Feshbach resonances in Kerr frequency combs

We show that both the power and repetition rate of a frequency comb generated in a nonlinear ring resonator, pumped with continuous-wave (cw) coherent light, are modulated. The modulation is brought about by the interaction of the cw background with optical pulses excited in the resonator, and occurs in resonators with nonzero high-order chromatic dispersion and wavelength-dependent quality factor. The modulation frequency corresponds to the detuning of the pump frequency from the eigenfrequency of the pumped mode in the resonator.

Figure 1

Numerically simulated modulation amplitudes of the phase $\Psi \left(f_m\right)$ (a) and power $P_{\mathrm{comb}}\left(f_m\right)$ (b) versus modulation frequency $f_m$. The low-frequency peak corresponds to the relaxation oscillation of the Kerr comb which depends on the bandwidth of the resonator modes, and the high-frequency peak corresponds to the frequency detuning $\left|\Delta \right|$.

Figure 2

Numerically simulated frequency combs for two detuning values ${\Delta }_0=-25$ (harmonically mode-locked comb, blue line) and ${\Delta }_0=-45$ (fundamentally mode-locked comb, red line) (a) and modulation amplitude of the phase parameter $\Psi \left(f_m\right)$ (b) versus modulation frequency $f_m$. The low-frequency peak in (b) corresponds to the relaxation oscillation of the Kerr comb which depends on the bandwidth of the resonator modes, and the high-frequency peak corresponds to the frequency detuning $\left|\Delta \right|$.