Kerr nonlinearity plays a pivotal role in nonlinear photonics. Recent advancement in wafer bonding techniques has led to the creation of a cubic silicon carbide-on-insulator (3C-SiCOI) platform with improved crystalline quality, offering exciting prospects for investigating the Kerr effect in 3C-SiC. In this paper, we demonstrate 3C-SiC's Kerr effects through design, fabrication, and experimental investigation. By using the cavity enhanced four-wave mixing based on microring resonator (MRRs) supporting transverse electric or magnetic (TE/TM) polarizations on the 3C-SiCOI platform, we experimentally retrieve the Kerr nonlinear index (n2) of 3C-SiC within diverse waveguide dimensions, revealing a value of 4.92 and 5.00 × 10−19 m2/W for TE and TM polarizations, respectively. We further confirm the thermal stability of the 3C-SiC in Kerr effects at elevated temperatures from 100 °C to 300 °C, showing negligible change of n2. Moreover, we demonstrated optical parametric oscillation (OPO) in the fabricated single mode MRR via a dual-pump configuration. With an input power of less than 50 mW, a distinct OPO spectrum covering the C band has been achieved. These results signify the emergence of 3C-SiCOI as a promising platform for Kerr applications.
Silicon carbide (SiC) has emerged as a promising platform for realizing diverse applications in integrated photonics across both classical and quantum areas, such as electro-optic modulation,1 quantum photonics,2–4 and nonlinear optics.2,5–8 With a high refractive index (∼2.57) and wide bandgap,2,9–11 SiC enables the development of optical waveguides with tight confinement, effectively reducing nonlinear losses including free carrier absorption and two-photon absorption.1,7 Moreover, its low thermo-optic coefficient,5,11 high thermal conductivity,12 and elevated electron mobility1 make it an excellent candidate for high-power applications.
Cubic SiC (3C-SiC) has an intrinsic zero-birefringence, and it can be epitaxially grown on a host substrate, such as silicon (Si), with the desired thickness. These enhance its flexibility and adaptability in photonic integration.1,7,9,13–15 Due to the non-centrosymmetry, 3C-SiC exhibits the Pockels effect, which has been utilized in the demonstration of a SiC modulator.1 Meanwhile, the optical Kerr nonlinearity holds great potential for advanced photonic applications, including mode locking,16 microwave frequency conversion,17,18 image processing,19 and logic gate.20 However, the current investigation of Kerr effects in 3C-SiC only includes the demonstration of four-wave mixing (FWM) by using a suspended microring resonator (MRR) with a propagation loss of 36.6 dB/cm and a loaded quality factor (Q-factor) of 7400.7 Recent advancements in wafer bonding techniques have enabled the development of the high-quality 3C-SiC-on-insulator (3C-SiCOI) platform,1,9 where a flip, bond, etch, and polish method is used to bond 3C-SiC onto an insulating wafer of thermal SiO2 on Si. This platform provides a suitable pathway for in-depth exploring the Kerr effect in 3C-SiC. By removing stacking faults and anti-phase boundaries at the SiC-Si interface,21 the 3C-SiCOI platform achieves an enhanced crystalline quality as evidenced by a lower crystal defect density and a larger grain size.1,9 This improvement leads to reduced scattering and absorption losses as light traverses through the SiC crystal,22–25 and also alters the photothermal nonlinear effect.5
In this paper, we demonstrate 3C-SiC's Kerr effects through design, fabrication, and experimental investigation. We demonstrate the cavity enhanced FWM with MRRs on the 3C-SiCOI platform operating under transverse electric or magnetic (TE/TM) polarizations, showing an improved conversion efficiency (CE) for both cases. This is attributed to the propagation loss of 3.9 and 3.5 dB/cm for fundamental TE and TM modes (TE00 and TM00) at single-mode operation, respectively, derived from the intrinsic Q-factors (Qi) of 119 432 for TE00 and 145 379 for TM00. We experimentally determine the Kerr nonlinear index, n2, of 3C-SiC at room temperature achieved by employing multiple MRRs with waveguide widths ranging from 800 nm to 2 μm, under various input power conditions across two polarization states. The obtained n2 values at an infrared wavelength are (4.92 ± 0.29) × 10−19 m2/W and (5.00 ± 0.30) × 10−19 m2/W for TE and TM polarizations, respectively. Moreover, the stability of the 3C-SiC's Kerr nonlinearity is assessed at elevated temperatures from 100 °C to 300 °C, revealing a negligible variation in the n2 value. In addition, we demonstrate the nonlinear capabilities of the 3C-SiCOI platform by achieving the optical parametric oscillation (OPO) through a dual-pump configuration in a single mode MRR. The result shows a distinct OPO spectrum covering the C band with less than 50 mW input power. Our work establishes the 3C-SiCOI platform as a promising and versatile candidate for advanced nonlinear photonics applications.
