Hybridization of solitons in realistic non-instantaneous fibers

Abstract

Non-local nonlinearities are an integral part of numerous physical systems. Yet, their dissipative nature makes it hard to identify and verify stable eigenstates rigorously. This work sheds new light onto the existence of temporally non-local solitons – a class of dissipative self-maintaining states in time theoretically predicted to emerge in media with a time-delayed (i.e., non-instantaneous) nonlinear response. Revisiting the non-instantaneous nonlinear Schrödinger equation introduced by Conti et al., I introduce a semi-analytical approach to reveal such non-instantaneous solitons in liquid-type media which exhibit realistic non-exponential response functions featuring both rise and decay times. I investigate the susceptibility of such states to typical perturbations, such as third-order dispersion, instantaneous Kerr nonlinearity, and causality of the material response. Empirical numeric experiments illustrate how non-instantaneous solitons may compete against and even fuse with instantaneous (Kerr-type) solitons to an inseparable hybrid solitary waves. While finding a numerical solution to define the nature of this mixed state remains a challenge, I introduce a phase balance condition and other benchmarks which will allow to identify the occurrence of such states in realistic liquid-core fiber systems in future work. The findings of this study give reason to hypothetize a new type of dissipative solitary state and provide new means to understanding information transport and system dynamics of highly non-instantaneous nonlinear systems, particularly liquid-core optical fibers and waveguides.