General coupled mode theory in non-Hermitian waveguides

TL;DR

This paper develops a generalized coupled mode theory for non-Hermitian waveguides, accurately modeling mode hybridization in systems with loss and gain, and enabling better design of non-Hermitian optical devices.

Contribution

It introduces a new coupled mode theory based on reaction conservation for non-Hermitian systems, extending standard theory to include loss, gain, and full vector fields.

Findings

Excellent agreement with finite element simulations

Applicable to parity-time symmetric waveguides

Enables study of nonreciprocal light propagation

Abstract

In the presence of loss and gain, the coupled mode equation on describing the mode hybridization of various waveguides or cavities, or cavities coupled to waveguides becomes intrinsically non-Hermitian. In such non-Hermitian waveguides, the standard coupled coupled mode theory fails. We generalize the coupled mode theory with a properly defined inner product based on reaction conservation. We apply our theory to the non-Hermitian parity-time symmetric waveguides, and obtain excellent agreement with results obtained by finite element fullwave simulations. The theory presented here is typically formulated in space to study coupling between waveguides, which can be transformed into time domain by proper reformulation to study coupling between non-Hermitian resonators. Our theory has the strength of studying non-Hermitian optical systems with inclusion of the full vector fields, thus is useful to study and design non-Hermitian devices that support asymmetric and even nonreciprocal light propagations