Lippmann-Schwinger integral equation approach to the emission of radiation by sources located inside finite-sized dielectric structures

A full-vectorial integral equation method is presented for calculating near fields and far fields generated by a given distribution of sources located inside finite-sized dielectric structures. Special attention is given to the treatment of the singularity of the dipole source field. A method is presented for removing the dipole source field singularity from the integral equations to be solved. It is also shown how the numerical task can be reduced in the case of structures with cylindrical symmetry. The methods are applied to calculate the near fields, far fields, and the emission rate of light from a dipole source located in the center of a cylindrically symmetric dielectric disk. The emission for certain disk diameters, where a resonance condition is fulfilled, is enhanced by 13 times as compared to the emission from the same dipole source located in free space. The methods have prospective uses for analyzing the emission of light by sources in some antennas and optical components such as vertical cavity surface emitting lasers, microdisk lasers, and light emitting diodes. The methods also have prospective uses in quantum electrodynamics for studies of spontaneous emission from, e.g., an excited atom located inside a dieletric structure.