Fig. 1. Chip-scale low timing jitter dispersion-managed silicon nitride microresonator. (a) Schematic illustration of DM soliton microcomb generation. Inset: scanning electron microscope images of the microresonator, zoomed waveguides, and the coupling gap. Scale bar: $130\mu \mathrm{m}$. (b) Simulated GVD along the microresonator. (c) Simulated GVD of waveguides with different widths at a fixed waveguide height and the cavity path-averaged GVD. (d) Measured GVD via swept-wavelength interferometry showing ${\beta }_2=-4.39{\mathrm{fs}}^2/\mathrm{mm}$. (e) Modeled timing jitter PSD and integrated jitter versus Fourier frequency for a constant-dispersion uniform-width ring microcomb, with ${\beta }_2=-4.39$, $-30.73$, and $-122.92{\mathrm{fs}}^2/\mathrm{mm}$, respectively, no Raman and thermal effects assumed. (f) Modeled timing jitter PSD and integrated jitter versus Fourier frequency for a constant-dispersion uniform-width ring microcomb with different mode crossing levels.

Fig. 2. Soliton microcomb formation in tapered dispersion-managed microresonators. (a), (c), and (e) Measured optical spectra of the single-soliton, double-soliton, and one-defect soliton crystal DM microcombs overlapped with the numerical model, showing negligible center frequency shifts (detailed in the Supplementary Material). Insets are zoomed optical spectra. (b) Measured intensity autocorrelation trace of the single-soliton DM microcomb. Inset: measured and modeled pulse widths. (d) Modeled intracavity waveform of the double-soliton with a temporal separation of $0.54\times T_R$. (f) Modeled intracavity waveform of the one-defect soliton crystal showing the modulated background (potential well) with a period of $1/12\times T_R$.

Fig. 3. RIN measurements of the dispersion-managed microcombs. (a) Experimental setup of the TE–TM dual-driven approach for the generation of thermally stabilized soliton microcomb and the relative intensity noise measurement. LD, laser diode; EDFA, erbium-doped fiber amplifier; PBS, polarization beam splitter; TE, transverse-electric; TM, transverse-magnetic; OBPF, optical bandpass filter; PD, photodiode; OSO, oscilloscope; and SSA, signal source analyzer. (b) Filtered optical spectrum of the single-soliton DM microcomb. (c), (d), and (e) RIN PSD and the corresponding integrated RIN of the microcombs at different dynamical states along with the lower bound set by the pump laser. The RIN PSD of the chaotic DM microcomb and the RIN PSD after loading broadband amplified spontaneous emission (ASE) noise are also illustrated. Inset of (c): Electrical noise optimization by adjusting the incident optical power of the PD to explore the dynamic soliton intensity fluctuations at different states. Inset of (d): Noise degradation of the double-soliton DM microcomb showing additional white high-frequency noise. Inset of (e): Noise degradation of the soliton crystal DM microcomb showing dynamic high-frequency noise.

Fig. 4. Measured repetition-rate frequency noise PSD and timing jitter PSD and the corresponding integrated RF linewidth and timing jitter of dispersion-managed soliton microcombs. (a) Experimental setup of the SHLI. WDM, wavelength division multiplexer; FS, fiber stretcher; EA, electronic amplifier; BPF, bandpass filter; PS, phase shifter; PID, proportional–integral–differential controller. Inset: schematic illustration of the SHLI. (b1), (b2), and (b3) Measured frequency noise PSD at different soliton states with a 49 m stabilized fiber link. The orange dashed lines with 10 dB/decade slopes indicate repetition-rate frequency free-walk induced by microresonator intracavity power fluctuations. The corresponding repetition-rate tone linewidth integrated from 1 MHz to 10 kHz is denoted with purple curves. The repetition-rate carrier frequency is 89 GHz. (c1), (c2), and (c3) Timing jitter PSD measurement of the soliton microcombs at different dynamical states with the calculated thermal-noise and quantum-noise limits. The timing jitter theoretical models from Refs. 56 and 57 are quantum-noise and thermal-noise limits of the soliton microcombs denoted, respectively, with solid orange and yellow lines. The corresponding integrated timing jitter is included. The comparison between the measured timing jitter PSD and prior works^{12,34,44,58,59} is included as well.