THEORY OF A SHORT OPTICAL CAVITY WITH DIELECTRIC MULTILAYER FILM MIRRORS

A theory for a one-dimensional optical cavity with multi-layer dielectric film mirrors is developed by the matrix method, where normalized orthogonal mode functions with a continuous spectrum are derived both inside and outside the cavity, and the field is quantized with them. The theory provides an exact means to study the mode characteristics of, and hence the spontaneous emission in a short optical cavity with mirrors of finite thickness. On the basis of this theory, we study in detail a short optical cavity with a length of half-wavelength and mirrors of quarter-wavelength single-layer dielectric film. The result shows that the resonant frequency is slightly different from that in a cavity of the same length and the same mirror reflectivity but with two delta-function like mirrors. furthermore, with the derived mode functions the spontaneous emission from a two-level atom in such a cavity is analyzed under a perturbation approximation, and the result shows that the spontaneous emission in the cavity is enhanced by the cavity quality factor Q when the atom is at the antinode and is inhibited by the factor 1 / Q when the atom is at the node.