Resonant-state expansion of light propagation in non-uniform waveguides

TL;DR

This paper introduces a new method based on resonant states for accurately and efficiently modeling light propagation in non-uniform waveguides, outperforming existing numerical techniques significantly.

Contribution

The authors develop a resonant-state expansion approach that transforms the wave equation into a matrix differential equation, enabling faster and more precise simulations of non-uniform waveguides.

Findings

Achieves 10 to 10,000 times speedup over traditional methods

Provides accurate modeling of complex non-uniform waveguide structures

Applicable to other wave phenomena like acoustics and quantum mechanics

Abstract

A new rigorous approach for precise and efficient calculation of light propagation along non-uniform waveguides is presented. Resonant states of a uniform waveguide, which satisfy outgoing-wave boundary conditions, form a natural basis for expansion of the local electromagnetic field. Using such an expansion at fixed frequency, we convert the wave equation for light propagation in a non-uniform waveguide into an ordinary second-order matrix differential equation for the expansion coefficients depending on the coordinate along the waveguide. We illustrate the method on several examples of non-uniform planar waveguides and evaluate its efficiency compared to the aperiodic Fourier modal method and the finite element method, showing improvements of one to four orders of magnitude. A similar improvement can be expected also for applications in other fields of physics showing wave phenomena, such as acoustics and quantum mechanics.