Hydrodynamic Optical Soliton Tunneling

TL;DR

This paper introduces the concept of hydrodynamic optical soliton tunneling, analyzing how dark solitons interact with evolving potential barriers like rarefaction waves and dispersive shock waves within the nonlinear Schrödinger framework.

Contribution

It develops a novel theoretical approach using Whitham modulation theory to describe soliton-barrier interactions and predicts new effects such as soliton reversal and cavitation.

Findings

Soliton tunneling and trapping depend on initial conditions and mean flow.

Interaction can cause soliton reversal and cavitation.

Theoretical framework matches numerical simulations.

Abstract

A conceptually new notion of hydrodynamic optical soliton tunneling is introduced in which a dark soliton is incident upon an evolving, broad potential barrier that arises from an appropriate variation of the input signal. The barriers considered include smooth rarefaction waves and highly oscillatory dispersive shock waves. Both the soliton and the barrier satisfy the same one-dimensional defocusing nonlinear Schr\"odinger (NLS) equation, which admits a convenient dispersive hydrodynamic interpretation. Under the scale separation assumption of Whitham modulation theory the highly nontrivial nonlinear interaction between the soliton and the evolving hydrodynamic barrier is described in terms of simple wave solutions to an appropriate asymptotic reduction of the Whitham-NLS system. One of the Riemann invariants of the reduced modulation system determines the characteristics of a soliton interacting with an initial mean flow that results in soliton tunneling or trapping. Another Riemann invariant yields the soliton tunneling phase shift. Under certain conditions, soliton interaction with hydrodynamic barriers gives rise to new effects that include reversal of the soliton propagation direction and spontaneous soliton cavitation, which further suggest possible methods of dark soliton control in optical fibers.