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In-Plane and Out-of-Plane Investigation of Resonant Tunneling Polaritons in Metal–Dielectric–Metal Cavities
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Nano Letters

Cite this: Nano Lett. 2023, 23, 4, 1489–1495
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https://doi.org/10.1021/acs.nanolett.2c04864
Published February 6, 2023

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Abstract

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Polaritons can be generated by tuning the optical transitions of a light emitter to the resonances of a photonic cavity. We show that a dye-doped cavity generates resonant tunneling polaritons with Epsilon-Near-Zero (ENZ) effective permittivity. We studied the polariton spectral dispersion in dye-doped metal-dielectric-metal (MDM) cavities as a function of the in-plane (k||) and out-of-plane (k⊥) components of the incident wavevector. The dependence on k|| was investigated through ellipsometry, revealing the ENZ modes. The k⊥ dependence was measured by varying the cavity thickness under normal incidence using a Surface Force Apparatus (SFA). Both methods revealed a large Rabi splitting well exceeding 100 meV. The SFA-based investigation highlighted the collective nature of strong coupling by producing a splitting proportional to the square root of the involved photons. This study demonstrates the possibility of generating ENZ polaritons and introduces the SFA as a powerful tool for the characterization of strong light–matter interactions.

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Keywords

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Light–matter interaction between a quantum system (light-emitting molecules, quantum dots, nanocrystals, etc.) and an electromagnetic resonator can be so strong that hybrid quasi-particles called polaritons are generated. (1−6) Several systems have been proposed as resonators but, among them, Fabry–Perot resonators are the most broadly used. (7−19) In a Fabry–Perot resonator with a single cavity, the resonances can be finely tuned by changing (i) the thickness tD of the dielectric(s) in the cavity, (ii) the refractive index nDof the dielectric layer(s), (iii) the incidence angle θi of the input radiation, and (iv) its polarization (20) (see schematic illustration in Section 1 in the Supporting Information (SI)).
In a planar Fabry–Perot cavity, monochromatic plane waves satisfy the dispersion relation k||2 + k⊥2 = (ω/c)2ε, where k|| = ki sin(θi) and k⊥ = ki cos(θi) are the in-plane and out-of-plane components of the incident wavevector (respectively parallel and normal to the layers), ε is the dielectric permittivity, ω is the frequency, and c is the speed of light. A resonance occurs when eq 1 is satisfied: (21,22)
λ(θi)≈λq1−sin2(θi)nD2
(1)
The resonant wavelength under normal incidence (λq) can be calculated from the equation
2nDtDλq+ϕ(λq)π=q
(2)
where q is the modal order (q = 1, 2, 3, ...) and ϕ is the phase shift under reflection at the dielectric/metal interface.
Combining eq 2 with eq 1 shows that the same resonance wavelength can be obtained by either varying the incidence angle θi with a fixed cavity thickness tD, or varying tD under normal incidence (θi = 0) (Section 1 in the SI).
It has been recently demonstrated that the resonances of a metal–dielectric–metal (MDM) resonator possess an epsilon-near-zero (ENZ) character, with a vanishing real part and a small imaginary part of the effective dielectric permittivity. (23) Since polaritons inherit properties from both the “matter” (emitter) and the “photon” (cavity mode) counterparts, it is plausible to expect that they could inherit the ENZ features of the MDM resonances.
In this Letter, we report on the spectral dispersion of MDM cavities made of Ag as metal and a PVP-Rhodamine 6G (R6G) blend as the dielectric (sketch in Figure 1b), and we experimentally demonstrate that the polaritons inherit the ENZ character of the cavity modes. Spectroscopic ellipsometry was used to determine the in-plane dispersion as a function of k|| (i.e., with respect to the incidence angle θi), whereas the out-of-plane dispersion was determined as a function of the cavity thickness tD under normal incidence. The latter measurement were performed with a surface forces apparatus (SFA), which is an instrument originally designed to quantify surface forces at the nanoscale, and was recently adapted to vary the dielectric thickness of MDM cavities from the micrometer scale down to a few nanometers. (24) The SFA experiments highlighted the collective nature of strong coupling as a dependence of the Rabi splitting on the number of photons in the cavity, an effect that is often overshadowed by the dependence on the number of emitters.

Figure 1

Figure 1. (a) Reflectance of an undoped MDM cavity (see inset) calculated with the SMM for s-polarization, and PVP and Ag layers with thicknesses of 350 and 35 nm, respectively. (b) Experimental and calculated s-polarization reflectance of the doped MDM cavity with R6G embedded in the PVP layer (see inset). (c) Analytically calculated (solid blue lines) and experimentally measured (blue stars) angular dispersion of resonances in the doped MDM cavity. Hybridization of the MDM cavity mode (black dash-dotted curve) with the LE and HE excitons of R6G (dashed horizontal lines) generates the low, middle, and high polariton branches (LP, MP, and HP), respectively. (d–l) Experimental reflectance at different incident angles θi.

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We first consider the interaction between the optical transitions of R6G molecules and ENZ cavity modes as a function of the parallel wavevector component k||. The angular dispersion of the MDM cavity is characterized by a blue-shift of the resonance wavelength as the angle of incidence θi is increased (eq 1 and Figure 1a). (22) Note that varying the angle of incidence provides the same information that can be obtained via k-space spectroscopy.
To highlight the effect of optical coupling, we calculated the angle-dependent reflectance of an undoped (i.e., dye-free) Ag/PVP/Ag MDM using Scattering Matrix Method (SMM) simulations, and we compared the results with our experiments obtained for a R6G-doped cavity with the same geometry (PVP and Ag layers with thicknesses of 35 and 315 nm, respectively; see Figures 1a and 1b). We consider the reflectance for the s-polarization. When the incidence angle increases, the resonance modes of the undoped cavity blue-shift (see Figure 1a).
Rhodamine 6G hosts two main active optical transitions peaked at wavelengths of 508 and 546 nm, which translate into a high-energy (HE) and a low-energy (LE) excitonic absorption peak, respectively (see Section 2 of the SI). (25) The HE exciton has an energy of ∼2.441 eV that can be related to vibronic sidebands. (25) It is characterized by a small transition dipole moment, as confirmed by the low oscillator amplitude in the Gaussian fit of the imaginary part of the refractive index of dye-doped PVP + Rhodamine 6G layer measured via spectroscopic ellipsometry (see Section 2 of the SI). The LE exciton, on the other hand, occurs at an energy of ∼2.27 eV and possesses a large transition dipole moment associated with S1 π–π* bonding. (25) Strong coupling between a single-transition “R6G-like” molecule and a cavity mode has been recently investigated theoretically by Gallego et al. (26) The authors considered rovibrational degrees of freedom and showed that dark hybrid states can be brightened in the strong coupling regime, leading to additional bright polaritonic states. However, this is not our case, since the two excitonic transitions, LE and HE, are already present in the absorption spectrum of R6G molecules, and we address a scenario of three coupled oscillators, in which two of them are represented by the two excitons and the third one is the cavity mode.
Off-resonance, the angular dispersion of the doped MDM cavity is similar to that of the undoped cavity, and the resonance wavelength blue-shifts as the incidence angle increases (see the band between 300 and 400 nm in Figure 1a). Near and on-resonance, when the cavity photon energy is close to an R6G transition, exciton-cavity polaritons are generated, and the dispersion of the resonant modes splits into polaritonic branches (Figure 1b). The splitting measured in reflection with s-polarization was accurately reproduced by SMM calculations (for the p-polarization, see Section 3 of ther SI), and the refractive index of both the Ag and R6G layers used in these calculations was measured via spectroscopic ellipsometry.
Figures 1b and 1c depict the polariton dispersions with avoided-crossing points between cavity modes and the LE and HE excitons of R6G at two distinct incidence angles: θin = ±35° and θin = ±50°, respectively. Since the HE and LE excitons have similar energies, they can both couple to the same cavity mode. This interaction can be modeled considering three coupled oscillators, producing three polaritonic dispersion branches, labeled as low (LP), middle (MP), and high (HP) polariton, according to their energy (see Figure 1c). For the interaction between the cavity mode and the LE exciton with large dipole moment, we obtained a large Rabi splitting 2ΩLE-ph = 260 meV, whereas for the HE mode with a small dipole, we found a smaller splitting of 2ΩHE-ph = 170 meV (obtained at the avoided-crossing points by fitting the reflectance curves as the sum of three gaussians). The anticrossings between all these polaritonic branches can be appreciated in Figure 1d–l, showing the s-polarized reflectance spectra acquired at angles spanning from 25° to 65°. Several ways have been proposed to characterize strong coupling, but the most broadly accepted condition is that the vacuum Rabi splitting 2Ω must be larger than the dissipative broadening of both the exciton (γe) and the cavity mode (γph), (27) e.g., 2Ω > (γe + γph)/2. In our case, we have 2ΩLE-ph = 260 meV, γLE = 112 meV, and γph(θ=35°) = 75 meV for the coupling between the LE exciton and the cavity mode occurring at ∼35°, whereas values of 2ΩHE-ph = 169 meV, γHE = 174 meV, and γph(θ=50°) = 96 meV for the coupling between the HE exciton and the cavity mode are observed at ∼50°. In the first case, we find (γLE + γph(θ=35°))/2 = 0.094 eV and, therefore, the condition 2ΩLE-ph > (γLE+γph(θ=35°))/2 is satisfied, confirming the strong coupling regime. In the latter case, we find (γHE+γph(θ=50°))/2 = 135 meV, again validating the condition for strong coupling.
As mentioned above, resonances in an MDM cavity can be interpreted as ENZ modes in a homogenized description of the complex effective permittivity. (23) This concept can be applied to the MDM multilayers studied in this work as well. We performed spectroscopic ellipsometry measurements and considered the R6G-doped MDM cavity as a homogenized material, and measured the pseudodielectric permittivity ε of the system as an effective material property. The real (ε′) and imaginary parts (ε′′) of ⟨ε⟩ are shown in Figures 2a and 2b, as solid black lines.