We explore the Kerr effect inside 3C-SiC crystal within a degenerated FWM scheme using MRRs on the 3C-SiCOI platform under TE and TM polarizations and characterize the value of n2 for each case. Figure 1(a) depicts the schematic diagram of this nonlinear process on the platform. The input TE or TM polarized photons at the pump and signal wavelengths undergo resonant enhancement, while simultaneously interacting with the correlated third-order nonlinear susceptibility (χ3) of 3C-SiC. The nonlinear interaction inside the cavity is enhanced, leading to the generation of an idler wave that surpasses the linear propagation loss of the waveguide,7,26,27 allowing the idler wave to be detected.
(a) The schematic of cavity enhanced FWM in 3C-SiCOI where red, blue, and green lines represent the pump, signal, and idler light, respectively. The scanning electron microscopy (SEM) picture of the fabricated (b) TE and (c) TM MRRs. Insets show the SEM for parts of MRR waveguides. Normalized transmission spectrum of the fabricated (d) TE and (e) TM MRR at room temperature after calibrating out the spectrum profile induced by VGCs. Insets inside are simulated mode profiles. Insets on the right are the Lorentz fits of the resonance line shape with corresponding 3-dB linewidth and intrinsic Q-factor (Qi) (circle: measurement and solid line: Lorentz fitting). (f) Measured free spectrum ranges (FSRs) with corresponding fitted lines at room temperature (circle: measurement and dashed line: fitting). (g) Calculated group velocity dispersion of both MRRs based on the measured FSRs (solid line: TE and dashed line: TM). (h) The microscope image of multiple fabricated TM MRRs. The inset shows one of the measured resonances with a 3-dB linewidth of 12 pm and a Qi of 217 877 (circle: measurement and solid line: Lorentz fitting).
(a) The schematic of cavity enhanced FWM in 3C-SiCOI where red, blue, and green lines represent the pump, signal, and idler light, respectively. The scanning electron microscopy (SEM) picture of the fabricated (b) TE and (c) TM MRRs. Insets show the SEM for parts of MRR waveguides. Normalized transmission spectrum of the fabricated (d) TE and (e) TM MRR at room temperature after calibrating out the spectrum profile induced by VGCs. Insets inside are simulated mode profiles. Insets on the right are the Lorentz fits of the resonance line shape with corresponding 3-dB linewidth and intrinsic Q-factor (Qi) (circle: measurement and solid line: Lorentz fitting). (f) Measured free spectrum ranges (FSRs) with corresponding fitted lines at room temperature (circle: measurement and dashed line: fitting). (g) Calculated group velocity dispersion of both MRRs based on the measured FSRs (solid line: TE and dashed line: TM). (h) The microscope image of multiple fabricated TM MRRs. The inset shows one of the measured resonances with a 3-dB linewidth of 12 pm and a Qi of 217 877 (circle: measurement and solid line: Lorentz fitting).
We exploit the Kerr effect in 3C-SiC via a cavity-enhanced FWM. To achieve this, we fabricate both TE and TM MRRs on the 3C-SiCOI platform, where a rib waveguide configuration is used to reduce the interaction between the optical mode and sidewalls of waveguides, therefore reducing the propagation losses and achieving a high Q-factor.28 The structure consists of 3C-SiC layers that are 530 and 700 nm thick for TE and TM waveguides, each with a 120 and 220 nm thick slab layer, respectively. Beneath the 3C-SiC layer, there is an oxide layer of 5 μm thickness. We fabricate identical devices with varied coupling gaps and examine extinction ratios (ERs) to determine the coupling condition for each resonance.29–33, Figures 1(b) and 1(c) show the scanning electron microscopy (SEM) images of the MRRs, displaying both having a waveguide width of 800 nm and a radius of 40 μm. Vertical grating couplers (VGCs) with a length of approximately 45 μm including the taper are used as optical input and output ports to couple light. The VGCs have grating periods of 1 μm and 990 nm with fill factors of 0.28 and 0.63 for TE and TM polarizations, respectively. They are optimized for maximum optical bandwidth and coupling efficiency for a 14.5° tilted single-mode optical fiber injecting TE/TM-polarized light. Each VGC has an approximate coupling loss of 7.5 dB. The measured optical spectra are shown in Figs. 1(d) and 1(e), revealing a single mode operation. The measured ER, determined by both the Qi and the external Q-factor (Qe) of the MRRs,33 varies with wavelength due to the wavelength dependencies of radiation, material absorption, and surface roughness.28–30 Through the Lorentzian fit of the line shape, we obtain a Qi of 119 432 and 145 379 for the TE and TM MRRs, respectively (see the supplementary material). This corresponds