Theory of spontaneous emission in an optical cavity

Spontaneous emission in a one-dimensional Fabry-Perot-type optical cavity is analyzed quantum mechanically. Via a monolayer dielectric cavity model, expressions describing the atomic-location dependence of the emission intensities and the spectra observed on both sides of the cavity are obtained. The probability amplitude for the upper atomic state is analyzed and its time-evolution equation is given. The probability amplitude is shown to be proportional to ''the electric field amplitude for a single emission event'' introduced classically by Huang et al. [Appl. Phys. Lett. 61, 2961 (1992)]. An expression for the emission spectrum applicable to a general one-dimensional cavity structure is obtained.