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 plana r cavity. In a paper by Brorson, Yokoyama, and Ippen, the authors deri ved the minimum lifetime in a planar cavity to be one-third of the fre e space (no cavity) lifetime, and the appropriate mirror spacing was f ound to be one-half wavelength. In a paper by Yamamoto, Machida, and B jork, it was concluded that the lifetime for a half-wavelength-long ca vity was only two-thirds of the free space lifetime. In this paper, th e 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-hal f wavelength. This will influence the emission mode pattern in a way t hat, in general, is undesirable for a surface emitting laser. It is al so shown that a strictly half-wavelength-long cavity has a lifetime of two-thirds of the free space lifetime. The model employed has the att ractive feature that it allows a smooth transition from a fully open s ystem with the atom interacting with a mode continuum, to the fully cl osed system with quantized photon modes.