van der Waals Decoration of Ultra-High-Q Silica Microcavities for χ(2)–χ(3) Hybrid Nonlinear Photonics

Optical nonlinear processes are indispensable in a wide range of applications, including ultrafast lasers, microscopy, and quantum information technologies. Among the diverse nonlinear processes, second-order effects usually overwhelm the higher-order ones, except in centrosymmetric systems, where the second-order susceptibility vanishes to allow the use of the third-order nonlinearity. Here we demonstrate a hybrid photonic platform whereby the balance between second- and third-order susceptibilities can be tuned flexibly. By decorating ultra-high-Q silica microcavities with atomically thin tungsten diselenide, we observe cavity-enhanced second-harmonic generation and sum-frequency generation with continuous-wave excitation at a power level of only a few hundred microwatts. We show that the coexistence of second- and third-order nonlinearities in a single device can be achieved by carefully choosing the size and location of the two-dimensional material. Our approach can be generalized to other types of cavities, unlocking the potential of hybrid systems with controlled nonlinear susceptibilities for novel applications.


INTRODUCTION
Since the landmark discovery of second-harmonic generation (SHG) [1] enabled by the invention of lasers [2], nonlinear optics have played a central role in the development of diverse photonics applications.Frequency conversion processes are of particular importance, being extensively employed in ultrafast optics [3], metrology [4,5], quantum state generation [6,7], as well as microscopy [8,9].To achieve these functionalities, both second-and third-order processes such as SHG, third-harmonic generation (THG), sum-frequency generation (SFG), parametric down conversion, and four-wave mixing (FWM) are utilized.
With such a variety of nonlinear effects, combinations of frequency conversion processes would allow for more flexible spectral synthesis.It is, however, generally difficult for second-and third-order processes to coexist.The efficiencies of nonlinear processes depend directly on the nonlinear susceptibility of conversion media but the origins are markedly different for second-and third-order susceptibilities.An essential requirement for second-order nonlinear processes to occur is inversion symmetry breaking, and typical materials include dielectric crystals (for example, lithium niobate and beta-barium borate), III-V semiconductors and organic crystals [10].Although third-order nonlinear susceptibility can simultaneously exist, second-order process dominates as higher-order nonlinearities are generally weak [10].
Conversely, second-order nonlinear susceptibility vanishes in centrosymmetric crystals and amorphous materials (e.g., liquids, gases, and amorphous solids), and only third-order processes can be utilized in these χ (3) materials.
In this regard, one promising strategy is to establish a hybrid system by combining a non-centrosymmetric nonlinear material with an ultrahigh-Q microcavity fabricated from a χ (3) material [11].The strength of second-order processes can be controlled through mode overlap with the non-centrosymmetric material, while exceptional enhancement of optical density in the tiny mode space can be facilitated to boost the third-order process to a practical level.As a candidate system, we propose ultrahigh-Q silica microcavities functionalized by transition metal dichalcogenides (TMDs).Silica whispering-gallery microcavities boast ultrahigh-Q properties (> 10 8 ) that ensure high-circulating optical intensities essential to induce various third-order optical nonlinear processes [12][13][14][15][16][17][18].Meanwhile, monolayer TMDs possess a comparable magnitude of second-order nonlinearity to commonly used nonlinear crystals [19][20][21] and are thus expected to be used for practical nonlinear applications [22][23][24][25][26].
Their atomically thin nature gives them mechanical flexibility to conform to the surface of the optical microcavities and the van der Waals character makes them compatible for the heterogeneous interface [27][28][29][30].
Here, we demonstrate a novel nonlinear photonic platform by functionalizing ultrahigh-Q silica microspheres with tungsten diselenide (WSe 2 ).Atomically thin layers of the twodimensional (2D) material are transferred onto the cavity with a minimal level of scattering loss.Cavity-enhanced second-harmonic (SH) generation is achieved by a continuous-wave (CW) excitation with only a few hundreds of microwatts thanks to strong light-matter interaction between a resonant optical field and integrated WSe 2 .We also observe efficient SFG with a two-color excitation scheme.In addition, pump power dependence shows self- locking of SH output, revealing the mechanism of the dynamic phase-matching process.It is confirmed that the SH process only occurs for odd layer numbers, and the coexistence of second-and third-order nonlinearities in a single device is achieved by controlling the second-order susceptibility of the device.We first functionalize a silica microsphere cavity (diameter ∼80 µm) by transferring mechanically exfoliated monolayer WSe 2 onto the cavity surface using the polydimethylsiloxane (PDMS)-assisted dry-transfer technique [31].The layer number of WSe 2 flakes are identified either through photoluminescence (PL) measurement [32] or by optical contrast in microscope images prior to the transfer [33].The degradation in the Q-factor