Modeling of spontaneous emission in presence of cylindrical nanoobjects: the scattering matrix approach

We propose a method of analysis of spontaneous emission of a quantum emitter (an atom, a luminescence center, a quantum dot) inside or in vicinity of a cylinder. At the focus of our method are analytical expressions for the scattering matrix of the cylindrical nanoobject. We propose the approach to electromagnetic field quantization based of eigenvalues and eigenvectors of the scattering matrix. The method is applicable for calculation and analysis of spontaneous emission rates and angular dependences of radiation for a set of different systems: semiconductor nanowires with quantum dots, plasmonic nanowires, cylindrical hollows in dielectrics and metals. Relative simplicity of the method allows obtaining analytical and semi-analytical expressions for both cases of radiation into external medium and into guided modes.