Calculation of atomic spontaneous emission rate in 1D finite photonic crystal with defects

TL;DR

This paper derives explicit formulas for atomic spontaneous emission rates in finite 1D photonic crystals with defects, using an effective resonator model to simplify analysis and interpretation.

Contribution

It introduces a novel application of the effective resonator model to calculate spontaneous emission rates in defective finite 1D photonic crystals.

Findings

Explicit formulas for different mode contributions

Numerical examples demonstrating model effectiveness

Simplified interpretation of emission phenomena

Abstract

We derive the expression for spontaneous emission rate in finite one-dimensional photonic crystal with arbitrary defects using the effective resonator model to describe electromagnetic field distributions in the structure. We obtain explicit formulas for contributions of different types of modes, i.e. radiation, substrate and guided modes. Formal calculations are illustrated with a few numerical examples, which demonstrate that the application of effective resonator model simplifies interpretation of results.