Low-loss prism-waveguide optical coupling for ultrahigh-Q low-index monolithic resonators

GUANGYAO LIU, VLADIMIR S. ILCHENKO, TIEHUI SU, YI-CHUN LING, SHAOQI FENG, KUANPING SHANG, YU ZHANG, WEI LIANG, ANATOLIY A. SAVCHENKOV, ANDREY B. MATSKO, LUTE MALEKI, AND S. J. BEN YOO* Department of Electrical Engineering and Computer Science, University of California-Davis, Davis, California 95616, USA OEwaves Inc., 465 North Halstead Street, Suite 140, Pasadena, California 91107, USA *Corresponding author: sbyoo@ucdavis.edu


INTRODUCTION
Kerr optical frequency combs [1][2][3][4][5], based on high-Q whisperinggallery-mode (WGM) resonators [6][7][8][9][10], have significantly stimulated the applications in optical clocks, optical synthesis, optical communications, optical sensing, cavity quantum electrodynamics, and precision navigation [11][12][13][14][15][16][17][18][19].Dielectric resonators on various platforms (e.g., silica, silicon nitride, lithium niobate) have been monolithically integrated with on-chip waveguides, achieving loaded Q as high as 100 million [20][21][22][23][24][25].On the other hand, crystalline resonators [26,27], suffering less from intrinsic and surface Rayleigh scattering, reported with record high-Q of 300 billion [28], have not yet been implemented with low-loss on-chip optical couplers.Such optical coupling to crystalline resonators should be based on a phase-and mode-matched power exchange between a resonator mode and a wave propagating in a specially engineered coupler (a waveguide or a prism).An ideal coupler should ensure phase synchronization, the optimal spatial overlap between the resonator and the coupler modes, mode selectivity, and criticality of the coupling [29][30][31].Mode selectivity is important for multi-mode structures as it allows interaction with a particular mode without disturbing the other modes of the structure.Previous demonstrations of optical coupling to ultrahigh-Q crystalline resonators utilized either free-space prisms, angle-cut fibers, or tapered fibers, suffering from the complexity of implementation onto a photonic platform that frequently calls for an active optical alignment [32][33][34][35].Primary challenges have been the material incompatibility between the crystalline resonator and the commonly used photonic platforms (e.g., silicon nitride, silica, silicon) [36,37], the low refractive index (e.g., 1.37) of the typical crystalline resonator [e.g., magnesium fluoride (MgF 2 )] compared to that of the conventional waveguide materials at telecommunication bands (e.g., 1.98 for silicon nitride, 3.48 for silicon), and the incompatible fabrication processes between traditional photonic platforms and the mechanically polished crystalline resonators.
Planar optical coupling is proved to be a robust and practical approach to implement WGM resonators with on-chip waveguides [38][39][40][41].Specifically, on-chip waveguides have been vertically coupled to crystalline resonators providing loaded Q exceeding 10 8 [42][43][44].In this work, we exploit the principle of evanescent wave coupling under total internal reflection (TIR) condition in traditional prism elements [45][46][47][48] and demonstrate, for the first time to our knowledge, a compact prism-waveguide coupler on a silicon nitride platform.This prism-waveguide coupler laterally couples light into and out of an ultrahigh-Q crystalline MgF 2 resonator with 1 dB loss and 1.9 × 10 9 loaded Q, realizing a new method for integration between crystalline resonators and on-chip waveguides [49].We further present a packaged module containing the prismwaveguide-coupled ultrahigh-Q MgF 2 resonator to generate a stable and low-noise optical frequency comb at the 26 GHz repetition rate.

