Light propagation in periodically modulated complex waveguides

TL;DR

This paper investigates light propagation in complex, periodically modulated waveguides, revealing conditions for exponential growth or decay and identifying stable nonlinear modes in certain non-$ ext{PT}$-symmetric structures.

Contribution

It provides a multiscale perturbation analysis of linear and nonlinear dynamics in complex waveguides, identifying classes with real spectra and stable nonlinear modes.

Findings

Many non-$ ext{PT}$-symmetric waveguides have partially complex spectra leading to exponential growth or decay.

Certain non-$ ext{PT}$-symmetric waveguides possess all-real linear spectra.

Stable nonlinear modes can form in $ ext{PT}$-symmetric waveguides both above and below phase transition.

Abstract

Light propagation in optical waveguides with periodically modulated index of refraction and alternating gain and loss are investigated for linear and nonlinear systems. Based on a multiscale perturbation analysis, it is shown that for many non-parity-time ($\mathcal{PT}$) symmetric waveguides, their linear spectrum is partially complex, thus light exponentially grows or decays upon propagation, and this growth or delay is not altered by nonlinearity. However, several classes of non-$\mathcal{PT}$-symmetric waveguides are also identified to possess all-real linear spectrum. In the nonlinear regime longitudinally periodic and transversely quasi-localized modes are found for $\mathcal{PT}$-symmetric waveguides both above and below phase transition. These nonlinear modes are stable under evolution and can develop from initially weak initial conditions.