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Europhysics Letters (EPL)

Spontaneous emission in three-dimensional photonic crystals with an incomplete band gap

Shi-Yao Zhu, G. X Li, Yuping Yang, Fangfei Li

Published Apr 1, 2003• 21 citations
Publisher

Abstract

The decay and radiation of an atom in a photonic crystal with an incomplete gap was investigated. If the transition frequency is close to a band edge, the Weisskopf-Wigner approximation is not applicable and the decay is nonexponential. The decay could be greatly enhanced or decreased by the self-emitted field.
DOI
10.1209/epl/i2003-00348-5

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We investigate the dynamical properties of the radiation field emitted from an excited two-level atom in a photonic crystal. If the transition frequency of the atom lies within a certain frequency range above the band edge, the emitted field consists of two components that show a different decay dynamics. In particular it is shown that one field component decreases faster than the atomic population with a decay constant depending on the distance from the atom. As a consequence, the decay rate of the electromagnetic field is spatially varying and, in general, can not be identified with the corresponding rate for the atomic population.
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In the first part of this introductory review we outline the developments in photonic band gap materials from the physics of photonic band gap formation to the fabrication and potential applications of photonic crystals. We briefly describe the analogies between electron and photon localization, present a simple model of a band structure calculation and describe some of the techniques used for fabricating photonic crystals. Also some applications in the field of photonics and optical circuitry are briefly presented. In the second part, we discuss the consequences for the interaction between an atom and the light field when the former is embedded in photonic crystals of a specific type, exhibiting a specific form of a gap in the density of states. We first briefly review the standard treatment (Weisskopf – Wigner theory) in describing the dynamics of spontaneous emission in free space from first principles, and then proceed by explaining the alterations needed to properly treat the case of a two-level atom embedded in a photonic band gap material.