DESIGN AND SIMULATIONS
A. Ultrahigh-QMgF 2 Resonator We used MgF 2 resonators [shown in Fig. 1(a)] with an intrinsic finesse of one million following the fabrication technique in the Method section.MgF 2 is characterized with excellent mechanical stability, relatively large hardness, as well as high optical transparency.The anomalous group velocity dispersion (GVD) at the communications band and a small thermo-refractive constant of this material are optimal for generation of optical mode-locked Kerr frequency combs.The anomalous GVD phase matches the nonlinear process.The small thermo-refractive constant increases the threshold of low-frequency thermo-optical instabilities, which often hinders mode locking of the comb harmonics.
Figures 1(a) and 1(b) show the photograph and the design of the resonator fabricated for the Kerr frequency comb oscillator.The final diameter and thickness of the resonator were 2.66 mm and 150 μm, respectively.Thickness (20 μm) of the mode localization area was designed for a 10 μm × 15 μm wedge-shaped WGM profile [simulation shown in Fig. 2(a)] for an optimal mode matching toward the prism-waveguide coupler mode.The loaded Q-factor was measured using the ring-down technique [28].The fabricated resonator was coupled nearly critically using a standard BK7 prism coupler to measure its Q-factor.The measured amplitude ring-down time was τ 10 μs [shown in Fig. 2(b)] at the 1.55 μm wavelength, which corresponds to 6 × 10 9 loaded Q-factor.

