Quantum theory of spontaneous emission in multilayer dielectric structures

TL;DR

This paper develops a quantum-electrodynamical formalism to accurately evaluate spontaneous emission in multilayer dielectric structures, addressing interference issues and applying it to silicon-based devices with results aligning with experimental data.

Contribution

It introduces a novel quantum model for spontaneous emission in multilayer dielectrics that avoids interference problems and is validated on silicon structures with experimental agreement.

Findings

Accurate emission rate calculations for multilayer structures.

Good agreement with experimental photoluminescence enhancement.

Model applicable to silicon-based photonic devices.

Abstract

We present a fully quantum-electrodynamical formalism suitable to evaluate the spontaneous emission rate and pattern from a dipole embedded in a non-absorbing and lossless multilayer dielectric structure. In the model here developed the electromagnetic field is quantized by a proper choice of a complete and orthonormal set of classical spatial modes, which consists of guided and radiative (partially and fully) states. In particular, by choosing a set of radiative states characterized by a single outgoing component, we get rid of the problem related to the quantum interference between different outgoing modes, which arises when the standard radiative basis is used to calculate spontaneous emission patterns. After the derivation of the local density of states, the analytical expressions for the emission rates are obtained within the framework of perturbation theory. First we apply our model to realistic Silicon-based structures such as a single Silicon/air interface and a Silicon waveguide in both the symmetric and asymmetric configurations. Then, we focus on the analysis of the spontaneous emission process in a silicon-on-insulator (SOI) Slot waveguide (a 6 layers model structure) doped with erbium ions (emitting at the telecom wavelength). In this latter case we find a very good agreement with the experimental evidence [M. Galli et al., Appl. Phys. Lett. 89, 241114 (2006)] of an enhanced TM/TE photoluminescence signal. Hence, this model is relevant to study the spontaneous emission in Silicon-based multilayer structures which nowadays play a fundamental role for the development of highly integrated multifunctional devices.