Dissipative Kerr soliton formation in dual-mode interaction Si₃N₄ microresonators

Dissipative Kerr soliton (DKS) microcombs are generated using a continuous wave pump laser with a high-quality factor (Q-factor) resonator.¹ The generation of DKS microcombs relies on nonlinear optical effects within a resonator platform, producing a broad spectrum of evenly spaced frequency lines. In recent years, DKS microcombs have been realized on various platforms with significant Kerr nonlinearity.^1–5 Among these platforms, the amorphous Si₃N₄ platform, with high effective nonlinearity, low optical losses, a broad transparency window, a wide bandgap of 5 eV, and fabrication compatibility, makes Si₃N₄ waveguides an attractive material used in integrated DKS microcomb.^6,7 Photonic chip-based DKS microcombs are widely used in ranging,^8–10 spectroscopy,^11,12 communication,^13,14 and microwave photonic.⁴ 

The larger cross-sectional area of multi-mode Si₃N₄ waveguides can result in reduced bending losses, which is beneficial for photonic integrated microresonators.^15,16 Photonic integrated microresonators with low loss rate are widely used in DKS generation. DKS are manifested as bright solitons or dark pulses, depending on the group velocity dispersion (GVD) of the microresonator.¹⁷ Therefore, comb structures in the frequency domain can be optimized through careful geometric dispersion engineering. Multi-mode waveguides offer additional flexibility in managing and engineering dispersion.¹⁸ However, in multi-mode waveguides, different spatial modes and their interactions affect local dispersion and introduce additional parasitic losses.^19,20 When two mode resonant frequencies approach each other, coupling between them leads to mode hybridization, shifting resonance frequencies. This phenomenon, known as “avoided modal crossing” (AMX), can disrupt group velocity dispersion by altering the dispersion properties of the involved modes.^19,21 AMX plays a crucial role in the microcomb field, facilitating the stabilization of bright solitons or the generation of dark pulses.^17,22 Auxiliary cavity geometries are also used to achieve precise control over the AMX positions for microcomb generation.^23,24 However, spatial mode coupling in multi-mode waveguides is often uncontrollable. Accidental AMXs often prevent the soliton formation.²⁵ Several methods have been proposed to suppress AMX in a multi-mode waveguides. A single-mode filtering section has been introduced to suppress higher-order mode families.¹⁹ Recently, racetrack-shaped microresonators with adiabatic bends connecting straight waveguides to suppress spatial mode interactions have been demonstrated.^15,26,27 To the best of our knowledge, there exists great research space in the generation of DKS microcomb in multi-mode Si₃N₄ waveguide microresonators without suppressing AMX, which motivates us carry out this work.

In this letter, DKS microcomb is generated in a multi-mode Si₃N₄ waveguide microresonator without suppressing spatial waveguide mode interaction. The multi-mode Si₃N₄ waveguide microresonator features high quality factor Q > 2.246 × 10⁶, free spectral range (FSR) about 47 GHz, and a large amount of AMXs. The spatial waveguide mode interaction is investigated in multi-mode Si₃N₄ waveguide microresonators. The result indicates that interaction between fundamental TE₀₀(TM₀₀) mode and higher-order TE₁₀(TM₁₀) mode will generates periodic AMXs, which can severely limit the device’s performance. The DKS microcomb generated in the dual-mode interaction microresonator is demonstrated using the auxiliary laser heating method.^28,29 In addition, performance of the DKS microcomb is illustrated by designing an integrated microcomb frequency measurement (MIFM) system to measure the frequency of frequency-modulated lasers. Compared to the standard H¹³C¹⁴N gas cell absorption wavelengths, the measurement error by the MIFM system does not exceed 11 pm.

The Si₃N₄ microring resonator (microresonator) used in this letter is fabricated by using the LIGENTEC AN800 process. Figure 1(a) shows the conceptual design of the microresonator Si₃N₄ waveguide with a thickness of 800 and 1700 nm width fully coated with SiO₂. If thickness of the straight waveguide is 800 nm and the width exceeds 800 nm, then higher-order modes occur.¹⁹ To verify higher-order modes existing in the used microresonator, a numerical simulation is developed in this letter. The numerically simulation results of mode profiles for four mode families are shown in Fig. 1(a). As shown in Fig. 1(a), the higher-order TE₁₀ and TM₁₀ modes are observed. With the same waveguide cross-sectional, a Si₃N₄ microresonator with a radius of 238.2 μm has been demonstrated to successfully generate soliton microcombs with a repetition frequency of 94.3 GHz.³⁰ In this letter, we utilized a Si₃N₄ microresonator with a radius of 455.6 μm for 47 GHz free-spectral-range (FSR) at the wavelength of 1550 nm.

Figure 1(b) shows the simulation results of the effective group index for the TE₀₀ mode and the TE₁₀ mode under the Si₃N₄ MMR with a radius of 455.6 μm. The wavelength-dependent destructive interference period δλ is shown in Fig. 1(c). From the simulation results, the destructive interference wavelength period for the TE₀₀–TE₁₀ modes is about 8.56 nm at 1550 nm. In addition, the period decreases as optical wavelength increase.