Figure 2

Figure 2. (a) Real part ε′ and (b) imaginary part ε″ of the experimentally measured pseudodielectric permittivity ⟨ε⟩ (solid black lines) of a R6G-doped MDM cavity, compared to the effective dielectric permittivity (black dots) analytically modeled through eq S2 in the SI. The measurement was done by ellipsometry at a 40° angle of incidence, the dispersion obtained from the analytic model is shown only within the polaritonic region, starting from 400 nm onward. (c) Experimentally measured reflectance R (red curve), transmittance T (green curve), and absorbance A (blue curve, obtained as A = 1 – R – T) for s-polarization. Low-loss ENZ modes correspond to transmittance (absorbance) peaks and reflectance dips with ε′ = 0 and small ε″. FB and SH-ENZ indicate the Ferrell–Berreman and second-harmonic ENZ mode, respectively. LP and HP are the lower and higher ENZ polaritons, respectively.

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Several transitions with zero ε′ are present in Figure 2a. The one at 327 nm is the well-known Ferrell–Berreman mode of Ag (Figure 2a, labeled “FB”). The resonance labeled SH-ENZ is a pure cavity mode, whose ENZ features have been demonstrated in refs (23), (28), and (29). The red-circled zero-crossing labeled as “Lossy ENZ” corresponds to the central wavelength of the Lorentzian oscillator used to model the bare cavity mode and it is not of interest for our work, as well as all the zero crossings found in correspondence of the peaks of ε″ (high losses). The zero-crossing points labeled as HP and LP in Figure 2a correspond to polaritonic modes that manifest ENZ features. Crucially, in correspondence to these wavelengths, dips in reflectance (R, red curve of Figure 2c) are present together with peaks in transmittance (T, green curve of Figure 2c) and in absorbance (A = 1 – R – T, blue curve of Figure 2c). In contrast, in correspondence to MP, no zero crossing was found. This behavior can be explained by considering the Hopfield coefficients of the three polaritons (see Section 5 of the SI), which reveal that HP and LP manifest mainly a photonic nature, while MP has a marked excitonic, lossy character. The relation of the ENZ properties of the polaritons to their photonic or excitonic character are also supported by the low-loss spectral region of the HP and LP modes (PVP-R6G compound), with extinction coefficient κ < 0.02 (see the red curve in Figure S2c in the SI, calculated from the ellipsometric measurements of Ψ and Δ (Figures S2a and S2b)). Therefore, the HP and LP polariton branches inherit high-quality ENZ features from the cavity mode, and the real part of the effective permittivity crosses zero at the polariton frequencies (or wavelengths in Figure 2a). In contrast, polaritons belonging to the MP branch always lie within the lossy, high-absorbance energy range of R6G and do not manifest ENZ behavior.
At the HP and LP wavelengths, the ENZ permittivity shows low losses (Figure 2b), so that the effective polariton wavevector (k = k0εeff1/2) almost completely vanishes, since εeff ≈ 0. This condition, which also sustains the propagation of polaritons generated in the dye-doped MDM cavity, is known as “resonant tunneling”.
To investigate the influence of the out-of-plane component of the incident wave vector on the polaritons, we used a SFA to measure the dispersion of MDM cavities as a function of a continuous variation of the cavity thickness tD. In this case, the cavity dielectric layer was a solution of PVP in ethanol, either pristine or doped with R6G molecules. The SFA technique is described in ref (30) and applications to multiple-beam interference and photonics can be found in ref (24). The fluid was confined between two cylindrical lenses with radius R = 2 cm, coated with a 30 nm Ag layer, facing each other at a distance d apart with their cylinder axes crossed at 90° (Figures 3a and 3b). The metal layers constituted the mirrors of a curved MDM cavity with a nonuniform thickness tD of the dielectric fluid. Around the point of closest surface approach, the separation distance between the two cylindrical surfaces is given by eq 3:
tD(r)=d+r22R
(3)
where r is the lateral distance from the point of closet surface approach (r = 0) and r ≪ R. This geometry is equivalent to that of a sphere of radius R facing a plane at a distance d (see Figures 3a and 3b).

Figure 3

Figure 3. (a) 3D sketch of the SFA crossed-cylinder geometry highlighting the formation of the Newton rings. (b) Cross-section of the SFA geometry along the axis of the bottom cylinder. R = 2 cm is the cylinder radius, and r is the lateral distance from the point of closest surface approach, i.e., r = 0, where the surface separation distance is d. The Ag layers on the glass cylinders (thickness 30 nm) together with the dielectric fluid between them form a curved MDM cavity with nonuniform thickness tD. (c) Color plots showing the logarithm of transmitted intensity as a function of the wavelength λ and position r for a fixed distance d between the surfaces in a PVP-ethanol mixture (without R6G). (d) Similar color plot obtained for a dye-doped solution containing 1.5 wt % of R6G. (e) Transmittance spectra taken from panel (d), showing the Rabi splitting measured for five consecutive harmonics. (f) Linear increase of the squared lateral position rq (2) measured from the spectra in panel (d), as a function of the relative order q – q0. (g) Parabolic increase of the Rabi splitting 2Ωq as a function of the lateral position rq.

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The light intensity I transmitted under normal incidence through the curved MDM cavity was collected using a microscope and directed with a right-angle prism into an imaging spectrograph coupled to a CCD camera. Therefore, the SFA setup is an ideal technique for directly revealing ENZ polaritons as it detects transmittance maxima corresponding to resonant tunneling cavity polaritons whose ENZ character was demonstrated above. (23)
This setup allowed to resolve I as a function of the wavelength λ and lateral position r over a field of view of ∼150 μm surrounding the point of closest surface approach (r = 0). Spectrograms I(r,λ) obtained for an undoped mixture of PVP and ethanol showed continuous resonance fringes with a parabolic shape reflecting the surface curvature (Figure 3c).
In eq 2, the phase shift ϕ due to reflection at the dielectric–metal interface varies slowly with the wavelength and, therefore, the resonance wavelength λq increases with tD following an approximately linear dependence. (24) Since tD increases parabolically with r (eq 3), the resonance fringe of order q, i.e., λq(r), presents a parabolic shape.
For R6G-doped PVP-ethanol solutions, the resonance fringes showed several anticrossings between the cavity modes (for different order q) and the RG6 excitons (∼510 nm). In Figure 3d, the splitting of up to five consecutive harmonics (high-order modes) were detected in the spectrograph field of view, demonstrating a rapid, single-shot measurement that captures the dispersion of several polariton modes.
To evaluate the coupling strength, we plotted the transmittance spectra at the five lateral positions rq, related to the mode of order q, corresponding to the different anticrossing points (Figure 3e) and measured the Rabi splitting 2Ωq via Gaussian fits of the transmittance peaks (see Section 6 in the SI). The analysis shows that the splitting increases nonlinerarly with the mode radius rq (Figure 3f). This finding can be interpreted by recalling the collective nature underlying the Rabi splitting. Indeed, according to the well-known Tavis–Cumming model, the Rabi splitting depends on (i) the numbers of photons mq, (ii) the number of the emitters Nq, and (iii) the modal volume Vq, as 2Ωq ∝ [(mq + 1)Nq/Vq]1/2. In most experiments, Nq is increased while Vq and mq are fixed. In our case, instead, the ratio c = Nq/Vq is constant, due to the uniform concentration of dye molecules in the polymeric solution. In contrast, the number of photons mq increases with the lateral position rq and, equivalently, with the cavity thickness tq (see Section 7 of the SI). As a result, in the SFA geometry, the Rabi splitting scales as 2Ωq = Atq1/2 (where A is a constant), or equivalently 2Ωq ∝ (d + rq2/2R)1/2. As shown by the fit in Figure 3g, this scaling relation is in good agreement with the experimental data for the fitting parameters d ≈ 0.77 μm and A ∼ 0.155 meV/μm1/2. This analysis confirms the square root proportionality of the Rabi splitting to the number of photons for the full set of modes observed in our single-shot experiment, evidencing the utility of the SFA to analyze often-overlooked contributions to light-matter coupling in MDM cavities.
In conclusion, in this work, we used a dye-doped MDM cavity to demonstrate that polaritons generated by the hybridization between excitons and ENZ cavity modes inherit the ENZ character of the cavity mode. We employed two distinct, but complementary, methods to measure the polariton dispersion by varying either the parallel (k||) or the perpendicular (k⊥) component of the wavevector in dye-doped MDM cavities.
The first method, based on the angular dispersion of an MDM cavity with fixed thickness, reveals the generation of three polaritonic branches: HP, LP, and MP. As demonstrated by the Hopfield coefficient calculation, HP and LP manifest a marked “cavity-like” behavior with a recognizable ENZ dispersion. In contrast, the third branch (MP) showed an “excitonic” lossy behavior with no ENZ behavior.
The second method is based on the use of the SFA to study the dependence of the strong coupling on k⊥ by exploiting the curvature of the optical lenses typically used in this setup that create a continuous lateral variation of the cavity thickness. SFA measurements allowed to detect the strong coupling of several consecutive cavity modes (harmonics) with the same exciton transition, within a rapid single-shot measurement. Such analysis revealed an often-overlooked aspect of the collective nature of the strong coupling process, that is the Rabi splitting proportionality to the square root of the number of the involved photons. Our reported Rabi splitting that increases as a function of the lateral position rq in the sphere-plane geometry is in very good agreement with the theoretical predictions.
Our work opens to polaritonics in the ENZ regime that integrates the highly appealing features of vanishing dielectric permittivity (energy tunneling, phase engineering, slow group velocity, etc.) to the field of strong light–matter interaction. Moreover, our approach proposes the SFA as a new experimental tool to investigate through single-shot measurements continuous variations of the salient parameters involved in the coupling dynamics.