is likely due to an increase in scattering loss resulting from the functionalization as is also observed in the integration of materials to other nanophotonic cavities [27,34,35].We anticipate minimal effect on the Q-factor from the absorption loss caused by the WSe 2 flake because the telecom band photon energy is significantly lower than the bandgap of monolayer WSe 2 (∼1.75 eV).It should be noted that the uniformity of transferred flakes is the key to maintaining high Q-factors as well as the flake size and the transfered position, and placing a small flake away from the equator of a microcavity would greatly reduce the scattering loss in high-Q modes.For most of this study, however, we place priority on using uniform and large WSe 2 flakes and transfer onto the equator of the device to maximize the interaction length between the optical modes and the WSe 2 material.
Efficient nonlinear optical processes are achieved by dynamically obtaining resonant phase-matching from thermal and Kerr nonlinearities.The phase-matching condition described here is different from the conventional phase-matching for frequency conversion processes in nonlinear crystals, which is usually satisfied by aligning the incident angle and polarization of the pump lasers.The situation becomes more complicated in a microcavity system due to resonance effects as well as inherent material and geometric cavity dispersion [36].Mode mismatch at the SH frequency is induced by the dispersion which hinders perfectly resonant phase-matching condition.In order to locate resonances with efficient frequency conversion, we carefully scan the pump wavelength while monitoring the visible spectrum with a thermoelectrically cooled charged coupled device (CCD) attached to a spectrometer.Continuous wavelength scan of the pump laser induces changes in the refractive index of the cavity via thermal and Kerr effects, thus giving rise to the redshift of the resonance modes.Since cavity modes with different resonant frequencies and spatial mode distribution experience different amounts of the redshift, the phase-matching condition can be fulfilled at certain pump wavelengths where efficient frequency conversion would occur.The SH power exhibits significant dependence on the pump powers of 0.5 mW, 1 mW, and 2 mW.
The colormaps are normalized to a common scale.
frequency of the SH light (773.1 nm) exactly matches twice the pump frequency (1545.5 nm) with a wavelength error of only 0.045%, and this fact confirms the occurrence of frequency doubling process via second-order optical nonlinearity.We stress that other third-order (Kerr) nonlinear processes, which could arise from bulk silica microcavities, are absent in this experiment because the threshold powers are far beyond our pump power level.The required pump powers for FWM and Raman oscillation are 12.6 mW and 36.1 mW, respectively, in the case of a loaded Q-factor of 5 × 10 6 , as threshold powers of these processes scale as 12,13].(See Methods for details in theoretical estimation of the threshold powers).
Next, we pump the device by using two CW lasers with different frequencies (i.e., twocolor excitation) at sub-milliwatt pump powers.This scheme allows us to observe SFG as shown in Figs.2(c) and 2(d).Two-color pump imposes a triply resonant condition on the sum-frequency process to be phase-matched, but it is easy to find the phase-matching condition by slowly tuning one laser while keeping the frequency of the other laser within a high-Q resonance.Figures 2(e) and 2(f) show a unique example, where two SH and one SF light are generated from two laser input because of five-fold resonant triple phase-matching.
In addition to second-order nonlinearities, we also observe excitonic photoluminescence (PL) from the monolayer WSe 2 .Figure 2 The dynamic phase-matching mentioned previously is highlighted in the pump power dependence of the SH power as shown in Fig. 3(a).We measure the SH power for the same cavity mode, and carefully tune the pump wavelength so that the SH light is maximized at each pump power.This measurement scheme allows us to find the perfect phase-matching condition at a certain pump power, which can be dynamically altered by the nonlinear resonance shifts.The double logarithm plot is presented in the inset of Fig. 3(a), where three distinct regimes can be recognized.Below a pump power of ∼2 mW, the SH powers exhibit a linear slope of ∼2.2, which is very close to the anticipated slope of 2 for a SHG process.
As the pump power is increased from 2 mW to 4.5 mW, the fitted slope drastically changes to ∼5.5, and further increase in the pump power (above 4.5 mW) induces saturation of the SH power.Such a kink behavior of the SHG intensity has not been reported in conventional SHG measurements of TMD flakes on substrates [37,38] or photonic nanostructures [26,35,39,40].
We therefore consider the influence of dynamic phase-matching condition in a double resonance system.Figure 3(b) shows the schematic for the mechanism under consideration, where the SH light is blue-detuned at low pump powers.In this scenario, SH light is considered to be almost in an off-resonance condition with a large detuning (state (i)), yielding a moderate conversion efficiency with a slope of approximately 2. As the pump power increases, thermal and Kerr nonlinearities induce significant redshift of the resonances [41].
