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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. 20, Iss. 9 — Sep. 1, 2003
  • pp: 1812–1817

Hyperbolic reflections as fundamental building blocks for multilayer optics

Alberto G. Barriuso, Juan J. Monzón, Luis L. Sánchez-Soto, and José F. Cariñena  »View Author Affiliations


JOSA A, Vol. 20, Issue 9, pp. 1812-1817 (2003)
http://dx.doi.org/10.1364/JOSAA.20.001812


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Abstract

We re-elaborate on the basic properties of lossless multilayers by using bilinear transformations. We study some interesting properties of the multilayer transfer function in the unit disk, showing that hyperbolic geometry turns out to be an essential tool for understanding multilayer action. We use a simple trace criterion to separate multilayers into three classes that represent rotations, translations, or parallel displacements. Moreover, we show that these three actions can be decomposed as a product of two reflections in hyperbolic lines. Therefore, we conclude that hyperbolic reflections can be considered as the basic pieces for a deeper understanding of multilayer optics.

© 2003 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: February 13, 2003
Revised Manuscript: April 11, 2003
Manuscript Accepted: April 11, 2003
Published: September 1, 2003

Citation
Alberto G. Barriuso, Juan J. Monzón, Luis L. Sánchez-Soto, and José F. Cariñena, "Hyperbolic reflections as fundamental building blocks for multilayer optics," J. Opt. Soc. Am. A 20, 1812-1817 (2003)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-20-9-1812

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