in size from tens of nanometers to tens of micrometers. Since their introduction in 1986, the optical tweezer has become an important tool for research in the fields of biol., phys. chem. and soft condensed matter physics. Recent advances promise to take optical tweezers out of the lab. and into the mainstream of manufg. and diagnostics; they may even become consumer products. The next generation of single-beam optical traps offers revolutionary new opportunities for fundamental and applied research.
  12. 12
    Moffitt, J.; Chemla, Y.; Smith, S. B.; Bustamante, C. Recent advances in optical tweezers. Annu. Rev. Biochem. 2008, 77, 205– 2,  DOI: 10.1146/annurev.biochem.77.043007.090225
    Google Scholar
    12
    Recent advances in optical tweezers
    Moffitt, Jeffrey R.; Chemla, Yann R.; Smith, Steven B.; Bustamante, Carlos
    Annual Review of Biochemistry (2008), 77 (), 205-228CODEN: ARBOAW; ISSN:0066-4154. (Annual Reviews Inc.)
    A review. It has been over 20 years since the pioneering work of Arthur Ashkin, and in the intervening years, the field of optical tweezers has grown tremendously. Optical tweezers are now being used in the investigation of an increasing no. of biochem. and biophys. processes, from the basic mech. properties of biol. polymers to the multitude of mol. machines that drive the internal dynamics of the cell. Innovation, however, continues in all areas of instrumentation and technique, with much of this work focusing on the refinement of established methods and on the integration of this tool with other forms of single-mol. manipulation or detection. Although tech. in nature, these developments have important implications for the expanded use of optical tweezers in biochem. research and thus should be of general interest. In this review, we address these recent advances and speculate on possible future developments.
  13. 13
    Ashkin, A.; Dziedzic, J. M. Optical trapping and manipulation of viruses and bacteria. Science 1987, 235 (4795), 1517,  DOI: 10.1126/science.3547653
    Google Scholar
    13
    Optical trapping and manipulation of viruses and bacteria
    Ashkin A; Dziedzic J M
    Science (New York, N.Y.) (1987), 235 (4795), 1517-20 ISSN:0036-8075.
    Optical trapping and manipulation of viruses and bacteria by laser radiation pressure were demonstrated with single-beam gradient traps. Individual tobacco mosaic viruses and dense oriented arrays of viruses were trapped in aqueous solution with no apparent damage using approximately 120 milliwatts of argon laser power. Trapping and manipulation of single live motile bacteria and Escherichia coli bacteria were also demonstrated in a high-resolution microscope at powers of a few milliwatts.
  14. 14
    Ashkin, A.; Dziedzic, J. M.; Bjorkholm, J. E.; Chu, S. Observation of a single-beam gradient force optical trap for dielectric particles. Opt. Lett. 1986, 11 (5), 288– 90,  DOI: 10.1364/OL.11.000288
    Google Scholar
    14
    Observation of a single-beam gradient force optical trap for dielectric particles
    Ashkin, A.; Dziedzic, J. M.; Bjorkholm, J. E.; Chu, Steven
    Optics Letters (1986), 11 (5), 288-90CODEN: OPLEDP; ISSN:0146-9592.
    Optical trapping of dielec. particles by a single-beam gradient force trap was demonstrated. This confirms the concept of neg. light pressure due to the gradient force. Trapping was obsd. over the entire range of particle size ∼25-10,000 nm in H2O. Use of the new trap extends the size range of macroscopic particles accessible to optical trapping and manipulation well into the Rayleigh size regime. Application of this trapping principle to atom trapping is considered.
  15. 15
    Pinheiro da Silva, B.; Buono, W. T.; Pereira, L. J.; Tasca, D. S.; Dechoum, K.; Khoury, A. Z.. Spin to orbital angular momentum transfer in nonlinear wave mixing. Frontiers in Optics; Optica Publishing Group, 2022. (Accessed 2023-10-17).
    Google Scholar
    There is no corresponding record for this reference.
  16. 16
    D'Ambrosio, V.; Carvacho, G.; Graffitti, F.; Vitelli, C.; Piccirillo, B.; Marrucci, L.; Sciarrino, F. Entangled vector vortex beams. Phys. Rev. A 2016, 94 (3), 030304,  DOI: 10.1103/PhysRevA.94.030304
    Google Scholar
    16
    Entangled vector vortex beams
    D'Ambrosio, Vincenzo; Carvacho, Gonzalo; Graffitti, Francesco; Vitelli, Chiara; Piccirillo, Bruno; Marrucci, Lorenzo; Sciarrino, Fabio
    Physical Review A (2016), 94 (3-A), 030304/1-030304/6CODEN: PRAHC3; ISSN:2469-9926. (American Physical Society)
    Light beams having a vectorial field structure, or polarization, that varies over the transverse profile and a central optical singularity are called vector vortex (VV) beams and may exhibit specific properties such as focusing into "light needles" or rotation invariance. VV beams have already found applications in areas ranging from microscopy to metrol., optical trapping, nano-optics, and quantum communication. Individual photons in such beams exhibit a form of single-particle quantum entanglement between different degrees of freedom. On the other hand, the quantum states of two photons can be also entangled with each other. Here, we combine these two concepts and demonstrate the generation of quantum entanglement between two photons that are both in VV states: a form of entanglement between two complex vectorial fields. This result may lead to quantum-enhanced applications of VV beams as well as to quantum information protocols fully exploiting the vectorial features of light.
  17. 17
    Naidoo, D.; Roux, F. S.; Dudley, A.; Litvin, I.; Piccirillo, B.; Marrucci, L.; Forbes, A. Controlled generation of higher-order Poincaré sphere beams from a laser. Nat. Photonics 2016, 10 (5), 327– 332,  DOI: 10.1038/nphoton.2016.37
    Google Scholar
    17
    Controlled generation of higher-order Poincare sphere beams from a laser
    Naidoo, Darryl; Roux, Filippus S.; Dudley, Angela; Litvin, Igor; Piccirillo, Bruno; Marrucci, Lorenzo; Forbes, Andrew
    Nature Photonics (2016), 10 (5), 327-332CODEN: NPAHBY; ISSN:1749-4885. (Nature Publishing Group)
    The angular momentum of light can be described by positions on a higher-order Poincare sphere, where superpositions of spin and orbital angular momentum states give rise to laser beams that have many applications, from microscopy to materials processing. Many techniques exist to create such beams but none so far allow their creation at the source. Here we report on a new class of laser that is able to generate all states on the higher-order Poincare sphere. We exploit geometric phase control inside a laser cavity to map polarization to orbital angular momentum, demonstrating that the orbital angular momentum degeneracy of a std. laser cavity may be broken, producing pure orbital angular momentum beams, and that generalized vector vortex beams may be created with high purity at the source. This work paves the way to new lasers for structured light based on intracavity geometric phase control.
  18. 18
    Li, Y.; Li, J.; Lü, B. Needle beam generation from an azimuthally polarized beam using a phase-only zone plate. Opt. Lett. 2017, 42 (4), 771– 774
    Google Scholar
    There is no corresponding record for this reference.
  19. 19
    Delaney, S.; Sanchez-Lopez, M. M.; Moreno, I.; Davis, J. A. Arithmetic with q-plates. Appl. Opt. 2017, 56 (3), 596– 600,  DOI: 10.1364/AO.56.000596
    Google Scholar
    19
    Arithmetic with q-plates
    Delaney Sam; Sanchez-Lopez Maria M; Moreno Ignacio; Davis Jeffrey A
    Applied optics (2017), 56 (3), 596-600 ISSN:.
    In this work we show the capability to form various q-plate equivalent systems using combinations of commercially available q-plates. We show operations like changing the sign of the q-value, or the addition and subtraction of q-plates. These operations only require simple combinations of q-plates and half-wave plates. Experimental results are presented in all cases. Following this procedure, experimental testing of higher and negative q-valued devices can be carried out using commonly available q-valued devices.
  20. 20
    Machavariani, G.; Lumer, Y.; Moshe, I.; Meir, A.; Jackel, S. Spatially-variable retardation plate for efficient generation of radiallyand azimuthally-polarized beams. Opt. Commun. 2008, 281, 732– 738,  DOI: 10.1016/j.optcom.2007.10.088
    Google Scholar
    20
    Spatially-variable retardation plate for efficient generation of radially- and azimuthally-polarized beams
    Machavariani, G.; Lumer, Y.; Moshe, I.; Meir, A.; Jackel, S.
    Optics Communications (2008), 281 (4), 732-738CODEN: OPCOB8; ISSN:0030-4018. (Elsevier B.V.)
    We investigate conversion of a linearly-polarized Gaussian beam to a radially- or an azimuthally-polarized doughnut (0, 1)* Laguerre-Gaussian (LG) beams, performed with a spatially-variable retardation (SVR) plate. The SVR plate is composed of eight sectors of a λ/2 retardation plate, each one with different orientation of the to crystal's slow axis. The anal. reveal that nearly-pure radially- or azimuthally-polarized LG(01)* beam with M2 = 2.2 can be obtained, while the transformation efficiency is 89.6%. In the expts., performed with Nd:YAG laser, we transformed a Gaussian beam with M2 = 1.3 to a radially- and azimuthally-polarized (0, 1)* Laguerre-Gaussian beams with M2 = 2.5. We carefully characterized the polarization state of the obtained radially- and azimuthally-polarized beams, measuring Stokes parameters. The polarization purity of the obtained beams, calcd. from the measured data, was as high as 96%.
  21. 21
    Cardano, F.; Karimi, E.; Slussarenko, S.; Marrucci, L.; de Lisio, C.; Santamato, E. Polarization pattern of vector vortex beams generated by q-plates with different topological charges. Appl. Opt. 2012, 51, C1– C6,  DOI: 10.1364/AO.51.0000C1
    Google Scholar
    There is no corresponding record for this reference.
  22. 22
    Wang, X. L.; Ding, J.; Ni, W. J.; Guo, C. S.; Wang, H. T. Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement. Opt. Lett. 2007, 32, 3549– 3551,  DOI: 10.1364/OL.32.003549
    Google Scholar
    22
    Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement
    Wang Xi-Lin; Ding Jianping; Ni Wei-Jiang; Guo Cheng-Shan; Wang Hui-Tian
    Optics letters (2007), 32 (24), 3549-51 ISSN:0146-9592.
    We describe a convenient approach for generating arbitrary vector beams in a 4-f system with a spatial light modulator (SLM) and a common path interferometric arrangement. A computer-generated hologram is introduced onto SLM for performing the beam conversion. Optical realization of a variety of polarization configurations confirms the reliability and flexibility of our method.
  23. 23
    Rong, Z. Y.; Han, Y. J.; Wang, S. Z.; Guo, C. S. Generation of arbitrary vector beams with cascaded liquid crystal spatial light modulators. Opt. Express 2014, 22, 1636– 1644,  DOI: 10.1364/OE.22.001636
    Google Scholar
    23
    Generation of arbitrary vector beams with cascaded liquid crystal spatial light modulators
    Rong Zhen-Yu; Han Yu-Jing; Wang Shu-Zhen; Guo Cheng-Shan
    Optics express (2014), 22 (2), 1636-44 ISSN:.
    A flexible approach is presented to generate vector beams with arbitrary polarization and complex amplitude by means of two cascaded transmissive liquid crystal spatial light modulators (LCSLMs). The configuration of the cascaded LCSLM system and its modulation characteristic are introduced. Theoretical analysis and experimental demonstration prove that the system in combination with a double-pass computer-generated hologram and a black-and-white pattern can generate vector beams with arbitrary polarization and complex amplitude by respectively controlling the complex amplitudes of two orthogonal polarization components of the beams. Using this system, we successfully generate radially polarized vector beams with helical phase distributions and vector Bessel beams with inhomogeneous amplitude distributions in experiments.
  24. 24
    Lim, B. C.; Phua, P. B.; Lai, W. J.; Hong, M. H. Fast switchable electro-optic radial polarization retarder. Opt. Lett. 2008, 33, 950– 952,  DOI: 10.1364/OL.33.000950
    Google Scholar
    24
    Fast switchable electro-optic radial polarization retarder
    Lim, B. C.; Phua, P. B.; Lai, W. J.; Hong, M. H.
    Optics Letters (2008), 33 (9), 950-952CODEN: OPLEDP; ISSN:0146-9592. (Optical Society of America)
    A fast and switchable electro-optic radial polarization retarder (EO-RPR) fabricated using the electro-optic ceramic Pb(Mg1/3Nb2/3)O3-PbTiO3 is presented. This EO-RPR is useful for fast and switchable generation of a pure cylindrical vector beam. When used together with a pair of half-wave plates, the EO-RPR can change circularly polarized light into any cylindrical vector beam of interest, such as radially or azimuthally polarized light. Radially and azimuthally polarized light with purities greater than 95% are generated exptl. The advantages of using EO-RPR include fast response time, low driving voltage, and transparency in a wide spectral range (500 to 7000 nm).
  25. 25
    Mushiake, Y.; Matsumura, K.; Nakajima, N. Generation of radially polarized optical beam mode by laser oscillation. Proc. IEEE 1972, 60, 1107– 1109,  DOI: 10.1109/PROC.1972.8865
    Google Scholar
    There is no corresponding record for this reference.
  26. 26
    Naidoo, D.; Aït-Ameur, K.; Brunel, M.; Forbes, A. Intra-cavity generation of superpositions of Laguerre–Gaussian beams. Appl. Phys. B: Laser Opt. 2012, 106, 683– 690,  DOI: 10.1007/s00340-011-4775-x
    Google Scholar
    There is no corresponding record for this reference.
  27. 27
    Tidwell, S. C.; Ford, D. H.; Kimura, W. D. Generating radially polarized beams interferometrically. Appl. Opt. 1990, 29, 2234– 2239,  DOI: 10.1364/AO.29.002234
    Google Scholar
    27
    Generating radially polarized beams interferometrically
    Tidwell, Steve C.; Ford, Dennis H.; Kimura, Wayne D.
    Applied Optics (1990), 29 (15), 2234-9CODEN: APOPAI; ISSN:0003-6935.
    Two interferometric techniques for converting a linearly polarized laser beam into a radially polarized beam with uniform azimuthal intensity are described. The techniques are based on the linear combination of orthogonally polarized beams, which have tailored intensity and phase profiles. Linearly polarized beams with intensity profiles tailored using a modified laser or an apodization filter were combined in sep. expts. to produce radially polarized light. A beam with an extinction ratio of -21.7 dB and azimuthal intensity variations of less than ±12% is produced using the modified laser output. The 2nd technique uses circularly polarized light and a unique spiral phase delay to produce the required phase profile. When focused, a radially polarized beam has a net longitudinal field useful for particle acceleration and, perhaps, other unique applications.
  28. 28
    Passilly, N.; Treussart, F.; Hierle, R.; de Saint Denis, R.; Ait-Ameur, K.; Roch, J.-F. Simple interferometric technique for generation of a radially polarized light beam. J. Opt. Soc. Am. A 2005, 22 (984), 984– 991,  DOI: 10.1364/JOSAA.22.000984
    Google Scholar
    28
    Simple interferometric technique for generation of a radially polarized light beam
    Passilly Nicolas; de Saint Denis Renaud; Ait-Ameur Kamel; Treussart Francois; Hierle Rolland; Roch Jean-Francois
    Journal of the Optical Society of America. A, Optics, image science, and vision (2005), 22 (5), 984-91 ISSN:1084-7529.
    We present a theoretical and experimental investigation of an interferometric technique for converting a linearly polarized Gaussian beam into a radially polarized doughnut beam. The experimental setup accomplishes the coherent summation of two orthogonally polarized TEM01 and TEM10 beams that are obtained from the transformation of a TEM00 beam by use of a simple binary diffractive optical element. We have shown that the degree of radial polarization is maximum at a given distance from the interferometer output port that depends on the diameter of the incident beam at the interferometer input port.
  29. 29
    Khonina, S. N.; Karpeev, S. V.; Alferov, S. V. Polarization converter for higher-order laser beams using a single binary diffractive optical element as beam splitter. Opt. Lett. 2012, 37 (2385), 2385– 2391,  DOI: 10.1364/OL.37.002385
    Google Scholar
    29
    Polarization converter for higher-order laser beams using a single binary diffractive optical element as beam splitter
