  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.
