Spontaneous emission rate and the density of states inside a one dimensional photonic crystal

TL;DR

This paper investigates the electromagnetic density of states and spontaneous emission rates inside a one-dimensional photonic crystal using semi-analytical methods and verifies results with numerical simulations, aiding thermal and radiation research.

Contribution

It introduces a semi-analytical approach using Green tensor formalism to calculate LDOS and DOS inside 1D photonic crystals, validated by FEM simulations.

Findings

Green tensor formalism effectively calculates LDOS and DOS inside 1D PC.

Approximate density of Bloch states matches exact calculations.

Results are consistent with FEM simulations in the visible range.

Abstract

Different densities of electromagnetic states inside a one dimensional photonic crystal (1D PC) are studied. Hertz vector formalism is used to calculate Green tensor inside a layered structure, semi-analytically. Based on the obtained Green tensor, the local density of electromagnetic states (LDOS) and the density of states (DOS) inside a 1D PC are calculated and discussed. The Green tensor is also used to approximate the density of Bloch states inside the 1D PC and is compared with its exact calculation based on the 1D PC dispersion relations. Using a practical 1D PC parameters in the visible range, the aforementioned quantities are calculated and verified with a full-wave solver based on finite element method (FEM). The formulations and the results are aimed to be helpful in thermal and spontaneous radiation studies.