Stable localized modes in asymmetric waveguides with gain and loss

TL;DR

This paper demonstrates that asymmetric waveguides with gain and loss can support stable optical beam propagation, with real propagation constants, through a novel relation between spectral problems and analysis of specific hyperbolic function-based waveguides.

Contribution

It introduces a new class of asymmetric waveguides supporting stable modes by linking two spectral problems and analyzes a specific hyperbolic function-based example.

Findings

Stable linear and nonlinear modes are demonstrated.

Propagation constants of modes are real, indicating stability.

A specific waveguide model with hyperbolic functions is analyzed.

Abstract

It is shown that asymmetric waveguides with gain and loss can support a stable propagation of optical beams. This means that the propagation constants of modes of the corresponding complex optical potential are real. A class of such waveguides is found from a relation between two spectral problems. A particular example of an asymmetric waveguide, described by the hyperbolic functions, is analyzed. The existence and stability of linear modes and of continuous families of nonlinear modes are demonstrated.