While the frequency of the SH light is twice the pump frequency (i.e., ω SH = 2ω p ), the resonance mode ω 2 for SH generally shows smaller shifts than the SH light (∆ω 2 < ∆ω SH ) due to the imperfect mode overlap between the pump and SH modes [42].The detuning of the SH light therefore decreases at a higher pump power, leading to a rapid increase in conversion efficiency (state (ii)).Once the SH power reaches its maximum when both cavity modes exactly match the on-resonance condition (state (iii)), a further increase in intracavity power results in the red detuning of SH light which would reduce the output (state (iv)).The maximum SH power for higher pump powers would then be obtained for the specific intracavity power where the double resonance condition is retained.Since the intracavity power is almost constant, the SH power saturates despite a further increase in the pump power.Such a complex power dependency is clearly observed in a separate experiment, where we record SH signals while continuously scanning the pump laser frequency at a certain pump power.As shown in Figs.3(c)-3(e), the SH signal becomes more and more frequent in the spectral map, and the intensity is drastically enhanced with the increase in the pump power.We note that no pump polarization dependence is observed.(Extended data are presented in Supplementary Note 3.) It is possible to calculate the conversion efficiency from the data in Fig. 3(a).When we define P SH as the detected SH power, the calculated maximum conversion efficiency P SH /P 2 p is 6.6 × 10 −4 %W −1 with the pump power P p of 4.5 mW.It should be noted that the internal (intracavity) conversion efficiency is expected to be over one order of magnitude higher than the above value because the waist of the nanofiber waveguide is optimized to the pump wavelength band in this experiment, thus resulting in poor coupling efficiency of SH light due to the phase mismatch between the visible band and the nanofiber coupler [43,44].We note that the collection efficiency can be improved by employing an additional nanofiber designed for SH wavelengths, i.e., add-drop configuration [17,42] or by exploiting a chaotic channel in deformed microcavities [44].
As mentioned earlier, symmetry plays an important role in determining the nonlinear susceptibility, and therefore the number of layers in the two-dimensional material is a crucial factor.The WSe 2 crystals used in this work possess the 2H-phase (semiconducting) structure, which is a more stable form than other crystal phases.The 2H-phase TMD crys-tals belonging to D 3h space group exhibit substantial second-order nonlinearity only for odd layer numbers, whereas the χ (2) nonlinearity vanishes in even layer numbers since the net nonlinear dipoles are cancelled out due to inversion symmetry [37,38].Considering these selection rules, we perform a comparative experiment in four different devices: pristine silica device, ML-WSe 2 functionalized device, 2L-WSe 2 functionalized device, and 3L-WSe 2 functionalized device.
Figure 4 shows the mapping of SH spectra in the visible wavelength region when the pump wavelength is scanned from 1500 nm to 1600 nm with a pump power of 3 mW.As .This is clear evidence that second-order nonlinearity originates from the integrated WSe 2 , not from intrinsic surface symmetry breaking of the cavity material [42].In a pristine device, third-order processes such as THG and third-order SFG associated with pump, FWM, and stimulated Raman scattering (SRS) are observed in the range of 500-620 nm (Fig. 4(a), left) thanks to unaltered ultrahigh-Q properties (> 5 × 10 7 ).We find that the number of SH signal peaks in the map is surprisingly high in both ML-and 3L-WSe 2 devices even though the Q-factors of most resonances are not as high as 10 7 .We attribute the efficient, highly populated SHG to giant second-order nonlinearity of TMD materials and relaxed resonant phase-matching condition due to cavity linewidth broadening.If we could achieve much higher Q-factors with larger overlap between the cavity mode and the material, the conversion efficiency is expected to substantially increase; nevertheless, the resonant phase-matching condition would become stricter as a trade-off.
We have shown thus far the results focused on the emergence of second-order nonlinearity, but one key advantage of this technique is its flexible controllability of nonlinear susceptibility.By carefully controlling the transferred position and the flake size of materials, it is possible to tune the balance between second-and third-order nonlinearity.Here, we intentionally place a small flake away from the equator of a cavity to keep Q-factors high enough (> 10 7 ) to simultaneously observe both second-and third-order nonlinear processes in the same device.can be recognized around 1630-1670 nm, which coincides with the Raman gain band of silica [13].For the visible wavelength band, the peaks around 520-600 nm arise from THG and third-order SFG processes involving the peaks seen in the pump band.The signals around 600 nm are believed to involve a cascaded Raman process [15,17,18].While these signals originate from third-order nonlinearity, the strong signal at a wavelength of 772 nm corresponds to the SH light of the pump light via second-order nonlinearity induced by monolayer WSe 2 .The spectral map is shown in Fig. 5(c), where the strong visible light is recognized as a result of simultaneous generation of second-and third-order processes.
The signals around 780-800 nm come from the second-order SFG process of the pump and Raman components, which are not observed in the previous experiments (Fig. 4).

