Quantum theory of dispersive electromagnetic modes

Drummond, P. D. and Hillery, M. (1999) Quantum theory of dispersive electromagnetic modes. Physical Review A, 59 1: 691-707. doi:10.1103/PhysRevA.59.691

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Author Drummond, P. D.
Hillery, M.
Title Quantum theory of dispersive electromagnetic modes
Journal name Physical Review A   Check publisher's open access policy
ISSN 1050-2947
1094-1622
Publication date 1999-01-01
Sub-type Article (original research)
DOI 10.1103/PhysRevA.59.691
Open Access Status File (Publisher version)
Volume 59
Issue 1
Start page 691
End page 707
Total pages 17
Place of publication College Park, MD, United States
Publisher American Physical Society
Language eng
Abstract A quantum theory of dispersion for an inhomogeneous solid is obtained, from a starting point of multipolar coupled atoms interacting with an electromagnetic field. The dispersion relations obtained are equivalent to the standard classical Sellmeir equations obtained from the Drude-Lorentz model. In the homogeneous (planewave) case, we obtain the detailed quantum mode structure of the coupled polariton fields, and show that the mode expansion in all branches of the dispersion relation is completely defined by the refractive index and the group velocity for the polaritons. We demonstrate a straightforward procedure for exactly diagonalizing the Hamiltonian in one-, two-, or three-dimensional environments, even in the presence of longitudinal phonon-exciton dispersion, and an arbitrary number of resonant transitions with different frequencies. This is essential, since it is necessary to include at least one phonon (IR) and one exciton (UV) mode, in order to represent dispersion in transparent solid media accurately. Our method of diagonalization does not require an explicit solution of the dispersion relation, but relies instead on the analytic properties of Cauchy contour integrals over all possible mode frequencies. When there is longitudinal-phonon dispersion, the relevant group-velocity term is modified so that it only includes the purely electromagnetic part of the group velocity. [S1050-2947(98)05811-9].
Keyword Optics
Physics, Atomic, Molecular & Chemical
Nondemolition Measurement
Optical Solitons
Quantization
Media
Q-Index Code C1
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Physical Sciences Publications
 
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Created: Tue, 10 Jun 2008, 23:50:16 EST