Purcell factor for a cylindrical nanocavity: ab initio analytical approach

The rigorous analytical approach for the calculation of the spontaneous decay rate for a quantum emitter located in a cylindrical cavity of arbitrary diameter and length is developed. The approach is based on the dyadic Green's function of the Helmholtz equation, which is obtained by introducing the fictitious surface current sheets at both ends of the nanocavity. The cases when an emitter is located on the cavity axis and when the cavity length exceeds essentially its diameter are considered in further detail. The general theory is illustrated by the calculations for the system, which models a quantum dot embedded in a GaAs nanowire. (C) 2012 Optical Society of America