B. Prism-Waveguide Couplers
The Si 3 N 4 material platform on silicon is attractive because of its relatively low loss and compact size, convenient for further integration of the laser and photodiode chips [50][51][52][53][54][55].In designing the Si 3 N 4 ∕SiO 2 waveguide platform suitable for the coupling to an ultrahigh-Q MgF 2 resonator, we considered the waveguide mode size and propagation loss as the most important parameters.The waveguide mode size at the interaction area [at the reflection normal line shown in Fig. 3(a)] should match that of the WGM [shown in Fig. 2(a)] in the resonator to maximize the mode overlap integral and thus reduce the coupling loss resulting from mode mismatch.Si 3 N 4 waveguide core thickness at 50 nm has the lowest mode-confinement factor (below 5%) at the core region compare to those with thicker cores, providing the largest mode size to match the designed resonator mode (10 μm × 15 μm).Besides, ultralow propagation loss has been achieved with a Si 3 N 4 waveguide platform with core thickness around 50 nm [56,57] utilizing wafer bonding and high-temperature annealing.We directly deposited a thick SiO 2 over-cladding layer via the low-pressure chemical vapor deposition technique, which is free of the complexity arising from wafer bonding.(Fabrication details are shown in Section 3 (Methods).
The mode shape of the single-mode 50-nm-thick Si 3 N 4 core waveguide (6 μm in width) is approximately 5 μm × 2 μm, much smaller and elongated compared to that of the WGM in the resonator.Thus, we utilized the 200-μm-long adiabatic taper structure [shown in green in Fig. 3(a)] to expand the mode to nearly a round shape with approximately 10 μm diameter where the waveguide core width tapers down to 200 nm, which is close to the resolution of the lithography tool used in the fabrication process.This achieves nearly ideal mode-matching to the fundamental  WGM in the resonator.We determined the 200 μm length to be the optimized adiabatic length for the taper structure by simulating the output power to preserve near 100% power transmission.The adiabatic taper structure also ensures the single-mode power transmission to provide better mode coupling selectivity toward the lowest-order WGM within the resonator compared to traditional freespace prisms that excite multimodes at the reflection surface.
To satisfy the prism-like evanescent wave coupling toward the resonator under the TIR condition, we selected a specific incident angle [θ, defined as an angle formed by the reflection surface normal and the center-line of the prism-waveguide coupler tip, shown in Fig. 3(a)] to fulfill the phase-matching condition at the chip-air interface.The effective index of the optical mode out of the prism-waveguide coupler tip is close to that of the SiO 2 cladding material (n waveguide 1.44) at 1.55 μm wavelength, and the effective index of the fundamental WGM inside the resonator is approximately 1.37 (n resonator 1.37).The analytical phase-matching condition for evanescent coupling requires that the propagation constant of the optical mode inside the resonator matches that of the prism-waveguide coupler tip along the lateral direction at the reflection surface; this leads to a relationship: θ arcsinn resonator ∕n waveguide .Thus the angle value is calculated to be approximately 71.5°.The TIR condition is automatically satisfied at this reflection angle, since the TIR critical angle for the material is 44°.
Figures 3(a) and 3(d) explain the model we used for numerical simulation of our prism-waveguide coupling system (see Supplement 1).
The first step shown in Fig. 3(a) presents the finite-difference timedomain (FDTD) simulation setup at the coupling region from the prism-waveguide toward the resonator.We used an estimatedchannel MgF 2 waveguide ring resonator to represent the ultrahigh-Q wedge disk resonator used in the experiment with a similar mode shape (10 μm × 15 μm) and kept the incident angle to be 71.5°.The air-gap distance [value G in Fig. 3(a)] between the prism-waveguide chip and the resonator is the most critical parameter to determine the self-coupling coefficient (r 1 ) and the crosscoupling coefficient (k 1 ) in the coupling region.The critical coupling condition for an add-drop resonator system [Fig.3(d)] (our measurement setup analogy) requires r 2 a r 1 , where a denotes the single-trip amplitude transmission coefficient within the resonator.The a value of our ultrahigh-Q MgF 2 resonator is close to 1 (ultralow scattering loss), which requires the gap value (G) to be finely tuned until the k 1 value is close to 0 to maintain critical coupling.The simulated results from Fig. 3(a) are used in the stable-state add-drop resonator model [58] shown in Fig. 3(d) to further derive the transmitted power at the drop port, assuming no loss at the second coupling region (free-space prism in our experiment).Figure 3(e) shows the normalized transmission power simulated at the drop port of the system utilizing prism-waveguide couplers for the ultrahigh-Q MgF 2 resonator.We could achieve the maximum transmission at the center wavelength at the gap value around 1 μm, which confirmed our expectation and the principle for prism-waveguide evanescent wave coupling to ultrahigh-Q crystalline resonators.We taped out the first type of single prism-waveguide mask shown in Fig. 3(b) with variations in the incidence angle (θ), distance (d ) between the tip of the single prism-waveguide and the edge of the chip, and the prism-waveguide tip width (tw) to mitigate the fabrication inaccuracy.Furthermore, to facilitate the power outcoupling from the resonator, we designed the second type of the paired prism-waveguide coupler masks [shown in Fig. 3(c)] containing mirror-positioned single prism-waveguide couplers (with the best configuration tested shown in the following Results section) with separation distance (2D) based on a trigonometric relationship between the incidence angle (θ) and the distance (d ).This separation distance is set to achieve the best phase-matching condition between both prism-waveguide coupler arms with the resonator.The combination of both input and output prism-waveguide couplers should function as a single free-space prism element for the specific crystalline resonator.Besides, we particularly made the input/output beam angle of this paired prism-waveguide couplers PIC to be 20°to suppress the surface reflection at the input edge for achieving selfinjection locking [59,60] toward a distributed feedback (DFB) laser chip using Rayleigh scattered light from the resonator.