CONCLUSIONS
In conclusion, we have demonstrated a novel approach for introducing second-order optical nonlinearity in ultrahigh-Q silica microcavities through functionalization by a twodimensional material.By integrating atomically thin TMD layers with broken crystal inversion symmetry onto the surface of amorphous silica microspheres, cavity-enhanced SHG and SFG arise from strong light-matter interaction via evanescent fields.The cavity-enhanced PL emission mediated by the SHG process reveals the distinct optical coupling between SH light and the excitonic resonance of the monolayer WSe 2 .The conversion efficiency of SH light is strongly dependent on the pump power as a result of the dynamic phase-matching process, leading to the drastic increase and saturation of the SH power.A carefully coordinated clean-stamp transfer technique allows for investigation of layer number dependence as well as manipulation of the relative strength of the second-and third-order optical nonlinearity in the device.
Practical levels of second-order nonlinearity in χ (3) materials has long been strongly desired.Surface symmetry breaking [42,45] and photo-induced effects [46,47] can introduce second-order nonlinear susceptibility but are limited in various aspects.In comparison, this study offers a powerful way to controllably enhance optical nonlinearity in high-Q microcavities, which would bring breakthroughs in nonlinear optics.The results presented in this work lead to an anticipation that optical nonlinearity can be artificially designed in hybrid systems where various nonlinear processes are combined to implement unconventional functionalities.
In addition, we note that this approach can be extended to other centrosymmetric high-Q cavity devices, including integrated ring resonators made of silicon or silicon nitride (Si 3 N 4 ), and thus paves the way to few-photon coherent nonlinear optics and quantum photon manipulation in various platforms.The combination of ultrahigh-Q cavities with nanomaterials opens up a novel regime in investigation of optical processes at high fields under CW excitation, potentially leading to intriguing physical phenomena as well as nanophotonic applications.

