Application of the generalized Kirchhoff's law to calculation of photoluminescence spectra of one-dimensional photonic crystals

TL;DR

This paper develops a generalized Kirchhoff's law-based method for calculating photoluminescence spectra of 1D photonic crystals, providing explicit formulas and insights into emission enhancement and suppression near photonic band-gap edges.

Contribution

It introduces a simple, explicit analytical approach for PL spectra calculation in 1D photonic crystals, connecting with existing LDOS-based methods and explaining emission behavior.

Findings

Derived an explicit expression for the spontaneous emission intensity enhancement factor.

Explained the variation of emission intensity near photonic band-gap edges.

Demonstrated the approach's applicability to structures with many layers.

Abstract

The approach based on the generalized Kirchhoff's law for calculating photoluminescence (PL) spectra of one-dimensional (1D) multi-layered structures, in particular, 1D photonic crystals has been developed. It is valid in the local thermodynamic equilibrium approximation and leads to simple and explicit expression for the photoluminescence intensity. In the framework of the present theory the analytical expression for the spontaneous emission intensity enhancement factor (IEF) for a 1D photonic crystal has been derived. It takes a particularly simple form in the case of a sufficiently large number of the layers and is well suitable for analysis; in particular, it explains the difference in the emission intensity at frequencies near different edges of photonic band-gaps (PBGs), where the intensity is relatively high, and specificity of suppression of the emission in a given frequency range. Also, the developed approach is discussed in connection with the standard method using the Fermi's golden rule and the concept of the local density of (optical) states (LDOS).