    Khonina Svetlana N; Karpeev Sergey V; Alferov Sergey V
    Optics letters (2012), 37 (12), 2385-7 ISSN:.
    We propose a new approach to generating a pair of initial beams for a polarization converter that operates by summing up two opposite-sign circularly polarized beams. The conjugated pairs of vortex beams matched with laser modes are generated using binary diffractive optical elements (DOEs). The same binary element simultaneously serves two functions: a beam shaper and a beam splitter. Two proposed optical arrangements are compared in terms of alignment complexity and energy efficiency. The DOEs in question have been designed and fabricated. Natural experiments that demonstrate the generation of vector higher-order cylindrical beams have been conducted.
  30. 30
    Yue, F.; Wen, D.; Xin, J.; Gerardot, B. D.; Li, J.; Chen, X. Vector Vortex Beam Generation with a Single Plasmonic Metasurface. ACS Photonics 2016, 3 (9), 1558– 1563,  DOI: 10.1021/acsphotonics.6b00392
    Google Scholar
    30
    Vector Vortex Beam Generation with a Single Plasmonic Metasurface
    Yue, Fuyong; Wen, Dandan; Xin, Jingtao; Gerardot, Brian D.; Li, Jensen; Chen, Xianzhong
    ACS Photonics (2016), 3 (9), 1558-1563CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
    Despite a plethora of applications ranging from quantum memories to high-resoln. lithog., the current technologies to generate vector vortex beams (VVBs) suffer from less efficient energy use, poor resoln., low damage threshold, and bulky size, preventing further practical applications. We propose and exptl. demonstrate an approach to generate VVBs with a single metasurface by locally tailoring phase and transverse polarization distribution. This method features the spin-orbit coupling and the superposition of the converted part with an addnl. phase pickup and the residual part without a phase change. By maintaining the equal components for the converted part and the residual part, the cylindrically polarized vortex beams carrying orbital angular momentum are exptl. demonstrated based on a single metasurface at subwavelength scale. The proposed approach provides unprecedented freedom in engineering the properties of optical waves with high-efficiency light utilization and a minimal footprint.
  31. 31
    Xu, Y.; Zhang, H.; Li, Q.; Zhang, X.; Xu, Q.; Zhang, W.; Hu, C.; Zhang, X.; Han, J.; Zhang, W. Generation of terahertz vector beams using dielectric metasurfaces via spin-decoupled phase control. Nanophotonics 2020, 9 (10), 3393– 3402,  DOI: 10.1515/nanoph-2020-0112
    Google Scholar
    There is no corresponding record for this reference.
  32. 32
    Liu, Y.; Ke, Y.; Zhou, J.; Liu, Y.; Luo, H.; Wen, S.; Fan, D. Generation of perfect vortex and vector beams based on Pancharatnam-Berry phase elements. Sci. Rep. 2017, 7, 44096,  DOI: 10.1038/srep44096
    Google Scholar
    32
    Generation of perfect vortex and vector beams based on Pancharatnam-Berry phase elements
    Liu Yachao; Ke Yougang; Zhou Junxiao; Liu Yuanyuan; Luo Hailu; Wen Shuangchun; Fan Dianyuan
    Scientific reports (2017), 7 (), 44096 ISSN:.
    Perfect vortex beams are the orbital angular momentum (OAM)-carrying beams with fixed annular intensities, which provide a better source of OAM than traditional Laguerre-Gaussian beams. However, ordinary schemes to obtain the perfect vortex beams are usually bulky and unstable. We demonstrate here a novel generation scheme by designing planar Pancharatnam-Berry (PB) phase elements to replace all the elements required. Different from the conventional approaches based on reflective or refractive elements, PB phase elements can dramatically reduce the occupying volume of system. Moreover, the PB phase element scheme is easily developed to produce the perfect vector beams. Therefore, our scheme may provide prominent vortex and vector sources for integrated optical communication and micromanipulation systems.
  33. 33
    Zeng, J.; Li, L.; Yang, X.; Gao, J. Generating and Separating Twisted Light by gradient-rotation Split-Ring Antenna Metasurfaces. Nano Lett. 2016, 16, 3101– 3108,  DOI: 10.1021/acs.nanolett.6b00360
    Google Scholar
    33
    Generating and Separating Twisted Light by gradient-rotation Split-Ring Antenna Metasurfaces
    Zeng, Jinwei; Li, Ling; Yang, Xiaodong; Gao, Jie
    Nano Letters (2016), 16 (5), 3101-3108CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
    Nanoscale compact optical vortex generators promise substantially significant prospects in modern optics and photonics, leading to many advances in sensing, imaging, quantum communication, and optical manipulation. However, conventional vortex generators often suffer from bulky size, low vortex mode purity in the converted beam, or limited operation bandwidth. Here, we design and demonstrate gradient-rotation split-ring antenna metasurfaces as unique spin-to-orbital angular momentum beam converters to simultaneously generate and sep. pure optical vortices in a broad wavelength range. Our proposed design has the potential for realizing miniaturized on-chip OAM-multiplexers, as well as enabling new types of metasurface devices for the manipulation of complex structured light beams.
  34. 34
    Zeng, J.; Luk, T. S.; Gao, J.; Yang, X. Spiraling light with magnetic metamaterial quarter-wave turbines. Sci. Rep. 2017, 7, 11824,  DOI: 10.1038/s41598-017-12143-7
    Google Scholar
    34
    Spiraling Light with Magnetic Metamaterial Quarter-Wave Turbines
    Zeng Jinwei; Gao Jie; Yang Xiaodong; Luk Ting S
    Scientific reports (2017), 7 (1), 11824 ISSN:.
    Miniaturized quarter-wave plate devices empower spin to orbital angular momentum conversion and vector polarization formation, which serve as bridges connecting conventional optical beam and structured light. Enabling the manipulability of additional dimensions as the complex polarization and phase of light, quarter-wave plate devices are essential for exploring a plethora of applications based on orbital angular momentum or vector polarization, such as optical sensing, holography, and communication. Here we propose and demonstrate the magnetic metamaterial quarter-wave turbines at visible wavelength to produce radially and azimuthally polarized vector vortices from circularly polarized incident beam. The magnetic metamaterials function excellently as quarter-wave plates at single wavelength and maintain the quarter-wave phase retardation in broadband, while the turbine blades consist of multiple polar sections, each of which contains homogeneously oriented magnetic metamaterial gratings near azimuthal or radial directions to effectively convert circular polarization to linear polarization and induce phase shift under Pancharatnum-Berry's phase principle. The perspective concept of multiple polar sections of magnetic metamaterials can extend to other analogous designs in the strongly coupled nanostructures to accomplish many types of light phase-polarization manipulation and structured light conversion in the desired manner.
  35. 35
    Yi, X.; Ling, X.; Zhang, Z.; Li, Y.; Zhou, X.; Liu, Y. Generation of cylindrical vector vortex beams by two cascaded metasurfaces. Opt. Express 2014, 22 (17207), 17207– 17215,  DOI: 10.1364/OE.22.017207
    Google Scholar
    35
    Generation of cylindrical vector vortex beams by two cascaded metasurfaces
    Yi Xunong; Ling Xiaohui; Zhang Zhiyou; Li Ying; Zhou Xinxing; Liu Yachao; Chen Shizhen; Luo Hailu; Wen Shuangchun
    Optics express (2014), 22 (14), 17207-15 ISSN:.
    We present a simple and efficient method to generate any cylindrical vector vortex (CVV) beams based on two cascaded metasurfaces. The metasurface works as a space-variant Panchratnam-Berry phase element and can produce any desirable vortex phase and vector polarization. The first metasurface is used to switch the sign of topological charges associated with vortex, and the second metasurface is applied to manipulate the local polarization. This method allows us to simultaneously manipulate polarization and phase of the CVV beams.
  36. 36
    Liu, Z.; Liu, Y.; Ke, Y.; Liu, Y.; Shu, W.; Luo, H. Generation of arbitrary vector vortex beams on hybrid-order Poincaré sphere. Photonics Res. 2017, 5 (1), 15– 21,  DOI: 10.1364/PRJ.5.000015
    Google Scholar
    There is no corresponding record for this reference.
  37. 37
    He, Y.; Li, Y.; Liu, J.; Zhang, X.; Cai, Y.; Chen, Y.; Chen, S.; Fan, D. Switchable phase and polarization singular beams generation using dielectric metasurfaces. Sci. Rep. 2017, 7 (1), 6814,  DOI: 10.1038/s41598-017-07217-5
    Google Scholar
    37
    Switchable phase and polarization singular beams generation using dielectric metasurfaces
    He Yanliang; Li Ying; Liu Junmin; Zhang Xiaoke; Cai Yao; Chen Yu; Chen Shuqing; Fan Dianyuan
    Scientific reports (2017), 7 (1), 6814 ISSN:.
    Singular beams which possess helical phase wavefront or spatially inhomogeneous polarization provide new freedom for optical field manipulation. However, conventional schemes to produce the singular beams have difficulty in realizing the flexible switch between different singular beams. In this work, we have experimentally demonstrated the capability of dielectric metasurfaces to generate three types of singular beams and switch between them at working wavelength of 1550 nm. We have shown vortex beam and cylindrical vector beam generation with single metasurface and cylindrical vector vortex beam generation with two cascaded metasurfaces. Moreover, experimental demonstration on switching cylindrical vector beam into vortex beam has also been done by combining one quarter-wave plate and a Glan laser polarizer. The experimental results match well with the analysis from the Jones matrix calculations. The average conversion efficiency of cylindrical vector beam to vortex beam was estimated to be 47.7%, which was about 2.3% lower than the theoretical prediction.
  38. 38
    He, Y.; Ye, H.; Liu, J.; Xie, Z.; Zhang, X.; Xiang, Y. Order-controllable cylindrical vector vortex beam generation by using spatial light modulator and cascaded metasurfaces. IEEE Photon J. 2017, 9 (5), 6101710,  DOI: 10.1109/JPHOT.2017.2741508
    Google Scholar
    There is no corresponding record for this reference.
  39. 39
    Wang, S.; Liu, Y.; Yang, S. A.; Lei, D. Y. Multifunctional vector beam generation using metasurface. Appl. Phys. Lett. 2019, 114 (12), 121103
    Google Scholar
    There is no corresponding record for this reference.
  40. 40
    Fu, P.; Ni, P.-N.; Wu, B.; Pei, X.-Z.; Wang, Q.-H.; Chen, P.-P.; Xu, C.; Kan, Q.; Chu, W.-G.; Xie, Y.-Y. Metasurface Enabled On-Chip Generation and Manipulation of Vector Beams from Vertical Cavity Surface-Emitting Lasers. Adv. Mater. 2023, 35 (12), 2204286,  DOI: 10.1002/adma.202204286
    Google Scholar
    40
    Metasurface Enabled On-Chip Generation and Manipulation of Vector Beams from Vertical Cavity Surface-Emitting Lasers
    Fu, Pan; Ni, Pei-Nan; Wu, Bo; Pei, Xian-Zhi; Wang, Qiu-Hua; Chen, Pei-Pei; Xu, Chen; Kan, Qiang; Chu, Wei-Guo; Xie, Yi-Yang
    Advanced Materials (Weinheim, Germany) (2023), 35 (12), 2204286CODEN: ADVMEW; ISSN:0935-9648. (Wiley-VCH Verlag GmbH & Co. KGaA)
    Metasurface polarization optics that consist of 2D array of birefringent nano-antennas have proven remarkable capabilities to generate and manipulate vectorial fields with subwavelength resoln. and high efficiency. Integrating this new type of metasurface with the std. vertical cavity surface-emitting laser (VCSEL) platform enables an ultracompact and powerful soln. to control both phase and polarization properties of the laser on a chip, which allows to structure a VCSEL into vector beams with on-demand wavefronts. Here, this concept is demonstrated by directly generating versatile vector beams from com. available VCSELs through on-chip integration of high-index dielec. metasurfaces. Exptl., the versatility of the approach for the development of vectorial VCSELs are validated by implementing a variety of functionalities, including directional emission of multibeam with specified polarizations, vectorial holog. display, and vector vortex beams generations. Notably, the proposed vectorial VCSELs integrated with a single layer of beam shaping metasurface bypass the requirements of multiple cascaded optical components, and thus have the potential to promote the advancements of ultracompact, lightweightand scalable vector beams sources, enriching and expanding the applications of VCSELs in optical communications, laser manipulation and processing, information encryption, and quantum optics.
  41. 41
    Cai, X.; Wang, J.; Strain, M. J.; Johnson-Morris, B.; Zhu, J.; Sorel, M.; O’Brien, J. L.; Thompson, M. G.; Yu, S. Integrated Compact Optical Vortex Beam Emitters. Science 2012, 338 (6105), 363– 366,  DOI: 10.1126/science.1226528
    Google Scholar
    41
    Integrated compact optical vortex beam emitters
    Cai, Xinlun; Wang, Jianwei; Strain, Michael J.; Johnson-Morris, Benjamin; Zhu, Jiangbo; Sorel, Marc; O'Brien, Jeremy L.; Thompson, Mark G.; Yu, Siyuan
    Science (Washington, DC, United States) (2012), 338 (6105), 363-366CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
    Emerging applications based on optical beams carrying orbital angular momentum (OAM) will probably require photonic integrated devices and circuits for miniaturization, improved performance, and enhanced functionality. We demonstrate silicon-integrated optical vortex emitters, using angular gratings to ext. light confined in whispering gallery modes with high OAM into free-space beams with well-controlled amts. of OAM. The smallest device has a radius of 3.9 μm. Exptl. characterization confirms the theor. prediction that the emitted beams carry exactly defined and adjustable OAM. Fabrication of integrated arrays and demonstration of simultaneous emission of multiple identical optical vortices provide the potential for large-scale integration of optical vortex emitters on complementary metal-oxide-semiconductor compatible silicon chips for wide-ranging applications.
  42. 42
    Zhen, B.; Hsu, C. W.; Lu, L.; Stone, A. D.; Soljacic, M. Topological Nature of Optical Bound States in the Continuum. Phys. Rev. Lett. 2014, 113, 257401,  DOI: 10.1103/PhysRevLett.113.257401
    Google Scholar
    42
    Topological nature of optical bound states in the continuum
    Zhen, Bo; Hsu, Chia Wei; Lu, Ling; Stone, A. Douglas; Soljacic, Marin
    Physical Review Letters (2014), 113 (25), 257401-1/1-257401-1/5, 5 pp.CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    Optical bound states in the continuum (BICs) have recently been realized in photonic crystal slabs, where the disappearance of out-of-plane radiation turns leaky resonances into guided modes with infinite lifetimes. We show that such BICs are vortex centers in the polarization directions of far-field radiation. They carry conserved and quantized topol. charges, defined by the winding no. of the polarization vectors, which ensure their robust existence and govern their generation, evolution, and annihilation. Our findings connect robust BICs in photonics to a wide range of topol. phys. phenomena.
  43. 43
    Yoda, T.; Notomi, M. Generation and Annihilation of Topologically Protected Bound States in the Continuum and Circularly Polarized States by Symmetry Breaking. Phys. Rev. Lett. 2020, 125, 053902,  DOI: 10.1103/PhysRevLett.125.053902
    Google Scholar
    43
    Generation and Annihilation of Topologically Protected Bound States in the Continuum and Circularly Polarized States by Symmetry Breaking
    Yoda, Taiki; Notomi, Masaya
    Physical Review Letters (2020), 125 (5), 053902CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
    We demonstrate by breaking the C6 symmetry for higher-order at-Γ bound states in the continuum (BICs) with topol. charge -2 in photonic crystals (i) deterministic generation of off-Γ BICs from the at-Γ BIC and (ii) a variety of pair-creation and annihilation processes of circularly polarized states with opposite topol. charges and the same handedness. To explain these phenomena, we introduce the handedness-wise topol. charge quantized to a half-integer. The handedness-wise charge gives a unified picture of various phenomena involving BICs and circularly polarized states.
  44. 44
    Iwahashi, S.; Kurosaka, Y.; Sakai, K.; Kitamura, K.; Takayama, N.; Noda, S. Higher-order vector beams produced by photonic-crystal lasers. Opt. Exp. 2011, 19, 11963,  DOI: 10.1364/OE.19.011963
