Raman-induced dynamics of ultrafast microresonator solitons

Abstract

Soliton microcombs are evolving towards octave-spanning for $f$-$2f$ self-referencing and expanding applications in spectroscopy and timekeeping. As spectra broaden and pulses shorten, the Raman-induced soliton self-frequency shift (SSFS) becomes a principal limitation: it reduces pump-to-comb conversion efficiency, constrains achievable span, and can, in extremes, preclude stationary operation. We develop a complementary theory of SSFS in microresonators that remains valid when the soliton duration $τ_s$ is shorter than the Raman response timescale. The theory predicts a reduced dependence of the SSFS on $τ_s$ which also expands the soliton existence range. Such predictions are validated by numerical simulations and by experiments on Si$_3$N$_4$ microresonators. Our results provide practical guidelines for engineering efficient and broadband soliton microcombs.

Figures (4)

• Figure 1: (a) Schematic of a microresonator soliton and the intracavity nonlinear processes. (b) Raman-induced SSFS $(\Omega/2\pi)$ in a soliton spectrum, manifested as a red-shift of the soliton’s spectral center relative to the pump. (c) Temporal illustration of soliton pulses and the material Raman response. (d) Simulated SSFS (gray dots) and analytical predictions (solid lines) versus soliton duration $\tau_s$. Lorentzian Raman response [Eq. \ref{['hR']}] with $\tau_2/\tau_1 = 1$ is used in the plot.
• Figure 2: (a) False-colored scanning electron microscope image of the Si$_3$N$_4$ microresonator. The Si$_3$N$_4$ structure and metal heater are shown in blue and gold, respectively. (b) Cross-sectional profile of the fundamental transverse-electric (TE$_{00}$) mode. (c) Transmission spectrum of a resonance near 1546 nm. The fitting reveals intrinsic and external-coupling quality factors of $6.2\times10^6$ and $2.6\times10^6$, respectively. (d) Measured integrated dispersion $D_\mathrm{int}$ (blue circles) with a polynomial fitting (red dashed line). The dispersion parameters are extracted from the fitting.
• Figure 3: (a) Experimental setup. CW: continuous wave; EDFA: erbium-doped fiber amplifier; BPF: band-pass filter; FPC: fiber polarization controller; PD: photodetector; OSC: oscilloscope; OSA: optical spectrum analyzer. (b) Optical spectra of soliton microcombs with different soliton durations. The spectral envelopes are fitted with $\mathrm{sech}^2$ functions (dashed lines), from which the soliton durations and SSFS values are extracted. (c) Measured SSFS (gray circles) and analytical predictions (solid lines) versus soliton duration $\tau_s$. As $\tau_s$ decreases, the measurements deviate from the scaling law of adiabatic limit (red, Eq. \ref{['adiabatic']}) and converge toward the prediction of non-adiabatic theory (blue, Eq. \ref{['uf_trans']}). The error bars indicate the 95% confidence interval from nonlinear least-squares fitting.
• Figure 4: Soliton existence range predicted by the adiabatic approximation (red dashed line), the full convolution model (blue solid line), and the model without Raman (black dashed line). The parameters used in simulating the diagram are: $\tau_1/2\pi = 12.2~\mathrm{fs},\tau_2=32~\mathrm{fs},f_R=0.05,D_1/2\pi = 500~\mathrm{GHz},\kappa/2\pi= 193~\mathrm{MHz}, \kappa_\mathrm{ext}/\kappa=0.5 ,D_2/2\pi = 5~\mathrm{MHz}$.