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30 April 2012 Spontaneous emission in a cylindrical nanocavity: ab initio analytical approach
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The rigorous analytical approach for the calculation of the spontaneous decay rate for an 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 Hertz vector potentials which describe the electromagnetic field in the system are found as Fourier integrals over the path in the complex plane of the propagation constant. The integral equation which determines the field Fourier transforms is derived. The Green's function is then used to calculate the field susceptibility and the spontaneous decay rate of an emitter located inside a nanocavity. The general theory is illustrated by the calculations for the system which models an InAs quantum dot embedded in a GaAs nanowire.
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Vladimir G. Bordo "Spontaneous emission in a cylindrical nanocavity: ab initio analytical approach", Proc. SPIE 8424, Nanophotonics IV, 84240L (30 April 2012);

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