    Google Scholar
    There is no corresponding record for this reference.
  45. 45
    Kodigala, A.; Lepetit, T.; Gu, Q.; Bahari, B.; Fainman, Y.; Kante, B. Lasing action from photonic bound states in continuum. Nature 2017, 541 (7636), 196– 199,  DOI: 10.1038/nature20799
    Google Scholar
    45
    Lasing action from photonic bound states in continuum
    Kodigala, Ashok; Lepetit, Thomas; Gu, Qing; Bahari, Babak; Fainman, Yeshaiahu; Kante, Boubacar
    Nature (London, United Kingdom) (2017), 541 (7636), 196-199CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
    In 1929, only three years after the advent of quantum mechanics, von Neumann and Wigner showed that Schrodinger's equation can have bound states above the continuum threshold. These peculiar states, called bound states in the continuum (BICs), manifest themselves as resonances that do not decay. For several decades afterwards the idea lay dormant, regarded primarily as a math. curiosity. In 1977, Herrick and Stillinger revived interest in BICs when they suggested that BICs could be obsd. in semiconductor superlattices. BICs arise naturally from Feshbach's quantum mech. theory of resonances, as explained by Friedrich and Wintgen, and are thus more phys. than initially realized. Recently, it was realized that BICs are intrinsically a wave phenomenon and are thus not restricted to the realm of quantum mechanics. They have since been shown to occur in many different fields of wave physics including acoustics, microwaves and nanophotonics. However, exptl. observations of BICs have been limited to passive systems and the realization of BIC lasers has remained elusive. Here we report, at room temp., lasing action from an optically pumped BIC cavity. Our results show that the lasing wavelength of the fabricated BIC cavities, each made of an array of cylindrical nanoresonators suspended in air, scales with the radii of the nanoresonators according to the theor. prediction for the BIC mode. Moreover, lasing action from the designed BIC cavity persists even after scaling down the array to as few as 8-by-8 nanoresonators. BIC lasers open up new avenues in the study of light-matter interaction because they are intrinsically connected to topol. charges and represent natural vector beam sources (i.e., there are several possible beam shapes), which are highly sought after in the fields of optical trapping, biol. sensing and quantum information.
  46. 46
    Doeleman, H. M.; Monticone, F.; den Hollander, W.; Alù, A.; Koenderink, A. F. Experimental observation of a polarization vortex at an optical bound state in the continuum. Nat. Photonics 2018, 12, 397– 401,  DOI: 10.1038/s41566-018-0177-5
    Google Scholar
    46
    Experimental observation of a polarization vortex at an optical bound state in the continuum
    Doeleman, Hugo M.; Monticone, Francesco; den Hollander, Wouter; Alu, Andrea; Koenderink, A. Femius
    Nature Photonics (2018), 12 (7), 397-401CODEN: NPAHBY; ISSN:1749-4885. (Nature Research)
    Optical bound states in the continuum (BICs) are states supported by a photonic structure that are compatible with free-space radiation, yet become perfectly bound for one specific in-plane momentum and wavelength1,2. Recently, it was predicted that light radiated by such modes around the BIC momentum-frequency condition should display a vortex in its far-field polarization profile, making the BIC topol. protected3. Here, we study a one-dimensional grating supporting a transverse magnetic mode with a BIC near 700 nm wavelength, verifying the existence of the BIC using reflection measurements, which show a vanishing reflection feature. Using k-space polarimetry, we measure the full polarization state of reflection around the BIC, highlighting the presence of a topol. vortex. We use an electromagnetic dipole model to explain the obsd. BIC through destructive interference between two radiation channels, characteristic of a Friedrich-Wintgen-type BIC4. Our findings shed light on the origin of BICs and verify their topol. nature.
  47. 47
    Wang, B.; Liu, W.; Zhao, M.; Wang, J.; Zhang, Y.; Chen, A.; Guan, F.; Liu, X.; Shi, L.; Zi, J. Generating optical vortex beams by momentum-space polarization vortices centered at bound states in the continuum. Nat. Photonics 2020, 14, 623,  DOI: 10.1038/s41566-020-0658-1
    Google Scholar
    47
    Generating optical vortex beams by momentum-space polarization vortices centred at bound states in the continuum
    Wang, Bo; Liu, Wenzhe; Zhao, Maoxiong; Wang, Jiajun; Zhang, Yiwen; Chen, Ang; Guan, Fang; Liu, Xiaohan; Shi, Lei; Zi, Jian
    Nature Photonics (2020), 14 (10), 623-628CODEN: NPAHBY; ISSN:1749-4885. (Nature Research)
    Abstr.: Optical vortices, beams with spiral wavefronts and screw phase dislocations, have been attracting increasing interest in various fields. Here, we theor. propose and exptl. realize an easy approach to generating optical vortices. We leverage the inherent momentum-space topol. vortex-like response of polarization (strong polarization anisotropy) around bound states in the continuum of two-dimensional periodic structures, for example photonic crystal slabs, to induce Pancharatnam-Berry phases and spin-orbit interaction in the beams. This new class of optical vortex generators operates in momentum space, meaning that the structure is almost homogeneous without a real-space center. In principle, any even-order optical vortex that is a diffraction-resistant high-order quasi-Bessel beam can be achieved at any desired working wavelength. The proposed approach expands the application of bound states in the continuum and topol. photonics.
  48. 48
    Huang, C.; Zhang, C.; Xiao, S.; Wang, Y.; Fan, Y.; Liu, Y.; Zhang, N.; Qu, G.; Ji, H.; Han, J.; Ge, L.; Kivshar, Y.; Song, Q. Ultrafast control of vortex microlasers. Science 2020, 367, 1018,  DOI: 10.1126/science.aba4597
    Google Scholar
    48
    Ultrafast control of vortex microlasers
    Huang, Can; Zhang, Chen; Xiao, Shumin; Wang, Yuhan; Fan, Yubin; Liu, Yilin; Zhang, Nan; Qu, Geyang; Ji, Hongjun; Han, Jiecai; Ge, Li; Kivshar, Yuri; Song, Qinghai
    Science (Washington, DC, United States) (2020), 367 (6481), 1018-1021CODEN: SCIEAS; ISSN:1095-9203. (American Association for the Advancement of Science)
    The development of classical and quantum information-processing technol. calls for on-chip integrated sources of structured light. Although integrated vortex microlasers have been previously demonstrated, they remain static and possess relatively high lasing thresholds, making them unsuitable for high-speed optical communication and computing. We introduce perovskite-based vortex microlasers and demonstrate their application to ultrafast all-optical switching at room temp. By exploiting both mode symmetry and far-field properties, we reveal that the vortex beam lasing can be switched to linearly polarized beam lasing, or vice versa, with switching times of 1 to 1.5 ps and energy consumption that is orders of magnitude lower than in previously demonstrated all-optical switching. Our results provide an approach that breaks the long-standing trade-off between low energy consumption and high-speed nanophotonics, introducing vortex microlasers that are switchable at terahertz frequencies.
  49. 49
    Cai, Z.; Wu, C.; Jiang, J.; Ding, Y.; Zheng, Z.; Ding, F. Phase-change metasurface for switchable vector vortex beam generation. Optics Express 2021, 29 (26), 42762– 42771,  DOI: 10.1364/OE.444956
    Google Scholar
    49
    Phase-change metasurface for switchable vector vortex beam generation
    Cai, Ziru; Wu, Cuo; Jiang, Jing; Ding, Yingtao; Zheng, Ziwei; Ding, Fei
    Optics Express (2021), 29 (26), 42762-42771CODEN: OPEXFF; ISSN:1094-4087. (Optica Publishing Group)
    Metasurfaces have attracted increasing attention due to their unprecedented capabilities of molding optical fields with exceedingly low losses. Despite significant achievements, most existing metasurfaces are passive and lack dynamic modulation post-fabrication. Here, we propose a tunable phase-change metasurface for switchable vector vortex beam generation in the mid-IR range. The phase-change meta-mol., consisting of two coupled Ge2Sb2Te5 (GST) bricks, is firstly designed to perform the switching between a quarter-wave plate and a usual transmissive plate over a wavelength range from 4.95 to 5.05 μm under the amorphous and cryst. phases of GST, resp. Furthermore, a general method is derived to achieve a switchable vector vortex beam generator at the target wavelength of 5 μm by spatially orienting GST meta-mols. to locally tailor phase and polarization distribution. Under the amorphous phase, radially polarized and azimuthally polarized beams, composed of the co-polarized circularly polarized (CP) component carrying orbital angular momentum (OAM) with a topol. charge of l = 0 and cross-polarized CP component carrying OAM with a topol. charge of l = ±2 are obtained for the left circularly polarized (LCP) and right circularly polarized (RCP) incident waves, resp. The mode purity values of the cross-polarized component and the co-polarized component are calcd. to be ∼ 0.949 and ∼ 0.955. When GST transits to its cryst. phase, the vector vortex beam disappears, and the incident CP beams pass through directly. Our finding paves the way for advanced applications targeting photonics integration with switchable functionalities.
  50. 50
    Tian, J.; Adamo, G.; Liu, H.; Wu, M.; Klein, M.; Deng, J.; Ang, N. S. S.; Paniagua-Dominguez, R.; Liu, H.; Kuznetsov, A. I.; Soci, C. Phase-Change Perovskite Microlaser with Tunable Polarization Vortex. Adv. Mater. 2023, 35, 2207430,  DOI: 10.1002/adma.202207430
    Google Scholar
    50
    Phase-Change Perovskite Microlaser with Tunable Polarization Vortex
    Tian, Jingyi; Adamo, Giorgio; Liu, Hailong; Wu, Mengfei; Klein, Maciej; Deng, Jie; Ang, Norman Soo Seng; Paniagua-Dominguez, Ramon; Liu, Hong; Kuznetsov, Arseniy I.; Soci, Cesare
    Advanced Materials (Weinheim, Germany) (2023), 35 (1), 2207430CODEN: ADVMEW; ISSN:0935-9648. (Wiley-VCH Verlag GmbH & Co. KGaA)
    Metasurfaces supporting optical bound states in the continuum (BICs) are emerging as simple and compact optical cavities to realize polarization-vortex lasers. The winding of the polarization around the singularity defines topol. charges which are generally set by the cavity design and cannot be altered without changing geometrical parameters. Here, a subwavelength-thin phase-change halide perovskite BIC metasurface functioning as a tunable polarization vortex microlaser is demonstrated. Upon the perovskite structural phase transitions, both its refractive index and gain vary substantially, inducing reversible and bistable switching between distinct polarization vortexes underpinned by opposite topol. charges. Dynamic tuning and switching of the resulting vector beams may find use in microscopy imaging, particle trapping and manipulation, and optical data storage.
  51. 51
    Shi, S.; Chen, C.; Prather, D. W. Plane-wave expansion method for calculating band structure of photonic crystal slabs with perfectly matched layers. J. Opt. Soc. Am. 2004, 21 (9), 1769– 1775,  DOI: 10.1364/JOSAA.21.001769
    Google Scholar
    51
    Plane-wave expansion method for calculating band structure of photonic crystal slabs with perfectly matched layers
    Shi Shouyuan; Chen Caihua; Prather Dennis W
    Journal of the Optical Society of America. A, Optics, image science, and vision (2004), 21 (9), 1769-75 ISSN:1084-7529.
    We present a new algorithm for calculation of the band structure of photonic crystal slabs. This algorithm combines the plane-wave expansion method with perfectly matched layers for the termination of the computational region in the direction out of the plane. In addition, the effective-medium tensor is applied to improve convergence. A general complex eigenvalue problem is then obtained. Two criteria are presented to distinguish the guided modes from the PML modes. As such, this scheme can accurately determine the band structure both above and below the light cone. The convergence of the algorithm presented has been studied. The results obtained by using this algorithm have been compared with those obtained by the finite-difference time-domain method and found to agree very well.
  52. 52
    Cao, Y.; Hou, Z.; Liu, Y. Convergence problem of plane-wave expansion method for phononic crystals. Phys. Lett. A 2004, 327 (2–3), 247– 253,  DOI: 10.1016/j.physleta.2004.05.030
    Google Scholar
    52
    Convergence problem of plane-wave expansion method for phononic crystals
    Cao, Yongjun; Hou, Zhilin; Liu, Youyan
    Physics Letters A (2004), 327 (2-3), 247-253CODEN: PYLAAG; ISSN:0375-9601. (Elsevier Science B.V.)
    A new formulation of eigenproblem for phononic crystals is developed. The convergence of the new formulation in the band-structure calcns. is examd. in detail and compared with that of the conventional plane wave expansion (CPWE) method. Numerical results show that the slow convergence of the CPWE method is not due to the slow convergence of the Fourier series for the elastic coeffs. (or displacement fields) in the interfaces of different materials, but to the inappropriate formulation of the eigenproblem used in the calcns. Numerical calcns. also show that the new formulation can provide much more accurate numerical results than the CPWE method for the systems of either very high or very low filling fractions, or of large elastic mismatch.
  53. 53
    David, A.; Benisty, H.; Weisbuch, C. Fast factorization rule and plane-wave expansion method for two-dimensional photonic crystals with arbitrary hole-shape. Phys. Rev. B 2006, 73, 075107,  DOI: 10.1103/PhysRevB.73.075107
    Google Scholar
    53
    Fast factorization rule and plane-wave expansion method for two-dimensional photonic crystals with arbitrary hole-shape
    David, Aurelien; Benisty, Henri; Weisbuch, Claude
    Physical Review B: Condensed Matter and Materials Physics (2006), 73 (7), 075107/1-075107/7CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
    A modified implementation of the plane-wave expansion for calcn. of photonic crystals band structures is introduced in order to circumvent the slow convergence stemming from field discontinuities. By using an adequate form of the Fourier transform of the dielec. const., a fast convergence rate is achieved for any photonic crystal pattern. This result, which generalizes previous convergence studies, is exemplified in the important case of photonic crystal with circular holes. We further consider more sophisticated structures, such as elliptical hole-shapes as well as supercell calcns. for waveguides. We also address calcns. of ultraflat photonic bands.
  54. 54
    Huang, S.-C.; Hong, K.-B.; Chiu, H.-L.; Lan, S.-W.; Chang, T.-C.; Li, H.; Lu, T.-C. Design of photonic crystal surface emitting lasers with indium-tin-oxide top claddings. Appl. Phys. Lett. 2018, 112 (6), 1105,  DOI: 10.1063/1.5016442
    Google Scholar
    There is no corresponding record for this reference.
  55. 55
    Miao, P.; Zhang, Z.; Sun, J.; Walasik, W.; Longhi, S.; Litchinitser, N. M.; Feng, L. Orbital angular momentum microlaser. Science 2016, 353, 464– 467,  DOI: 10.1126/science.aaf8533
    Google Scholar
    55
    Orbital angular momentum microlaser
    Miao, Pei; Zhang, Zhifeng; Sun, Jingbo; Walasik, Wiktor; Longhi, Stefano; Litchinitser, Natalia M.; Feng, Liang
    Science (Washington, DC, United States) (2016), 353 (6298), 464-467CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
    Structured light provides an addnl. degree of freedom for modern optics and practical applications. The effective generation of orbital angular momentum (OAM) lasing, esp. at a micro- and nanoscale, could address the growing demand for information capacity. By exploiting the emerging non-Hermitian photonics design at an exceptional point, we demonstrate a microring laser producing a single-mode OAM vortex lasing with the ability to precisely define the topol. charge of the OAM mode. The polarization assocd. with OAM lasing can be further manipulated on demand, creating a radially polarized vortex emission. Our OAM microlaser could find applications in the next generation of integrated optoelectronic devices for optical communications in both quantum and classical regimes.

