Influence of disorder on a Bragg microcavity

TL;DR

This study uses the resonant-state expansion to analyze how disorder, modeled by random thickness variations, affects the resonance energy, linewidth, and quality factor of a planar Bragg microcavity, revealing proportional broadening and inverse quadratic quality factor decay.

Contribution

It applies the resonant-state expansion to quantify disorder effects on microcavity modes, demonstrating the accuracy of first-order perturbation theory for moderate disorder levels.

Findings

Inhomogeneous broadening grows proportionally with disorder magnitude.

Quality factor decreases inversely with the square of disorder magnitude.

First-order perturbation theory accurately predicts resonance energy for moderate disorder.

Abstract

Using the resonant-state expansion for leaky optical modes of a planar Bragg microcavity, we investigate the influence of disorder on its fundamental cavity mode. We model the disorder by randomly varying the thickness of the Bragg-pair slabs (composing the mirrors) and the cavity, and calculate the resonant energy and linewidth of each disordered microcavity exactly, comparing the results with the resonant-state expansion for a large basis set and within its first and second orders of perturbation theory. We show that random shifts of interfaces cause a growth of the inhomogeneous broadening of the fundamental mode that is proportional to the magnitude of disorder. Simultaneously, the quality factor of the microcavity decreases inversely proportional to the square of the magnitude of disorder. We also find that first-order perturbation theory works very accurately up to a reasonably large disorder magnitude, especially for calculating the resonance energy, which allows us to derive qualitatively the scaling of the microcavity properties with disorder strength.