A. Ultrahigh-Q Magnesium Fluoride Resonator Fabrication Technique
We start with a high-quality crystalline MgF 2 wafer and produce a thin cylindrical preform.The crystalline cylinder is then ground using a diamond slurry.The shape of the surface is set to be optimal for the waveguide platform (Si 3 N 4 ) that the resonator is intended for.We have achieved ultrahigh finesse by careful selection of the parameters that control the mechanical shaping of the resonator utilizing the algorithm best for MgF 2 at the specific crystal cut.The control of the surface quality is achieved when no Rayleigh scattering in the resonator is observed.Electron microscopy tests show that in this case, the roughness of the resonator surface is of the order of a crystalline lattice period.ASML 5500/300 DUV lithography tool on 6 in.(150 mm) p-type silicon wafers.We started with depositing 5-μm-thick low-temperature-oxide (LTO) at 450°C by low-pressure chemical vapor deposition (LPCVD) as the Si 3 N 4 waveguide bottom cladding.We then deposited 50-nm-thick stoichiometric Si 3 N 4 at 800°C by LPCVD as the waveguide core [shown in step 1 in Fig. 4(a)].We defined the alignment marks for facet etching process on the Si 3 N 4 layer followed by step 2 in Fig. 4(a) to pattern the Si 3 N 4 waveguide core by inductively coupled plasma (ICP) etching.Another 5-μm-thick LTO oxide was deposited as the waveguide overcladding in step 3 in Fig. 4(a).We deposited 500-nm-thick amorphous silicon (a-Si) by LPCVD as the hard mask for facet etching through a 10-μm-thick SiO 2 layer together with a 150-μm-thick silicon substrate.We performed lithography on 5-μm-thick DUV photoresist for the assistance of facet deep etching.In step 4 in Fig. 4(a), we conducted a xenon difluoride (XeF 2 ) etching to remove an approximately 30-μm-thick silicon substrate underneath the tip of the prism-waveguide couplers [transparent regions in Fig. 4(b)].Finally, dicing with 5 μm accuracy using a diamond saw was performed on the wafer to shape PICs into the exact 0.5 mm × 4 mm rectangular die [Fig.4(b)] to facilitate coupling to the resonator in a compact platform.

A. Demonstration of Single Prism-Waveguide Coupled to Ultrahigh-QMgF 2 Resonator
We finalized the PIC facet by deep etching through the cladding material (SiO 2 ) and 150 μm deep into the silicon substrate followed by an isotropic XeF 2 etching, which removes the silicon substrate from the tip of the prism-waveguide coupler to avoid resonator WGM coupling into the high-refractive-index silicon substrate.We measured the transmission spectrum of the resonator using a tunable narrow linewidth laser.The resonator was overloaded, and the measurement had shown that the loaded Q-factor was on the order of a billion [Fig.5(b)].The transmission loss through the resonator did not exceed 3 dB.The low insertion loss suggests that the Q-factor of the resonator did not degrade noticeably during the packaging procedure.To evaluate the performance of the designed single prismwaveguide couplers, we prepared a setup [shown in Fig. 5(a)] allowing us to (1) estimate the efficiency of waveguide insertion; (2) qualify the waveguide transmission loss; (3) couple light into WGM of the resonator from the prism-waveguide coupler; (4) couple light out of WGM using a conventional prism; (5) measure the full power exiting the WGM; and (6) deconstruct the overall transmission loss of the full optical train, and estimate the efficiency of coupling between the prism-waveguide coupler to the WGM in the resonator.The insert in Fig. 5(a) depicts the actual interface between the angled tip of the prism-waveguide coupler and the adjacent MgF 2 resonator.Light delivered by a single-mode fiber (SMF-28) was collimated and focused using Thorlabs aspheric lenses C230 and C280 with focal distances approximate 9 mm and 18 mm, respectively; the resulting system formed the focal spot with a full width at 1∕e 2 diameter of approximate 5 μm, well matched to the input mode of the silicon nitride waveguide.We used a straight waveguide [green straight line in Fig. 5(a)] to assess the insertion loss by comparing the optical power output of the waveguide (with light collected using integrating sphere), to the optical power in the input fiber.This comparison yielded the value of the overall insertion loss between the fiber and the output beam of the waveguide at the level 3.8 this value included residual reflections, modal mismatches, and waveguide propagation losses.After that, the input launcher optics were aligned to send the light into the prismwaveguide coupler [green curved line shown in Fig. 5(a)].The MgF 2 resonator was positioned in the proximity of the waveguide chip edge with angled waveguide tips, and adjusted using Thorlabs NanoMax 302 three-axis translation stage with additional lead zirconate titanate (PZT) drives.An identical translation stage was used to bring the conventional glass coupling prism to couple the light out of the WGM of the resonator.The light exiting the prism was intercepted by a large area multimode fiber ["light pipe" in Fig. 5(a)] and sent into a photodetector for observation of the WGM, measurement of the loaded Q-factor using a tunable laser at 1550 nm (New Focus Velocity 6302), and evaluation of transmission losses.To validate the symmetry of input and output coupling, an additional optical launcher ["WG Launcher 2" in Fig. 5(a)] was used to match the WGM field at the TIR surface of the prism.By varying and equalizing the two gaps, we maximized the optical throughput of the setup and estimated the transmission loss of the prism-waveguide-toresonator-to-outcoupling prism as a function of loaded bandwidth.The latter has been measured using calibration of the laser sweep assisted by a fiber interferometer.We measured the minimum coupling loss of 1 dB at a heavily loaded bandwidth of 3.2 MHz via the best single prism-waveguide coupler with the following geometric specs: incident angle θ 71.5°, distance d 2 μm, and prismwaveguide tip width tw 200 nm.While the intrinsic unloaded bandwidth of resonator, measured shown in Fig. 5(b), was 100 KHz (Q near 1.9 billion at 1.55 μm wavelength).