Cited By

Click to copy section linkSection link copied!
Citation Statements
Explore this article's citation statements on scite.ai
powered by  Scite

This article is cited by 3 publications.

  1. Rui Tang, Hong Zhang, Yi-Han Cheng. Tailoring Electronic and Magnetic Properties of YcoO3 via Anharmonic Phononic Coupling and Vector Vortex Beam Interaction. The Journal of Physical Chemistry Letters 2025, 16 (11) , 2815-2822. https://doi.org/10.1021/acs.jpclett.5c00298
  2. Xiaobo Zhou, Zhuang Li, Yufeng Zhou, Chenghao Bai, Xianyu Ao. Lasing from Doubly Degenerate Bound States in the Continuum. The Journal of Physical Chemistry Letters 2024, 15 (42) , 10703-10709. https://doi.org/10.1021/acs.jpclett.4c02604
  3. Wenzheng Zhao, Weimin Wang, Zhao-xian Chen, Xingsheng Luan, Jun-long Kou, Yan-qing Lu. Evolution of Degenerate Pairs of Bound States in the Continuum With Broken Symmetry. IEEE Photonics Journal 2024, 16 (2) , 1-7. https://doi.org/10.1109/JPHOT.2024.3378672
Download PDF
Go to ACS Photonics
Get e-Alerts
Get e-Alerts

ACS Photonics

Cite this: ACS Photonics 2023, 10, 12, 4112–4120
Click to copy citationCitation copied!
https://doi.org/10.1021/acsphotonics.3c00561
Published November 28, 2023

Copyright © 2023 The Authors. Published by American Chemical Society. This publication is licensed under

CC-BY 4.0 .

Article Views

1730

Altmetric

-

Citations

3
Learn about these metrics

Article Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.

Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.

The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated.

  • Abstract

    High Resolution Image
    Download MS PowerPoint Slide

    Figure 1

    Figure 1. Figure showing how the polarization vector twists around the vortex center in A and B representations.

    High Resolution Image
    Download MS PowerPoint Slide

    Figure 2

    Figure 2. PCSEL structure and images of the device. (a) Schematic diagram of the designed PCSEL structure. The laser structure is mainly composed of an active layer, two SCH layers, two cladding layers, and a PC region. ITO layer is cladded on a PC for protection and current spreading purposes. (b) Top view of the OM image of the actual device. The diameters of the aperture, PC region, ITO cladding, and mesa are 120, 125, 210, and 260 μm, respectively. (c and d) Top-view SEM images of the PC structure with honeycomb (c) and hexagonal lattices (d). The black regions are etching holes that are expected to remain unfilled after ITO deposition.

    High Resolution Image
    Download MS PowerPoint Slide

    Figure 3

    Figure 3. L–I–V characteristics and spectra. (a, b) Measured L–I–V curves of Hon-PCSEL (a) and Hex-PCSEL (b) under pulsed electrical pumping. The different line styles stand for different PC lattice constants. (c and d) Measured emission spectra of Hon-PCSEL (c) and Hex-PCSEL (d). The different colors stand for different PC lattice constants. The maximum intensity has been normalized to the same value.

    High Resolution Image
    Download MS PowerPoint Slide

    Figure 4

    Figure 4. AREL spectra below (left) and above (right) the lasing threshold of (a) Hon-PCSELs with a lattice constant of 318.7 nm, (b) Hon-PCSELs with a lattice constant of 322.7 nm, (c) Hex-PCSELs with a lattice constant of 318 nm, and (d) Hex-PCSELs with a lattice constant of 320 nm. The upper-right inset in (a) is the first Brillouin zone of the reciprocal lattice. The AREL measurements are conducted along the Γ-M direction. The Hon-PCSELs are measured with the pulse duration 1 μs and duty cycle 0.1%, while the Hex-PCSELs are additionally measured with a pulse duration 10 μs above the threshold. The scattered points are the TE and TM photonic bands calculated by the PWEM method. We define the modes with low to high frequencies as the A ∼ F modes.

    High Resolution Image
    Download MS PowerPoint Slide

    Figure 5

    Figure 5. Far-field pattern and polarization direction of PCSELs with a honeycomb lattice. (a) Measured FFP of Hon-PCSEL with the lattice constant 318.7 nm. The pink arrows represent the polarization directions. The figures in the right panel depict the measured FFPs with the polarizer oriented along the pink arrows. The TC is identified to be −2. (b and c) The calculated magnitudes of the x- and y-components of the polarization vector of the TE F mode. The black lines represent zero intensity of this component. (d) Orientation of the electric field of the TE F mode at different k points. The orientation is indicated by its azimuthal angle (radian) relative to the x-axis. The TE F mode shows a TC of −2. (e–h) Measured FFP, calculated magnitude, and orientation of electric field for Hon-PCSEL with the lattice constant 322.7 nm. The TC is identified to be +1 and is consistent with the TE A mode in the calculation.

    High Resolution Image
    Download MS PowerPoint Slide

    Figure 6

    Figure 6. (a) measured spectra of Hex-PCSEL with the lattice constant 318 nm under different pulse duration conditions, where the repetition rate is fixed to be 1 kHz. The numbers on the right-hand side represent the ratio of integrated power of the TE B mode relative to the TE F mode. (b) The fwhm of the two main peaks in (a). (c) Spectra measured with the heat plate temperatures 300 and 340 K. The pulse width is fixed to be 200 ns, and the current is ranging from 200 to 500 mA.

    High Resolution Image
    Download MS PowerPoint Slide

    Figure 7

    Figure 7. (a and e) Measured FFPs of Hex-PCSELs under 1 and 10 μs pulse duration conditions. The figures in the right panel depict the measured FFPs with the polarizer oriented along the pink arrows. The TC is −2 in the 1 μs case, while it becomes +1 in the 10 μs case. (b–e and f–h) Calculation results of the TE F mode and the TE B mode of Hex-PCSELs.

    High Resolution Image
    Download MS PowerPoint Slide

  • References

    This article references 55 other publications.

