Optical parametric oscillation in silicon carbide nanophotonics

Silicon carbide (SiC) is rapidly emerging as a leading platform for the implementation of nonlinear and quantum photonics. Here, we find that commercial SiC, which hosts a variety of spin qubits, possesses low optical absorption that can enable SiC integrated photonics with quality factors exceeding $10^7$. We fabricate microring resonators with quality factors as high as 1.1 million, and observe low-threshold (8.5 $\pm$ 0.5 mW) optical parametric oscillation as well as optical microcombs spanning 200 nm. Our demonstration is an essential milestone in the development of photonic devices that harness the unique optical properties of SiC, paving the way toward the monolithic integration of nonlinear photonics with spin-based quantum technologies.

Silicon carbide (SiC) is a promising material for realizing quantum and nonlinear photonics technologies. [1][2][3][4] Uniquely combining a wide transparency window (UV to mid-IR), 5 a strong second-and third-order (χ (2) , χ (3) ) optical nonlinearity, 6, 7 and a high refractive index, SiC is also host to a variety of optically-addressable spin qubits, 2,8 which are actively studied for applications in quantum computation 8,9 and sensing. 10 SiC photonics have been in development for over a decade, and have recently seen major breakthroughs, including low-loss waveguides and high quality (Q) factor resonators; 3, 4, 11 efficient on-chip frequency conversion via the χ (2) nonlinearity; 3,4 and integration of single spin qubits with nanophotonic cavities. 4,12 This puts SiC on the forefront of efforts toward a monolithic platform combining quantum and nonlinear photonics. However, the observation of optical parametric oscillation (OPO) in SiC remains an outstanding challenge. On-chip OPO enables efficient wideband spectral translation, 13 frequency comb formation for metrology 14 and spectroscopy, 15 and on-chip generation of non-classical light states. 16 Furthermore, the monolithic integration of optical spin defects with a near-threshold OPO light source can enable the demonstration of new physical effects in cavity quantum electrodynamics, such as synthetic strong coupling, 17 with important implications for integrated spin-based quantum technologies.
Here, we demonstrate on-chip χ (3) optical parametric oscillation (OPO) and microcomb formation in high-purity semiinsulating (HPSI) 4H-SiC-on-insulator microring resonators. This is enabled by resonator dispersion engineering, improved fabrication techniques resulting in Q factors as high as 1.1 mil-lion, and compact inverse-designed vertical couplers for a broadband, high-efficiency free-space interface. We also perform a careful study of the intrinsic material absorption of SiC, providing crucial information on the dominant sources of loss in high-Q photonic devices based on SiC.
The device fabrication follows the process described in Ref., 4 with modifications to improve the pattern-transfer fidelity and device Q factors. Instead of using HSQ e-beam resist, which suffers from low reactive-ion etching selectivity against SiC, an aluminum hard mask (deposited via evaporation and patterned with ZEP e-beam resist) is used. Combined with a low-power SF6 etch, this yields a hard-mask selectivity of 9 (compared to 2 for HSQ). Using this method, devices in SiC films as thick as 1.5 µm can be fabricated. Figure 1a shows microring resonator devices before oxide encapsulation. Q factors as high as 1.1 · 10 6 are measured (Fig. 1c), which corresponds to waveguide loss of 0.38 dB/cm. Routing light to and from the chip is done via efficient and broadband inverse-designed vertical couplers, 18, 19 with a peak singlemode coupling efficiency of 31%, as illustrated in Fig. 1(d-f). Accurate pattern transfer and high aspect ratio nanostructures enabled by the new fabrication approach were essential for the demonstration of the close agreement between the simulated and measured efficiency at the target wavelength of 1550 nm.
The waveguide loss of 0.38 dB/cm presented here approaches the previously reported upper bound of 0.3 dB/cm on the intrinsic absorption of 4H-SiC. 21 To identify the dominant source of loss in high-Q SiC devices, we perform high resolution characterization of the intrinsic absorption of SiC via photothermal common-path interferometry (PCI), which has been used to detect absolute absorption down to 1 ppm/cm. 20 In PCI, a low-power probe beam is used to sense the heating effect from the absorption of a high-power pump beam, as shown in Fig. 2a. The pump beam, with comparatively smaller waist, is chopped, periodically modulating the heating effect, which induces self-interference of the probe beam via the photothermal effect. We perform absorption measurements on sublimation-grown HPSI 4H-SiC (Shanghai Famous Trade Co. LTD) with resistivity exceeding 10 5 Ω·m (Fig. 2b). The measured absorption is shown in Table 1. We note that the absolute accuracy of PCI requires a lowtransparency calibration sample or precise knowledge of material properties, including the refractive index, the thermo-  In order to generate degenerate four-wave mixing OPO, one must achieve frequency and phase matching between the pump, signal, and idler modes in the resonator. The frequency matching condition 2ωp = ωs + ωi follows from conservation of energy. The phase matching condition ensures proper volumetric mode overlap and, for OPO within one mode family of a microring, reduces to the statement of conservation of angular momentum 2µp = µs + µi, where µ is the azimuthal mode number. 