Nonlinear photonic crystals near the supercollimation point

TL;DR

This paper explores how nonlinearity and diffraction interact in photonic crystals near the supercollimation point, revealing stable solitons governed by a nonlinear Schrödinger equation and analyzing their collision behavior.

Contribution

It introduces a nonlinear diffraction model for photonic crystals at the supercollimation point and studies soliton stability and interactions within this framework.

Findings

Solitons are stable within a specific existence domain.

Nonlinear diffraction significantly affects soliton collision dynamics.

The stability criterion follows the Vakhitov-Kolokolov condition.

Abstract

We uncover a strong coupling between nonlinearity and diffraction in a photonic crystal at the supercollimation point. We show this is modeled by a nonlinear diffraction term in a nonlinear schroedinger type equation, in which the properties of solitons are investigated. Linear stability analysis shows solitons are stable in an existence domain that obeys the Vakhitov-Kolokolov criterium. In addition, we investigate the influence of the nonlinear diffraction on soliton collision scenarios.