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Journal of Modern Optics

Spontaneous emission between mirrors

Peter W. Milonni

Published Sep 10, 2007• 6 citations
Publisher

Abstract

Some of the physics of spontaneous emission in cavities is revisited, including the enhancement of the decay rate by the cavity Q, the nature of inhibited spontaneous emission, and the ‘excess noise’ in lossy laser cavities.
DOI
10.1080/09500340701391142

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A single inverted two-level atom is used as a theoretical model for a quantum noise detector to investigate fundamental properties of excess noise in an unstable optical resonator. For a symmetric unstable spherical mirror cavity, we develop an analytic quantum description of the field in terms of a complete set of normalizable biorthogonal quasimodes and adjoint modes. Including the interaction with a single two-level atom leads to a description analogous to the Jaynes-Cummings model with modified coupling constants. One finds a strong position and geometry-dependent atomic decay probability proportional to the square root K\sqrt{K}K​ of the excess noise factor K at the cavity center. Introducing an additional homogeneous gain one recovers the K-fold emission enhancement that has been predicted before for the linewidth of an unstable cavity laser. We find that excess noise may be viewed as a spatial redistribution of the field quantum noise inside the resonator. Taking a position average of the atomic decay rate over the cavity volume leads to a cancellation of the excess noise enhancement.
The spontaneous emission of an excited atom in a lossy cavity with nonorthogonal eigenmodes is analyzed. The quantum Langevin formalism is used to describe the dynamics of the spontaneous decay. The analysis shows that the spontaneous decay is modified by the Q value and the effective mode volume factor of each cavity eigenmode. The effective mode volume is generalized for cavities with nonorthogonal modes, which can be a very significant modification in the microcavity regime. It is shown that the spontaneous decay is not enhanced by the excess noise factor as claimed by other analyses.