    1. 1
      Allen, L.; Beijersbergen, M. W.; Spreeuw, R. J.; Woerdman, J. P. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. Phys. Rev. A 1992, 45 (11), 8185,  DOI: 10.1103/PhysRevA.45.8185
      1
      Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes
      Allen; Beijersbergen; Spreeuw; Woerdman
      Physical review. A, Atomic, molecular, and optical physics (1992), 45 (11), 8185-8189 ISSN:1050-2947.
      There is no expanded citation for this reference.
    2. 2
      He, H.; Friese, M. E.; Heckenberg, N. R.; Rubinsztein-Dunlop, H. Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity. Phys. Rev. Lett. 1995, 75 (5), 826,  DOI: 10.1103/PhysRevLett.75.826
      2
      Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity
      He, H.; Friese, M. E. J.; Heckenberg, N. R.; Rubinsztein-Dunlop, H.
      Physical Review Letters (1995), 75 (5), 826-9CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      Black or reflective particles can be trapped in the dark central min. of a doughnut laser beam produced using a high efficiency computer generated hologram. Such beams carry angular momentum due to the helical wave-front structure assocd. with the central phase singularity even when linearly polarized. Trapped absorptive particles spin due to absorption of this angular momentum transferred from the singularity beam. The direction of spin can be reversed by changing the sign of the singularity.
    3. 3
      Mair, A.; Vaziri, A.; Weihs, G.; Zeilinger, A. Entanglement of the orbital angular momentum states of photons. Nature 2001, 412 (6844), 313– 316,  DOI: 10.1038/35085529
      3
      Entanglement of the orbital angular momentum states of photons
      Mair A; Vaziri A; Weihs G; Zeilinger A
      Nature (2001), 412 (6844), 313-6 ISSN:0028-0836.
      Entangled quantum states are not separable, regardless of the spatial separation of their components. This is a manifestation of an aspect of quantum mechanics known as quantum non-locality. An important consequence of this is that the measurement of the state of one particle in a two-particle entangled state defines the state of the second particle instantaneously, whereas neither particle possesses its own well-defined state before the measurement. Experimental realizations of entanglement have hitherto been restricted to two-state quantum systems, involving, for example, the two orthogonal polarization states of photons. Here we demonstrate entanglement involving the spatial modes of the electromagnetic field carrying orbital angular momentum. As these modes can be used to define an infinitely dimensional discrete Hilbert space, this approach provides a practical route to entanglement that involves many orthogonal quantum states, rather than just two Multi-dimensional entangled states could be of considerable importance in the field of quantum information, enabling, for example, more efficient use of communication channels in quantum cryptography.
    4. 4
      Wang, J.; Yang, J. Y.; Fazal, I. M.; Ahmed, N.; Yan, Y.; Huang, H.; Willner, A. E. Terabit free-space data transmission employing orbital angular momentum multiplexing. Nat. Photonics 2012, 6 (7), 488– 496,  DOI: 10.1038/nphoton.2012.138
      4
      Terabit free-space data transmission employing orbital angular momentum multiplexing
      Wang, Jian; Yang, Jeng-Yuan; Fazal, Irfan M.; Ahmed, Nisar; Yan, Yan; Huang, Hao; Ren, Yongxiong; Yue, Yang; Dolinar, Samuel; Tur, Moshe; Willner, Alan E.
      Nature Photonics (2012), 6 (7), 488-496CODEN: NPAHBY; ISSN:1749-4885. (Nature Publishing Group)
      The recognition in the 1990s that light beams with a helical phase front have orbital angular momentum has benefited applications ranging from optical manipulation to quantum information processing. Recently, attention has been directed towards the opportunities for harnessing such beams in communications. Here, we demonstrate that four light beams with different values of orbital angular momentum and encoded with 42.8 × 4 Gbit s-1 quadrature amplitude modulation (16-QAM) signals can be multiplexed and demultiplexed, allowing a 1.37 Tbit s-1 aggregated rate and 25.6 bit s-1 Hz-1 spectral efficiency when combined with polarization multiplexing. Moreover, we show scalability in the spatial domain using two groups of concentric rings of eight polarization-multiplexed 20 × 4 Gbit s-1 16-QAM-carrying orbital angular momentum beams, achieving a capacity of 2.56 Tbit s-1 and spectral efficiency of 95.7 bit s-1 Hz-1. We also report data exchange between orbital angular momentum beams encoded with 100 Gbit s-1 differential quadrature phase-shift keying signals. These demonstrations suggest that orbital angular momentum could be a useful degree of freedom for increasing the capacity of free-space communications.
    5. 5
      Gibson, G.; Courtial, J.; Padgett, M. J.; Vasnetsov, M.; Pas’ko, V.; Barnett, S. M.; Franke-Arnold, S. Free-space information transfer using light beams carrying orbital angular momentum. Opt. Express 2004, 12 (22), 5448– 5456,  DOI: 10.1364/OPEX.12.005448
      5
      Free-space information transfer using light beams carrying orbital angular momentum
      Gibson Graham; Courtial Johannes; Padgett Miles; Vasnetsov Mikhail; Pas'ko Valeriy; Barnett Stephen; Franke-Arnold Sonja
      Optics express (2004), 12 (22), 5448-56 ISSN:.
      We demonstrate the transfer of information encoded as orbital angular momentum (OAM) states of a light beam. The transmitter and receiver units are based on spatial light modulators, which prepare or measure a laser beam in one of eight pure OAM states. We show that the information encoded in this way is resistant to eavesdropping in the sense that any attempt to sample the beam away from its axis will be subject to an angular restriction and a lateral offset, both of which result in inherent uncertainty in the measurement. This gives an experimental insight into the effects of aperturing and misalignment of the beam on the OAM measurement and demonstrates the uncertainty relationship for OAM.
    6. 6
      Wang, Y.; Zhang, J.; Ren, Y.; Cheng, L.; Zhu, B.; Zhao, Z. Demonstration of high-speed free-space optical communication using orbital angular momentum (OAM) modes. Opt. Commun. 2018, 426, 327– 332
      There is no corresponding record for this reference.
    7. 7
      Goyal, S. K.; Roux, F. S.; Forbes, A. Theoretical and experimental study of bit error rate performance of a spatially multiplexed free-space optical communication system using multiple orbital angular momentum modes. Opt. Express 2012, 20 (13), 1405– 1419
      There is no corresponding record for this reference.
    8. 8
      Lavery, M. P. J.; Speirits, F. C.; Barnett, S. M.; Padgett, M. J. Detection of a spinning object using light’s orbital angular momentum.. Science 2013, 341 (6145), 537– 540,  DOI: 10.1126/science.1239936
      8
      Detection of a Spinning Object Using Light's Orbital Angular Momentum
      Lavery, Martin P. J.; Speirits, Fiona C.; Barnett, Stephen M.; Padgett, Miles J.
      Science (Washington, DC, United States) (2013), 341 (6145), 537-540CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
      The linear Doppler shift is widely used to infer the velocity of approaching objects, but this shift does not detect rotation. By analyzing the orbital angular momentum of the light scattered from a spinning object, we obsd. a frequency shift proportional to product of the rotation frequency of the object and the orbital angular momentum of the light. This rotational frequency shift was still present when the angular momentum vector was parallel to the observation direction. The multiplicative enhancement of the frequency shift may have applications for the remote detection of rotating bodies in both terrestrial and astronomical settings.
    9. 9
      Qiu, S.; Liu, T.; Li, Z.; Wang, C.; Ren, Y.; Shao, Q.; Xing, C. Influence of lateral misalignment on the optical rotational Doppler effect. Appl. Opt. 2019, 58 (10), 2650,  DOI: 10.1364/AO.58.002650
      9
      Influence of lateral misalignment on the optical rotational Doppler effect
      Qiu Song; Liu Tong; Li Zhimeng; Wang Chen; Ren Yuan; Shao Qiongling; Xing Chaoyang
      Applied optics (2019), 58 (10), 2650-2655 ISSN:.
      The discovery of the optical rotational Doppler effect associated with orbital angular momentum of light paves a new way to detect the rotational speed of spinning objects. In this paper, we investigate the influence of lateral misalignment, i.e., the distance between the beam axis of a probe light and the rotation axis of a spinning object, on the rotational Doppler effect. First, we analyze the mechanism of the rotational Doppler effect of optical vortices based on the linear Doppler effect. Specifically, we consider the general case where the center of the optical vortex does not coincide with the rotation axis, and deduce the generalized formula of rotational Doppler shift based on a local scattering model. It is found that the bandwidth of the rotational Doppler signal depends proportionally on the amount of lateral misalignment, whereas the value of rotational Doppler shift remains constant. A proof-of-concept experiment is performed, and the measured results agree well with theoretical predictions. These findings may be useful for practical application of the optical rotational Doppler effect in remote sensing and metrology.
    10. 10
      Schmiegelow, C. T.; Schulz, J.; Kaufmann, H.; Ruster, T.; Poschinger, U. G.; Schmidt-Kaler, F. Transfer of optical orbital angular momentum to a bound electron. Nat. Commun. 2016, 7 (1), 129,  DOI: 10.1038/ncomms12998
      There is no corresponding record for this reference.
    11. 11
      Grier, D. G. A revolution in optical manipulation. Nature 2003, 424 (6950), 810,  DOI: 10.1038/nature01935
      11
      A revolution in optical manipulation
      Grier, David G.
      Nature (London, United Kingdom) (2003), 424 (6950), 810-816CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
      A review. Optical tweezers use the forces exerted by a strongly focused beam of light to trap and move objects ranging in size from tens of nanometers to tens of micrometers. Since their introduction in 1986, the optical tweezer has become an important tool for research in the fields of biol., phys. chem. and soft condensed matter physics. Recent advances promise to take optical tweezers out of the lab. and into the mainstream of manufg. and diagnostics; they may even become consumer products. The next generation of single-beam optical traps offers revolutionary new opportunities for fundamental and applied research.
    12. 12
      Moffitt, J.; Chemla, Y.; Smith, S. B.; Bustamante, C. Recent advances in optical tweezers. Annu. Rev. Biochem. 2008, 77, 205– 2,  DOI: 10.1146/annurev.biochem.77.043007.090225
      12
      Recent advances in optical tweezers
      Moffitt, Jeffrey R.; Chemla, Yann R.; Smith, Steven B.; Bustamante, Carlos
      Annual Review of Biochemistry (2008), 77 (), 205-228CODEN: ARBOAW; ISSN:0066-4154. (Annual Reviews Inc.)
      A review. It has been over 20 years since the pioneering work of Arthur Ashkin, and in the intervening years, the field of optical tweezers has grown tremendously. Optical tweezers are now being used in the investigation of an increasing no. of biochem. and biophys. processes, from the basic mech. properties of biol. polymers to the multitude of mol. machines that drive the internal dynamics of the cell. Innovation, however, continues in all areas of instrumentation and technique, with much of this work focusing on the refinement of established methods and on the integration of this tool with other forms of single-mol. manipulation or detection. Although tech. in nature, these developments have important implications for the expanded use of optical tweezers in biochem. research and thus should be of general interest. In this review, we address these recent advances and speculate on possible future developments.
    13. 13
      Ashkin, A.; Dziedzic, J. M. Optical trapping and manipulation of viruses and bacteria. Science 1987, 235 (4795), 1517,  DOI: 10.1126/science.3547653
      13
      Optical trapping and manipulation of viruses and bacteria
      Ashkin A; Dziedzic J M
      Science (New York, N.Y.) (1987), 235 (4795), 1517-20 ISSN:0036-8075.
      Optical trapping and manipulation of viruses and bacteria by laser radiation pressure were demonstrated with single-beam gradient traps. Individual tobacco mosaic viruses and dense oriented arrays of viruses were trapped in aqueous solution with no apparent damage using approximately 120 milliwatts of argon laser power. Trapping and manipulation of single live motile bacteria and Escherichia coli bacteria were also demonstrated in a high-resolution microscope at powers of a few milliwatts.
    14. 14
      Ashkin, A.; Dziedzic, J. M.; Bjorkholm, J. E.; Chu, S. Observation of a single-beam gradient force optical trap for dielectric particles. Opt. Lett. 1986, 11 (5), 288– 90,  DOI: 10.1364/OL.11.000288
      14
      Observation of a single-beam gradient force optical trap for dielectric particles
      Ashkin, A.; Dziedzic, J. M.; Bjorkholm, J. E.; Chu, Steven
      Optics Letters (1986), 11 (5), 288-90CODEN: OPLEDP; ISSN:0146-9592.
      Optical trapping of dielec. particles by a single-beam gradient force trap was demonstrated. This confirms the concept of neg. light pressure due to the gradient force. Trapping was obsd. over the entire range of particle size ∼25-10,000 nm in H2O. Use of the new trap extends the size range of macroscopic particles accessible to optical trapping and manipulation well into the Rayleigh size regime. Application of this trapping principle to atom trapping is considered.
    15. 15
      Pinheiro da Silva, B.; Buono, W. T.; Pereira, L. J.; Tasca, D. S.; Dechoum, K.; Khoury, A. Z.. Spin to orbital angular momentum transfer in nonlinear wave mixing. Frontiers in Optics; Optica Publishing Group, 2022. (Accessed 2023-10-17).
      There is no corresponding record for this reference.
    16. 16
      D'Ambrosio, V.; Carvacho, G.; Graffitti, F.; Vitelli, C.; Piccirillo, B.; Marrucci, L.; Sciarrino, F. Entangled vector vortex beams. Phys. Rev. A 2016, 94 (3), 030304,  DOI: 10.1103/PhysRevA.94.030304
      16
      Entangled vector vortex beams
      D'Ambrosio, Vincenzo; Carvacho, Gonzalo; Graffitti, Francesco; Vitelli, Chiara; Piccirillo, Bruno; Marrucci, Lorenzo; Sciarrino, Fabio
      Physical Review A (2016), 94 (3-A), 030304/1-030304/6CODEN: PRAHC3; ISSN:2469-9926. (American Physical Society)
