Quasimode theory of quantum optical processes in photonic band gap materials

Dalton, B. J. and Garraway, B. M. (2002) Quasimode theory of quantum optical processes in photonic band gap materials. Journal of Modern Optics, 49 5/6: 947-958. doi:10.1080/09500340110109034

Author Dalton, B. J.
Garraway, B. M.
Title Quasimode theory of quantum optical processes in photonic band gap materials
Journal name Journal of Modern Optics   Check publisher's open access policy
ISSN 0950-0349
Publication date 2002
Sub-type Article (original research)
DOI 10.1080/09500340110109034
Volume 49
Issue 5/6
Start page 947
End page 958
Total pages 12
Place of publication [England]
Publisher Taylor & Francis
Collection year 2002
Language eng
Subject C1
240201 Theoretical Physics
780102 Physical sciences
0205 Optical Physics
0206 Quantum Physics
Abstract This paper deals with atomic systems coupled to a structured reservoir of quantum EM field modes, with particular relevance to atoms interacting with the field in photonic band gap materials. The case of high Q cavities has been treated elsewhere using Fano diagonalization based on a quasimode approach, showing that the cavity quasimodes are responsible for pseudomodes introduced to treat non-Markovian behaviour. The paper considers a simple model of a photonic band gap case, where the spatially dependent permittivity consists of a constant term plus a small spatially periodic term that leads to a narrow band gap in the spectrum of mode frequencies. Most treatments of photonic band gap materials are based on the true modes, obtained numerically by solving the Helmholtz equation for the actual spatially periodic permittivity. Here the field modes are first treated in terms of a simpler quasimode approach, in which the quasimodes are plane waves associated with the constant permittivity term. Couplings between the quasimodes occur owing to the small periodic term in the permittivity, with selection rules for the coupled modes being related to the reciprocal lattice vectors. This produces a field Hamiltonian in quasimode form. A matrix diagonalization method may be applied to relate true mode annihilation operators to those for quasimodes. The atomic transitions are coupled to all the quasimodes, and the true mode atom-EM field coupling constants (one-photon Rabi frequencies) are related to those for the quasimodes and also expressions are obtained for the true mode density. The results for the one-photon Rabi frequencies differ from those assumed in other work. Expressions for atomic decay rates are obtained using the Fermi Golden rule, although these are valid only well away from the band gaps.
Keyword Optics
Macroscopic Canonical Quantization
Spontaneous Emission
Mode Theory
Q-Index Code C1

Document type: Journal Article
Sub-type: Article (original research)
Collection: Centre for Advanced Imaging Publications
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Created: Tue, 14 Aug 2007, 17:13:43 EST