Input-Output from Optical Cavities: Quasi-Mode Theory

Abstract

Many situations in quantum optics and cavity quantum electrodynamics involve interaction processes between the quantum EM field and radiating atoms in the presence of passive, lossless, non dispersive, linear, classical optical systems such as cavities, beam splitters. Such optical devices lead to important (though classical) effects in the treatment of the physical processes involved.The classical optics device can be modelled via the spatially dependent electric permittivity e(R) (and magnetic permeability, for magnetic media) functions for the media constituting the device. The associated vector mode functions, being the exact solutions of the generalised Helmholtz equation involving the true permittivity (and permeability) functions, incorporate the device characteristics into the quantum EM field description, enabling macroscopic canonical quantization of the EM field and radiative atomic charges to be carried out1. Canonical quantization based on such “true” or “universe” mode functions shows the quantum EM field to be equivalent to uncoupled quantum harmonic oscillators, one for each mode and thereby justifying the photon model for quantum optics in such non free space situations1. The true mode approach provides a useful foundation for development of formal theory in quantum optics. In situations where optical cavities are involved, the true mode functions generally fall into at least two categories — the “internal” mode functions that are large inside and small outside the cavity, and the “external” mode functions where the reverse applies. Many physical processes such as the input and output of energy and other measurable quantities between the inside and the outside of optical cavities can be studied via true mode functions. Essentially, atoms excited inside the cavity interchange energy with internal modes and the escape of this energy from the cavity depends on these modes having small but non-zero amplitudes outside.