Preventing critical collapse of higher-order solitons by tailoring unconventional optical diffraction and nonlinearities

Abstract

Self-trapped modes suffer critical collapse in two-dimensional cubic systems. To overcome such a collapse, linear periodic potentials or competing nonlinearities between self-focusing cubic and self-defocusing quintic nonlinear terms are often introduced. Here, we combine both schemes in the context of an unconventional and nonlinear fractional Schrödinger equation with attractive-repulsive cubic-quintic nonlinearity and an optical lattice. We report theoretical results for various two-dimensional trapped solitons, including fundamental gap and vortical solitons as well as the gap-type soliton clusters. The latter soliton family resembles the recently-found gap waves. We uncover that, unlike the conventional case, the fractional model exhibiting fractional diffraction order strongly influences the formation of higher band gaps. Hence, a new route for the study of self-trapped modes in these newly emergent higher band gaps is suggested. Regimes of stability and instability of all the soliton families are obtained with the help of linear-stability analysis and direct simulations.

Flat-floor Bubbles, Dark Solitons, and Vortices Stabilized by Inhomogeneous Nonlinear Media

“…It was checked that the numerical mesh with ∆x = ∆r = 0.1 and ∆z = 0.002 was sufficient for producing fully reliable results. It is relevant to mention that numerical methods for producing stationary and dynamical solutions to NLS/GP equations with a spatially varying nonlinearity coefficients were developed and used in many previous works [1,28,39,40,41,42], [48]- [62].…”

“…In this connection, it is relevant to mention that linear lattices, i.e., spatially periodic linear potentials, are commonly used for the creation and stabilization of solitons. In particular, linear lattices in combination with self-repulsive cubic nonlinearity [12] give rise to various families of gap solitons, including fundamental [13,14], subwavelength [15,16], parity-time-symmetric [17,18], subfundamental [19], composite [20,21], surface [22], moving [23,24], dark [25], discrete [26], and multipole [27] ones, as well as clusters built of them [28]. Further, gap solitons were predicted in moiré lattices [29,30] and in systems with quintic and cubic-quintic nonlinearities [31].…”

Dark gap solitons in periodic nonlinear media with competing cubic-quintic nonlinearities

“…Periodic potentials, such as photonic crystals and lattices in the context of optics and optical lattices in BECs, have demonstrated as a versatile toolbox for operating and controlling the dynamics of optical and matter waves [3,4,5,6,40,41,42,43] . Worthwhile mentioning is the generation of bright gap solitons [44,45,46,47,48] under the condition of self-defocusing nonlinearity which, as mentioned above, admits only the dark solitons and cannot allow the existence of bright solitons in uniform media [49]. The underlying nonlinear physics is that the periodic potentials, counterintuitively, can invert the sign of the effective dispersion of the media, and thus support bright gap solitons [50,51,52].…”

“…Although the bright gap solitons have been previously reported in the physical systems of cubic-quintic nonlinearity and optical lattices [46,47], their opposite nonlinear excitations-the dark gap solitons-however, are yet to be explored in such systems. Furthermore, the dark gap solitons in periodic nonlinear media are currently not being surveyed extensively [61,62,63,64] and, therefore, the underlying soliton physics is yet to be disclosed.…”

Families of fundamental and multipole solitons in a cubic-quintic nonlinear lattice in fractional dimension

“…The experimental implementation of the FSE in condensed-matter [56,57] and optical [58] setups, where nonlinearity is a natural feature, has drawn interest to the possibility of existence of solitons in fractional dimensions [59][60][61][62]. In particular, "accessible solitons" [63,64] and self-trapped states of vectorial [65], gap [66], nonlocal [67], vortical [68], and multi-peak types [69] have been predicted in FSE models, as well as soliton clusters [70,71], symmetry breaking of solitons [72,73], coupled solitons [74] and dissipative solitons in a fractional complex-Ginzburg-Landau model [75]. In the case of the ubiquitous cubic (Kerr) self-focusing, the solitons are unstable at α ≤ 1, as the combination of such values with the Kerr nonlinearity gives rise to the collapse.…”