Semi-analytical quasi-normal mode theory for the local density of states in coupled photonic crystal cavity-waveguide structures

TL;DR

This paper develops and validates a semi-analytical quasi-normal mode theory to accurately compute the local density of states in coupled photonic crystal cavity-waveguide structures, achieving high precision with minimal error.

Contribution

It introduces a semi-analytical QNM-based method for LDOS calculation in coupled photonic crystal structures, validated against numerical methods with high accuracy.

Findings

The theory accurately reproduces asymmetric spectra of single cavities.

It captures complex spectra with peaks and dips in multi-cavity systems.

Relative errors are below 1% within the relevant bandwidth.

Abstract

We present and validate a semi-analytical quasi-normal mode (QNM) theory for the local density of states (LDOS) in coupled photonic crystal (PhC) cavity-waveguide structures. By means of an expansion of the Green's function on one or a few QNMs, a closed-form expression for the LDOS is obtained, and for two types of two-dimensional PhCs, with one and two cavities side-coupled to an extended waveguide, the theory is validated against numerically exact computations. For the single cavity, a slightly asymmetric spectrum is found, which the QNM theory reproduces, and for two cavities a non-trivial spectrum with a peak and a dip is found, which is reproduced only when including both the two relevant QNMs in the theory. In both cases, we find relative errors below 1% in the bandwidth of interest.