A roundtrip matrix method for calculating the leaky resonant modes of open nanophotonic structures

TL;DR

This paper introduces a simplified and intuitive numerical method based on scattering matrices to accurately compute leaky resonant modes of open nanophotonic structures, facilitating better analysis of their optical properties.

Contribution

The paper develops a novel roundtrip matrix approach using scattering matrices for calculating quasi-normal modes in open nanophotonic structures, improving simplicity and implementation.

Findings

Successfully computed quasi-normal modes for 2D photonic crystal cavities

Reconstructed scattering spectra from complex mode frequencies

Demonstrated method's applicability to various cavity configurations

Abstract

We present a numerical method for calculating quasi-normal modes of open nanophotonic structures. The method is based on scattering matrices and a unity eigenvalue of the roundtrip matrix of an internal cavity, and we develop it in detail with electromagnetic fields expanded on Bloch modes of periodic structures. This procedure is simpler to implement numerically and more intuitive than previous scattering matrix methods, and any routine based on scattering matrices can benefit from the method. We demonstrate the calculation of quasi-normal modes for two-dimensional photonic crystals where cavities are side-coupled and in-line-coupled to an infinite W1 waveguide and show that the scattering spectrum of these types of cavities can be reconstructed from the complex quasi-normal mode frequency.