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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 19, Iss. 3 — Mar. 1, 2002
  • pp: 603–609

Understanding multilayers from a geometrical viewpoint

Teresa Yonte, Juan J. Monzón, Luis L. Sánchez-Soto, José F. Cariñena, and Carlos López-Lacasta  »View Author Affiliations

JOSA A, Vol. 19, Issue 3, pp. 603-609 (2002)

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We reelaborate on the basic properties of lossless multilayers. We show that the transfer matrices for these multilayers have essentially the same algebraic properties as the Lorentz group SO(2, 1) in a (2+1)-dimensional space–time as well as the group SL(2, ℝ) underlying the structure of the ABCD law in geometrical optics. By resorting to the Iwasawa decomposition, we represent the action of any multilayer as the product of three matrices of simple interpretation. This group-theoretical structure allows us to introduce bilinear transformations in the complex plane. The concept of multilayer transfer function naturally emerges, and its corresponding properties in the unit disk are studied. We show that the Iwasawa decomposition is reflected at this geometrical level in three simple actions that can be considered the basic pieces for a deeper understanding of the multilayer behavior. We use the method to analyze in detail a simple practical example.

© 2002 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

Original Manuscript: April 18, 2001
Revised Manuscript: July 10, 2001
Manuscript Accepted: August 7, 2001
Published: March 1, 2002

Teresa Yonte, Juan J. Monzón, Luis L. Sánchez-Soto, José F. Cariñena, and Carlos López-Lacasta, "Understanding multilayers from a geometrical viewpoint," J. Opt. Soc. Am. A 19, 603-609 (2002)

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