29 The spectral characteristics of the OPO and subsequent microcomb are determined by the dispersion relative to the pump mode (µp = 0) where the k th -order dispersion is D k . Here, D1 is the free spectral range (FSR) of the resonator. When D2 dominates all higher-order terms and is positive (negative), the mode dispersion is said to be anomalous (normal).
We engineer microrings to possess anomalous dispersion in the TE10 mode across the telecommunications band for broadband microcomb generation. 30 The dispersion calculations include material anisotropy, 5 and are performed in cylindrical coordinates to include the effect of the microring bending radius. For 100 µm diameter microrings, a target height of 530 nm and a width of 1850 nm (with a sidewall angle of 10 • ) are chosen. To predict the OPO behavior, we obtain a transmission spectrum across the full range of the tunable laser (1520-1570 nm), and extract the dispersion of the TE10 mode by measuring the frequencies of the resonances. To measure dispersion with high precision, we rely on a Mach Zehnder interferometer "ruler", the free spectral range of which is measured using an adaption of the radio-frequency spectroscopy method. 31 Figure 3a shows the integrated dispersion Dint = ω(µ) − (ω0 + D1µ) with respect to mode number, to visualize all k ≥ 2 dispersion terms. Numerical simulation of the integrated dispersion for the target microring dimensions is plotted for comparison, showing agreement.
The intrinsic (loaded) Q factor of the TE10 mode is measured to be 2.7 · 10 5 (1.8 · 10 5 ). At the OPO threshold power, primary sidebands emerge at µ = ±12. As more power is injected into the microring, a primary comb at the multi-FSR sideband spacing emerges (Fig. 3b). At 75 mW, spectrallyseparated sub-combs are formed around the primary lines. At the maximum injected power, the sub-combs fill out and interfere around the pump, which is evidence of chaotic comb generation. 30 The thermo-optic effect we observe in our devices may require the use of active capture techniques 32 for soliton formation, and lithographic control of device structure can eliminate avoided mode crossings, which may otherwise impede soliton capture. Using the experimental parameters of our device, we simulate the soliton frequency comb using the Lugiato-Lefever equation, 33 neglecting Raman and χ (2) effects. The simulated soliton is shown in the last plot in Fig. 3b.
Finally, we measure the OPO power threshold in our devices and use it to determine the nonlinear refractive index (n2) of 4H-SiC. The power threshold of the OPO is defined as the power injected into the pump mode at which the primary sideband emerges. This threshold is determined by the loss and the confinement of the three modes where n is the modal refractive index, V is the mode volume, and η = QL,p/Qc,p where Qc,p accounts for coupling losses from the pump mode to the waveguide. 34 In this demonstration, we use the TE00 mode of a 55 µm diameter ring resonator with the same cross-section as before. Although the dispersion is normal for the fundamental TE mode, pumping at an avoided mode crossing allows us to achieve frequency matching 35 and to generate OPO, while benefiting from the higher quality factors of the fundamental mode. By optimiz- ing the pump power such that the OPO threshold is reached exactly on resonance, we measure a threshold of 8.5±0.5 mW.
Using the simulated mode volume and measured quality factors, we extract a nonlinear refractive index for 4H-SiC of n2 = 6.9 ± 1.1 × 10 −15 cm 2 /W at 1550 nm, consistent with previous studies. 7,36 In conclusion, we have demonstrated optical parametric oscillation and frequency combs in SiC nanophotonics by leveraging the high field enhancement of our microrings. In light of the recent integration of single spin qubits into 4H-SiC-oninsulator nanostructures, 4 our platform holds promise for the monolithic realization of nonlinear and quantum photonics.

Funding Information
This research is funded in part by the National Science Foundation under award NSF/EFRI-1741660; and the DARPA PIPES program under contract number HR0011-19-2-0016. Part of this work was performed at the Stanford Nanofabrication Facility (SNF) and the Stanford Nano Shared Facilities (SNSF), supported by the National Science Foundation under award ECCS-1542152. M.A.G. acknowledges support from the Albion Hewlett Stanford Graduate Fellowship (SGF) and the NSF Graduate Research Fellowship. K.Y.Y. acknowledges support from a Quantum and Nano Science and Engineering postdoctoral fellowship. D.L. acknowledges support from the Fong SGF and the National Defense Science and Engineering Graduate Fellowship.