Quantum Electrodynamics in Resonant Cavities
Abstract
In this work we study the radiative properties of an atom inside a resonant cavity. By using a phenomenological model in which field modes are represented as damped harmonic oscillators, we study the atomic spontaneous emission process from the viewpoint of coupled harmonic oscillators. To examine this model, we show explicitly for a onedimensional model of an open cavity that cavity modes are characterized by complex frequencies; their wave functions are determined by a complex boundary condition on the open side of the cavity. A completeness relation for these wave functions is provided, and a new representation of fields is discussed. Within this formalism, cavity modes in a threedimensional open cavity, such as a laser cavity, are determined by a mixed boundaryvalue problem of the wave equation. We develop an integral representation for the wave functions, and integral equations for the mode structure. When a short wavelength approximation is made, the exact integral equations are shown to yield the wellknown FoxLi integral equations for modes in laser resonators. Calculations using the exact formalism are also presented for situations in which the FoxLi formulation does not apply. We then discuss the influence of the resonant cavity on the spontaneous emission as exhibited by the position and orientation dependence of the radiation process. The spectral response function is introduced from first principles; it determines the radiative properties of an atom. Sample calculations of this function are presented for some cavities in which the mode functions can be found explicitly. An alternative means of calculating this function is to use an integral representation for it. Its application to an atom in a laser cavity leads to a multiple reflection expansion, and to a result in agreement with the phenomenological picture introduced earlier. The latter approach is presented in detail for the interesting case of a concentric laser cavity.
 Publication:

Ph.D. Thesis
 Pub Date:
 1993
 Bibcode:
 1993PhDT.......122H
 Keywords:

 LASER;
 Physics: Optics; Physics: Atomic