Polychromatic Cherenkov Radiation Induced Group Velocity Symmetry Breaking in Counterpropagating Dissipative Kerr Solitons

High-order-dispersion-induced dispersive waves emitted by dissipative Kerr solitons are frequently observed in microresonator frequency comb generation. Also known as soliton Cherenkov radiation, this type of dispersive wave plays a critical role in comb spectrum broadening as well as the formation of soliton bound states. Here, we report the experimental observation of symmetry breaking in the group velocity of counterpropagating solitons in a crystalline microresonator. Induced by the polychromatic Cherenkov radiation, soliton bound states are formed, showing different group velocities with different spatiotemporal separations between constituent solitons. By bidirectionally pumping the microresonator with laser fields of equal power and frequency, we demonstrate the degeneracy lifting of repetition rates of the counterpropagating solitons. Our work not only shines new light on the impact of dispersive waves in nonlinear cavities, but also introduces a novel approach to develop compact dual-comb spectrometers.

Figure 1

Under symmetric pumping conditions, CW and CCW DKS can have different soliton group velocities if (a) the $CP$ states are of unequal soliton numbers, or (b) the $CP$ states are multisoliton states with equal soliton numbers but unequal intersoliton separations.

Figure 2

(a) Experimental setup. (b) Optical spectra of the single-soliton states in the CW (blue) and CCW (red) directions. A picture of the microresonator is shown in the inset. (c) Soliton repetition rate spectrogram obtained from the combination of two $CP$ soliton states while scanning the detuning over 16 MHz. The step size of the scanning is 100 kHz. At each step, after the detuning is changed, stable microcomb optical spectra and repetition rate spectrum are acquired.

Figure 3

(a) Microcomb spectra of a CW single-soliton state (blue) and a CCW dual-soliton state (red). (b) Evolution of the $CP$ DKS repetition rates when the pump-resonance detuning is scanned. In the regions where the degeneracy is lifted (indicated by the lower yellow strips), the higher (lower) repetition rate corresponds to the CW (CCW) DKS because the signal shows slightly higher (lower) amplitude. Around the two prominent repetition rate signals we observe multiple modulation sidebands, which we attribute to the collision between CW and CCW solitons in the microresonator. (c) The upper figure shows the relative CR intensities in a mode (order number $\mu =246$) in the CW (blue) and the CCW (red) microcombs. Strong bistabilities with increasing detuning (open circles and solid lines) and decreasing detuning (shallow circles with dashed lines) are indicated by the shaded areas. The lower figure plots the relative intensity difference with different detuning sweeping directions. The black dotted line indicates the equal relative intensities. (d) The nondegenerate (left) and the degenerate (right) repetition rate spectra that correspond to the red and green dots shown in the lower panel in (b). The resolution bandwidth is 500 Hz. (e) The rf comb obtained when the repetition rate degeneracy is lifted. The line spacing of the rf comb is equal to the frequency difference between the repetition rates of the CW and CCW solitons. The inset shows a portion of the comb in the frequency range of 0–0.1 MHz.

Figure 4

(a) Comb spectra of the dual-soliton states in the CW (blue) and CCW (red) directions, showing identical intersoliton separations. The insets display the estimated temporal separations in the dual-soliton states. (b) Soliton repetition rate spectrogram of the identical $CP$ DKS, showing a single repetition rate signal the whole time. (c) Comb spectra of the CW and CCW dual-soliton states that are of different temporal arrangements. (d) The repetition rate spectrogram of the dissimilar dual-soliton states exhibit several regimes where degeneracy is lifted.