Quantum theory of spontaneous emission in multilayer dielectric structures

This paper is a theoretical one dealing with spontaneous emission in one-dimensional photonic structures. We present a fully quantum-electrodynamical formalism suitable to evaluate the spontaneous emission rate and pattern from a dipole embedded in a nonabsorbing 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 Si/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 six-layer model structure) doped with Er3+ ions. 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.