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

1. 通过定义包含空腔的整个空间中的场模式，改进了传统的空腔量子电动力学，将输出耦合和传播效应纳入其中。以介质板为空腔模型。二能级原子在偶极子和旋转波近似下与模相互作用。一维分析正交模态是通过施加一个周期边界条件，在与板垂直的方向上具有大周期得到的。模态函数的归一化常数的傅里叶展开式表示在腔表面的多次反射。在薛定谔图中得到了描述发射过程的时滞微分方程。它代表多重反射或镜像的效果。在此基础上，表明发射光谱不仅可以用原子衰变表示，而且可以用空间响应函数表示。通过对空腔空间系统施加三维周期边界条件，推导出正交模态函数。将原子场系统限制在零激励和单激励子空间中，导出了海森堡图像中的延迟微分方程。它反映了多重反射或镜像的效果。在马尔可夫近似下，得到了自发发射增强因子。双原子发射用海森堡图分析了两个受激原子在腔内的自发发射，并计算了总发射率。出现了对应于单原子发射的项和代表原子相互作用的项。对后一项的数值分析表明，随着原子间距离在平面微腔模直径上的增加，后一项的大小逐渐减小，从而阐明了模直径的含义。

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.