OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 24, Iss. 11 — Nov. 1, 2007
  • pp: 3564–3572

Analytical investigation of one-dimensional magnetoelectric photonic crystals. The 2 × 2 matrix approach

K. A. Vytovtov and Yu. S. Tarasenko  »View Author Affiliations

JOSA A, Vol. 24, Issue 11, pp. 3564-3572 (2007)

View Full Text Article

Enhanced HTML    Acrobat PDF (165 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The wave behavior within a one-dimensional magnetoelectric photonic crystal is studied. A very simple, accurate analytical method of investigating the wave transmission along an arbitrary direction is developed. The method is based on the 2 × 2 translation matrix instead of the well-known 4 × 4 matrices. The TE- and TM-wave decomposition of a total wave in a one-dimensional magnetoelectric stack is presented in an accurate analytical form, to our knowledge for the first time, and the physical interpretation of the translation matrix determinant is given, also as far as we know for the first time.

© 2007 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(000.3870) General : Mathematics
(080.2730) Geometric optics : Matrix methods in paraxial optics
(210.3820) Optical data storage : Magneto-optical materials
(260.1180) Physical optics : Crystal optics
(260.2110) Physical optics : Electromagnetic optics
(350.7420) Other areas of optics : Waves

ToC Category:
Physical Optics

Original Manuscript: July 26, 2007
Revised Manuscript: September 19, 2007
Manuscript Accepted: September 20, 2007
Published: October 23, 2007

K. A. Vytovtov and Yu. S. Tarasenko, "Analytical investigation of one-dimensional magnetoelectric photonic crystals. The 2×2 matrix approach," J. Opt. Soc. Am. A 24, 3564-3572 (2007)

Sort:  Year  |  Journal  |  Reset  


  1. E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987). [CrossRef] [PubMed]
  2. D. Felbacq, B. Guizal, and F. Zolla, "Wave propagation in one-dimensional photonic crystals," Opt. Commun. 152, 119-126 (1998). [CrossRef]
  3. S. Khorasan and K. Mehrany, "Differential transfer-matrix method for solution of one-dimensional linear nonhomogeneous optical structures," J. Opt. Soc. Am. B 20, 91-96 (2003). [CrossRef]
  4. C. Jamois, R. B. Wehrspohn, L. C. Andreani, C. Hermann, O. Hess, and U. Gosele, "Silicon-based two-dimensional photonic crystal waveguides," Photonics Nanostruct. Fundam. Appl. 1, 1-13 (2003). [CrossRef]
  5. E. B. McDaniel, J. W. P. Hsu, L. S. Goldner, R. J. Jonucci, E. L. Shirley, and G. W. Bryant, "Local characterization of transmission properties of a two-dimensional crystal," Phys. Rev. B 55, 10878-10882 (1997). [CrossRef]
  6. A. Chutinan and S. Noda, "Spiral three-dimensional photonic-band-gap structure," Phys. Rev. B 57, R2006-R2008 (1998). [CrossRef]
  7. S. R. Kennedy, M. J. Brett, H. Miguez, O. Toader, and S. John, "Optical properties of a three-dimensional silicon square spiral photonic crystal," Photonics Nanostruct. Fundam. Appl. 1, 37-42 (2003). [CrossRef]
  8. L. I. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, and Th. Rasing, "Magnetic photonic crystals," J. Phys. D 36, 277-287 (2003). [CrossRef]
  9. A. Figotin and I. Vitebsky, "Nonreciprocal magnetic photonic crystals," Phys. Rev. E 63, 066609-1-066609-17 (2001). [CrossRef]
  10. Ph. Russell, T. Birks, and F. D. Lloyd-Lucas, Photonic Bloch Waves and Photonic Band Gaps (Plenum, 1995).
  11. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991). [CrossRef]
  12. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley-Interscience, 1984).
  13. K. Sakoda, Optical Properties of Photonic Crystals (Springer, 2001).
  14. I. H. Zabel and D. Stroud, "Photonic band structures of optically anisotropic periodic arrays," Phys. Rev. B 48, 5004-5021 (1993). [CrossRef]
  15. P. Yeh, "Extended Jones matrix method," J. Opt. Soc. Am. 72, 507-513 (1982). [CrossRef]
  16. P. Yeh, "Electromagnetic propagation in birefringent layered media," J. Opt. Soc. Am. 69, 742-756 (1979). [CrossRef]
  17. D. W. Berreman, "Optics in stratified and anisotropic media: 4×4-matrix formulation," J. Opt. Soc. Am. 62, 502-510 (1972). [CrossRef]
  18. S. Teitler and B. W. Henvis, "Refraction in stratified, anisotropic media," J. Opt. Soc. Am. 60, 830-834 (1970). [CrossRef]
  19. D. Ager and H. P. Hughes, "Optical properties of stratified systems including lamellar gratings," Phys. Rev. B 44, 13452-13465 (1991). [CrossRef]
  20. M. Qiu and S. He, "Optimal design of a two-dimensional photonic crystal of square lattice with a large complete two-dimensional bandgap," J. Opt. Soc. Am. B 17, 1027-1030 (2000). [CrossRef]
  21. K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, "Photonic band gaps in three dimensions: new layer-by-layer periodic structures," Solid State Commun. 89, 413-416 (1994). [CrossRef]
  22. J. K. Hale, Oscillations in Nonlinear Systems (McGraw-Hill, 1963).
  23. G. Kauderer, Nichtlineare Mechanik (Springer-Verlag, 1958). [CrossRef]
  24. R. C. Jones, "New calculus for the treatment of optical system I. Description and discussion of the calculus," J. Opt. Soc. Am. 31, 488-493 (1941). [CrossRef]
  25. F. Gharadjedaghi and J. Robert, "Comportement electro-optique d'une structure nématique en hélice--application à l'affichage," Rev. Phys. Appl. 11, 467-473 (1976). [CrossRef]
  26. A. Lien, "The general and simplified Jones matrix representations for the high pretilt twisted nematic cell," J. Appl. Phys. 67, 2853-2856 (1990). [CrossRef]
  27. H. L. Ong, "Electro-optics of a twisted nematic liquid crystal display by 2×2 propagation matrix at oblique incidence," Jpn. J. Appl. Phys., Part 1 30, L1028-L1031 (1991). [CrossRef]
  28. M. Mansuripur, "Analysis of multilayered thin-film structures containing magneto-optic and anisotropic media at oblique incidence using 2×2 matrices," J. Appl. Phys. 67, 6466-6475 (1990). [CrossRef]
  29. M. Mansuripur, The Principles of Magneto-Optical Recording (Cambridge U. Press, 1995). [CrossRef]
  30. I. Abdulhalim, "Analytic propagation matrix method for anisotropic magnetooptic layered media," J. Opt. A, Pure Appl. Opt. 2, 557-564 (2000). [CrossRef]
  31. H. Wohler and M. E. Becker, "Numerical modeling of LCD electro-optical performance," Opto-Electron. Rev. 10, 23-33 (2002).
  32. B. Lax and K. J. Button, Microwave Ferrite and Ferrimagnetics (McGraw-Hill, 1962).
  33. L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media (Pergamon, 1984).
  34. N. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light, 5th ed. (Pergamon, 1975), Sec. 11.3.
  35. P. Lancaster and M. Tismenetsky, The Theory of Matrices With Applications, 2nd ed. (Academic, 1985).
  36. J. A. Kong, Electromagnetic Wave Theory, 2nd ed. (Wiley, 1990).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited