Accurate quantification of the Purcell effect in the presence of a dielectric microdisk of nanoscale thickness

The spontaneous emission of a molecular dipole in the presence of a thin dielectric microdisk is studied as a 3D solution of Maxwell's equations with two-sided generalised boundary conditions on the disk median plane, local energy finiteness and a radiation condition at infinity. Results presented show that the radiative and non-radiative decay rates display resonance maxima associated with the disk natural frequencies which can be explained through the effective-refractive-index approximation. The numerical solution is based on a set of coupled integral equations of the Fredholm second kind, with smooth kernel functions, obtained with the aid of the method of analytical regularisation.