to linear propagation losses of 3.9 dB/cm for the TE00 and 3.5 dB/cm for the TM00 modes, calculated based on Qi, the resonance wavelength, and the group index.30 These values are lower than the loss observed in Ref. 1, attributable to the enhanced confinement resulting from the optimized waveguide geometry. The effective mode area of TE and TM waveguides is calculated to be 0.43 and 0.55 μm2, respectively. We then evaluate the dispersion characteristics of both fabricated MRRs by measuring the free spectral range (FSR) as given in Fig. 1(f). The results show that the obtained FSR increases in accordance with the wavelength. As illustrated in Fig. 1(g), we further evaluate the group velocity dispersion with the measured FSR, showing anomalous dispersion characteristics in both devices. This enables seamless phase matching condition between adjacent resonances within the infrared wavelength,26 facilitating strong Kerr effects inside the MRR. To have a comprehensive investigation of the Kerr effect on 3C-SiCOI platform, MRRs with varying waveguide widths from 800 nm to 2 μm are fabricated. Figure 1(h) displays the microscope image of multiple fabricated TM MRRs, and the inset shows that one of the measured MRRs with 2 μm waveguide width, exhibiting a 3-dB linewidth of 12 pm and a Qi of 217 877.
We employ a signal-pump scheme with the fabricated MRRs to conduct the cavity enhanced FWM experiment based on the structure shown in Fig. 1(a). As a demonstrative example, we use the MRRs shown in Figs. 1(b) and 1(c) to showcase this nonlinear process (see the supplementary material). Figures 2(a) and 2(b) display the measured FWM spectra of both devices under the on-resonance condition at different on-chip powers. Clear idler peaks are measured in each case, where the amplitude increases following the increase in the pump power. To quantitively analyze this trend, we calculate the overall CE by comparing the amplitudes of the idler under the on-resonance condition and the amplitudes of the signal under the off resonance condition. The results show that as the input pump power increases, the measured CE exhibits a quadratic increasing trend, as displayed in the insets of Figs. 2(a) and 2(b). Note that as the input power continues to rise, the CE can be gradually saturating due to instability caused by the absorption-induced wavelength shift.33,34 At a low pump power of 2.9 mW, we achieved a CE of −47 dB and −49 dB for the TE and TM MRRs, respectively. These values are over 20 dB higher than the one obtained from the suspended 3C-SiC platform.7 By calculating the effective nonlinearity,7,33,34 the nonlinearity of TE and TM waveguides is obtained as 4.62 and 3.77 W−1m−1, respectively. Subsequently, we determine n2 of 3C-SiC to be 4.95 × 10−19 m2/W for the TE mode and 5.08 × 10−19 m2/W for the TM mode. The slight anisotropy of Kerr nonlinearity is due to the nonzero off diagonal χ3 tensor elements, which introduce anisotropy in n2 for the zinc blende structure of 3C-SiC.35–37
Measured output spectrum of (a) TE MRR and (b) TM MRR when the pump and probe lasers are both on resonance with different pump power. Inset: conversion efficiency under corresponding pump power (circle: measurement and dashed line: fitting). (c) Statistics of Kerr nonlinear index (n2) for 3C-SiC under both TE and TM polarizations. The vertical axis represents the fraction of the total number of n2 measured from each FWM experiment utilizing fabricated TE and TM MRRs (bar: measurement and dashed line: distribution).
Measured output spectrum of (a) TE MRR and (b) TM MRR when the pump and probe lasers are both on resonance with different pump power. Inset: conversion efficiency under corresponding pump power (circle: measurement and dashed line: fitting). (c) Statistics of Kerr nonlinear index (n2) for 3C-SiC under both TE and TM polarizations. The vertical axis represents the fraction of the total number of n2 measured from each FWM experiment utilizing fabricated TE and TM MRRs (bar: measurement and dashed line: distribution).
To further evaluate the Kerr nonlinear response of 3C-SiC, we conduct numerous n2 measurements (totaling 97) utilizing multiple fabricated MRRs under two polarization states. These MRRs have waveguide widths ranging from 800 nm to 2 μm, and we also vary input power during the experiment. Figure 2(c) displays the histogram of the n2 values, where the dashed line represents the distribution of the results. The mean values of n2 are 4.92 × 10−19 m2/W for TE polarization and 5.00 × 10−19 m2/W for TM polarization with a standard deviation of 0.29 × 10−19 and 0.30 × 10−19, respectively. The similarity in the obtained n2 values shows the versatility of the 3C-SiCOI platform in supporting both TE and TM modes for integrated photonics applications.
