Nonlinear-mode-coupling-induced soliton crystal dynamics in optical microresonators

Dissipative Kerr solitons based on microresonators have wide applications from optical communications to optical ranging for the high-repetition rate and broad bandwidth. Restricted by the bending losses and dispersion control of the optical waveguide, it could be hard to further realize ultrahigh-repetetion rate reaching several terahertz by simply reducing the size of microresonators. Soliton crystals, which completely fill the microresonator with a series of equidistant temporal pulses, can be an effective approach to realize ultrahigh-repetition rate in the common cavity length. In this paper, we investigate the generation of soliton crystals in the presence of nonlinear mode coupling, which can induce a modulation on the background wave and modify the cavity dynamics. Under the condition of suitable wave vector mismatch and nonlinear-coupling-coefficient, high-deterministic perfect soliton crystals can be realized. Besides, the drifting behavior of the soliton crystals is demonstrated to be determined by the match between the wave vector mismatch and nonlinear coupling coefficient. Finally, we successfully observe the recrystallization of the perfect soliton crystals.

Figure 1

Schematic diagram of nonlinear-mode-coupling-induced SCs formation in monolithic Kerr MRRs. The MRR is externally driven by a CW pump laser and the dimensions of the MRR satisfy the PMC between the fundamental and the harmonic waves.

Figure 2

(a) Spectra of fundamental (red vertical lines with squares) and harmonic (blue vertical lines with circles) waves in the PSCs state. (b) Temporal waveforms of fundamental (red solid line) and harmonic (blue dashed line) waves in the PSCs state. (c)–(d) Intracavity waveform evolutions of fundamental and second-harmonic waves, respectively.

Figure 3

(a) Intracavity power of the fundamental wave with respect to round-trip phase detuning ${\delta }_0$, Blue lines: PSCs, black lines: SCs with one vacancy. (b) A statistical overview of the generated soliton states out of 50 scans with the same parameters in Fig. 2. (c)–(d) Two kinds of spectra evolutions of the fundamental wave for PSCs and SCs with one vacancy, respectively.

Figure 4

(a)–(b) Intracavity waveform evolutions of fundamental wave induced by FD-SH mode coupling when $\mathrm{\Delta }k=-4.68\times {10}^3{\mathrm{m}}^{-1}$, $\kappa =3{\mathrm{W}}^{-1}{\mathrm{m}}^{-1}$, and $\mathrm{\Delta }k=-4.603\times {10}^3{\mathrm{m}}^{-1}$, $\kappa =3.6{\mathrm{W}}^{-1}{\mathrm{m}}^{-1}$, respectively. (c)–(d) Intracavity waveform evolutions induced by AMXs with $\mathrm{\Delta }=-12.7$ MHz and $133.7\mathrm{MHz}$, respectively.

Figure 5

(a) Drifting direction depending on the range of the wave vector mismatch $\mathrm{\Delta }k$ and the second-order coupling coefficient $\kappa$. (b)–(c) Temporal evolutions of the left-drifting and right-drifting PSCs corresponding to the black circle and triangle marked as B and C, respectively.

Figure 6

(a)–(b) The statistical overviews of the generated soliton states out of 50 scans when $P_{\mathrm{in}}=32$ mW and $P_{\mathrm{in}}=50$ mW, respectively. The characteristic generation of SCs with on vacancy when $P_{\mathrm{in}}=50$ mW: (c) Spectra of the fundamental (red vertical lines with squares) and the harmonic (blue vertical lines with circles) waves, (d) Temporal waveforms of the fundamental (red solid line) and the harmonic (blue dashed line) waves in SCs state. (e)–(f) Intracavity waveforms evolution of fundamental and second-harmonic waves, respectively.

Figure 7

Vacancy: (a) Temporal waveforms, (b) spectrum. Superstructure: (c) Temporal waveforms, (d) spectrum.

Figure 8

(a) Temporal evolution of the PSCs melting and recrystallization through the backward tuning to the chaotic state and forward tuning back to the initial PSCs state. (b)–(e) The spectra at different tuning stages corresponding to the specific round trips in (a).