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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • 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)

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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

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

Konstantin A. Vytovtov, "Analytical investigation of stratified isotropic media," J. Opt. Soc. Am. A 22, 689-696 (2005)

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  1. C. Elachi, “Wave in active and passive periodic structures: a review,” Proc. IEEE 64, 1666–1698 (1976). [CrossRef]
  2. P. Yeh, A. Yariv, C. Hong, “Electromagnetic propagation in periodic stratified media. I. General theory,” J. Opt. Soc. Am. 67, 423–438 (1977). [CrossRef]
  3. P. Yeh, A. Yariv, C. Hong, “Electromagnetic propagation in periodic stratified media. II. Birefringence, phase matching, and x-ray lasers,” J. Opt. Soc. Am. 67, 438–448 (1977). [CrossRef]
  4. M. Born, E. Wolf, Principles of Optics, 3rd ed. (Pergamon, New York, 1965).
  5. P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).
  6. T. Tamir, “Scattering of electromagnetic waves by a sinusoidally stratified half-space: part II,” Can. J. Phys. 44, 2461–2494 (1966). [CrossRef]
  7. G. A. Gevorkyan, “On the theory of propagation of electromagnetic waves in a waveguide with a multiperiodically modulated dielectric filling,” Physica A 241, 236–239 (1997). [CrossRef]
  8. P. C. Waterman, “Scattering by periodic surfaces,” J. Acoust. Soc. Am. 57, 791–802 (1975). [CrossRef]
  9. S. L. Chuang, J. A. Kong, “Wave scattering from a periodic dielectric surface for a general angle of incidence,” Radio Sci. 17, 545–557 (1982). [CrossRef]
  10. A. Boag, Y. Leviatan, A. Boag, “Analysis of two-dimensional electromagnetic scattering from nonplanar periodic surfaces using a strip current model,” IEEE Trans. Antennas Propag. 37, 1437–1451 (1989). [CrossRef]
  11. J. J. Pesque, D. P. Bouche, R. Mittra, “Optimization of multilayer antireflection coatings using an optimal control method,” IEEE Trans. Microwave Theory Tech. 40, 1789–1796 (1992). [CrossRef]
  12. G. A. Ybara, S. M. Wu, G. L. Bilbro, S. H. Ardalan, C. P. Hearn, R. T. Neece, “Optimal signal prossing of frequency-stepped SW radar data,” IEEE Trans. Microwave Theory Tech. 43, 94–105 (1995). [CrossRef]
  13. L. Brillouin, M. Parodi, Propagation des Ondes dans les Milieux Périodiques (Masson et Cie, Editeurs, Paris, 1956).
  14. N. Blombergen, A. J. Sievers, “Nonlinear optical properties of periodic laminar structures,” Appl. Phys. Lett. 17, 483–485 (1970). [CrossRef]
  15. A. A. Bulgakov, S. A. Bulgakov, M. Nieto-Vesperinas, “Inhomogeneous waves and energy localization in dielectric superlattices,” Phys. Rev. B 58, 4438–4448 (1998). [CrossRef]
  16. F. Abelès, “Recherches sur la propagation des ondes electromagnétiques sinusoidales dans les milieux stratifiés. Application aux conches minces,” Ann. Phys. (Paris) 5, 596–640, 706–782 (1950).
  17. G. Gambill, “Criteria for parametric instability for linear differential systems with periodic coefficients,” Riv. Mat. Univ. Parma 6, 37–43 (1955).
  18. J. K. Hale, Oscillations in Nonlinear Systems (McGraw-Hill, New York, 1963).
  19. A. H. Nayfer, Introduction to Pertrubation Techniques (Wiley, New York, 1981).
  20. L. R. Lewis, A. Hessel, “Propagation characteristics of a periodic array of dielectric slabs,” IEEE Trans. Microwave Theory Tech. 19, 276–286 (1971). [CrossRef]
  21. J. C. W. A. Costa, A. J. Giarola, “Electromagnetic wave propagation in multilayered dielectric periodic structures,” IEEE Trans. Antennas Propag. 41, 1432–1438 (1993). [CrossRef]
  22. J. W. Strutt, Rayleigh, “On the maintenance of vibrations by forces of double frequency, and on the propagation of waves through a medium endowed with a periodic structure,” Philos. Mag. 24, 145–159 (1887). [CrossRef]
  23. F. Bloch, “Quantenmechanik der elektronen in kristallgittern,” Z. Phys. 52, 555–500 (1928). [CrossRef]
  24. J. R. Pierce, “Coupling of modes of propagation,” J. Appl. Phys. 25, 179–183 (1954). [CrossRef]
  25. D. L. Jaggard, C. Elachi, “Floquet and coupled-waves analysis of higher-order Bragg coupling in a periodic medium,” J. Opt. Soc. Am. 66, 674–682 (1976). [CrossRef]
  26. D. W. Berreman, “Optics in straified and anisotropic media: 4×4-matrix formulation,” J. Opt. Soc. Am. 62, 502–510 (1972). [CrossRef]
  27. S. Teitler, B. W. Henvis, “Refraction in stratified, anisotropic media,” J. Opt. Soc. Am. 60, 830–834 (1970). [CrossRef]
  28. D. Ager, H. P. Hughes, “Optical properties of stratified systems including lamellar gratings,” Phys. Rev. B 44, 13452–13465 (1991). [CrossRef]
  29. W. C. Chew, Waves and Fields in Inhomogeneous Media (Van Nostrand Reinhold, New York, 1990), 136–140.
  30. K. Vytovtov, “A model of a two-dimensional linear parametric system with a step pumping,” in Proceedings XXXII Sympozjon PTMTS Modelowanie w Mechanice (Gliwice, Poland, 1998), pp. 377–380.
  31. Yu. M. Terent’ev, K. A. Vytovtov, “Investigation of wave behavior in periodical magnetized ferrite,” Electromagn. Waves Electron. Syst. 4, 37–42 (1999).
  32. Yu. M. Terent’ev, K. A. Vytovtov, “Transformation matrix of N-layer periodic medium with anisotropic layers,” J. Commun. Technol. Electron. 45, 255–257 (2000).
  33. K. A. Vytovtov, “The analytical method of investigation of periodic layered media with uniaxial bianisotropy,” J. Commun. Technol. Electron. 46, 144–150 (2001).
  34. K. A. Vytovtov, “Propagation conditions of a harmonic waves within bianisotropic periodic layered media,” in Proceedings of 30th European Microwave Conference (Paris, 2000), Vol. 2, pp. 238–241.

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