Next, we evaluate the Kerr nonlinearity of 3C-SiC at different temperatures. Figures 3(a) and 3(b) show the measured optical spectra across a temperature range from room temperature (25 °C) to 300 °C. These spectra are obtained by heating the chips shown in Figs. 1(b) and 1(c) onto the hotplate. With the rising temperature, the resonance positions shift toward longer wavelengths, while their line shape remains stable, thanks to the high thermal conductivity (490 W/(m · K)) of the 3C-SiC.12 Figures 3(c) and 3(d) show the FSRs at different temperatures, where circles represent FSRs measured at the MRR's resonance wavelengths. The results show that the measured FSRs with respect to the resonance wavelengths follow the same trend, implying the MRRs remain anomalous dispersion characteristics26 under all examined temperature conditions.
Measured resonance line shape of the fabricated (a) TE MRR and (b) TM MRR under different temperatures ranging from 25 °C to 300 °C. (c) and (d) Measurements of FSR in terms of wavelength with corresponding trend line (circle: measurement and dashed line: fitting).
Measured resonance line shape of the fabricated (a) TE MRR and (b) TM MRR under different temperatures ranging from 25 °C to 300 °C. (c) and (d) Measurements of FSR in terms of wavelength with corresponding trend line (circle: measurement and dashed line: fitting).
We then conduct the cavity enhanced FWM at high temperature for n2 characterization. Figure 4 illustrates the n2 values obtained at various temperatures and input power levels for both TE and TM MRRs. The inset of Fig. 4 illustrates one of the measured FWM spectra at 300 °C, exhibiting a distinct idler well above the noise floor. The results in Fig. 4 demonstrate uniform n2 values across high temperatures, with the mean values of (4.94 ± 0.45) × 10−19 m2/W and (4.93 ± 0.38) × 10−19 m2/W for TE and TM polarizations respectively. These n2 values are consistent with those obtained at room temperature, showing the thermal stability of the 3C-SiC in Kerr nonlinear response.
Experimentally retrieved n2 at different optical pump power across high temperatures (symbols: measurement and dashed line: mean value). The insets show the measured FWM at 300 °C for (i) TE and (ii) TM polarizations.
Experimentally retrieved n2 at different optical pump power across high temperatures (symbols: measurement and dashed line: mean value). The insets show the measured FWM at 300 °C for (i) TE and (ii) TM polarizations.
Following the characterization of n2 in 3C-SiC, we proceed to demonstrate OPO utilizing one TM mode MRR with an 80 μm diameter and an 800 nm waveguide width in a dual-pump scheme (see the supplementary material). This geometry of the waveguide ensures the OPO operating in a single mode scheme, thereby avoiding the crossings or interferences between different orders of optical modes.26,38 Figure 5(a) shows the measured transmission spectrum of the MRR, illustrating a 3-dB optical bandwidth of 35 nm, mainly limited by the operational bandwidth of the VGCs. Two erbium-doped fiber amplifiers (Amonics), whose gain profiles are also presented in Fig. 5(a), are used to boost the pump power and compensate for the insertion loss of the VGC in the dual-pump OPO demonstration. By assessing the FSR between the adjacent resonance modes,38 the integrated dispersion (Dint) is then calculated. As shown in Fig. 5(b), Dint meets the dispersion requirement necessary for OPO.26,38 The pump locations are selected near the two MRR resonances closest to 1550 nm. One pump is slightly red detuned to the resonance, while the other pump gradually scans the adjacent resonance from shorter to longer wavelength until a photothermal self-lock situation is reached. Figure 5(c) shows the OPO spectrum with multiple symmetric peaks acquired under different input power conditions. As shown in cases 1–3, the number of measured peaks increases with higher input power levels. At input pump powers of 17.36 and 15.70 dBm (case 3), the measured OPO spectrum spans almost the entire C band and shows a good agreement with the simulation results obtained from Lugiato–Lefever equation model (case 4). The occurrence of an OPO across a broader bandwidth is feasible by reducing the fiber-to-chip coupling loss and extending the optical bandwidth through edge coupling. With a coupling loss of less than 1 dB,39 a comb spectrum spanning over 234 nm based on our current 3C-SiCOI platform can be achieved under the same input power applied in case 3, as shown in Fig. 5(d). Leveraging the platform's capacity to operate at high optical power, it holds promise for generating a broadband frequency comb or even a comb soliton by increasing the optical power launched into the chip and further reducing the waveguide loss.