Methods

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Fabrication and Characterization of ENZ Cavities

The layered metal–dielectric–metal (MDM) structure was fabricated by a multistep process. A 30-nm-thick silver layer was deposited using DC magnetron sputtering in an argon atmosphere (P = 4 × 10–2 mbar and a deposition power of 20 W). 14 mM R6G in ethanol-PVP solution was spin-coated at 2500 rpm for 1 min on top of the Ag layer to obtain a 315-nm-thick dye-doped PVP layer. The spin-coated sample was annealed for 10 min at 70 °C to ensure an ethanol-free PVP layer. After that, the top 30-nm Ag layer was deposited via DC magnetron sputtering with deposition parameters equal to the aforementioned ones. After deposition of each layer, thickness and optical constant were measured by ellipsometry. s- and p-polarized reflectance of the ENZ cavities was measured by spectroscopic ellipsometry in an angular range between 25° and 85° with a step of 2°.

SFA Experiments

A surface force apparatus (SFA) Mark III by Surforce LLC, USA was used in the experiments. (24,30) One of the Ag-coated cylindrical lenses was fixed on a rigid support, whereas the other one was attached to the free end of a double cantilever spring. The surfaces of the lenses were sufficiently far apart from each other to avoid any mechanical interaction and moved freely in contact with a 40 μL droplet of a PVP-ethanol solution. The droplet was infiltrated between the Ag-coated lenses by capillarity, and it was either doped with a concentration of 1.5 wt % R6G or left undoped.
Transmission spectra were obtained by illuminating the MDM cavity (consisting of the metal layers on the lens surfaces and the dielectric solution) under normal incidence with white light from a halogen lamp. The transmitted light was collected through the entrance slit of an imaging spectrograph (PI Acton Spectra Pro 2300i) aligned with one of the cylindrical lenses, and recorded with a high-sensitivity CCD camera (Andor Newton DU940P-FI). Only a small region of the surface surrounding the contact position was probed, such that r ≤ 0.15 mm ≪ R, equivalent to a sphere-plane geometry. (31) A CCD camera image recorded the transmitted intensity I as a function of the wavelength λ and position r (Figure 3). Multibeam interference created resonance peaks in a spectrogram, i.e., local maxima of the 2d intensity function I(λ, r), corresponding to constructive interference. Spectrograms such as those shown in Figures 3c and 3d were obtained by combining multiple CCD images taken in different but overlapping spectral intervals. Each image was recorded within <1 s, whereas a spectrogram was completed within <20 s.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.nanolett.2c04864.

  • Schematic illustration of a metal-dielectric-metal (MDM) resonator; refractive index calculation of PVP-R6G; P-polarization reflectance analysis of the dye-doped MDM cavity; ENZ fit of R6G-doped MDM cavity via ellipsometry measurements and analytical model of the effective dielectric permittivity; three oscillator coupling model and Hopfield coefficients calculation; Gaussian fit of the transmittance spectra acquired via SFA measurements; determination of the number of photons per mode q in the cavity (PDF)

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Author Information

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  • Corresponding Authors
  • Authors
    • Aniket Patra - Dipartimento di Fisica, Università della Calabria, via P. Bucci 33b, 87036 Rende CS, Italy;  Optoelectronics Research Line, Istituto Italiano di Tecnologia, via Morego 30, 16163 Genova, Italy;  Orcidhttps://orcid.org/0000-0002-4126-6660
    • Roman Krahne - Optoelectronics Research Line, Istituto Italiano di Tecnologia, via Morego 30, 16163 Genova, Italy;  Orcidhttps://orcid.org/0000-0003-0066-7019
    • Antonio De Luca - Dipartimento di Fisica, Università della Calabria, via P. Bucci 33b, 87036 Rende CS, Italy;  Consiglio Nazionale delle Ricerche−Istituto di Nanotecnologia (CNR-Nanotec), via P. Bucci 33c, 87036 Rende, Italy
  • Author Contributions

    V.C., A.P., B.Z., A.D.L., and R.K. conceived the work. V.C. and A.P. conceived and demonstrated the ENZ nature of the polaritons generated within ENZ cavities. B.Z. conceived and performed the SFA experiments. A.P. fabricated the samples. A.P. and V.C. carried out the ellipsometry measurements. V.C. fitted the ellipsometries and evaluated the ENZ nature of the polaritons. A.P. carried out the reflectance measurements together with the SMM simulations and the analytical model. V.C. identified the Rabi splitting increase as a function of the lateral displacement in the SFA experiments and suggested its square root dependence law. B.Z. calculated the number of photons in a cavity mode and fitted the Rabi splitting data as a parabolic function of the ring radius. A.D.L. and R.K. supervised the work contributing to the interpretation of the experiments and theoretical calculations. V.C. performed the calculation of the Hopfield coefficients and discussed the conclusions stemming from it.

  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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The authors are thankful to Prof. Francesco Plastina and Dr. Nicolino Lo Gullo for the insightful and fruitful discussions on the role of the number of photons in both the Jaynes-Cummings and Tavis-Cummings model. The results obtained in this study had the support of “Progetto STAR 2 – PIR01_00008”–Ministero dell’Università e Ricerca/Italian Ministry of University and Research. V. C. thanks the research project “Componenti Optoelettronici Biodegradabili ed Eco-Sostenibili verso la nanofotonica “green” (D.M. n. 1062, 10.08.2021, PON “Ricerca e Innovazione” 2014-2020), contract identification code 1062_R17_GREEN).