B. Demonstration of Prism-Waveguide-Assisted Optical Injection Locking of DFB Laser to Resonator
As the next step in the experimental evaluation of our novel prism-waveguide coupling system for MgF 2 resonators, we performed and evaluated parameters of optical injection locking of a DFB laser.This was considered a crucial step to achieve waveguide-based optical frequency comb generator based on the ultrahigh-Q MgF 2 resonator.To validate the quality of the coupler, we created an external DFB semiconductor laser utilizing the self-injection locking method for locking the laser to the  3) are the prism-waveguide coupler PIC, (4) and ( 5) are fiber launchers.
WGM resonator [61,62].The coupler loss impacts the back scattering significantly because it limits the amount of light both entering the mode and exiting the mode in the direction of the laser.To demonstrate the self-injection locking we used the setup depicted in Fig. 6, in which MgF 2 resonator (1 in Fig. 6) was simultaneously coupled to two single prism-waveguide coupler chips (2 and 3 in Fig. 6).The best prism-waveguide coupler in PIC (2 in Fig. 6) was coupled to the powered DFB laser assembly (4 in Fig. 6) (Emcore 702) equipped with a two-lens beam transformer that provides mode matching between the laser beam and the waveguide mode.The focused DFB laser assembly was suspended on a mechanical extender tip mounted on the micro-positioner for active alignment.The second, weakly coupled, prism-waveguide PIC (3 in Fig. 6) was used for tapping the light output of the resonator, and a light pipe (5 in Fig. 6) was used for collection and transferring the light to the photodetector.An additional light pipe was used to monitor the input coupling at the reflection port of the first prismwaveguide coupler.With proper alignment and optimally chosen gaps, optical injection locking was achieved with optical resonance feedback from the resonator, and a locking range of 5 GHz was obtained with our prism-waveguide coupler.This observation confirmed the high quality of the prism-waveguide coupler, as the locking is usually not observed if the coupler loss exceeds 5 dB.These parameters are similar to those obtained in existing WGM-resonator-stabilized injection-locked lasers that use freespace optics and prism couplers [62].

C. Demonstration of Packaged Kerr Frequency Comb Source via Paired Prism-Waveguide Couplers
Based on the successful demonstration of laser injection locking with the MgF 2 resonator via single prism-waveguide coupler PICs, we followed the design shown in Fig. 3(c) and the fabrication process in Section 3 (Methods) to deliver the paired prism-waveguide couplers PIC using the best single prismwaveguide coupler configuration tested above.Figure 4(b) shows photographs taken with the aid of a microscope of the fabricated 0.5 mm × 3.8 mm paired prism-waveguide coupler PIC.The silicon substrate was removed (shown in the light-colored region around the PIC) to avoid unnecessary WGM power leakage.Figure 7(a) depicts the configuration of the packaged comb unit based on paired prism-waveguide coupler PIC coupling toward the MgF 2 resonator.The PIC was rotated 20°to eliminate the input facet reflection for a laser injection-locking condition.A Kerr optical frequency comb is generated in the resonator when the laser light is efficiently coupled to the WGM, the power of the light exceeds the comb generation threshold, and the frequency of the pump is locked to the mode of the resonator.We increased the laser current to approximately 80 mA for self-injection locking with a WGM.Figures 7(b) and 7(c) show the schematic illustration and the actual photograph of the packaged Kerr frequency comb unit.The frequency comb was observed when the detuning value was properly selected and phase adjusted for positive optical feedback.The 26 GHz optical frequency comb was observed using an optical spectrum analyzer [Fig.7(d)].After confirmation of the optimal optical comb regime, the light was sent to a highspeed photodetector (U2t V2140), where we observed generation of a spectrally pure RF signal confirming coherence of the optical comb harmonics and utility of the device as a packaged photonic source of low-phase-noise microwave signals.

