Coexistence of stable dark- and bright-soliton Kerr combs in normal-dispersion resonators

Abstract

Using the Lugiato-Lefever model, we analyze the effects of third-order chromatic dispersion on the existence and stability of dark-and bright-soliton Kerr frequency combs in the normal dispersion regime. While in the absence of third-order dispersion only dark solitons exist over an extended parameter range, we find that third-order dispersion allows for stable dark and bright solitons to coexist. Reversibility is broken and the shape of the switching waves connecting the top and bottom homogeneous solutions is modified. Bright solitons come into existence thanks to the generation of oscillations in the switching-wave profiles. Temporal oscillatory instabilities of dark solitons are suppressed in the presence of sufficiently strong third-order dispersion, while bright solitons are never found to oscillate in time. As a result of third-order dispersion both bright and dark solitons are found to move with a velocity that depends on their width.

Localized structures in dispersive and doubly resonant optical parametric oscillators

“…This term breaks the reflection symmetry x → −x, inducing the drift of the LSs and the modification of the collapsed snaking as reported in Ref. [70]. Although these effects are very relevant regarding real physical systems, their study is beyond the scope of the present work and will be examined elsewhere.…”

“…A natural extension of this work must include the effect of the temporal walk-off, which breaks the x → −x symmetry inducing asymmetry and drift. We expect that for weak walkoff the collapsed snaking is modified in the same fashion as in the context of Kerr cavities in the presence of third-order dispersion [70].…”

Dissipative Kerr solitons in optical microresonators

“…In (124), it was demonstrated that the dynamics of platicons in the presence of the third-order dispersion is quite peculiar and drastically different from bright solitons. In (125), a possibility of stable coexistence of dark and bright solitons in case of nonzero third-order dispersion was revealed.…”

Advances in soliton microcomb generation

“…92,93 Although the original nonlinear Schrödinger equation admits a solution in the form of bright solitons in the anomalous-dispersion regime, dark solitons are in the normal-dispersion regime. 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."…”

“…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.…”