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    Many-Body and Correlation Effects on Parametric Polariton Amplification in Semiconductor Microcavities
    Savasta, Salvatore; Di Stefano, Omar; Girlanda, Raffaello
    Physical Review Letters (2003), 90 (9), 096403/1-096403/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    The complexity induced by the Coulomb interaction between electrons dets. the noninstantaneous character of exciton-exciton collisions. The exciton-photon coupling in semiconductor microcavities is able to alter the exciton dynamics during collisions strongly affecting the effective scattering rates. Anal. clarifies the origin of the great enhancement of parametric gain obsd. when increasing the polariton splitting. It also demonstrates that exciton-exciton collisions in semiconductors can be controlled and engineered to produce almost decoherence-free collisions for the realization of all-optical microscopic devices.
  7. 7
    Takahashi, H.; Kassa, E.; Christoforou, C.; Keller, M. Strong Coupling of a Single Ion to an Optical Cavity. Phys. Rev. Lett. 2020, 124, 013602,  DOI: 10.1103/PhysRevLett.124.013602
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    Strong Coupling of a Single Ion to an Optical Cavity
    Takahashi, Hiroki; Kassa, Ezra; Christoforou, Costas; Keller, Matthias
    Physical Review Letters (2020), 124 (1), 013602CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
    Strong coupling between an atom and an electromagnetic resonator is an important condition in cavity quantum electrodynamics. While strong coupling in various phys. systems has been achieved so far, it remained elusive for single at. ions. Here, we achieve a coupling strength of 2πx(12.3±0.1) MHz between a single Ca40+ ion and an optical cavity, exceeding both at. and cavity decay rates which are 2πx11.5 and 2πx(4.1±0.1) MHz, resp. We use cavity assisted Raman spectroscopy to precisely characterize the ion-cavity coupling strength and observe a spectrum featuring the normal mode splitting in the cavity transmission due to the ion-cavity interaction. Our work paves the way towards new applications of cavity quantum electrodynamics utilizing single trapped ions in the strong coupling regime for quantum optics and quantum technologies.
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    Carusotto, I.; Ciuti, C. Quantum Fluids of Light. Rev. Mod. Phys. 2013, 85, 299– 366,  DOI: 10.1103/RevModPhys.85.299
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    Kaeek, M.; Damari, R.; Roth, M.; Fleischer, S.; Schwartz, T. Strong Coupling in a Self-Coupled Terahertz Photonic Crystal. ACS Photonics 2021, 8, 1881– 1888,  DOI: 10.1021/acsphotonics.1c00309
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    Strong Coupling in a Self-Coupled Terahertz Photonic Crystal
    Kaeek, Maria; Damari, Ran; Roth, Michal; Fleischer, Sharly; Schwartz, Tal
    ACS Photonics (2021), 8 (7), 1881-1888CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
    Vibrational strong coupling is a phenomenon in which a vibrational transition in a material placed inside a photonic structure is hybridized with its optical modes to form composite light-matter excitations known as vibro-polaritons. Here, we demonstrate a new concept of vibrational strong coupling: we show that a monolithic photonic crystal, made of a resonant material, can exhibit strong coupling between the optical modes confined in the structure and the terahertz vibrational excitations of the same material. We study this system both exptl. and numerically to characterize the dispersion of the photonic modes for various sample thicknesses and reveal their coupling with the vibrational resonances. Finally, our time-domain THz measurements allow us to isolate the free induction decay signal from the grating modes as well as from the vibro-polaritons.
  10. 10
    Gogna, R.; Zhang, L.; Wang, Z.; Deng, H. Photonic Crystals for Controlling Strong Coupling in van Der Waals Materials. Opt. Express 2019, 27, 22700– 22700,  DOI: 10.1364/OE.27.022700
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    Photonic crystals for controlling strong coupling in van der Waals materials
    Gogna, Rahul; Zhang, Long; Wang, Zhaorong; Deng, Hui
    Optics Express (2019), 27 (16), 22700-22707CODEN: OPEXFF; ISSN:1094-4087. (Optical Society of America)
    The design of photonic structures plays a crucial role in the engineering of light-matter interactions. Planar microcavities have been widely used to establish strong light-matter coupling in semiconductor quantum wells, leading to intense research on exciton-polariton systems in the past few decades. However, planar cavities are limited in material compatibility, inflexible for mode engineering, and bulky for integration. Here we demonstrate dielec. slab photonic crystals as a flexible and compact platform for polaritons, where excitons are strongly coupled to photons confined in the leaky modes of the slab. We show our structure is well-suited for van der Waals materials, features unusual adjustable dispersions, and allows for multi-wavelength operation on a single chip.
  11. 11
    Vora, P. M.; Bracker, A. S.; Carter, S. G.; Kim, M.; Kim, C. S.; Gammon, D. Strong Coupling of a Quantum Dot Molecule to a Photonic Crystal Cavity. Phys. Rev. B 2019, 99, 165420,  DOI: 10.1103/PhysRevB.99.165420
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    11
    Strong coupling of a quantum dot molecule to a photonic crystal cavity
    Vora, Patrick M.; Bracker, Allan S.; Carter, Samuel G.; Kim, Mijin; Kim, Chul Soo; Gammon, Daniel
    Physical Review B (2019), 99 (16), 165420CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)
    Quantum dot mols. (QDMs) have widely tunable exciton transition energies and transition strengths that can be controlled with an applied elec. field. We use these properties to demonstrate in situ tuning of the vacuum Rabi splitting for a quantum dot mol. embedded in a photonic crystal cavity. Both components of the anisotropic exchange doublet have a component parallel to the cavity and are strongly coupled. This produces two QDM-cavity polaritons with properties dominated by the cavity and a third mixed-spin hybrid state with little cavity component and unusual polarization.
  12. 12
    Heintz, J.; Markešević, N.; Gayet, E. Y.; Bonod, N.; Bidault, S. Few-Molecule Strong Coupling with Dimers of Plasmonic Nanoparticles Assembled on DNA. ACS Nano 2021, 15, 14732– 14743,  DOI: 10.1021/acsnano.1c04552
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    12
    Few-Molecule Strong Coupling with Dimers of Plasmonic Nanoparticles Assembled on DNA
    Heintz, Jeanne; Markesevic, Nemanja; Gayet, Elise Y.; Bonod, Nicolas; Bidault, Sebastien
    ACS Nano (2021), 15 (9), 14732-14743CODEN: ANCAC3; ISSN:1936-0851. (American Chemical Society)
    Hybrid nanostructures, in which a known no. of quantum emitters are strongly coupled to a plasmonic resonator, should feature optical properties at room temp. such as few-photon nonlinearities or coherent superradiant emission. We demonstrate here that this coupling regime can only be reached with dimers of gold nanoparticles in stringent exptl. conditions, when the interparticle spacing falls below 2 nm. Using a short transverse DNA double-strand, we introduce five dye mols. in the gap between two 40 nm gold particles and actively decrease its length down to sub-2 nm values by screening electrostatic repulsion between the particles at high ionic strengths. Single-nanostructure scattering spectroscopy then evidence the observation of a strong-coupling regime in excellent agreement with electrodynamic simulations. Furthermore, we highlight the influence of the planar facets of polycryst. gold nanoparticles on the probability of observing strongly coupled hybrid nanostructures.
  13. 13
    Huang, Y.; Wu, F.; Yu, L. Rabi Oscillation Study of Strong Coupling in a Plasmonic Nanocavity. New J. Phys. 2020, 22, 063053,  DOI: 10.1088/1367-2630/ab9222
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    Rabi oscillation study of strong coupling in a plasmonic nanocavity
    Huang, Yuming; Wu, Fan; Yu, Li
    New Journal of Physics (2020), 22 (June), 063053CODEN: NJOPFM; ISSN:1367-2630. (IOP Publishing Ltd.)
    Strong interaction between emitters and plasmonic nanocavity has various applications in quantum fields at room temp. As Rabi oscillation gives the direct proof to the energy exchange in strong coupling, it is more intuitive and necessary to analyze the interaction in time domain. In this paper, we give the Rabi oscillation in a high-dissipation plasmonic nanocavity by using full-quantum method and draw a new strong coupling criterion about mode vol. which provides a significant guidance in plasmonic nanocavitys nanofabrication. Moreover, we reveal the relation between Rabi oscillation and Rabi splitting, which is beneficial for exploring emitter-plasmon hybrid systems time-domain property through frequency-domain response. An emitter-hexagon hybrid system with ultrasmall mode vol. is designed to verify our theory. The numerical simulation shows good agreements with our theor. results. Our work has applications in quantum information and quantum computing in the future.
  14. 14
    Maccaferri, N.; Barbillon, G.; Koya, A. N.; Lu, G.; Acuna, G. P.; Garoli, D. Recent Advances in Plasmonic Nanocavities for Single-Molecule Spectroscopy. Nanoscale Adv. 2021, 3, 633– 642,  DOI: 10.1039/D0NA00715C
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    Recent advances in plasmonic nanocavities for single-molecule spectroscopy
    Maccaferri, Nicolo; Barbillon, Gregory; Koya, Alemayehu Nana; Lu, Guowei; Acuna, Guillermo P.; Garoli, Denis
    Nanoscale Advances (2021), 3 (3), 633-642CODEN: NAADAI; ISSN:2516-0230. (Royal Society of Chemistry)
    A review. Plasmonic nanocavities are able to engineer and confine electromagnetic fields to subwavelength vols. In the past decade, they have enabled a large set of applications, in particular for sensing, optical trapping, and the investigation of phys. and chem. phenomena at a few or single-mol. levels. This extreme sensitivity is possible thanks to the highly confined local field intensity enhancement, which depends on the geometry of plasmonic nanocavities. Indeed, suitably designed structures providing engineered local optical fields lead to enhanced optical sensing based on different phenomena such as surface enhanced Raman scattering, fluorescence, and F.ovrddot.orster resonance energy transfer. In this mini-review, we illustrate the most recent results on plasmonic nanocavities, with specific emphasis on the detection of single mols.
  15. 15
    Al-Ani, I. A. M.; As’Ham, K.; Huang, L.; Miroshnichenko, A. E.; Lei, W.; Hattori, H. T. Strong Coupling of Exciton and High-Q Mode in All-Perovskite Metasurfaces. Advanced Optical Materials 2022, 10, 2101120,  DOI: 10.1002/adom.202101120
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    15
    Strong Coupling of Exciton and High-Q Mode in All-Perovskite Metasurfaces
    Al-Ani, Ibrahim A. M.; As'Ham, Khalil; Huang, Lujun; Miroshnichenko, Andrey E.; Lei, Wen; Hattori, Haroldo T.
    Advanced Optical Materials (2022), 10 (1), 2101120CODEN: AOMDAX; ISSN:2195-1071. (Wiley-VCH Verlag GmbH & Co. KGaA)
