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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 17, Iss. 8 — Aug. 1, 2000
  • pp: 1475–1481

Fresnel formulas as Lorentz transformations

Juan José Monzón and Luis L. Sánchez-Soto  »View Author Affiliations


JOSA A, Vol. 17, Issue 8, pp. 1475-1481 (2000)
http://dx.doi.org/10.1364/JOSAA.17.001475


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Abstract

From a matrix formulation of the boundary conditions we obtain the fundamental invariant for an interface and a remarkably simple factorization of the interface matrix, which enables us to express the Fresnel coefficients in a new and compact form. This factorization allows us to recast the action of an interface between transparent media as a hyperbolic rotation. By exploiting the local isomorphism between SL(2, C) and the (3+1)-dimensional restricted Lorentz group SO(3, 1), we construct the equivalent Lorentz transformation that describes any interface.

© 2000 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(120.5700) Instrumentation, measurement, and metrology : Reflection
(120.7000) Instrumentation, measurement, and metrology : Transmission
(230.4170) Optical devices : Multilayers

History
Original Manuscript: October 19, 1999
Revised Manuscript: April 13, 2000
Manuscript Accepted: April 13, 2000
Published: August 1, 2000

Citation
Juan José Monzón and Luis L. Sánchez-Soto, "Fresnel formulas as Lorentz transformations," J. Opt. Soc. Am. A 17, 1475-1481 (2000)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-17-8-1475

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