Kerr optical frequency comb generation using whispering-gallery-mode resonators in the pulsed-pump regime

Kerr comb generation is usually based on the nonlinear dynamics of the intracavity field in a whispering-gallery-mode resonator pumped by a continuous-wave laser. However, using a pulsed instead of a continuous-wave pump opens an alternative research avenue from both the theoretical and experimental viewpoints, as it permits us to tailor the spectral properties of ultrashort pulse trains with a single passive nonlinear element. In this article we study the dynamics of Kerr optical frequency combs when the whispering-gallery-mode resonator is pumped by a synchronous pulse train. We propose a model that is based on an extension of the Lugiato-Lefever equation, which accounts for both the pulsed nature of the pump and the mismatch between the free-spectral range of the resonator and the repetition rate of the pulse train. We lay a particular emphasis on the effect of pump-cavity desynchronization on the spectral shape of the output combs. The numerical simulations are successfully compared with experimental measurements where the optical pulses are generated via time-lens soliton compression, and the resonator is a millimeter-size magnesium fluoride resonator with a billion quality factor at the pump wavelength.

Figure 1

Experimental setup used to drive a WGM resonator with quasisynchronous ultrashort optical pulses. The mm-size WGM resonator in this experiment is made of magnesium fluoride, and has an FSR of approximately 6 GHz with $Q$ in excess of ${10}^9$ at 1550 nm. PC: Polarization controller; IM: Intensity modulator; PM: Phase modulator; EDFA: Erbium-doped fiber amplifier; RFA: Radio frequency amplifier; PS: Phase shifter; SMF-28: Single-mode fiber spool; WGMR: WGM resonator; Att: Optical attenuator; OSA: Optical spectrum analyzer.

Figure 2

(a) Numerical simulation based on Eq. (3) for the time-lens soliton compression as the quasisinusoidal prepulses are propagating along the fiber spool. The parameters of the simulation for the initial condition in Eq. (2) are ${\kappa }_o{G}_o{P}_{{}_{\mathrm{L}}}=420$ mW, $V_0=2$ V, $\mathrm{\Delta }\mathrm{\Phi }=0$, and $\eta =3$. (b) Comparison between the experimental and simulated autocorrelation (AC) plots for the compressed (output) optical pulses. This plot permits us to evaluate the full-width at half-maximum to a value around 4 ps.

Figure 3

Kerr comb spectra at the output of the WGMR for a repetition rate mismatch of $\pm 30$ kHz relative to the FSR. Top: Numerical simulation using Eq. (9) with parameter $\alpha =0$, $F=8$, $\beta =-0.005$, and considering a Gaussian pulse with a 4.2 ps width. Bottom: Experimental spectra using the experimental setup presented in Fig. 1.

Figure 4

Experimental and numerical spectra for various values of the frequency mismatch $f_{{}_{\mathrm{\Delta }}}$. The parameters for the numerical simulations were $\alpha =0$ and $\beta =-0.008$. The input pulse was a Gaussian with a 4.2 ps pulse width.

Figure 5

Numerical simulation showing the variation of the pulse shape power $P$ for various values of the frequency mismatch $f_{{}_{\mathrm{\Delta }}}$. The parameters for the numerical simulations are the same as those in Fig. 4.