    Recently developed halide perovskite semiconductors are viewed as an excellent platform to realize exciton-polariton at room temp. due to their large oscillation strength. Here, the optimized strong coupling between the exciton of perovskite and quasi-bound state in the continuum (QBIC) with high-quality factor (Q-factor), supported by all-perovskite metagrating, including magnetic dipole (MD)-QBIC and toroidal dipole (TD)-QBIC is demonstrated. By taking advantage of extreme elec. field confinement enabled by a high-Q mode, it is found that the max. Rabi splitting can be enhanced up to a record high value of 400 meV, almost twice the Rabi splitting reported in the same perovskite-based subwavelength metasurface. The simulation results reveal that both the Q-factor of QBIC mode and the thickness of the perovskite metasurface play dominant roles in the enhanced strong coupling. It is also demonstrated that adding a protection layer of poly(Me methacrylate) on the top of the perovskite metagrating has a negligible effect on the maximized Rabi-splitting. These results suggest a new approach for studying exciton-polaritons and may pave the way toward flexible, large-scale, and low-cost integrated polaritonic devices and the realization of polariton lasing at room temp.
  16. 16
    Qin, M.; Xiao, S.; Liu, W.; Ouyang, M.; Yu, T.; Wang, T.; Liao, Q. Strong Coupling between Excitons and Magnetic Dipole Quasi-Bound States in the Continuum in WS2-TiO2 Hybrid Metasurfaces. Opt. Express 2021, 29, 18026– 18036,  DOI: 10.1364/OE.427141
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    16
    Strong coupling between excitons and magnetic dipole quasi-bound states in the continuum in WS2-TiO2 hybrid metasurfaces
    Qin, Meibao; Xiao, Shuyuan; Liu, Wenxing; Ouyang, Mingyu; Yu, Tianbao; Wang, Tongbiao; Liao, Qinghua
    Optics Express (2021), 29 (12), 18026-18036CODEN: OPEXFF; ISSN:1094-4087. (Optical Society of America)
    Enhancing the light-matter interactions in two-dimensional materials via optical metasurfaces has attracted much attention due to its potential to enable breakthrough in advanced compact photonic and quantum information devices. Here, we theor. investigate a strong coupling between excitons in monolayer WS2 and quasi-bound states in the continuum (quasi-BIC). In the hybrid structure composed of WS2 coupled with asym. titanium dioxide nanobars, a remarkable spectral splitting and typical anticrossing behavior of the Rabi splitting can be obsd., and such strong coupling effect can be modulated by shaping the thickness and asymmetry parameter of the proposed metasurfaces, and the angle of incident light. It is found that the balance of line width of the quasi-BIC mode and local elec. field enhancement should be considered since both of them affect the strong coupling, which is crucial to the design and optimization of metasurface devices. This work provides a promising way for controlling the light-matter interactions in strong coupling regime and opens the door for the future novel quantum, low-energy, distinctive nanodevices by advanced meta-optical engineering.
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    Réveret, F.; Disseix, P.; Leymarie, J.; Vasson, A.; Semond, F.; Leroux, M.; Massies, J. Influence of the Mirrors on the Strong Coupling Regime in Planar GaN Microcavities. Phys. Rev. B 2008, 77, 195303,  DOI: 10.1103/PhysRevB.77.195303
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    Influence of the mirrors on the strong coupling regime in planar GaN microcavities
    Reveret, F.; Disseix, P.; Leymarie, J.; Vasson, A.; Semond, F.; Leroux, M.; Massies, J.
    Physical Review B: Condensed Matter and Materials Physics (2008), 77 (19), 195303/1-195303/8CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
    The optical properties of bulk λ/2 GaN microcavities working in the strong light-matter coupling regime are studied by using angle-dependent reflectivity and photoluminescence at 5 and 300 K. The structures have an Al0.2Ga0.8N/AlN distributed Bragg reflector as the bottom mirror and either an Al mirror or a dielec. Bragg mirror as the top one. First, the influence of the no. of pairs of the bottom mirror on the Rabi splitting is studied. The increase in the mirror penetration depth is correlated with a redn. of the Rabi splitting. Second, the emission of the lower polariton branch is obsd. at low temp. in a microcavity contg. 2 Bragg mirrors and exhibiting a quality factor of 190. Simulations using the transfer-matrix formalism, taking into account the real structure of the samples studied, are in good agreement with exptl. results.
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    Cao, J.; De Liberato, S.; Kavokin, A. V. Strong Light–Matter Coupling in Microcavities Characterised by Rabi-Splittings Comparable to the Bragg Stop-Band Widths. New J. Phys. 2021, 23, 113015,  DOI: 10.1088/1367-2630/ac3260
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    Schneider, C.; Glazov, M. M.; Korn, T.; Höfling, S.; Urbaszek, B. Two-Dimensional Semiconductors in the Regime of Strong Light-Matter Coupling. Nat. Commun. 2018, 9, 2695,  DOI: 10.1038/s41467-018-04866-6
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    Two-dimensional semiconductors in the regime of strong light-matter coupling
    Schneider Christian; Hofling Sven; Glazov Mikhail M; Korn Tobias; Hofling Sven; Urbaszek Bernhard
    Nature communications (2018), 9 (1), 2695 ISSN:.
    The optical properties of transition metal dichalcogenide monolayers are widely dominated by excitons, Coulomb-bound electron-hole pairs. These quasi-particles exhibit giant oscillator strength and give rise to narrow-band, well-pronounced optical transitions, which can be brought into resonance with electromagnetic fields in microcavities and plasmonic nanostructures. Due to the atomic thinness and robustness of the monolayers, their integration in van der Waals heterostructures provides unique opportunities for engineering strong light-matter coupling. We review first results in this emerging field and outline future opportunities and challenges.
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    Kasap, S. O. Optoelectronics and Photonics: Principles and Practices; Prentice Hall, 2001; p 340.
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    Hecht, E. Optics, 4th Edition; Addison–Wesley Professional, 2002.
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    Caligiuri, V.; Biffi, G.; Palei, M.; Martín-García, B.; Pothuraju, R. D.; Bretonnière, Y.; Krahne, R. Angle and Polarization Selective Spontaneous Emission in Dye-Doped Metal/Insulator/Metal Nanocavities. Adv. Opt. Mater. 2020, 8, 1901215– 1901215,  DOI: 10.1002/adom.201901215
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    22
    Angle and Polarization Selective Spontaneous Emission in Dye-Doped Metal/Insulator/Metal Nanocavities
    Caligiuri, Vincenzo; Biffi, Giulia; Palei, Milan; Martin-Garcia, Beatriz; Pothuraju, Renuka Devi; Bretonniere, Yann; Krahne, Roman
    Advanced Optical Materials (2020), 8 (1), 1901215CODEN: AOMDAX; ISSN:2195-1071. (Wiley-VCH Verlag GmbH & Co. KGaA)
    Directing and polarizing the emission of a fluorophore is of fundamental importance in the perspective of novel photonic sources based on emerging nanoemitter technologies. These two tasks are usually accomplished by a sophisticated and demanding structuring of the optical environment in which the emitter is immersed, or by nontrivial chem. engineering of its geometry and/or band structure. Here, the wavelength and polarization selective spontaneous emission from a dye-embedded in a metal/insulator/metal (d-MIM) nanocavity is demonstrated. A push-pull chromophore with large Stokes shift is embedded in a MIM cavity whose resonances are tuned with the spectral emission band of the chromophore. Angular and polarization resolved spectroscopy expts. reveal that the radiated field is reshaped according to the angular dispersion of the nanocavity, and that its spectrum manifests two bands with different polarization corresponding to the p- and s-polarized resonances of the cavity. The d-MIM cavities are a highly versatile system for polarization and wavelength division multiplexing applications at the nanoscale, as well as for near-field focused emission and nanolenses.
  23. 23
    Caligiuri, V.; Palei, M.; Biffi, G.; Artyukhin, S.; Krahne, R. A Semi-Classical View on Epsilon-Near-Zero Resonant Tunneling Modes in Metal/Insulator/Metal Nanocavities. Nano Lett. 2019, 19, 3151– 3160,  DOI: 10.1021/acs.nanolett.9b00564
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    23
    A Semi-Classical View on Epsilon-Near-Zero Resonant Tunneling Modes in Metal/Insulator/Metal Nanocavities
    Caligiuri, Vincenzo; Palei, Milan; Biffi, Giulia; Artyukhin, Sergey; Krahne, Roman
    Nano Letters (2019), 19 (5), 3151-3160CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
    Metal/Insulator/Metal nanocavities (MIMs) are highly versatile systems for nanometric light confinement and waveguiding, and their optical properties are mostly interpreted in terms of surface plasmon polaritons. Although classic electromagnetic theory accurately describes their behavior, it often lacks phys. insight, leaving some fundamental aspects of light interaction with these structures unexplored. A quantum mech. description is elaborated of the MIM cavity as a double barrier quantum well. The square of the imaginary part κ of the refractive index ~n of the metal was identified as the optical potential, and MIM cavity resonances are suppressed if the ratio n/κ exceeds a certain limit, which shows that low n and high κ values are desired for strong and sharp cavity resonances. The spectral regions of cavity mode suppression correspond to the interband transitions of the metals, where the optical processes are intrinsically non-Hermitian. The quantum treatment allows to describe the tunnel effect for photons and reveals that the MIM cavity resonances can be excited by resonant tunneling via illumination through the metal, without the need of momentum matching techniques such as prisms or grating couplers. By combining this anal. with ellipsometry on exptl. MIM structures and by developing a simple harmonic oscillator model of the MIM for the calcn. of its effective permittivity, the cavity eigenmodes coincide with low-loss zeros of the effective permittivity. Therefore, the MIM resonances correspond to epsilon-near-zero (ENZ) eigenmodes that can be excited via resonant tunneling. The approach provides a toolbox for the engineering of ENZ resonances throughout the entire visible range, which the authors demonstrate exptl. and theor. In particular, the authors apply the quantum mech. approach to asym. MIM superabsorbers and use it for configuring broadly tunable refractive index sensors. The work elucidates the role of MIM cavities as photonic analogs to tunnel diodes and opens new perspectives for metamaterials with designed ENZ response.
  24. 24
    Zappone, B.; Caligiuri, V.; Patra, A.; Krahne, R.; De Luca, A. Understanding and Controlling Mode Hybridization in Multicavity Optical Resonators Using Quantum Theory and the Surface Forces Apparatus. ACS Photonics 2021, 8, 3517– 3525,  DOI: 10.1021/acsphotonics.1c01055
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    24
    Understanding and Controlling Mode Hybridization in Multicavity Optical Resonators Using Quantum Theory and the Surface Forces Apparatus
    Zappone, Bruno; Caligiuri, Vincenzo; Patra, Aniket; Krahne, Roman; De Luca, Antonio
    ACS Photonics (2021), 8 (12), 3517-3525CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
