General theory for spontaneous emission in active dielectric microstructures: Example of a fiber amplifier

A model for spontaneous emission in active dielectric microstructures is given in terms of the classical electric field Green’s tensor and the quantum-mechanical operators for the generating currents. A formalism is given for calculating the Green’s tensor, which does not rely on the existence of a complete power orthogonal set of electromagnetic modes, and the formalism may therefore be applied to microstructures with gain and/or absorption. The Green’s tensor is calculated for an optical fiber amplifier, and the spontaneous emission in fiber amplifiers is studied with respect to the position, transition frequency, and vector orientation of a spatially localized current source. Radiation patterns are studied using a Poynting vector approach taking into account amplification or absorption from an active medium in the fiber.