      Light beams having a vectorial field structure, or polarization, that varies over the transverse profile and a central optical singularity are called vector vortex (VV) beams and may exhibit specific properties such as focusing into "light needles" or rotation invariance. VV beams have already found applications in areas ranging from microscopy to metrol., optical trapping, nano-optics, and quantum communication. Individual photons in such beams exhibit a form of single-particle quantum entanglement between different degrees of freedom. On the other hand, the quantum states of two photons can be also entangled with each other. Here, we combine these two concepts and demonstrate the generation of quantum entanglement between two photons that are both in VV states: a form of entanglement between two complex vectorial fields. This result may lead to quantum-enhanced applications of VV beams as well as to quantum information protocols fully exploiting the vectorial features of light.
    17. 17
      Naidoo, D.; Roux, F. S.; Dudley, A.; Litvin, I.; Piccirillo, B.; Marrucci, L.; Forbes, A. Controlled generation of higher-order Poincaré sphere beams from a laser. Nat. Photonics 2016, 10 (5), 327– 332,  DOI: 10.1038/nphoton.2016.37
      17
      Controlled generation of higher-order Poincare sphere beams from a laser
      Naidoo, Darryl; Roux, Filippus S.; Dudley, Angela; Litvin, Igor; Piccirillo, Bruno; Marrucci, Lorenzo; Forbes, Andrew
      Nature Photonics (2016), 10 (5), 327-332CODEN: NPAHBY; ISSN:1749-4885. (Nature Publishing Group)
      The angular momentum of light can be described by positions on a higher-order Poincare sphere, where superpositions of spin and orbital angular momentum states give rise to laser beams that have many applications, from microscopy to materials processing. Many techniques exist to create such beams but none so far allow their creation at the source. Here we report on a new class of laser that is able to generate all states on the higher-order Poincare sphere. We exploit geometric phase control inside a laser cavity to map polarization to orbital angular momentum, demonstrating that the orbital angular momentum degeneracy of a std. laser cavity may be broken, producing pure orbital angular momentum beams, and that generalized vector vortex beams may be created with high purity at the source. This work paves the way to new lasers for structured light based on intracavity geometric phase control.
    18. 18
      Li, Y.; Li, J.; Lü, B. Needle beam generation from an azimuthally polarized beam using a phase-only zone plate. Opt. Lett. 2017, 42 (4), 771– 774
      There is no corresponding record for this reference.
    19. 19
      Delaney, S.; Sanchez-Lopez, M. M.; Moreno, I.; Davis, J. A. Arithmetic with q-plates. Appl. Opt. 2017, 56 (3), 596– 600,  DOI: 10.1364/AO.56.000596
      19
      Arithmetic with q-plates
      Delaney Sam; Sanchez-Lopez Maria M; Moreno Ignacio; Davis Jeffrey A
      Applied optics (2017), 56 (3), 596-600 ISSN:.
      In this work we show the capability to form various q-plate equivalent systems using combinations of commercially available q-plates. We show operations like changing the sign of the q-value, or the addition and subtraction of q-plates. These operations only require simple combinations of q-plates and half-wave plates. Experimental results are presented in all cases. Following this procedure, experimental testing of higher and negative q-valued devices can be carried out using commonly available q-valued devices.
    20. 20
      Machavariani, G.; Lumer, Y.; Moshe, I.; Meir, A.; Jackel, S. Spatially-variable retardation plate for efficient generation of radiallyand azimuthally-polarized beams. Opt. Commun. 2008, 281, 732– 738,  DOI: 10.1016/j.optcom.2007.10.088
      20
      Spatially-variable retardation plate for efficient generation of radially- and azimuthally-polarized beams
      Machavariani, G.; Lumer, Y.; Moshe, I.; Meir, A.; Jackel, S.
      Optics Communications (2008), 281 (4), 732-738CODEN: OPCOB8; ISSN:0030-4018. (Elsevier B.V.)
      We investigate conversion of a linearly-polarized Gaussian beam to a radially- or an azimuthally-polarized doughnut (0, 1)* Laguerre-Gaussian (LG) beams, performed with a spatially-variable retardation (SVR) plate. The SVR plate is composed of eight sectors of a λ/2 retardation plate, each one with different orientation of the to crystal's slow axis. The anal. reveal that nearly-pure radially- or azimuthally-polarized LG(01)* beam with M2 = 2.2 can be obtained, while the transformation efficiency is 89.6%. In the expts., performed with Nd:YAG laser, we transformed a Gaussian beam with M2 = 1.3 to a radially- and azimuthally-polarized (0, 1)* Laguerre-Gaussian beams with M2 = 2.5. We carefully characterized the polarization state of the obtained radially- and azimuthally-polarized beams, measuring Stokes parameters. The polarization purity of the obtained beams, calcd. from the measured data, was as high as 96%.
    21. 21
      Cardano, F.; Karimi, E.; Slussarenko, S.; Marrucci, L.; de Lisio, C.; Santamato, E. Polarization pattern of vector vortex beams generated by q-plates with different topological charges. Appl. Opt. 2012, 51, C1– C6,  DOI: 10.1364/AO.51.0000C1
      There is no corresponding record for this reference.
    22. 22
      Wang, X. L.; Ding, J.; Ni, W. J.; Guo, C. S.; Wang, H. T. Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement. Opt. Lett. 2007, 32, 3549– 3551,  DOI: 10.1364/OL.32.003549
      22
      Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement
      Wang Xi-Lin; Ding Jianping; Ni Wei-Jiang; Guo Cheng-Shan; Wang Hui-Tian
      Optics letters (2007), 32 (24), 3549-51 ISSN:0146-9592.
      We describe a convenient approach for generating arbitrary vector beams in a 4-f system with a spatial light modulator (SLM) and a common path interferometric arrangement. A computer-generated hologram is introduced onto SLM for performing the beam conversion. Optical realization of a variety of polarization configurations confirms the reliability and flexibility of our method.
    23. 23
      Rong, Z. Y.; Han, Y. J.; Wang, S. Z.; Guo, C. S. Generation of arbitrary vector beams with cascaded liquid crystal spatial light modulators. Opt. Express 2014, 22, 1636– 1644,  DOI: 10.1364/OE.22.001636
      23
      Generation of arbitrary vector beams with cascaded liquid crystal spatial light modulators
      Rong Zhen-Yu; Han Yu-Jing; Wang Shu-Zhen; Guo Cheng-Shan
      Optics express (2014), 22 (2), 1636-44 ISSN:.
      A flexible approach is presented to generate vector beams with arbitrary polarization and complex amplitude by means of two cascaded transmissive liquid crystal spatial light modulators (LCSLMs). The configuration of the cascaded LCSLM system and its modulation characteristic are introduced. Theoretical analysis and experimental demonstration prove that the system in combination with a double-pass computer-generated hologram and a black-and-white pattern can generate vector beams with arbitrary polarization and complex amplitude by respectively controlling the complex amplitudes of two orthogonal polarization components of the beams. Using this system, we successfully generate radially polarized vector beams with helical phase distributions and vector Bessel beams with inhomogeneous amplitude distributions in experiments.
    24. 24
      Lim, B. C.; Phua, P. B.; Lai, W. J.; Hong, M. H. Fast switchable electro-optic radial polarization retarder. Opt. Lett. 2008, 33, 950– 952,  DOI: 10.1364/OL.33.000950
      24
      Fast switchable electro-optic radial polarization retarder
      Lim, B. C.; Phua, P. B.; Lai, W. J.; Hong, M. H.
      Optics Letters (2008), 33 (9), 950-952CODEN: OPLEDP; ISSN:0146-9592. (Optical Society of America)
      A fast and switchable electro-optic radial polarization retarder (EO-RPR) fabricated using the electro-optic ceramic Pb(Mg1/3Nb2/3)O3-PbTiO3 is presented. This EO-RPR is useful for fast and switchable generation of a pure cylindrical vector beam. When used together with a pair of half-wave plates, the EO-RPR can change circularly polarized light into any cylindrical vector beam of interest, such as radially or azimuthally polarized light. Radially and azimuthally polarized light with purities greater than 95% are generated exptl. The advantages of using EO-RPR include fast response time, low driving voltage, and transparency in a wide spectral range (500 to 7000 nm).
    25. 25
      Mushiake, Y.; Matsumura, K.; Nakajima, N. Generation of radially polarized optical beam mode by laser oscillation. Proc. IEEE 1972, 60, 1107– 1109,  DOI: 10.1109/PROC.1972.8865
      There is no corresponding record for this reference.
    26. 26
      Naidoo, D.; Aït-Ameur, K.; Brunel, M.; Forbes, A. Intra-cavity generation of superpositions of Laguerre–Gaussian beams. Appl. Phys. B: Laser Opt. 2012, 106, 683– 690,  DOI: 10.1007/s00340-011-4775-x
      There is no corresponding record for this reference.
    27. 27
      Tidwell, S. C.; Ford, D. H.; Kimura, W. D. Generating radially polarized beams interferometrically. Appl. Opt. 1990, 29, 2234– 2239,  DOI: 10.1364/AO.29.002234
      27
      Generating radially polarized beams interferometrically
      Tidwell, Steve C.; Ford, Dennis H.; Kimura, Wayne D.
      Applied Optics (1990), 29 (15), 2234-9CODEN: APOPAI; ISSN:0003-6935.
      Two interferometric techniques for converting a linearly polarized laser beam into a radially polarized beam with uniform azimuthal intensity are described. The techniques are based on the linear combination of orthogonally polarized beams, which have tailored intensity and phase profiles. Linearly polarized beams with intensity profiles tailored using a modified laser or an apodization filter were combined in sep. expts. to produce radially polarized light. A beam with an extinction ratio of -21.7 dB and azimuthal intensity variations of less than ±12% is produced using the modified laser output. The 2nd technique uses circularly polarized light and a unique spiral phase delay to produce the required phase profile. When focused, a radially polarized beam has a net longitudinal field useful for particle acceleration and, perhaps, other unique applications.
    28. 28
      Passilly, N.; Treussart, F.; Hierle, R.; de Saint Denis, R.; Ait-Ameur, K.; Roch, J.-F. Simple interferometric technique for generation of a radially polarized light beam. J. Opt. Soc. Am. A 2005, 22 (984), 984– 991,  DOI: 10.1364/JOSAA.22.000984
      28
      Simple interferometric technique for generation of a radially polarized light beam
      Passilly Nicolas; de Saint Denis Renaud; Ait-Ameur Kamel; Treussart Francois; Hierle Rolland; Roch Jean-Francois
      Journal of the Optical Society of America. A, Optics, image science, and vision (2005), 22 (5), 984-91 ISSN:1084-7529.
      We present a theoretical and experimental investigation of an interferometric technique for converting a linearly polarized Gaussian beam into a radially polarized doughnut beam. The experimental setup accomplishes the coherent summation of two orthogonally polarized TEM01 and TEM10 beams that are obtained from the transformation of a TEM00 beam by use of a simple binary diffractive optical element. We have shown that the degree of radial polarization is maximum at a given distance from the interferometer output port that depends on the diameter of the incident beam at the interferometer input port.
    29. 29
      Khonina, S. N.; Karpeev, S. V.; Alferov, S. V. Polarization converter for higher-order laser beams using a single binary diffractive optical element as beam splitter. Opt. Lett. 2012, 37 (2385), 2385– 2391,  DOI: 10.1364/OL.37.002385
      29
      Polarization converter for higher-order laser beams using a single binary diffractive optical element as beam splitter
      Khonina Svetlana N; Karpeev Sergey V; Alferov Sergey V
      Optics letters (2012), 37 (12), 2385-7 ISSN:.
      We propose a new approach to generating a pair of initial beams for a polarization converter that operates by summing up two opposite-sign circularly polarized beams. The conjugated pairs of vortex beams matched with laser modes are generated using binary diffractive optical elements (DOEs). The same binary element simultaneously serves two functions: a beam shaper and a beam splitter. Two proposed optical arrangements are compared in terms of alignment complexity and energy efficiency. The DOEs in question have been designed and fabricated. Natural experiments that demonstrate the generation of vector higher-order cylindrical beams have been conducted.
    30. 30
      Yue, F.; Wen, D.; Xin, J.; Gerardot, B. D.; Li, J.; Chen, X. Vector Vortex Beam Generation with a Single Plasmonic Metasurface. ACS Photonics 2016, 3 (9), 1558– 1563,  DOI: 10.1021/acsphotonics.6b00392
      30
      Vector Vortex Beam Generation with a Single Plasmonic Metasurface
      Yue, Fuyong; Wen, Dandan; Xin, Jingtao; Gerardot, Brian D.; Li, Jensen; Chen, Xianzhong
      ACS Photonics (2016), 3 (9), 1558-1563CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
      Despite a plethora of applications ranging from quantum memories to high-resoln. lithog., the current technologies to generate vector vortex beams (VVBs) suffer from less efficient energy use, poor resoln., low damage threshold, and bulky size, preventing further practical applications. We propose and exptl. demonstrate an approach to generate VVBs with a single metasurface by locally tailoring phase and transverse polarization distribution. This method features the spin-orbit coupling and the superposition of the converted part with an addnl. phase pickup and the residual part without a phase change. By maintaining the equal components for the converted part and the residual part, the cylindrically polarized vortex beams carrying orbital angular momentum are exptl. demonstrated based on a single metasurface at subwavelength scale. The proposed approach provides unprecedented freedom in engineering the properties of optical waves with high-efficiency light utilization and a minimal footprint.
    31. 31
      Xu, Y.; Zhang, H.; Li, Q.; Zhang, X.; Xu, Q.; Zhang, W.; Hu, C.; Zhang, X.; Han, J.; Zhang, W. Generation of terahertz vector beams using dielectric metasurfaces via spin-decoupled phase control. Nanophotonics 2020, 9 (10), 3393– 3402,  DOI: 10.1515/nanoph-2020-0112
      There is no corresponding record for this reference.
    32. 32
      Liu, Y.; Ke, Y.; Zhou, J.; Liu, Y.; Luo, H.; Wen, S.; Fan, D. Generation of perfect vortex and vector beams based on Pancharatnam-Berry phase elements. Sci. Rep. 2017, 7, 44096,  DOI: 10.1038/srep44096
      32
      Generation of perfect vortex and vector beams based on Pancharatnam-Berry phase elements
      Liu Yachao; Ke Yougang; Zhou Junxiao; Liu Yuanyuan; Luo Hailu; Wen Shuangchun; Fan Dianyuan
      Scientific reports (2017), 7 (), 44096 ISSN:.