    Optical fields in metal-dielec. multilayers display typical features of quantum systems, such as energy level quantization and avoided crossing, underpinned by an isomorphism between the Helmholtz and Schr.ovrddot.odinger wave equations. This article builds on the fundamental concepts and methods of quantum theory to facilitate the understanding and design of multicavity resonators. It also introduces the surface forces app. (SFA) as a powerful tool for rapid, continuous, and extensive characterization of mode dispersion and hybridization. Instead of fabricating many different resonators, two equal metal-dielec.-metal microcavities were created on glass lenses and displaced relative to each other in a transparent silicone oil using the SFA. The fluid thickness was controlled in real time with nanometer accuracy from more than 50μm to less than 20 nm, reaching mech. contact between the outer cavities in a few minutes. The fluid gap acted as a third microcavity providing optical coupling and producing a complex pattern of resonance splitting as a function of the variable thickness. An optical wave in this sym. three-cavity resonator emulated a quantum particle with nonzero mass in a potential comprising three square wells. Interference between the wells produced a 3-fold splitting of degenerate energy levels due to hybridization. The exptl. results could be explained using the std. methods and formalism of quantum mechanics, including symmetry operators and the variational method. Notably, the interaction between square wells produced bonding, antibonding, and nonbonding states that are analogous to hybridized MOs and are relevant to the design of "epsilon-near-zero" devices with vanishing dielec. permittivity.
  25. 25
    Chapman, M.; Euler, W. B. Rhodamine 6G Structural Changes in Water/Ethanol Mixed Solvent. J. Fluoresc. 2018, 28, 1431– 1437,  DOI: 10.1007/s10895-018-2318-0
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    Rhodamine 6G Structural Changes in Water/Ethanol Mixed Solvent
    Chapman, Mingyu; Euler, William B.
    Journal of Fluorescence (2018), 28 (6), 1431-1437CODEN: JOFLEN; ISSN:1053-0509. (Springer)
    In water rhodamine 6G (Rh6G) tends to form aggregates at higher concns. while in ethanol the aggregation is minimal. The extent of aggregation can be controlled by changing the water to ethanol ratio. In ethanol the absorption spectra have a low energy peak and a higher energy shoulder, which are assigned to the S1 π-π* transition and vibronic side band, resp., of Rh6G monomers. In water the same two peaks absorption peaks are obsd. at low concns. but at higher concns. a new peak grows in, which is assigned to an H-dimer. Emission spectra are in agreement with these assignments, but also develop a third peak at higher concns. that is assigned to emission from excimer aggregates. For the first time, the monomer and dimer av. diams. were measured by light scattering to be 1.4 ± 0.2 nm and 3.3 ± 0.6 nm, which form in the ground state, leading to the obsd. excited states. In a mixed solvent the extent of aggregation can be controlled by selecting the ethanol to water ratio, even at the highest concns.
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    Galego, J.; Garcia-Vidal, F. J.; Feist, J. Cavity-Induced Modifications of Molecular Structure in the Strong-Coupling Regime. Phys. Rev. X 2015, 5, 041022,  DOI: 10.1103/PhysRevX.5.041022
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    Cavity-induced modifications of molecular structure in the strong-coupling regime
    Galego, Javier; Garcia-Vidal, Francisco J.; Feist, Johannes
    Physical Review X (2015), 5 (4), 041022/1-041022/14CODEN: PRXHAE; ISSN:2160-3308. (American Physical Society)
    In most theor. descriptions of collective strong coupling of org. mols. to a cavity mode, the mols. are modeled as simple two-level systems. This picture fails to describe the rich structure provided by their internal rovibrational (nuclear) degrees of freedom. We investigate a first-principles model that fully takes into account both electronic and nuclear degrees of freedom, allowing an exploration of the phenomenon of strong coupling from an entirely new perspective. First, we demonstrate the limitations of applicability of the Born-Oppenheimer approxn. in strongly coupled mol.-cavity structures. For the case of two mols., we also show how dark states, which within the two-level picture are effectively decoupled from the cavity, are indeed affected by the formation of collective strong coupling. Finally, we discuss ground-state modifications in the ultrastrong-coupling regime and show that some mol. observables are affected by the collective coupling strength, while others depend only on the single-mol. coupling const.
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    Cacciola, A.; Di Stefano, O.; Stassi, R.; Saija, R.; Savasta, S. Ultrastrong Coupling of Plasmons and Excitons in a Nanoshell. ACS Nano 2014, 8, 11483– 11492,  DOI: 10.1021/nn504652w
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    Ultrastrong coupling of plasmons and excitons in a nanoshell
    Cacciola, Adriano; Di Stefano, Omar; Stassi, Roberto; Saija, Rosalba; Savasta, Salvatore
    ACS Nano (2014), 8 (11), 11483-11492CODEN: ANCAC3; ISSN:1936-0851. (American Chemical Society)
    The strong coupling regime of hybrid plasmonic-mol. systems is a subject of great interest for its potential to control and engineer light-matter interactions at the nanoscale. Recently, the so-called ultrastrong coupling regime, which is achieved when the light-matter coupling rate reaches a considerable fraction of the emitter transition frequency, has been realized in semiconductor and superconducting systems and in org. mols. embedded in planar microcavities or coupled to surface plasmons. Here we explore the possibility to achieve this regime of light-matter interaction at nanoscale dimensions. We demonstrate by accurate scattering calcns. that this regime can be reached in nanoshells constituted by a core of org. mols. surrounded by a silver or gold shell. These hybrid nanoparticles can be exploited for the design of all-optical ultrafast plasmonic nanocircuits and -devices.
  28. 28
    Caligiuri, V.; Palei, M.; Biffi, G.; Krahne, R. Hybridization of Epsilon-near-Zero Modes via Resonant Tunneling in Layered Metal-Insulator Double Nanocavities. Nanophotonics 2019, 8, 1505– 1508,  DOI: 10.1515/nanoph-2019-0054
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    28
    Hybridization of epsilon-near-zero modes via resonant tunneling in layered metal-insulator double nanocavities
    Caligiuri, Vincenzo; Palei, Milan; Biffi, Giulia; Krahne, Roman
    Nanophotonics (2019), 8 (9), 1505-1512CODEN: NANOLP; ISSN:2192-8614. (Walter de Gruyter GmbH)
    The coupling between multiple nanocavities in close vicinity leads to the hybridization of their modes. Stacked metal-insulator-metal (MIM) nanocavities constitute a highly versatile and very interesting model system to study and engineer such mode coupling, as they can be realized by lithog.-free fabrication methods with fine control on the optical and geometrical parameters. Here, we study the hybridization of ENZ resonances in MIMIM nanocavities, obtaining a very large mode splitting reaching 0.477 eV, Q-factors of the order of 40 in the visible spectral range, and fine control on the resonance wavelength and mode linewidth by tuning the thickness of the dielec. and metallic layers. Interestingly, the asymmetry of the mode splitting in a sym. MIMIM cavity is not reflected in the classical model of coupled oscillators, which can be directly related to quantum mech. tunneling for the coupling of the two cavities. Interpreting the cavity resonances as resonant tunneling modes elucidates that they can be excited without momentum matching techniques. The broad tunability of high-quality ENZ resonances together with their strong coupling efficiency makes such MIMIM cavities an ideal platform for exploring light-matter interaction, for example, by the integration of quantum emitters in dielec. layers.
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    Caligiuri, V.; Biffi, G.; Patra, A.; Pothuraju, R. D.; De Luca, A.; Krahne, R. One-Dimensional Epsilon-Near-Zero Crystals. Adv. Photonics Res. 2021, 2, 2100053,  DOI: 10.1002/adpr.202100053
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    One-Dimensional Epsilon-Near-Zero Crystals
    Caligiuri, Vincenzo; Biffi, Giulia; Patra, Aniket; Pothuraju, Renuka Devi; De Luca, Antonio; Krahne, Roman
    Advanced Photonics Research (2021), 2 (7), 2100053CODEN: APRDF2; ISSN:2699-9293. (Wiley-VCH Verlag GmbH & Co. KGaA)
    Alternating multilayer architectures are an ideal framework to tailor the properties of light. In photonic crystals, dielecs. with different refractive indexes are periodically arranged to provide a photonic bandgap. Herein, it is shown that a periodic arrangement of metal/insulator layers gives rise to an Epsilon-Near-Zero (ENZ) crystal with distinct bands of vanishing permittivity. The analogy of metal/insulator/metal (MIM) cavities to wave mechanics that describes them as quantum-wells for photons is elaborated, and the Kronig-Penney (KP) model is applied to MIM multilayers. This KP modeling allows to ext. the d. of ENZ states, evidencing a significant increase at the band edges, which makes ENZ crystals appealing for lasing applications. The ENZ bandwidth can be tuned by the thickness of the metal layers and can span the entire visible range, and the interactions between bands of two different cavity subsystems in more complex ENZ crystals enable more elaborate ENZ band engineering. Finally, the difference between the ENZ crystals and hyperbolic metamaterials is elucidated and the conditions that sep. these two regimes are quantified. The ENZ crystals constitute a new paradigm in the study of metal/insulator multilayers, and showcase a promising platform for light-matter interaction in photonic and plasmonic technologies.
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  1. Qingtai Xie, Jinpeng Wang, Jie Hong, Jing-Feng Liu, Guanghui Liu, Feng Wu, Yongzhu Chen, Gengyan Chen. Strong radiative coupling between two quantum emitters with arbitrary mutual orientation via a silver nano-arc. Physica Scripta 2024, 99 (8) , 085129. https://doi.org/10.1088/1402-4896/ad63e0
  2. Giuseppe Emanuele Lio, Antonio Ferraro, Bruno Zappone, Janusz Parka, Ewa Schab‐Balcerzak, Cesare Paolo Umeton, Francesco Riboli, Rafał Kowerdziej, Roberto Caputo. Unlocking Optical Coupling Tunability in Epsilon‐Near‐Zero Metamaterials Through Liquid Crystal Nanocavities. Advanced Optical Materials 2024, 12 (13) https://doi.org/10.1002/adom.202302483
  3. Hannah J Hayler, Timothy S Groves, Aurora Guerrini, Astrid Southam, Weichao Zheng, Susan Perkin. The surface force balance: direct measurement of interactions in fluids and soft matter. Reports on Progress in Physics 2024, 87 (4) , 046601. https://doi.org/10.1088/1361-6633/ad2b9b
  4. Aniket Patra, Vincenzo Caligiuri, Renuka D. Pothuraju, Bruno Zappone, Antonio De Luca, Roman Krahne. Metal-Dielectric-Metal Nanocavities with Vanishing Permittivity: Resonance Coupling and Strong Light-Matter Interaction. 2023, 19-20. https://doi.org/10.1109/NMDC57951.2023.10344059
  5. V Caligiuri, S Siprova, A Patra, G E Lio, R Termine, S Cilurzo, A Golemme, A De Luca. Coexisting and cooperating light–matter interaction regimes in a polaritonic photovoltaic system. Journal of Optics 2023, 25 (10) , 105401. https://doi.org/10.1088/2040-8986/acf2ac
  6. Ben Johns. Dispersion engineering of infrared epsilon-near-zero modes by strong coupling to optical cavities. Nanophotonics 2023, 12 (16) , 3301-3312. https://doi.org/10.1515/nanoph-2023-0215
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  • Abstract

