Universal Kerr-thermal dynamics of self-injection-locked microresonator dark pulses

Abstract

Microcombs, formed in optical microresonators driven by continuous-wave lasers, are miniaturized optical frequency combs. Leveraging integrated photonics and laser self-injection locking (SIL), compact microcombs can be constructed via hybrid integration of a semiconductor laser with a chip-based microresonator. While the current linear SIL theory has successfully addressed the linear coupling between the laser cavity and the external microresonator, it fails to describe the complicated nonlinear processes, especially for dark-pulse microcomb formation. Here, we investigate -- theoretically, numerically and experimentally -- the Kerr-thermal dynamics of a semiconductor laser self-injection-locked to an integrated silicon nitride microresonator. We unveil intriguing yet universal dark-pulse formation and switching behaviour with discrete steps, and establish a theoretical model scrutinizing the synergy of laser-microresonator mutual coupling, Kerr nonlinearity and photo-thermal effect. Numerical simulation confirms the experimental result and identifies the origins. Exploiting this unique phenomenon, we showcase an application on low-noise photonic microwave generation with phase noise purified by 23.5 dB. Our study not only adds critical insight of pulse formation in laser-microresonator hybrid systems, but also enables all-passive, photonic-chip-based microwave oscillators with high spectral purity.

Figures (3)

• Figure 1: Principle and schematic of SIL, Kerr nonlinearity and photo-thermal effect in the laser-microresonator coupled system. a. Frequency- and time-domain picture describing the synergy of SIL, photo-thermal effect and Kerr nonlinearity, which yields narrowing of the pump laser's linewidth, red-shift of the microresonator's resonance grid, and formation of a platicon microcomb. Res. mode: resonance mode. b. Experimental setup. A DFB laser chip edge-coupled to a Si$_3$N$_4$ microresonator chip. A printed circuit board (PCB) provides stable current to the laser and stabilizes the laser temperature. Output light from the Si$_3$N$_4$ microresonator is collected by a lensed fiber. $E_{\mathrm{L}}$: light amplitude in the laser cavity. $E^{+}$/$E^{-}$: light amplitude in the clockwise/counter-clockwise direction in the microresonator. $E_{\mathrm{out}}$: light amplitude at the microresonator output. $\varphi$: feedback phase of $E^{-}$.
• Figure 2: Experimental result in comparison with numerical simulation. a. Experimentally measured output laser power with forward (green) or backward (yellow) tuning. b. Experimentally measured beat frequency between the output laser and a frequency-fixed reference laser, with forward (blue) or backward (red) tuning. c. Zoom-in profiles of the gray-shaded region in b with forward (blue) or backward (red) tuning. Discrete steps with backward tuning are numbered with 1 to 4. d, e. Numerical simulation results corresponding to experimental data in a, b. Horizontal axes are the frequency detuning (in the unit of $\kappa /2$) between the free-running laser frequency and the cold resonance frequency. Effective (Eff.) detuning is the frequency detuning (in the unit of $\kappa /2$) between the laser frequency at the microresonator output and the cold resonance frequency. f. Zoom-in profile of the gray-shaded zoom in d, e. Gray curves outline the full detuning range of platicon steps.
• Figure 3: Optical spectra of different platicon states and the resulted noise-quenching effect. a. Experimentally measured (blue lines) and simulated (red curves) optical spectra of the platicon states labeled in Fig. \ref{['Fig:2']}c, f. They agree not only on the spectral envelopes but also on the number of fringes (marked with arrows). Insets: simulated time-domain pulse shapes of the corresponding platicon states. The fringes, marked with arrows, are related to the oscillating tails at the bottom of the dark pulse. b. Measured platicon's repetition rate $f_\mathrm{rep}$ (blue) and phase noise $S_{\phi}$ at 10 kHz Fourier offset frequency (red) of the 10.7-GHz microwave, with backward tuning. $f_0 =10.68545$ GHz. Vertical dashed lines highlight that the local minimum of $S_{\phi}$ coincides with the local maximum of $f_\mathrm{rep}$. Horizontal dashed lines highlight that this coincidence is associated with $\mathrm{d}f_\mathrm{rep}/\mathrm{d}I=0$. c. Phase noise $S_{\phi}$ spectra of the local maximum and minimum points marked with green and black dots in b. Phase noise quenching up to 23.5 dB is observed. Inset shows the beat note of the lowest $S_{\phi}$ (black data) with 10 Hz RBW.