Dual Integral Equations and Analytical Regularization Technique in the Study of Purcell Effect for a Thin Dielectric Disk

We consider spontaneous radiation of atomic or molecular dipole in the presence of a thin dielectric microdisk as a boundary‐value problem for 3D Maxwell’s equations, local energy finiteness, and a radiation condition at infinity. The problem is reduced first to dual integral equations (IEs) and then to regularized IEs and the latter are solved with a meshless Nystrom algorithm. Results show that the radiative and non‐radiative decay rates display resonance maxima associated with the disk natural frequencies explained through the effective‐refractive‐index approximation.