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    Figure 1

    Figure 1. (a) Reflectance of an undoped MDM cavity (see inset) calculated with the SMM for s-polarization, and PVP and Ag layers with thicknesses of 350 and 35 nm, respectively. (b) Experimental and calculated s-polarization reflectance of the doped MDM cavity with R6G embedded in the PVP layer (see inset). (c) Analytically calculated (solid blue lines) and experimentally measured (blue stars) angular dispersion of resonances in the doped MDM cavity. Hybridization of the MDM cavity mode (black dash-dotted curve) with the LE and HE excitons of R6G (dashed horizontal lines) generates the low, middle, and high polariton branches (LP, MP, and HP), respectively. (d–l) Experimental reflectance at different incident angles θi.

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    Figure 2

    Figure 2. (a) Real part ε′ and (b) imaginary part ε″ of the experimentally measured pseudodielectric permittivity ⟨ε⟩ (solid black lines) of a R6G-doped MDM cavity, compared to the effective dielectric permittivity (black dots) analytically modeled through eq S2 in the SI. The measurement was done by ellipsometry at a 40° angle of incidence, the dispersion obtained from the analytic model is shown only within the polaritonic region, starting from 400 nm onward. (c) Experimentally measured reflectance R (red curve), transmittance T (green curve), and absorbance A (blue curve, obtained as A = 1 – R – T) for s-polarization. Low-loss ENZ modes correspond to transmittance (absorbance) peaks and reflectance dips with ε′ = 0 and small ε″. FB and SH-ENZ indicate the Ferrell–Berreman and second-harmonic ENZ mode, respectively. LP and HP are the lower and higher ENZ polaritons, respectively.

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    Figure 3

    Figure 3. (a) 3D sketch of the SFA crossed-cylinder geometry highlighting the formation of the Newton rings. (b) Cross-section of the SFA geometry along the axis of the bottom cylinder. R = 2 cm is the cylinder radius, and r is the lateral distance from the point of closest surface approach, i.e., r = 0, where the surface separation distance is d. The Ag layers on the glass cylinders (thickness 30 nm) together with the dielectric fluid between them form a curved MDM cavity with nonuniform thickness tD. (c) Color plots showing the logarithm of transmitted intensity as a function of the wavelength λ and position r for a fixed distance d between the surfaces in a PVP-ethanol mixture (without R6G). (d) Similar color plot obtained for a dye-doped solution containing 1.5 wt % of R6G. (e) Transmittance spectra taken from panel (d), showing the Rabi splitting measured for five consecutive harmonics. (f) Linear increase of the squared lateral position rq (2) measured from the spectra in panel (d), as a function of the relative order q – q0. (g) Parabolic increase of the Rabi splitting 2Ωq as a function of the lateral position rq.

