Geometrical interpretation of optical absorption

We reinterpret the transfer matrix for an absorbing system in very simple geometrical terms. In appropriate variables, the system appears as performing a Lorentz transformation in a (1 + 3)-dimensional space. Using homogeneous coordinates, we map that action on the unit sphere, which is at the realm...

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Bibliographic Details
Published in:Physical review. A, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 2011-08, Vol.84 (2), Article 023830
Main Authors: Monzón, J. J., Barriuso, A. G., Sánchez-Soto, L. L., Montesinos-Amilibia, J. M.
Format: Article
Language:English
Subjects:
ABSORPTIVITY
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
COORDINATES
GEOMETRY
LORENTZ TRANSFORMATIONS
MATHEMATICAL METHODS AND COMPUTING
OPTICAL DISPERSION
THREE-DIMENSIONAL CALCULATIONS
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Summary:We reinterpret the transfer matrix for an absorbing system in very simple geometrical terms. In appropriate variables, the system appears as performing a Lorentz transformation in a (1 + 3)-dimensional space. Using homogeneous coordinates, we map that action on the unit sphere, which is at the realm of the Klein model of hyperbolic geometry. The effects of absorption appear then as a loxodromic transformation, that is, a rhumb line crossing all the meridians at the same angle.
ISSN:1050-2947
1094-1622
DOI:10.1103/PhysRevA.84.023830