Device fabrication
A silica microsphere cavity is fabricated from a standard single-mode fiber (SMF-28) via arc-discharging using a commercial fiber fusion splicer.The cavity size can be roughly controlled by the discharge power, position, and duration.The arc-melting process ensures the surface uniformity and smoothness, enabling ultrahigh Q-factors of up to 10 8 .Before the cavity fabrication, we reduce the fiber diameter to approximately 20-30 µm by adiabatically stretching the optical fiber.This preprocess allows the fabrication of a microsphere with a diameter of less than 100 µm.Atomically thin WSe 2 flakes are prepared by mechanical exfoliation of a bulk WSe 2 crystal (HQ Graphene).The WSe 2 flake is deposited on the microsphere surface using a dry-transfer technique assisted by a PDMS sheet.Precise position alignment is accomplished by using a motorized position system and a high-magnification microscope.

Experimental setup details
A wavelength-tunable CW laser (Santec, TSL-710) at the telecom band is used as a pump light source.The polarization of the input light is adjusted to the desired cavity modes by using a fiber polarization controller (FPC).A tapered fiber waveguide (diameter of ∼1 µm) is used to couple the pump light to a cavity via evanescent coupling.The distance between the fiber and the cavity is carefully controlled by using a high-precision positioner since the coupling strength is determined by the distance and the coupling position [43,48].
The pump (telecom band) and visible (400-900 nm) spectra are measured by an optical spectrum analyzer (OSA) and a thermoelectrically-cooled charge coupled device (CCD) camera attached to a high-resolution spectrometer, respectively.The transmission spectrum is recorded by using a photodetector (PD) and a data acquisition (DAQ) system triggered with laser wavelength sweeping.The laser power is kept less than 10 µW to avoid thermal broadening of a resonance for the transmission measurement.The spectral mapping is recorded with a spectrometer while slowly scanning the pump laser wavelength.
Theoretical estimation of threshold power for third-order nonlinear processes Threshold pump power for parametric FWM and Raman oscillation is obtained by taking into account the power build-up factor in a microcavity coupled to an external waveguide, respectively [12,13], where n is the refractive index, V eff is the effective mode volume, n 2 is the nonlinear refractive index, c is the speed of light in a vacuum, η is the coupling efficiency to the waveguide (η = 0.5 is the critical coupling condition), and g R = 6.2×10 −14 is the Raman gain coefficient of silica.For a silica microsphere with a diameter of 80 µm, the parameters are assumed to be n = 1.44, n 2 = 2.2 × 10 −20 , and V eff = 3287 µm 3 .The effective mode volume is calculated by FEM simulation.

FIG. 1 .
FIG. 1. Functionalization of a high-Q silica microcavity by atomically thin 2D material.(a) Conceptual illustration of a monolayer-material-integrated silica microcavity realizing strong lightmatter interaction.(b) Simulated normalized intensity of the optical mode across the equator of a silica microsphere with a radius of 40 µm.The calculations are conducted by using a finite element method (FEM) software (COMSOL Multiphysics).The cavity modes exhibit a slight difference in the profiles, and TM modes exhibit evanescent fields slightly higher than TE modes.The inset shows the optical mode profile, where the white line indicates the boundary between the silica and surrounding air.(c) False-color scanning electron micrograph image of a WSe 2 integrated high-Q microsphere.The scale bar represents 50 µm.(d) Experimental setup.FPC, fiber polarization controller; DUT, device under test; PD, photodetector; DAQ, data acquisition; OSA, optical spectrum analyzer; CCD, charged-coupled device installed to a spectrometer.(e, f) Histogram of cavity linewidths in pristine and functionalized microcavities.The degradation of Q-factors is mainly attributed to an increase in surface scattering loss.

FIG. 2 .
FIG. 2. Observation of second-order nonlinear processes in material integrated microresonators.(a, b) Optical spectra of pump wavelength and generated SH light.The frequency of the SH light exactly matches twice the frequency of the pump light, indicating the nonlinear frequency-doubling process.The energy diagram of an SH process is shown in the inset.(c, d) Optical spectra of two different pump wavelengths and generated second-order sum-frequency (SF) light.The frequency of SF light corresponds to the sum of pump frequencies as depicted in the inset.(e, f) Measured spectra of pump wavelengths and corresponding visible light, where the two-color excitation scheme enables simultaneous generation of SFG and SHG.The difference in signal powers is owing to the phase-matching condition for near-infrared and visible cavity modes.(g) Optical spectra of SHGmediated photoluminescence (PL) emission in a WSe 2 -functionalized cavity.The SH light at a wavelength of 715 nm excites excitonic PL in a monolayer WSe 2 , where the broad emission is optically coupled to numerous cavity modes.The inset shows the energy diagram of the process.CB: conduction band, VB: valence band.

