Switching dynamics of dark-pulse Kerr frequency comb states in optical microresonators

Dissipative Kerr solitons are localized structures that exist in nonlinear optical cavities. They lead to the formation of microcombs—chip-scale frequency combs that could facilitate precision frequency synthesis and metrology by capitalizing on advances in silicon photonics. Previous demonstrations have mainly focused on anomalous dispersion cavities. Notwithstanding, localized structures also exist in the normal dispersion regime in the form of circulating dark pulses, but their physical dynamics is far from being understood. Here, we explore dark-pulse Kerr combs generated in normal dispersion optical microresonators and report the discovery of reversible switching between coherent dark-pulse combs, whereby distinct states can be accessed deterministically. Furthermore, we reveal that the formation of dark-pulse Kerr combs is associated with the appearance of another resonance, a feature that has never been observed for dark pulses and is ascribed to soliton behavior. These results contribute to understanding the nonlinear physics in normal dispersion nonlinear cavities and provide insight into the generation of microcombs with high conversion efficiency.

Figure 1

Linear characterization of the multimode silicon nitride microresonator. (a) Microscope image of the silicon nitride microresonator. (b) Measured transmission scan of the microresonator, where two clear transverse modes appear. (c) Integrated dispersion, i.e., frequency deviation of the resonance locations of the main mode (black dots), ${\omega }_{\mu }$, with respect to an ideal grid, $D_{\mathrm{int}}=({\omega }_{\mu }-{\omega }_0-2\pi D_1\mu )/2\pi$, where $\mu$ is the mode number and $D_1$ the free spectral range. The main mode displays normal dispersion, while at $\mu =0$ the dispersion changes locally to anomalous due to the linear coupling between two transverse modes in the resonator. (d) Linear mode coupling effect. The transmission spectrum is divided into blocks with a spacing difference of 1 FSR [dotted lines in (b)] to plot this diagram and calculate the linear coupling strength. The red and blue circles represent the resonance frequencies of the two transverse modes in different FSR blocks. The gray solid lines depict the no mode coupling ($\kappa =0$) case, found by linearly fitting $\mu$ versus the resonance frequencies in the region far from $\mu =0$. Mode coupling shifts the resonances apart from each other at $\mu =0$, leading to an avoided mode crossing. The measured linear coupling coefficient between the modes is $\kappa =22.7{\mathrm{m}}^{-1}$, while the measured group velocity dispersion of the main mode is ${\beta }_2=139{\mathrm{ps}}^2/\mathrm{km}$.

Figure 2

Deterministic switching of dark pulses. (a) Setup for comb generation and measurement. The setup within the dashed lines is used in Sec. 4. PC: Polarization controller, EDFA: Erbium-doped fiber amplifier; PM: Power meter; ATT: Attenuator; PD: Photodiode; IM: Intensity modulator; OSA: Optical spectrum analyzer; OSC: Oscilloscope; VNA: Vector network analyzer. (b) Measured comb power when the pump is forward and backward tuned, shown in blue (dark gray) and yellow (light gray), respectively. The frequency axis indicates the pump location with respect to its initial frequency. The frequency scan is calibrated by means of an auxiliary interferometer. (c) Zoomed-in view of (b), where smoothed steplike patterns are observed as the pump is tuned, indicating switching between dark-pulse comb states. The inset shows the radio-frequency spectrum (dashed red) and noise floor (solid blue) of the generated comb. (d) The blue frequency lines are the comb spectra measured at different pump detunings, corresponding to the comb states marked in (b). The comb envelope of each state is simulated and shown in red, with the corresponding simulated time-domain waveforms underneath. The arrows point the number of low intensity oscillations. For state F, the phase of the pulse is also shown in dashed blue.

Figure 3

(a) Simulation of average intracavity power for different linear coupling coefficients $\kappa$, as the pump is forward tuned. (b) Zoomed-in view of the dashed region in (a), clearly showing smooth steps similar to those observed in our experiments [Fig. 2].

Figure 4

(a) Schematic diagram of the method used for the measurement of the system response. The pump approaches the hybridized resonances 1 and 2 from the blue side. Once the pump crosses resonance 2, a dark-pulse comb is generated and another resonance, labeled 3, emerges. (b) System response as the pump is tuned into resonance. (c) Zoomed-in view of (b), where the existence of dark pulses is highlighted. The appearance of an extra resonance can be clearly observed in this regime. (d) VNA traces and corresponding measured comb spectra and simulated time-domain waveforms (inset) for various pump detunings indicated by dashed lines in (b). Note that the origin of the frequency axis here is the pump laser, providing a direct indication of the location of the resonances and effective pump-laser detuning. (e) Measured and simulated VNA traces associated with the main mode for pump detunings III and IV in (b). The experimental traces are the zoomed-in view of states III and IV in (d).

Figure 5

Hot-cavity spectroscopy of a dark-pulse Kerr comb in a different silicon nitride microresonator with similar characteristics, in terms of dispersion, $Q$ and avoided mode crossing. (a) System response as the pump is tuned into resonance from the blue side. The appearance of a third resonance can be clearly observed in the dark-pulse regime (highlighted region). (b) Dark-pulse Kerr comb spectrum measured at the pump detuning indicated by a dashed line in (a).