On the spontaneous lifetime change in an ideal planar microcavity-transition from a mode continuum to quantized modes

The spontaneous emission lifetime of an atom is known to be influenced by its environment. In general, the lifetime will be different if the atom is suspended in free space than if it is placed inside a cavity. A simple cavity geometry in which to explore this effect is the planar cavity. In a paper by Brorson, Yokoyama, and Ippen, the authors derived the minimum lifetime in a planar cavity to be one-third of the free space (no cavity) lifetime, and the appropriate mirror spacing was found to be one-half wavelength. In a paper by Yamamoto, Machida, and Bjork, it was concluded that the lifetime for a half-wavelength-long cavity was only two-thirds of the free space lifetime. In this paper, the discrepancy between these results is clarified and it is shown that the shortest lifetime is indeed one-third of the free space lifetime; but to achieve this, the cavity has to be slightly longer than one-half wavelength. This will influence the emission mode pattern in a way that, in general, is undesirable for a surface emitting laser. It is also shown that a strictly half-wavelength-long cavity has a lifetime of two-thirds of the free space lifetime. The model employed has the attractive feature that if allows a smooth transition from a fully open system with the atom interacting with a mode continuum, to the fully closed system with quantized photon modes.>