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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Henry M. Van Driel
  • Vol. 24, Iss. 7 — Jul. 1, 2007
  • pp: 1603–1609

Band structure and Bloch states in birefringent one-dimensional magnetophotonic crystals: an analytical approach

Miguel Levy and Amir A Jalali  »View Author Affiliations

JOSA B, Vol. 24, Issue 7, pp. 1603-1609 (2007)

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An analytical formulation for the band structure and Bloch modes in elliptically birefringent magnetophotonic crystals is presented. The model incorporates both the effects of gyrotropy and linear birefringence generally present in magneto-optic thin-film devices. Full analytical expressions are obtained for the dispersion relation and Bloch modes in a layered-stack photonic crystal, and their properties are analyzed. It is shown that other models recently discussed in the literature are contained as special limiting cases of the formulation presented herein.

© 2007 Optical Society of America

OCIS Codes
(230.3810) Optical devices : Magneto-optic systems
(260.1440) Physical optics : Birefringence
(260.2030) Physical optics : Dispersion

ToC Category:
Physical Optics

Original Manuscript: February 27, 2007
Manuscript Accepted: March 21, 2007
Published: June 15, 2007

Miguel Levy and Amir A Jalali, "Band structure and Bloch states in birefringent one-dimensional magnetophotonic crystals: an analytical approach," J. Opt. Soc. Am. B 24, 1603-1609 (2007)

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  1. A. Figotin and I. Vitebsky, "Nonreciprocal magnetic photonic crystals," Phys. Rev. E 63, 066609 (2001). [CrossRef]
  2. A. Fedyanin, O. Aktsipetrov, D. Kobayashi, K. Nishimura, H. Uchida, and M. Inoue, "Enhanced Faraday and nonlinear magneto-optical Kerr effects in magnetophotonic crystals," J. Magn. Magn. Mater. 282, 256-259 (2004). [CrossRef]
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  4. A. Baryshev, T. Kodama, K. Nishimura, H. Uchida, and M. Inoue, "Three-dimensional magnetophotonic crystals based on artificial opals," J. Appl. Phys. 95, 7336-7338 (2004). [CrossRef]
  5. M. Inoue, K. Arai, T. Fuji, and M. Abe, "One-dimensional magnetophotonic crystals," J. Appl. Phys. 85, 5768-5770 (1999). [CrossRef]
  6. M. Levy, H. Yang, M. Steel, and J. Fujita, "Flat-top response in one-dimensional magnetic photonic bandgap structures with Faraday rotation enhancement," J. Lightwave Technol. 19, 1964-1969 (2001). [CrossRef]
  7. M. Steel, M. Levy, and R. M. Osgood, "Photonic bandgaps with defects and the enhancement of Faraday rotation," J. Lightwave Technol. 18, 1297-1308 (2000). [CrossRef]
  8. M. Levy and R. Li, "Polarization rotation enhancement and scattering mechanisms in waveguide magnetophotonic crystals," Appl. Phys. Lett. 89, 121113 (2006). [CrossRef]
  9. S. Kahl and A. Grishin, "Enhanced Faraday rotation in all-garnet magneto-optical photonic crystal," Appl. Phys. Lett. 84, 1438-1440 (2004). [CrossRef]
  10. A. Figotin, Y. A. Godin, and I. Vitebsky, "Two-dimensional tunable photonic crystals," Phys. Rev. B 57, 2841-2848 (1998). [CrossRef]
  11. A. Figotin and I. Vitebskiy, "Electromagnetic unidirectionality in magnetic photonic crystals," Phys. Rev. B 67, 165210 (2003). [CrossRef]
  12. M. Inoue, K. Arai, T. Fujii, and M. Abe, "Magneto-optical properties of one-dimensional photonic crystals composed of magnetic and dielectric layers," J. Appl. Phys. 83, 6768-6770 (1998). [CrossRef]
  13. H. Yang, M. Levy, R. Li, P. Moran, C. Gutierrez, and A. Bandyopadhyay, "Linear birefringence control and magnetization in sputter-deposited magnetic garnet films," IEEE Trans. Magn. 40, 3533-3537 (2004). [CrossRef]
  14. X. Huang, R. Li, H. Yang, and M. Levy, "Multimodal and birefringence effects in magnetic photonic crystals," J. Magn. Magn. Mater. 300, 112-116 (2006). [CrossRef]
  15. The use of TE/TM terminology in this context is meant to illustrate the fact that different waveguide modes with different polarization states possess different modal refractive indices. The authors are aware that the polarization state of light in gyrotropic films, especially under material stresses and the geometrical confinement generated by asymmetric optical waveguide channels should be described in terms of waveguide modes that account for elliptical birefringence. A full treatment of the polarization state of Bloch modes is presented in this work.
  16. M. Levy, "Normal modes and birefringent magnetophotonic crystals," J. Appl. Phys. 99, 073104 (2006). [CrossRef]
  17. R. Li and M. Levy, "Bragg grating magnetic photonic crystal waveguides," Appl. Phys. Lett. 86, 251102 (2005). [CrossRef]
  18. L. Landau, E. Lifshitz, and L. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, 1984).
  19. P. Yeh, "Electromagnetic propagation in birefringent layered media," J. Opt. Soc. Am. 69, 742-756 (1979). [CrossRef]
  20. S. Visnovsky, K. Postava, and T. Yamaguchi, "Magneto-optic polar Kerr and Faraday effects in periodic multilayers," Opt. Express 9, 158-171 (2001). [CrossRef] [PubMed]
  21. We use the greek letter λ to represent the eigenvalue of the Bloch equation. It is not used as a symbol for wavelength.
  22. T. R. Zaman, X. Guo, and R. J. Ram, "Faraday rotation in an InP waveguide," Appl. Phys. Lett. 90, 023514 (2007). [CrossRef]
  23. Y. Hwang, H. Kim, S. Cho, Y. Um, H. Park, and G. Jeen, "Magneto-optical properties for bulk Cd0.63−yMn0.37HgyTe single crystals," J. Appl. Phys. 100, 063509 (2006). [CrossRef]
  24. S. I. Khartsev and A. M. Grishin, "Heteroepitaxial Bi3Fe5O12/La3Ga5O12 films for magneto-optical photonic crystals," Appl. Phys. Lett. 86, 141108 (2005). [CrossRef]

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