To further elucidate mode interaction between the TE₀₀ mode and the TE₁₀ mode, simulations are conducted on resonant frequencies of the two modes under Si₃N₄ MMR with different radius, respectively. Figure 1(d) shows the simulation results of the resonant frequencies over the wavelength range of 1500–1600 nm within different radius. The resonant frequency is conducted by m = c∗n_eff/ω. As shown in Fig. 1(d), the resonant frequencies of these two modes have a small difference in their FSRs; the resonant frequency of these two modes will periodically approach each other in the frequency domain. The coupling between these two mode families can additionally lead to AMX, when the resonant frequencies approach each other. It is observed that the number of AMX increases with larger resonator radius under a certain wavelength range. These AMXs can not only locally alter the dispersion but also potentially prohibit DKS microcomb generation, even in the presence of the overall anomalous dispersion.²⁵ 

The dual-mode interaction Si₃N₄ microresonator used in this letter has a waveguide cross section of 1700 × 800 nm² (height × width) and a radius of 455.6 μm. From the simulation results, it can be concluded that within the 1500–1600 nm wavelength range, there are 12 AMXs.

In this section, we implemented DKS microcomb experiments based on the aforementioned Si₃N₄ microresonator. The Si₃N₄ microresonator is characterized. To future discuss the performance and advantages of the generated DKS microcomb, frequency measurement experiments are presented.

Figure 2 shows the characterization of microresonator parameters in the 1500–1600 nm range. The integrated dispersion is defined as D_int = ω_μ − ω₀ − D₁μ, where μ is the relative mode number of the center mode, ω_μ/2π is the μth resonance frequency, and D₁/2π is the FSR of the center mode. As shown in Fig. 2(a), the Si₃N₄ microresonator exhibits overall anomalous group velocity dispersion (GVD). Figure 2(b) shows local deviations in the integrated dispersion of TE₀₀ mode, caused by the influence of AMXs. Two mode families are identified from the transmission spectrum near one AMX. As shown in Fig. 2(c), the higher-order TE₁₀ mode (red dots) exhibits Fano resonance.³¹ When the TE₀₀ mode (black dots), with a narrow resonance linewidth, approaches a TE₁₀ mode, AMX occurs, resulting in a shift in the resonance frequency of the TE₀₀ mode. The interaction between these two modes leads to a partial broadening of the resonance linewidth of the TE₀₀ mode.

Figure 3(a) shows the experimental setup for DKS microcomb generation. Auxiliary heating is used to balance thermal effects. When generating DKS microcombs, it is necessary to note that the dispersion local disturbances and the reduction in the Q factor of some resonant modes are caused by AMX (supplementary material Sec. II). The resonance at 1550.19 nm located near the midpoint between two AMXs is selected as the pump mode, which can obtain a larger range of anomalous dispersion. The resonance mode at 1560.08 nm with a relatively lower Q factor is selected as the auxiliary mode, which enables a wider tuning range of the auxiliary laser and helps prevent the generation of undesired spectral sidebands.³² From the transmission spectrum, it is observed that after tuning the auxiliary laser to the appropriate position, clear soliton steps appears when the pump laser is scanned from blue detuning to red detuning.

Figure 3(b) shows that the measured optical spectrum of the DKS microcomb general features a characteristic sech² shape. However, near the wavelength where AMX occurs, the spectral envelopes feature modulations such as the transmission spectrum. This effect is due to the increased parasitic coupling loss near the AMX points (supplementary material Sec. III).

In the experiment, the FM laser was scanned from 1539–1561 nm at the rate of 20 nm/s covering 27 H¹³C¹⁴N absorption lines. The center wavelength of the DKS microcomb is 1550.12 nm, and the repetition frequency is 47.12 GHz. The fitting results between the frequency and phase are compared to the frequencies of the H¹³C¹⁴N absorption lines. By extracting the phase of the MZI signal corresponding to each absorption line position, the frequency is calculated. Figure 4(c) shows the comparison between the calculated frequency after fitting and the standard frequency. The comparison results indicate that the wavelength residual does not exceed 11 pm. These results highlight the feasibility of the MIFM system for application in FM laser frequency measurement.

In summary, we have generated DKS microcomb in a dual-mode interaction Si₃N₄ microresonator without suppressing AMXs, and an MIFM system has been designed for FM laser frequency measurement. Through numerical simulation and theoretical analysis, we have demonstrated the periodic AMXs in a dual-mode interaction Si₃N₄ microresonator caused by the group index difference between TE₀₀ mode and TE₁₀ mode. The presence of AMXs can significantly distort local dispersion, posing a challenge to soliton formation. By using an auxiliary heating method, the DKS microcomb has been successfully generated in the dual-mode interaction Si₃N₄ microresonator. Our results demonstrate the effective application of the DKS microcomb as a frequency ruler in frequency-modulated (FM) laser frequency measurements, proving its compatibility with established frequency metrology standards. This approach not only mitigates the dispersion-related challenges caused by AMXs but also enhances the precision and reliability of on-chip frequency measurements.

The successful generation of the integrated on-chip DKS microcomb represents a significant advancement in the field, providing a robust and scalable solution for future frequency metrology systems. The ability to integrate such high-performance microcombs on a silicon photonic platform opens new avenues for compact, cost-effective, and versatile frequency measurement tools. As the technology continues to evolve, we anticipate its widespread adoption in various applications, including telecommunications, spectroscopy, and precision metrology, further driving innovation in integrated photonics.

See the supplementary material for additional information.

This work was supported by the National Key Research and Development Program of China (Grant No. 2022YFF0705701) and the National Natural Science Foundation of China (Grant No. 52375546).

The authors have no conflicts to disclose.

Yurun Zhai: Formal analysis (equal); Writing – original draft (equal). Junchen Liu: Writing – review & editing (equal). Linhua Jia: Writing – review & editing (equal). Fumin Zhang: Funding acquisition (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.