Spontaneous emission in a confined structure with output coupling -Vacuum field and radiated field-

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1. ModelConventional cavity quantum electrodynamics is improved in that the output coupling and propagation effects are incorporated by defining field modes in the whole space cotaining the cavity. As a cavity model dielectric slab is taken. A two level atom interacts with the modes under dipole and rotating-wave approximation.2. One-dimensional analysisOrthoganal modes are derived by imposing a periodic boundary condition with a large period in the directions normal to the slab. The normalization constants of the mode functions have Fourier expansions representing multiple reflectins at the cavity surfaces. A delay-differential equation describing the emission process is obtained in the Schroedinger picture. It represents the effects of multiple reflection or mirror images. Based on this the emission spectum is shown to be expressed not only by the atomic decay but also by the spatial response function.3. Three-dimensional analysisBy imposing a three-dimensional periodic boundary conditions on the cavity-space system, orthogonal mode functions are derived. Limiting the atom-field system to the zero- and one-excitation subspace, a delay differential equation is derived in the Heisenderg picture. It reflects the effects of multiple reflecton or mirror images. Under a Markov approximation the spontaneous emission enhancement factors is obtained.4. Two atom emissionSpontaneous emission by two excited atoms in the cavity is analyzed in the Heisenberg picture and the total emission rate is calculated. There appear terms corresponding to one-atom emission and terms representing mutual interaction of the atoms. Numerical analysis of the latter terms show that the magnitude of the terms fall off as the inter-atomic distance increases over the mode diameter of the planar microcavity, thus elucidating the meaning of the mode diameter.