Figure 1 (
Figure1(a) shows a conceptual illustration of a 2D-material functionalized silica microcavity, capable of serving as a second-order nonlinear photonic platform.Strong light-matter interaction assisted by cavity resonance permits efficient nonlinear optical processes that originate from the atomically thin layered material with low-power CW excitation.The frequency converted light that resonates with another longitudinal resonance mode, in a situation referred to as a doubly-resonant condition, allows the cavity-enhanced signals to couple into the same waveguide coupler utilized for excitation.The normalized mode intensity of a microsphere cavity is shown in Fig.1(b), where the inset shows the optical mode profile.Although the optical density is maximized at a few microns inside from the surface of the cavity, evanescent field exists at the boundary, which interacts with a surface integrated 2D material.These simulation results indicate that the evanescent tails, accounting for up to a few percentages of the total light intensity, can interact efficiently with the surface layer for both primary polarization modes, namely the transverse-electric (TE) and transverse-magnetic (TM) modes.The light-matter interaction on the surface layer generally increases in a smaller cavity because the ratio of the evanescent field to the total intensity is inversely related to the cavity radius.(The relationship between the evanescent field ratio and the cavity radius is further detailed in Supplementary Note 1.)

Figure 1 (
c) shows a false-color image of the WSe 2 functionalized silica microsphere cavity.(The details on the sample fabrication are presented in Methods and Supplementary Note 2.)To characterize the influence of WSe 2 flake on the Q-factor of a microcavity, we compare the transmission spectra before and after the transfer process.The experimental setup is presented in Fig.1(d).All resonances observed within 1530 to 1570 nm are numerically fitted to a Lorentzian function.This allows for the statistical analysis of loaded FWHM linewidth (=ω/Q) as shown in Figs.1(e) and 1(f).The median value in a pristine (i.e., before transfer) microsphere is 2 MHz, which corresponds to an ultrahigh Q-factor of 1 × 10 8 .After the transfer of a WSe 2 flake, the most probable loaded linewidth broadens to approximately 40 MHz, corresponding to a Q-factor of 5 × 10 6 even though the highest Q values remain about 10 7 .

Figure 2 FIG. 3 .
Figure 2 presents optical spectra in the visible and the corresponding pump wavelength bands.By carefully tuning the pump laser wavelength to a cavity resonance with a pump power of 500 µW, second-harmonic (SH) light is clearly observed (Fig. 2(a) and 2(b)).The

FIG. 4 .
FIG. 4. Layer dependence of SH light intensity.(a) Spectral mapping of signal intensity in the visible wavelength region in a pristine silica microsphere.Third-order nonlinear processes (e.g., THG, TSFG) are observed in the 500-600 nm wavelength range, whereas no strong signal appears in the 740-810 nm wavelength range due to the absence of the second-order nonlinearity.(b) Spectral mapping in a monolayer WSe 2 functionalized microcavity.The strong SH signals are observed over a wide range of pump wavelengths (1500-1600 nm).(c) Mapping in a 2L-WSe 2 functionalized sample.No clear SH light is measured in the map because the inversion symmetry exists in a 2H-stacked bilayer WSe 2 , thus the χ (2) nonlinearity vanishes.(d) Mapping in a 3L-WSe 2 device.The distinct SH light is observed again similar to the monolayer case since the inversion symmetry is broken for 3L-WSe 2 crystal structures.The measurements are performed with a fixed pump power of 3 mW.
(g) shows a spectrum of SHG at a wavelength of 715 nm and the associated PL emission when pumping the device at a wavelength of 1530 nm.The multiple spikes seen in the PL spectrum indicate that broad excitonic PL couples to the high-Q cavity modes and the intensities are enhanced due to Purcell effect or modulated by the differing collection efficiencies.The energy diagram is depicted in the inset of Fig.2(g).We emphasize that the observation of this unique resonance energy transfer, i.e, SHG-mediated PL and subsequent resonant enhancement, has only become possible by our WSe 2 -functionalized high-Q devices.This result also proves the strong interaction between a monolayer WSe 2 and whispering-gallery modes via an evanescent field.
we anticipate, strong SH light appears only in the ML and 3L-WSe 2 devices (Figs.4(b) and 4(d)), whereas there is no distinct signal in the pristine and 2L-WSe 2 devices (Figs.4(a) and 4(c))

Figures 5 (FIG. 5 .
Figures 5(a) and 5(b) show the observed optical spectra in the pump and the visible wavelength bands in this WSe 2 functionalized microcavity.In the pump wavelength band, FWM sidebands are observed in the vicinity of the pump light and a few Raman peaks