      Perfect vortex beams are the orbital angular momentum (OAM)-carrying beams with fixed annular intensities, which provide a better source of OAM than traditional Laguerre-Gaussian beams. However, ordinary schemes to obtain the perfect vortex beams are usually bulky and unstable. We demonstrate here a novel generation scheme by designing planar Pancharatnam-Berry (PB) phase elements to replace all the elements required. Different from the conventional approaches based on reflective or refractive elements, PB phase elements can dramatically reduce the occupying volume of system. Moreover, the PB phase element scheme is easily developed to produce the perfect vector beams. Therefore, our scheme may provide prominent vortex and vector sources for integrated optical communication and micromanipulation systems.
    33. 33
      Zeng, J.; Li, L.; Yang, X.; Gao, J. Generating and Separating Twisted Light by gradient-rotation Split-Ring Antenna Metasurfaces. Nano Lett. 2016, 16, 3101– 3108,  DOI: 10.1021/acs.nanolett.6b00360
      33
      Generating and Separating Twisted Light by gradient-rotation Split-Ring Antenna Metasurfaces
      Zeng, Jinwei; Li, Ling; Yang, Xiaodong; Gao, Jie
      Nano Letters (2016), 16 (5), 3101-3108CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
      Nanoscale compact optical vortex generators promise substantially significant prospects in modern optics and photonics, leading to many advances in sensing, imaging, quantum communication, and optical manipulation. However, conventional vortex generators often suffer from bulky size, low vortex mode purity in the converted beam, or limited operation bandwidth. Here, we design and demonstrate gradient-rotation split-ring antenna metasurfaces as unique spin-to-orbital angular momentum beam converters to simultaneously generate and sep. pure optical vortices in a broad wavelength range. Our proposed design has the potential for realizing miniaturized on-chip OAM-multiplexers, as well as enabling new types of metasurface devices for the manipulation of complex structured light beams.
    34. 34
      Zeng, J.; Luk, T. S.; Gao, J.; Yang, X. Spiraling light with magnetic metamaterial quarter-wave turbines. Sci. Rep. 2017, 7, 11824,  DOI: 10.1038/s41598-017-12143-7
      34
      Spiraling Light with Magnetic Metamaterial Quarter-Wave Turbines
      Zeng Jinwei; Gao Jie; Yang Xiaodong; Luk Ting S
      Scientific reports (2017), 7 (1), 11824 ISSN:.
      Miniaturized quarter-wave plate devices empower spin to orbital angular momentum conversion and vector polarization formation, which serve as bridges connecting conventional optical beam and structured light. Enabling the manipulability of additional dimensions as the complex polarization and phase of light, quarter-wave plate devices are essential for exploring a plethora of applications based on orbital angular momentum or vector polarization, such as optical sensing, holography, and communication. Here we propose and demonstrate the magnetic metamaterial quarter-wave turbines at visible wavelength to produce radially and azimuthally polarized vector vortices from circularly polarized incident beam. The magnetic metamaterials function excellently as quarter-wave plates at single wavelength and maintain the quarter-wave phase retardation in broadband, while the turbine blades consist of multiple polar sections, each of which contains homogeneously oriented magnetic metamaterial gratings near azimuthal or radial directions to effectively convert circular polarization to linear polarization and induce phase shift under Pancharatnum-Berry's phase principle. The perspective concept of multiple polar sections of magnetic metamaterials can extend to other analogous designs in the strongly coupled nanostructures to accomplish many types of light phase-polarization manipulation and structured light conversion in the desired manner.
    35. 35
      Yi, X.; Ling, X.; Zhang, Z.; Li, Y.; Zhou, X.; Liu, Y. Generation of cylindrical vector vortex beams by two cascaded metasurfaces. Opt. Express 2014, 22 (17207), 17207– 17215,  DOI: 10.1364/OE.22.017207
      35
      Generation of cylindrical vector vortex beams by two cascaded metasurfaces
      Yi Xunong; Ling Xiaohui; Zhang Zhiyou; Li Ying; Zhou Xinxing; Liu Yachao; Chen Shizhen; Luo Hailu; Wen Shuangchun
      Optics express (2014), 22 (14), 17207-15 ISSN:.
      We present a simple and efficient method to generate any cylindrical vector vortex (CVV) beams based on two cascaded metasurfaces. The metasurface works as a space-variant Panchratnam-Berry phase element and can produce any desirable vortex phase and vector polarization. The first metasurface is used to switch the sign of topological charges associated with vortex, and the second metasurface is applied to manipulate the local polarization. This method allows us to simultaneously manipulate polarization and phase of the CVV beams.
    36. 36
      Liu, Z.; Liu, Y.; Ke, Y.; Liu, Y.; Shu, W.; Luo, H. Generation of arbitrary vector vortex beams on hybrid-order Poincaré sphere. Photonics Res. 2017, 5 (1), 15– 21,  DOI: 10.1364/PRJ.5.000015
      There is no corresponding record for this reference.
    37. 37
      He, Y.; Li, Y.; Liu, J.; Zhang, X.; Cai, Y.; Chen, Y.; Chen, S.; Fan, D. Switchable phase and polarization singular beams generation using dielectric metasurfaces. Sci. Rep. 2017, 7 (1), 6814,  DOI: 10.1038/s41598-017-07217-5
      37
      Switchable phase and polarization singular beams generation using dielectric metasurfaces
      He Yanliang; Li Ying; Liu Junmin; Zhang Xiaoke; Cai Yao; Chen Yu; Chen Shuqing; Fan Dianyuan
      Scientific reports (2017), 7 (1), 6814 ISSN:.
      Singular beams which possess helical phase wavefront or spatially inhomogeneous polarization provide new freedom for optical field manipulation. However, conventional schemes to produce the singular beams have difficulty in realizing the flexible switch between different singular beams. In this work, we have experimentally demonstrated the capability of dielectric metasurfaces to generate three types of singular beams and switch between them at working wavelength of 1550 nm. We have shown vortex beam and cylindrical vector beam generation with single metasurface and cylindrical vector vortex beam generation with two cascaded metasurfaces. Moreover, experimental demonstration on switching cylindrical vector beam into vortex beam has also been done by combining one quarter-wave plate and a Glan laser polarizer. The experimental results match well with the analysis from the Jones matrix calculations. The average conversion efficiency of cylindrical vector beam to vortex beam was estimated to be 47.7%, which was about 2.3% lower than the theoretical prediction.
    38. 38
      He, Y.; Ye, H.; Liu, J.; Xie, Z.; Zhang, X.; Xiang, Y. Order-controllable cylindrical vector vortex beam generation by using spatial light modulator and cascaded metasurfaces. IEEE Photon J. 2017, 9 (5), 6101710,  DOI: 10.1109/JPHOT.2017.2741508
      There is no corresponding record for this reference.
    39. 39
      Wang, S.; Liu, Y.; Yang, S. A.; Lei, D. Y. Multifunctional vector beam generation using metasurface. Appl. Phys. Lett. 2019, 114 (12), 121103
      There is no corresponding record for this reference.
    40. 40
      Fu, P.; Ni, P.-N.; Wu, B.; Pei, X.-Z.; Wang, Q.-H.; Chen, P.-P.; Xu, C.; Kan, Q.; Chu, W.-G.; Xie, Y.-Y. Metasurface Enabled On-Chip Generation and Manipulation of Vector Beams from Vertical Cavity Surface-Emitting Lasers. Adv. Mater. 2023, 35 (12), 2204286,  DOI: 10.1002/adma.202204286
      40
      Metasurface Enabled On-Chip Generation and Manipulation of Vector Beams from Vertical Cavity Surface-Emitting Lasers
      Fu, Pan; Ni, Pei-Nan; Wu, Bo; Pei, Xian-Zhi; Wang, Qiu-Hua; Chen, Pei-Pei; Xu, Chen; Kan, Qiang; Chu, Wei-Guo; Xie, Yi-Yang
      Advanced Materials (Weinheim, Germany) (2023), 35 (12), 2204286CODEN: ADVMEW; ISSN:0935-9648. (Wiley-VCH Verlag GmbH & Co. KGaA)
      Metasurface polarization optics that consist of 2D array of birefringent nano-antennas have proven remarkable capabilities to generate and manipulate vectorial fields with subwavelength resoln. and high efficiency. Integrating this new type of metasurface with the std. vertical cavity surface-emitting laser (VCSEL) platform enables an ultracompact and powerful soln. to control both phase and polarization properties of the laser on a chip, which allows to structure a VCSEL into vector beams with on-demand wavefronts. Here, this concept is demonstrated by directly generating versatile vector beams from com. available VCSELs through on-chip integration of high-index dielec. metasurfaces. Exptl., the versatility of the approach for the development of vectorial VCSELs are validated by implementing a variety of functionalities, including directional emission of multibeam with specified polarizations, vectorial holog. display, and vector vortex beams generations. Notably, the proposed vectorial VCSELs integrated with a single layer of beam shaping metasurface bypass the requirements of multiple cascaded optical components, and thus have the potential to promote the advancements of ultracompact, lightweightand scalable vector beams sources, enriching and expanding the applications of VCSELs in optical communications, laser manipulation and processing, information encryption, and quantum optics.
    41. 41
      Cai, X.; Wang, J.; Strain, M. J.; Johnson-Morris, B.; Zhu, J.; Sorel, M.; O’Brien, J. L.; Thompson, M. G.; Yu, S. Integrated Compact Optical Vortex Beam Emitters. Science 2012, 338 (6105), 363– 366,  DOI: 10.1126/science.1226528
      41
      Integrated compact optical vortex beam emitters
      Cai, Xinlun; Wang, Jianwei; Strain, Michael J.; Johnson-Morris, Benjamin; Zhu, Jiangbo; Sorel, Marc; O'Brien, Jeremy L.; Thompson, Mark G.; Yu, Siyuan
      Science (Washington, DC, United States) (2012), 338 (6105), 363-366CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
      Emerging applications based on optical beams carrying orbital angular momentum (OAM) will probably require photonic integrated devices and circuits for miniaturization, improved performance, and enhanced functionality. We demonstrate silicon-integrated optical vortex emitters, using angular gratings to ext. light confined in whispering gallery modes with high OAM into free-space beams with well-controlled amts. of OAM. The smallest device has a radius of 3.9 μm. Exptl. characterization confirms the theor. prediction that the emitted beams carry exactly defined and adjustable OAM. Fabrication of integrated arrays and demonstration of simultaneous emission of multiple identical optical vortices provide the potential for large-scale integration of optical vortex emitters on complementary metal-oxide-semiconductor compatible silicon chips for wide-ranging applications.
    42. 42
      Zhen, B.; Hsu, C. W.; Lu, L.; Stone, A. D.; Soljacic, M. Topological Nature of Optical Bound States in the Continuum. Phys. Rev. Lett. 2014, 113, 257401,  DOI: 10.1103/PhysRevLett.113.257401
      42
      Topological nature of optical bound states in the continuum
      Zhen, Bo; Hsu, Chia Wei; Lu, Ling; Stone, A. Douglas; Soljacic, Marin
      Physical Review Letters (2014), 113 (25), 257401-1/1-257401-1/5, 5 pp.CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      Optical bound states in the continuum (BICs) have recently been realized in photonic crystal slabs, where the disappearance of out-of-plane radiation turns leaky resonances into guided modes with infinite lifetimes. We show that such BICs are vortex centers in the polarization directions of far-field radiation. They carry conserved and quantized topol. charges, defined by the winding no. of the polarization vectors, which ensure their robust existence and govern their generation, evolution, and annihilation. Our findings connect robust BICs in photonics to a wide range of topol. phys. phenomena.
    43. 43
      Yoda, T.; Notomi, M. Generation and Annihilation of Topologically Protected Bound States in the Continuum and Circularly Polarized States by Symmetry Breaking. Phys. Rev. Lett. 2020, 125, 053902,  DOI: 10.1103/PhysRevLett.125.053902
      43
      Generation and Annihilation of Topologically Protected Bound States in the Continuum and Circularly Polarized States by Symmetry Breaking
      Yoda, Taiki; Notomi, Masaya
      Physical Review Letters (2020), 125 (5), 053902CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
      We demonstrate by breaking the C6 symmetry for higher-order at-Γ bound states in the continuum (BICs) with topol. charge -2 in photonic crystals (i) deterministic generation of off-Γ BICs from the at-Γ BIC and (ii) a variety of pair-creation and annihilation processes of circularly polarized states with opposite topol. charges and the same handedness. To explain these phenomena, we introduce the handedness-wise topol. charge quantized to a half-integer. The handedness-wise charge gives a unified picture of various phenomena involving BICs and circularly polarized states.
    44. 44
      Iwahashi, S.; Kurosaka, Y.; Sakai, K.; Kitamura, K.; Takayama, N.; Noda, S. Higher-order vector beams produced by photonic-crystal lasers. Opt. Exp. 2011, 19, 11963,  DOI: 10.1364/OE.19.011963
      There is no corresponding record for this reference.
    45. 45
      Kodigala, A.; Lepetit, T.; Gu, Q.; Bahari, B.; Fainman, Y.; Kante, B. Lasing action from photonic bound states in continuum. Nature 2017, 541 (7636), 196– 199,  DOI: 10.1038/nature20799
      45
      Lasing action from photonic bound states in continuum
      Kodigala, Ashok; Lepetit, Thomas; Gu, Qing; Bahari, Babak; Fainman, Yeshaiahu; Kante, Boubacar
      Nature (London, United Kingdom) (2017), 541 (7636), 196-199CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
      In 1929, only three years after the advent of quantum mechanics, von Neumann and Wigner showed that Schrodinger's equation can have bound states above the continuum threshold. These peculiar states, called bound states in the continuum (BICs), manifest themselves as resonances that do not decay. For several decades afterwards the idea lay dormant, regarded primarily as a math. curiosity. In 1977, Herrick and Stillinger revived interest in BICs when they suggested that BICs could be obsd. in semiconductor superlattices. BICs arise naturally from Feshbach's quantum mech. theory of resonances, as explained by Friedrich and Wintgen, and are thus more phys. than initially realized. Recently, it was realized that BICs are intrinsically a wave phenomenon and are thus not restricted to the realm of quantum mechanics. They have since been shown to occur in many different fields of wave physics including acoustics, microwaves and nanophotonics. However, exptl. observations of BICs have been limited to passive systems and the realization of BIC lasers has remained elusive. Here we report, at room temp., lasing action from an optically pumped BIC cavity. Our results show that the lasing wavelength of the fabricated BIC cavities, each made of an array of cylindrical nanoresonators suspended in air, scales with the radii of the nanoresonators according to the theor. prediction for the BIC mode. Moreover, lasing action from the designed BIC cavity persists even after scaling down the array to as few as 8-by-8 nanoresonators. BIC lasers open up new avenues in the study of light-matter interaction because they are intrinsically connected to topol. charges and represent natural vector beam sources (i.e., there are several possible beam shapes), which are highly sought after in the fields of optical trapping, biol. sensing and quantum information.
