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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. 22, Iss. 4 — Apr. 1, 2005
  • pp: 689–696

Analytical investigation of stratified isotropic media

Konstantin A. Vytovtov  »View Author Affiliations


JOSA A, Vol. 22, Issue 4, pp. 689-696 (2005)
http://dx.doi.org/10.1364/JOSAA.22.000689


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Abstract

A rigorous analytical approach for investigating a stratified medium with an arbitrary finite number of homogeneous isotropic layers in a period is developed. The approach is based on the translation matrix method. It is well known that the translation matrix for a period must be found as the product of the layer matrices. It is proved that this matrix can be represented as a finite sum of trigonometric matrices, and thus the dispersion relation of a stratified medium is written in an analytical form. All final expressions are obtained in terms of the constitutive parameters. To this author’s knowledge, this is the first time that the new sign function that allows us to develop the presented analytical results has been described. The condition of the existence of a wave with an arbitrary period divisible by a structure period is found in analytical form. It is proved that changing the layer arrangement within the period does not affect the structure of the transmission and absorption bands.

© 2005 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(000.6800) General : Theoretical physics
(080.2710) Geometric optics : Inhomogeneous optical media
(080.2720) Geometric optics : Mathematical methods (general)
(080.2730) Geometric optics : Matrix methods in paraxial optics
(260.2110) Physical optics : Electromagnetic optics

History
Original Manuscript: June 7, 2004
Revised Manuscript: September 20, 2004
Manuscript Accepted: September 20, 2004
Published: April 1, 2005

Citation
Konstantin A. Vytovtov, "Analytical investigation of stratified isotropic media," J. Opt. Soc. Am. A 22, 689-696 (2005)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-22-4-689

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