Spatiotemporal evolution of continuous-wave field and dark soliton formation in a microcavity with normal dispersion

Abstract

Stable dark soliton and dark pulse formation in normally dispersive and red-detuned microcavities are investigated by numerically solving the normalized Lugiato-Lefever equation. The soliton essence is proved by fitting the calculated field intensity profile with the analytical formula of a dark soliton. Meanwhile, we find that a dark soliton can be generated either from the nonlinear evolution of an optical shock wave or narrowing of a locally broad dark pulse with smoother fronts. Explicit analytical expression is obtained to describe the oscillatory fronts of the optical shock wave. Furthermore, from the calculation results, we show that for smaller frequency detunings, e.g., α < 3, in addition to the dark soliton formation, a single dark pulse with an oscillatory dip can also arise and propagate stably in the microcavity under proper pump detuning and pump strength combination. The existence region together with various field intensity profiles and the corresponding spectra of single dark pulse are demonstrated.

Advances in soliton microcomb generation

“…94,95 It is worth noting that mode-locking transitions do not necessarily correspond to dark or bright pulse (soliton) generation in microresontors with normal dispersion. 96,97 This is in contrast to the situations for the negative-dispersion regime where all soliton forms are actually "bright solitons." Actually, in the field of traditional modelocked fiber lasers, it has been proved that different types of bright pulses can emit from a laser cavity in the normaldispersion regime, including dissipative solitons with rectangular spectrum (Gaussian in time domain), Gaussian spectrum (flat-topped pulses), broadband spectrum (wave-breaking-free pulses), and noise-like pulses (low-coherence pulse clusters).…”

“…95 In other words, it can be considered that there does not exist a rigid "barrier" to distinguish the two states (depending on the pulse duration and duty cycle). Since rich phenomena have been discovered exhibiting distinct features from different aspects and with rather complicated excitation dynamics, there have been various prediction and explanations related to the physical origin of the observed temporal behaviors for microcombs with normal dispersion in the literature, such as "platicons" (flat-topped bright solitonic pulses), 99 dark pulses, 23,92 and dark solitons 93,95,96 or just normal-dispersion microcombs. 97 In this part, we mainly focus on the mode-locked character, rather than a strict physical clarification for this kind of pulse.…”

Analysis of dark soliton generation in the microcavity with mode-interaction*

“…And weak white Gaussian noise is feasible for the initial condition. [11] When the frequency detuning of the microcavity is large, combining with the initial field of the noise, multiple dark solitons can generate. When the frequency detuning δ 0 is set to 4, ∆ f 1 = −230 MHz, and ∆ f 2 = 230 MHz, the field evolves into four dark solitons, which is illustrated in Fig.…”

“…A dark soliton can be generated either from the nonlinear evolution of an optical shock wave or the narrowing of a locally broad dark pulse with smoother fronts. [11] Relying on numerically solving the spatiotemporal evolution of dark solitons, the effects of operating parameters on the dark soliton field are also studied. The increment of the microcavity second-order dispersion causes the dark soliton pulse to broaden.…”

Two-color flat-top solitons in microresonator-based optical parametric oscillators

“…In our work we studied numerically the generation of the particular type of the solitonic structures, two-color flat-top solitonic pulses, platicons, in the microresonator-based optical parametric oscillator via frequency scan that is the conventional method of the dissipative Kerr solitons generation in experiments [9]. Dark solitons [35][36][37][38][39][40] and platicons [41][42][43][44][45][46] are well-studied in Kerr microresonators and it was shown that in terms of the pump-to-comb conversion efficiency the generation of platicons may be significantly more efficient than the generation of bright solitons [47,48] that is very promising for the coherent optical communications [49,50]. In [51] platicon generation in the quadratically nonlinear microresonators was studied for the second harmonic generation process.…”