    46. 46
      Doeleman, H. M.; Monticone, F.; den Hollander, W.; Alù, A.; Koenderink, A. F. Experimental observation of a polarization vortex at an optical bound state in the continuum. Nat. Photonics 2018, 12, 397– 401,  DOI: 10.1038/s41566-018-0177-5
      46
      Experimental observation of a polarization vortex at an optical bound state in the continuum
      Doeleman, Hugo M.; Monticone, Francesco; den Hollander, Wouter; Alu, Andrea; Koenderink, A. Femius
      Nature Photonics (2018), 12 (7), 397-401CODEN: NPAHBY; ISSN:1749-4885. (Nature Research)
      Optical bound states in the continuum (BICs) are states supported by a photonic structure that are compatible with free-space radiation, yet become perfectly bound for one specific in-plane momentum and wavelength1,2. Recently, it was predicted that light radiated by such modes around the BIC momentum-frequency condition should display a vortex in its far-field polarization profile, making the BIC topol. protected3. Here, we study a one-dimensional grating supporting a transverse magnetic mode with a BIC near 700 nm wavelength, verifying the existence of the BIC using reflection measurements, which show a vanishing reflection feature. Using k-space polarimetry, we measure the full polarization state of reflection around the BIC, highlighting the presence of a topol. vortex. We use an electromagnetic dipole model to explain the obsd. BIC through destructive interference between two radiation channels, characteristic of a Friedrich-Wintgen-type BIC4. Our findings shed light on the origin of BICs and verify their topol. nature.
    47. 47
      Wang, B.; Liu, W.; Zhao, M.; Wang, J.; Zhang, Y.; Chen, A.; Guan, F.; Liu, X.; Shi, L.; Zi, J. Generating optical vortex beams by momentum-space polarization vortices centered at bound states in the continuum. Nat. Photonics 2020, 14, 623,  DOI: 10.1038/s41566-020-0658-1
      47
      Generating optical vortex beams by momentum-space polarization vortices centred at bound states in the continuum
      Wang, Bo; Liu, Wenzhe; Zhao, Maoxiong; Wang, Jiajun; Zhang, Yiwen; Chen, Ang; Guan, Fang; Liu, Xiaohan; Shi, Lei; Zi, Jian
      Nature Photonics (2020), 14 (10), 623-628CODEN: NPAHBY; ISSN:1749-4885. (Nature Research)
      Abstr.: Optical vortices, beams with spiral wavefronts and screw phase dislocations, have been attracting increasing interest in various fields. Here, we theor. propose and exptl. realize an easy approach to generating optical vortices. We leverage the inherent momentum-space topol. vortex-like response of polarization (strong polarization anisotropy) around bound states in the continuum of two-dimensional periodic structures, for example photonic crystal slabs, to induce Pancharatnam-Berry phases and spin-orbit interaction in the beams. This new class of optical vortex generators operates in momentum space, meaning that the structure is almost homogeneous without a real-space center. In principle, any even-order optical vortex that is a diffraction-resistant high-order quasi-Bessel beam can be achieved at any desired working wavelength. The proposed approach expands the application of bound states in the continuum and topol. photonics.
    48. 48
      Huang, C.; Zhang, C.; Xiao, S.; Wang, Y.; Fan, Y.; Liu, Y.; Zhang, N.; Qu, G.; Ji, H.; Han, J.; Ge, L.; Kivshar, Y.; Song, Q. Ultrafast control of vortex microlasers. Science 2020, 367, 1018,  DOI: 10.1126/science.aba4597
      48
      Ultrafast control of vortex microlasers
      Huang, Can; Zhang, Chen; Xiao, Shumin; Wang, Yuhan; Fan, Yubin; Liu, Yilin; Zhang, Nan; Qu, Geyang; Ji, Hongjun; Han, Jiecai; Ge, Li; Kivshar, Yuri; Song, Qinghai
      Science (Washington, DC, United States) (2020), 367 (6481), 1018-1021CODEN: SCIEAS; ISSN:1095-9203. (American Association for the Advancement of Science)
      The development of classical and quantum information-processing technol. calls for on-chip integrated sources of structured light. Although integrated vortex microlasers have been previously demonstrated, they remain static and possess relatively high lasing thresholds, making them unsuitable for high-speed optical communication and computing. We introduce perovskite-based vortex microlasers and demonstrate their application to ultrafast all-optical switching at room temp. By exploiting both mode symmetry and far-field properties, we reveal that the vortex beam lasing can be switched to linearly polarized beam lasing, or vice versa, with switching times of 1 to 1.5 ps and energy consumption that is orders of magnitude lower than in previously demonstrated all-optical switching. Our results provide an approach that breaks the long-standing trade-off between low energy consumption and high-speed nanophotonics, introducing vortex microlasers that are switchable at terahertz frequencies.
    49. 49
      Cai, Z.; Wu, C.; Jiang, J.; Ding, Y.; Zheng, Z.; Ding, F. Phase-change metasurface for switchable vector vortex beam generation. Optics Express 2021, 29 (26), 42762– 42771,  DOI: 10.1364/OE.444956
      49
      Phase-change metasurface for switchable vector vortex beam generation
      Cai, Ziru; Wu, Cuo; Jiang, Jing; Ding, Yingtao; Zheng, Ziwei; Ding, Fei
      Optics Express (2021), 29 (26), 42762-42771CODEN: OPEXFF; ISSN:1094-4087. (Optica Publishing Group)
      Metasurfaces have attracted increasing attention due to their unprecedented capabilities of molding optical fields with exceedingly low losses. Despite significant achievements, most existing metasurfaces are passive and lack dynamic modulation post-fabrication. Here, we propose a tunable phase-change metasurface for switchable vector vortex beam generation in the mid-IR range. The phase-change meta-mol., consisting of two coupled Ge2Sb2Te5 (GST) bricks, is firstly designed to perform the switching between a quarter-wave plate and a usual transmissive plate over a wavelength range from 4.95 to 5.05 μm under the amorphous and cryst. phases of GST, resp. Furthermore, a general method is derived to achieve a switchable vector vortex beam generator at the target wavelength of 5 μm by spatially orienting GST meta-mols. to locally tailor phase and polarization distribution. Under the amorphous phase, radially polarized and azimuthally polarized beams, composed of the co-polarized circularly polarized (CP) component carrying orbital angular momentum (OAM) with a topol. charge of l = 0 and cross-polarized CP component carrying OAM with a topol. charge of l = ±2 are obtained for the left circularly polarized (LCP) and right circularly polarized (RCP) incident waves, resp. The mode purity values of the cross-polarized component and the co-polarized component are calcd. to be ∼ 0.949 and ∼ 0.955. When GST transits to its cryst. phase, the vector vortex beam disappears, and the incident CP beams pass through directly. Our finding paves the way for advanced applications targeting photonics integration with switchable functionalities.
    50. 50
      Tian, J.; Adamo, G.; Liu, H.; Wu, M.; Klein, M.; Deng, J.; Ang, N. S. S.; Paniagua-Dominguez, R.; Liu, H.; Kuznetsov, A. I.; Soci, C. Phase-Change Perovskite Microlaser with Tunable Polarization Vortex. Adv. Mater. 2023, 35, 2207430,  DOI: 10.1002/adma.202207430
      50
      Phase-Change Perovskite Microlaser with Tunable Polarization Vortex
      Tian, Jingyi; Adamo, Giorgio; Liu, Hailong; Wu, Mengfei; Klein, Maciej; Deng, Jie; Ang, Norman Soo Seng; Paniagua-Dominguez, Ramon; Liu, Hong; Kuznetsov, Arseniy I.; Soci, Cesare
      Advanced Materials (Weinheim, Germany) (2023), 35 (1), 2207430CODEN: ADVMEW; ISSN:0935-9648. (Wiley-VCH Verlag GmbH & Co. KGaA)
      Metasurfaces supporting optical bound states in the continuum (BICs) are emerging as simple and compact optical cavities to realize polarization-vortex lasers. The winding of the polarization around the singularity defines topol. charges which are generally set by the cavity design and cannot be altered without changing geometrical parameters. Here, a subwavelength-thin phase-change halide perovskite BIC metasurface functioning as a tunable polarization vortex microlaser is demonstrated. Upon the perovskite structural phase transitions, both its refractive index and gain vary substantially, inducing reversible and bistable switching between distinct polarization vortexes underpinned by opposite topol. charges. Dynamic tuning and switching of the resulting vector beams may find use in microscopy imaging, particle trapping and manipulation, and optical data storage.
    51. 51
      Shi, S.; Chen, C.; Prather, D. W. Plane-wave expansion method for calculating band structure of photonic crystal slabs with perfectly matched layers. J. Opt. Soc. Am. 2004, 21 (9), 1769– 1775,  DOI: 10.1364/JOSAA.21.001769
      51
      Plane-wave expansion method for calculating band structure of photonic crystal slabs with perfectly matched layers
      Shi Shouyuan; Chen Caihua; Prather Dennis W
      Journal of the Optical Society of America. A, Optics, image science, and vision (2004), 21 (9), 1769-75 ISSN:1084-7529.
      We present a new algorithm for calculation of the band structure of photonic crystal slabs. This algorithm combines the plane-wave expansion method with perfectly matched layers for the termination of the computational region in the direction out of the plane. In addition, the effective-medium tensor is applied to improve convergence. A general complex eigenvalue problem is then obtained. Two criteria are presented to distinguish the guided modes from the PML modes. As such, this scheme can accurately determine the band structure both above and below the light cone. The convergence of the algorithm presented has been studied. The results obtained by using this algorithm have been compared with those obtained by the finite-difference time-domain method and found to agree very well.
    52. 52
      Cao, Y.; Hou, Z.; Liu, Y. Convergence problem of plane-wave expansion method for phononic crystals. Phys. Lett. A 2004, 327 (2–3), 247– 253,  DOI: 10.1016/j.physleta.2004.05.030
      52
      Convergence problem of plane-wave expansion method for phononic crystals
      Cao, Yongjun; Hou, Zhilin; Liu, Youyan
      Physics Letters A (2004), 327 (2-3), 247-253CODEN: PYLAAG; ISSN:0375-9601. (Elsevier Science B.V.)
      A new formulation of eigenproblem for phononic crystals is developed. The convergence of the new formulation in the band-structure calcns. is examd. in detail and compared with that of the conventional plane wave expansion (CPWE) method. Numerical results show that the slow convergence of the CPWE method is not due to the slow convergence of the Fourier series for the elastic coeffs. (or displacement fields) in the interfaces of different materials, but to the inappropriate formulation of the eigenproblem used in the calcns. Numerical calcns. also show that the new formulation can provide much more accurate numerical results than the CPWE method for the systems of either very high or very low filling fractions, or of large elastic mismatch.
    53. 53
      David, A.; Benisty, H.; Weisbuch, C. Fast factorization rule and plane-wave expansion method for two-dimensional photonic crystals with arbitrary hole-shape. Phys. Rev. B 2006, 73, 075107,  DOI: 10.1103/PhysRevB.73.075107
      53
      Fast factorization rule and plane-wave expansion method for two-dimensional photonic crystals with arbitrary hole-shape
      David, Aurelien; Benisty, Henri; Weisbuch, Claude
      Physical Review B: Condensed Matter and Materials Physics (2006), 73 (7), 075107/1-075107/7CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
      A modified implementation of the plane-wave expansion for calcn. of photonic crystals band structures is introduced in order to circumvent the slow convergence stemming from field discontinuities. By using an adequate form of the Fourier transform of the dielec. const., a fast convergence rate is achieved for any photonic crystal pattern. This result, which generalizes previous convergence studies, is exemplified in the important case of photonic crystal with circular holes. We further consider more sophisticated structures, such as elliptical hole-shapes as well as supercell calcns. for waveguides. We also address calcns. of ultraflat photonic bands.
    54. 54
      Huang, S.-C.; Hong, K.-B.; Chiu, H.-L.; Lan, S.-W.; Chang, T.-C.; Li, H.; Lu, T.-C. Design of photonic crystal surface emitting lasers with indium-tin-oxide top claddings. Appl. Phys. Lett. 2018, 112 (6), 1105,  DOI: 10.1063/1.5016442
      There is no corresponding record for this reference.
    55. 55
      Miao, P.; Zhang, Z.; Sun, J.; Walasik, W.; Longhi, S.; Litchinitser, N. M.; Feng, L. Orbital angular momentum microlaser. Science 2016, 353, 464– 467,  DOI: 10.1126/science.aaf8533
      55
      Orbital angular momentum microlaser
      Miao, Pei; Zhang, Zhifeng; Sun, Jingbo; Walasik, Wiktor; Longhi, Stefano; Litchinitser, Natalia M.; Feng, Liang
      Science (Washington, DC, United States) (2016), 353 (6298), 464-467CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
      Structured light provides an addnl. degree of freedom for modern optics and practical applications. The effective generation of orbital angular momentum (OAM) lasing, esp. at a micro- and nanoscale, could address the growing demand for information capacity. By exploiting the emerging non-Hermitian photonics design at an exceptional point, we demonstrate a microring laser producing a single-mode OAM vortex lasing with the ability to precisely define the topol. charge of the OAM mode. The polarization assocd. with OAM lasing can be further manipulated on demand, creating a radially polarized vortex emission. Our OAM microlaser could find applications in the next generation of integrated optoelectronic devices for optical communications in both quantum and classical regimes.

  • Supporting Information

    Supporting Information

    The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsphotonics.3c00561.

    • Additional polarization simulation results in k-space, FFP measured with a polarizer, and self-interference measurement results (PDF)


    Terms & Conditions

    Most electronic Supporting Information files are available without a subscription to ACS Web Editions. Such files may be downloaded by article for research use (if there is a public use license linked to the relevant article, that license may permit other uses). Permission may be obtained from ACS for other uses through requests via the RightsLink permission system: http://pubs.acs.org/page/copyright/permissions.html.