Field quantization, photons and non-Hermitean modes

Brown, S. A. and Dalton, B. J. (2002) Field quantization, photons and non-Hermitean modes. Journal of Modern Optics, 49 7: 1009-1041. doi:10.1080/09500340110095625


Author Brown, S. A.
Dalton, B. J.
Title Field quantization, photons and non-Hermitean modes
Journal name Journal of Modern Optics   Check publisher's open access policy
ISSN 0950-0340
Publication date 2002-01-01
Sub-type Article (original research)
DOI 10.1080/09500340110095625
Open Access Status Not Open Access
Volume 49
Issue 7
Start page 1009
End page 1041
Total pages 33
Place of publication [England]
Publisher Taylor & Francis
Language eng
Subject C1
240201 Theoretical Physics
780102 Physical sciences
0205 Optical Physics
0206 Quantum Physics
Abstract Field quantization in unstable optical systems is treated by expanding the vector potential in terms of non-Hermitean (Fox-Li) modes. We define non-Hermitean modes and their adjoints in both the cavity and external regions and make use of the important bi-orthogonality relationships that exist within each mode set. We employ a standard canonical quantization procedure involving the introduction of generalized coordinates and momenta for the electromagnetic (EM) field. Three-dimensional systems are treated, making use of the paraxial and monochromaticity approximations for the cavity non-Hermitean modes. We show that the quantum EM field is equivalent to a set of quantum harmonic oscillators (QHOs), associated with either the cavity or the external region non-Hermitean modes, and thus confirming the validity of the photon model in unstable optical systems. Unlike in the conventional (Hermitean mode) case, the annihilation and creation operators we define for each QHO are not Hermitean adjoints. It is shown that the quantum Hamiltonian for the EM field is the sum of non-commuting cavity and external region contributions, each of which can be expressed as a sum of independent QHO Hamiltonians for each non-Hermitean mode, except that the external field Hamiltonian also includes a coupling term responsible for external non-Hermitean mode photon exchange processes. The non-commutativity of certain cavity and external region annihilation and creation operators is associated with cavity energy gain and loss processes, and may be described in terms of surface integrals involving cavity and external region non-Hermitean mode functions on the cavity-external region boundary. Using the essential states approach and the rotating wave approximation, our results are applied to the spontaneous decay of a two-level atom inside an unstable cavity. We find that atomic transitions leading to cavity non-Hermitean mode photon absorption are associated with a different coupling constant to that for transitions leading to photon emission, a feature consequent on the use of non-Hermitean mode functions. We show that under certain conditions the spontaneous decay rate is enhanced by the Petermann factor.
Keyword Optics
Cavity Quantum Electrodynamics
Macroscopic Canonical Quantization
Excess Noise
Spontaneous Emission
Laser
Q-Index Code C1

Document type: Journal Article
Sub-type: Article (original research)
Collection: Centre for Advanced Imaging Publications
 
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Created: Wed, 15 Aug 2007, 03:13:45 EST