Jackiw-Rebbi states in interfaced binary waveguide arrays with Kerr nonlinearity

TL;DR

This paper explores the optical analogs of Jackiw-Rebbi states in binary waveguide arrays with Kerr nonlinearity, revealing unique profile behaviors and stability conditions for different nonlinear media.

Contribution

It provides exact calculations of nonlinear Jackiw-Rebbi states and uncovers their distinct envelope behavior compared to other localized structures.

Findings

Higher amplitude states can envelope lower amplitude ones

Positive nonlinear media support stable states over wide amplitudes

Negative nonlinear media support only low amplitude states

Abstract

We systematically investigate the optical analogs of quantum relativistic Jackiw-Rebbi states in binary waveguide arrays in the presence of Kerr nonlinearity with both self-focusing and self-defocusing cases. The localized profiles of these nonlinear Jackiw-Rebbi states can be calculated exactly by using the shooting method. We show that these nonlinear Jackiw-Rebbi states have a very interesting feature which is totally different from all other well-known nonlinear localized structures, including optical solitons. Namely, the profiles of nonlinear JR states with higher peak amplitudes can totally envelope the ones with lower peak amplitudes. We demonstrate that media with the positive nonlinear coefficient can support stable Jackiw-Rebbi states for a wide range of peak amplitudes, whereas media with the negative nonlinear coefficient are only able to support Jackiw-Rebbi states with low peak amplitudes. A general rule for the detuning of nonlinear Jackiw-Rebbi states in binary waveguide arrays is found.