CONCLUSION
We have demonstrated the first on-chip prism-waveguide couplers on a compact silicon nitride platform for phase-and mode-matched evanescent coupling to a low-index ultrahigh-Q crystalline resonator.This prism-waveguide-coupled MgF 2 resonator achieves 1.9 billion loaded Q-factor with 1 dB coupling loss.We further realized a packaged planar-waveguide-coupled Kerr optical frequency comb source at 26 GHz repetition rate where the laser chip was self-injection-locked to this prismwaveguide-coupled MgF 2 resonator.

Fig. 1 .
Fig. 1.(a) Camera photo of a transparent ultrahigh-Q MgF 2 resonator on the holding pedestal.(b) Geometric dimension of the cross-section view of a half-resonator with 1330 μm radius, 150 μm height, and 20-μm-high wedge region for the WGM shown in red.

Fig. 3 .
Fig. 3. (a) Geometric configuration of prism-waveguide couplers maintaining phase synchronized coupling toward the resonator (used in FDTD simulation): G denotes the gap distance between the photonic integrated chip (PIC) and resonator; D denotes the distance between the tip of prism-waveguide coupler and the reflection surface normal; d denotes the distance between the tip of the prism-waveguide coupler and the edge of PIC; tw denotes the tip core width; θ denotes the reflection angle; L denotes the length of the taper structure.(b) Testing PIC (10 mm × 4.5 mm) containing individual prism-waveguide couplers with variations in θ, d, and tw.(c) PIC (3.6 mm × 0.42 mm) containing a pair of prism-waveguide couplers (single prism-waveguide coupler with the best performance tested through mask shown in (b) and an end-to-end waveguide for alignment assistance).(d) Add-drop resonator system, analogy to our testing setup for single prism-waveguide coupler: bottom red dashed rectangular region represents prism-waveguide-to-resonator coupling area with self-coupling ratio r 1 , cross-coupling ratio k 1 , and additional loss γ; top red dashed rectangular region represents free-space prism to resonator coupling area with self-coupling ratio r 2 , cross-coupling ratio k 2 , and no additional loss (ideal prism) (e) The semi-numerical simulation results of the drop port transmission power at different gap values [G in (a)] between the prism-waveguide chip and the resonator at 1550 nm.

Fig. 5 .Fig. 6 .
Fig. 5. (a) Measurement setup for single prism-waveguide coupler and straight calibration waveguides (shown in green lines).The insert is the microscope picture of the fabricated chip containing prism-waveguide couplers aligned to a resonator where silicon substrate released region [step 4 in Fig. 4(a)] is shown in blue dotted rectangle.(b) Normalized transmitted power received at the light pipe from (a) in weak loading regime, indicating the unloaded bandwidth of 100 kHz, Q-factor 1.9 × 10 9 .

Fig. 7 .
Fig. 7. (a) 3D schematic illustration of paired-prism-waveguide couplers coupled to the resonator for comb generation.(b) Illustration of the packaged Kerr frequency comb source.(c) Photo of packaged planar-waveguide coupled comb source.(d) Representative Kerr frequency comb output from the package.