(a) Normalized transmission profile of the fabricated MRR and gain spectrum of two erbium-doped fiber amplifiers (EDFAs). (b) Dispersion characteristics of the 3C-SiC waveguide (circle: measurement and solid line: fitting). The inset shows the simulated field profile of the TM MRR's coupling region. (c) Measured dual pump OPO spectra with three cases of different input power for 1547 and 1551 nm pumps. Case 1: 13.80 and 12.52 dBm; case 2: 15.30 and 14.02 dBm; and case 3: 17.36 and 15.70 dBm. Case 4 shows the simulation results from Lugiato–Lefever equation (LLE) under the same conditions as case 3. (d) LLE simulation results for the fabricated TM MRR under the same input power as case 3 incorporating reduced coupling losses (solid line: simulation and dashed line: Sech2 fitting).
(a) Normalized transmission profile of the fabricated MRR and gain spectrum of two erbium-doped fiber amplifiers (EDFAs). (b) Dispersion characteristics of the 3C-SiC waveguide (circle: measurement and solid line: fitting). The inset shows the simulated field profile of the TM MRR's coupling region. (c) Measured dual pump OPO spectra with three cases of different input power for 1547 and 1551 nm pumps. Case 1: 13.80 and 12.52 dBm; case 2: 15.30 and 14.02 dBm; and case 3: 17.36 and 15.70 dBm. Case 4 shows the simulation results from Lugiato–Lefever equation (LLE) under the same conditions as case 3. (d) LLE simulation results for the fabricated TM MRR under the same input power as case 3 incorporating reduced coupling losses (solid line: simulation and dashed line: Sech2 fitting).
In conclusion, we investigate Kerr effects on the 3C-SiCOI platform through the cavity enhanced FWM process under both TE and TM polarizations. We achieve a reduced optical loss in the 3C-SiC waveguide under single-mode operation, therefore facilitating an enhanced wavelength conversion process inside the cavity. By using MRRs with different waveguide widths, n2 values of (4.92 ± 0.29) × 10−19 m2/W and (5.00 ± 0.30) × 10−19 m2/W are obtained for TE and TM polarizations, respectively, highlighting the platform's robust response in Kerr nonlinearity to the variation of polarizations in light. Furthermore, we confirm the thermal stability of 3C-SiC in its Kerr nonlinear response, noting negligible variations in n2 even at high temperatures ranging from 100 °C to 300 °C. Finally, we demonstrate a dual-pump OPO with a single mode TM 3C-SiC MRR. Further enhancements in performance can be achieved by improving the crystalline quality in the 3C-SiCOI waveguide and reducing chip-to-fiber coupling loss.
SUPPLEMENTARY MATERIAL
See the supplementary material for more details.
This study received fundings from the University of Sydney (Sydney Research Accelerator Prize, Harvard University Mobility Scheme, Research Training Program Scholarship).
Device fabrication and characterization were carried out at the Research and Prototype Foundry, a core research facility at the University of Sydney, a part of the Australian National Fabrication Facility. We thank Dr. N. Sinclair, Dr. K. Powell, and Professor M. Lončar from John A. Paulson School of Engineering and Applied Sciences at Harvard University, Dr J. Deng from Center for Nanoscale Systems at Harvard University, and Professor A. Gaeta from Columbia University for discussions. D.M. and X.Y. thank Dr. J. Wang from the University of Sydney for his assistance in device design. D.M. acknowledges the support of Research Training Program Scholarships from the University of Sydney.
AUTHOR DECLARATIONS
Conflict of Interest
The authors have no conflicts to disclose.
Author Contributions
Liwei Li and Bin-Kai Liao contributed equally to this work.
Debin Meng: Conceptualization (equal); Data curation (lead); Formal analysis (lead); Investigation (equal); Methodology (lead); Validation (equal); Visualization (equal); Writing – original draft (lead); Writing – review & editing (equal). Liwei Li: Data curation (supporting); Investigation (lead); Methodology (equal); Validation (supporting); Visualization (lead); Writing – review & editing (equal). Bin-Kai Liao: Data curation (equal); Formal analysis (equal); Methodology (supporting); Validation (lead); Writing – original draft (equal); Writing – review & editing (equal). Xiaoke Yi: Conceptualization (lead); Funding acquisition (lead); Methodology (equal); Supervision (lead); Writing – original draft (equal); Writing – review & editing (equal).
DATA AVAILABILITY
The data that support the findings of this study are available from the corresponding author upon reasonable request.