Exact bidirectional X-wave solutions in fiber Bragg gratings

TL;DR

This paper derives exact bidirectional X-wave solutions in fiber Bragg gratings using coupled-mode theory, revealing their properties, symmetries, and potential for high-contrast focusing.

Contribution

It introduces a novel set of exact solutions for bidirectional pulses in fiber Bragg gratings expressed via Bessel functions, expanding understanding of waveforms in these systems.

Findings

Solutions include bidirectional and unidirectional pulses

Solutions exhibit specific symmetry and asymptotic behaviors

Potential for high-contrast pulse focusing

Abstract

We find exact solutions describing bidirectional pulses propagating in fiber Bragg gratings. They are derived by solving the coupled-mode theory equations and are expressed in terms of products of modified Bessel functions with algebraic functions. Depending on the values of the two free parameters the general bidirectional X-wave solution can also take the form of a unidirectional pulse. We analyze the symmetries and the asymptotic properties of the solutions and also discuss about additional waveforms that are obtained by interference of more than one solutions. Depending on their parameters such pulses can create a sharp focus with high contrast.