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      There is no corresponding record for this reference.
    22. 22
      Caligiuri, V.; Biffi, G.; Palei, M.; Martín-García, B.; Pothuraju, R. D.; Bretonnière, Y.; Krahne, R. Angle and Polarization Selective Spontaneous Emission in Dye-Doped Metal/Insulator/Metal Nanocavities. Adv. Opt. Mater. 2020, 8, 1901215– 1901215,  DOI: 10.1002/adom.201901215
      22
      Angle and Polarization Selective Spontaneous Emission in Dye-Doped Metal/Insulator/Metal Nanocavities
      Caligiuri, Vincenzo; Biffi, Giulia; Palei, Milan; Martin-Garcia, Beatriz; Pothuraju, Renuka Devi; Bretonniere, Yann; Krahne, Roman
      Advanced Optical Materials (2020), 8 (1), 1901215CODEN: AOMDAX; ISSN:2195-1071. (Wiley-VCH Verlag GmbH & Co. KGaA)
      Directing and polarizing the emission of a fluorophore is of fundamental importance in the perspective of novel photonic sources based on emerging nanoemitter technologies. These two tasks are usually accomplished by a sophisticated and demanding structuring of the optical environment in which the emitter is immersed, or by nontrivial chem. engineering of its geometry and/or band structure. Here, the wavelength and polarization selective spontaneous emission from a dye-embedded in a metal/insulator/metal (d-MIM) nanocavity is demonstrated. A push-pull chromophore with large Stokes shift is embedded in a MIM cavity whose resonances are tuned with the spectral emission band of the chromophore. Angular and polarization resolved spectroscopy expts. reveal that the radiated field is reshaped according to the angular dispersion of the nanocavity, and that its spectrum manifests two bands with different polarization corresponding to the p- and s-polarized resonances of the cavity. The d-MIM cavities are a highly versatile system for polarization and wavelength division multiplexing applications at the nanoscale, as well as for near-field focused emission and nanolenses.
    23. 23
      Caligiuri, V.; Palei, M.; Biffi, G.; Artyukhin, S.; Krahne, R. A Semi-Classical View on Epsilon-Near-Zero Resonant Tunneling Modes in Metal/Insulator/Metal Nanocavities. Nano Lett. 2019, 19, 3151– 3160,  DOI: 10.1021/acs.nanolett.9b00564
      23
      A Semi-Classical View on Epsilon-Near-Zero Resonant Tunneling Modes in Metal/Insulator/Metal Nanocavities
      Caligiuri, Vincenzo; Palei, Milan; Biffi, Giulia; Artyukhin, Sergey; Krahne, Roman
      Nano Letters (2019), 19 (5), 3151-3160CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
      Metal/Insulator/Metal nanocavities (MIMs) are highly versatile systems for nanometric light confinement and waveguiding, and their optical properties are mostly interpreted in terms of surface plasmon polaritons. Although classic electromagnetic theory accurately describes their behavior, it often lacks phys. insight, leaving some fundamental aspects of light interaction with these structures unexplored. A quantum mech. description is elaborated of the MIM cavity as a double barrier quantum well. The square of the imaginary part κ of the refractive index ~n of the metal was identified as the optical potential, and MIM cavity resonances are suppressed if the ratio n/κ exceeds a certain limit, which shows that low n and high κ values are desired for strong and sharp cavity resonances. The spectral regions of cavity mode suppression correspond to the interband transitions of the metals, where the optical processes are intrinsically non-Hermitian. The quantum treatment allows to describe the tunnel effect for photons and reveals that the MIM cavity resonances can be excited by resonant tunneling via illumination through the metal, without the need of momentum matching techniques such as prisms or grating couplers. By combining this anal. with ellipsometry on exptl. MIM structures and by developing a simple harmonic oscillator model of the MIM for the calcn. of its effective permittivity, the cavity eigenmodes coincide with low-loss zeros of the effective permittivity. Therefore, the MIM resonances correspond to epsilon-near-zero (ENZ) eigenmodes that can be excited via resonant tunneling. The approach provides a toolbox for the engineering of ENZ resonances throughout the entire visible range, which the authors demonstrate exptl. and theor. In particular, the authors apply the quantum mech. approach to asym. MIM superabsorbers and use it for configuring broadly tunable refractive index sensors. The work elucidates the role of MIM cavities as photonic analogs to tunnel diodes and opens new perspectives for metamaterials with designed ENZ response.
    24. 24
      Zappone, B.; Caligiuri, V.; Patra, A.; Krahne, R.; De Luca, A. Understanding and Controlling Mode Hybridization in Multicavity Optical Resonators Using Quantum Theory and the Surface Forces Apparatus. ACS Photonics 2021, 8, 3517– 3525,  DOI: 10.1021/acsphotonics.1c01055
      24
      Understanding and Controlling Mode Hybridization in Multicavity Optical Resonators Using Quantum Theory and the Surface Forces Apparatus
      Zappone, Bruno; Caligiuri, Vincenzo; Patra, Aniket; Krahne, Roman; De Luca, Antonio
      ACS Photonics (2021), 8 (12), 3517-3525CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
      Optical fields in metal-dielec. multilayers display typical features of quantum systems, such as energy level quantization and avoided crossing, underpinned by an isomorphism between the Helmholtz and Schr.ovrddot.odinger wave equations. This article builds on the fundamental concepts and methods of quantum theory to facilitate the understanding and design of multicavity resonators. It also introduces the surface forces app. (SFA) as a powerful tool for rapid, continuous, and extensive characterization of mode dispersion and hybridization. Instead of fabricating many different resonators, two equal metal-dielec.-metal microcavities were created on glass lenses and displaced relative to each other in a transparent silicone oil using the SFA. The fluid thickness was controlled in real time with nanometer accuracy from more than 50μm to less than 20 nm, reaching mech. contact between the outer cavities in a few minutes. The fluid gap acted as a third microcavity providing optical coupling and producing a complex pattern of resonance splitting as a function of the variable thickness. An optical wave in this sym. three-cavity resonator emulated a quantum particle with nonzero mass in a potential comprising three square wells. Interference between the wells produced a 3-fold splitting of degenerate energy levels due to hybridization. The exptl. results could be explained using the std. methods and formalism of quantum mechanics, including symmetry operators and the variational method. Notably, the interaction between square wells produced bonding, antibonding, and nonbonding states that are analogous to hybridized MOs and are relevant to the design of "epsilon-near-zero" devices with vanishing dielec. permittivity.
    25. 25
      Chapman, M.; Euler, W. B. Rhodamine 6G Structural Changes in Water/Ethanol Mixed Solvent. J. Fluoresc. 2018, 28, 1431– 1437,  DOI: 10.1007/s10895-018-2318-0
      25
      Rhodamine 6G Structural Changes in Water/Ethanol Mixed Solvent
      Chapman, Mingyu; Euler, William B.
      Journal of Fluorescence (2018), 28 (6), 1431-1437CODEN: JOFLEN; ISSN:1053-0509. (Springer)
      In water rhodamine 6G (Rh6G) tends to form aggregates at higher concns. while in ethanol the aggregation is minimal. The extent of aggregation can be controlled by changing the water to ethanol ratio. In ethanol the absorption spectra have a low energy peak and a higher energy shoulder, which are assigned to the S1 π-π* transition and vibronic side band, resp., of Rh6G monomers. In water the same two peaks absorption peaks are obsd. at low concns. but at higher concns. a new peak grows in, which is assigned to an H-dimer. Emission spectra are in agreement with these assignments, but also develop a third peak at higher concns. that is assigned to emission from excimer aggregates. For the first time, the monomer and dimer av. diams. were measured by light scattering to be 1.4 ± 0.2 nm and 3.3 ± 0.6 nm, which form in the ground state, leading to the obsd. excited states. In a mixed solvent the extent of aggregation can be controlled by selecting the ethanol to water ratio, even at the highest concns.
    26. 26
      Galego, J.; Garcia-Vidal, F. J.; Feist, J. Cavity-Induced Modifications of Molecular Structure in the Strong-Coupling Regime. Phys. Rev. X 2015, 5, 041022,  DOI: 10.1103/PhysRevX.5.041022
      26
      Cavity-induced modifications of molecular structure in the strong-coupling regime
      Galego, Javier; Garcia-Vidal, Francisco J.; Feist, Johannes
      Physical Review X (2015), 5 (4), 041022/1-041022/14CODEN: PRXHAE; ISSN:2160-3308. (American Physical Society)
      In most theor. descriptions of collective strong coupling of org. mols. to a cavity mode, the mols. are modeled as simple two-level systems. This picture fails to describe the rich structure provided by their internal rovibrational (nuclear) degrees of freedom. We investigate a first-principles model that fully takes into account both electronic and nuclear degrees of freedom, allowing an exploration of the phenomenon of strong coupling from an entirely new perspective. First, we demonstrate the limitations of applicability of the Born-Oppenheimer approxn. in strongly coupled mol.-cavity structures. For the case of two mols., we also show how dark states, which within the two-level picture are effectively decoupled from the cavity, are indeed affected by the formation of collective strong coupling. Finally, we discuss ground-state modifications in the ultrastrong-coupling regime and show that some mol. observables are affected by the collective coupling strength, while others depend only on the single-mol. coupling const.
    27. 27
      Cacciola, A.; Di Stefano, O.; Stassi, R.; Saija, R.; Savasta, S. Ultrastrong Coupling of Plasmons and Excitons in a Nanoshell. ACS Nano 2014, 8, 11483– 11492,  DOI: 10.1021/nn504652w
      27
      Ultrastrong coupling of plasmons and excitons in a nanoshell
      Cacciola, Adriano; Di Stefano, Omar; Stassi, Roberto; Saija, Rosalba; Savasta, Salvatore
      ACS Nano (2014), 8 (11), 11483-11492CODEN: ANCAC3; ISSN:1936-0851. (American Chemical Society)
      The strong coupling regime of hybrid plasmonic-mol. systems is a subject of great interest for its potential to control and engineer light-matter interactions at the nanoscale. Recently, the so-called ultrastrong coupling regime, which is achieved when the light-matter coupling rate reaches a considerable fraction of the emitter transition frequency, has been realized in semiconductor and superconducting systems and in org. mols. embedded in planar microcavities or coupled to surface plasmons. Here we explore the possibility to achieve this regime of light-matter interaction at nanoscale dimensions. We demonstrate by accurate scattering calcns. that this regime can be reached in nanoshells constituted by a core of org. mols. surrounded by a silver or gold shell. These hybrid nanoparticles can be exploited for the design of all-optical ultrafast plasmonic nanocircuits and -devices.
    28. 28
      Caligiuri, V.; Palei, M.; Biffi, G.; Krahne, R. Hybridization of Epsilon-near-Zero Modes via Resonant Tunneling in Layered Metal-Insulator Double Nanocavities. Nanophotonics 2019, 8, 1505– 1508,  DOI: 10.1515/nanoph-2019-0054
      28
      Hybridization of epsilon-near-zero modes via resonant tunneling in layered metal-insulator double nanocavities
      Caligiuri, Vincenzo; Palei, Milan; Biffi, Giulia; Krahne, Roman
      Nanophotonics (2019), 8 (9), 1505-1512CODEN: NANOLP; ISSN:2192-8614. (Walter de Gruyter GmbH)
      The coupling between multiple nanocavities in close vicinity leads to the hybridization of their modes. Stacked metal-insulator-metal (MIM) nanocavities constitute a highly versatile and very interesting model system to study and engineer such mode coupling, as they can be realized by lithog.-free fabrication methods with fine control on the optical and geometrical parameters. Here, we study the hybridization of ENZ resonances in MIMIM nanocavities, obtaining a very large mode splitting reaching 0.477 eV, Q-factors of the order of 40 in the visible spectral range, and fine control on the resonance wavelength and mode linewidth by tuning the thickness of the dielec. and metallic layers. Interestingly, the asymmetry of the mode splitting in a sym. MIMIM cavity is not reflected in the classical model of coupled oscillators, which can be directly related to quantum mech. tunneling for the coupling of the two cavities. Interpreting the cavity resonances as resonant tunneling modes elucidates that they can be excited without momentum matching techniques. The broad tunability of high-quality ENZ resonances together with their strong coupling efficiency makes such MIMIM cavities an ideal platform for exploring light-matter interaction, for example, by the integration of quantum emitters in dielec. layers.
    29. 29
      Caligiuri, V.; Biffi, G.; Patra, A.; Pothuraju, R. D.; De Luca, A.; Krahne, R. One-Dimensional Epsilon-Near-Zero Crystals. Adv. Photonics Res. 2021, 2, 2100053,  DOI: 10.1002/adpr.202100053
      29
      One-Dimensional Epsilon-Near-Zero Crystals
      Caligiuri, Vincenzo; Biffi, Giulia; Patra, Aniket; Pothuraju, Renuka Devi; De Luca, Antonio; Krahne, Roman
      Advanced Photonics Research (2021), 2 (7), 2100053CODEN: APRDF2; ISSN:2699-9293. (Wiley-VCH Verlag GmbH & Co. KGaA)
      Alternating multilayer architectures are an ideal framework to tailor the properties of light. In photonic crystals, dielecs. with different refractive indexes are periodically arranged to provide a photonic bandgap. Herein, it is shown that a periodic arrangement of metal/insulator layers gives rise to an Epsilon-Near-Zero (ENZ) crystal with distinct bands of vanishing permittivity. The analogy of metal/insulator/metal (MIM) cavities to wave mechanics that describes them as quantum-wells for photons is elaborated, and the Kronig-Penney (KP) model is applied to MIM multilayers. This KP modeling allows to ext. the d. of ENZ states, evidencing a significant increase at the band edges, which makes ENZ crystals appealing for lasing applications. The ENZ bandwidth can be tuned by the thickness of the metal layers and can span the entire visible range, and the interactions between bands of two different cavity subsystems in more complex ENZ crystals enable more elaborate ENZ band engineering. Finally, the difference between the ENZ crystals and hyperbolic metamaterials is elucidated and the conditions that sep. these two regimes are quantified. The ENZ crystals constitute a new paradigm in the study of metal/insulator multilayers, and showcase a promising platform for light-matter interaction in photonic and plasmonic technologies.
    30. 30
      Israelachvili, J. N.; McGuiggan, P. M. Adhesion and Short-Range Forces between Surfaces. Part i: New Apparatus for Surface Force Measurements. J. Mater. Res. 1990, 5, 2223– 2231,  DOI: 10.1557/JMR.1990.2223
      30
      Adhesion and short-range forces between surfaces. Part I: New apparatus for surface force measurements
      Israelachvili, Jacob N.; McGuiggan, Patricia M.
      Journal of Materials Research (1990), 5 (10), 2223-31CODEN: JMREEE; ISSN:0884-2914.
      A new miniature Surface Forces App. (SFA Mark III) is described for measuring the forces between surfaces in vapors and liqs. The app. employs techniques similar to those used in current SFAs, but is easier to operate and is generally more user-friendly. Four stages of increasingly sensitive distance controls replace the 3 control stages of previous apparatuses. The first 3 stages allow for rapid manual control of surface sepn. to within 10 Å, while the fourth piezo-control stage has a sensitivity of < 1 Å. All 4 distance controls were specially designed to produce perfectly linear displacements of the surfaces. In addn., the SFA Mark III is more robust, less susceptible to thermal drifts, easier to clean, and requires smaller quantities of liq. than conventional SFAs.
    31. 31
      Israelachvili, J. N. Intermolecular and Surface Forces; Academic Press: Waltham, MA, USA, 2011.
      There is no corresponding record for this reference.

  • Supporting Information

    Supporting Information

    The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.nanolett.2c04864.

    • Schematic illustration of a metal-dielectric-metal (MDM) resonator; refractive index calculation of PVP-R6G; P-polarization reflectance analysis of the dye-doped MDM cavity; ENZ fit of R6G-doped MDM cavity via ellipsometry measurements and analytical model of the effective dielectric permittivity; three oscillator coupling model and Hopfield coefficients calculation; Gaussian fit of the transmittance spectra acquired via SFA measurements; determination of the number of photons per mode q in the cavity (PDF)


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