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Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry van Driel
  • Vol. 29, Iss. 12 — Dec. 1, 2012
  • pp: 3231–3239

Transverse-magnetic-polarized Floquet–Bloch waves in one-dimensional photonic crystals

G. V. Morozov and D. W. L. Sprung  »View Author Affiliations


JOSA B, Vol. 29, Issue 12, pp. 3231-3239 (2012)
http://dx.doi.org/10.1364/JOSAB.29.003231


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Abstract

Using binary and sinusoidal photonic crystals as examples, it is shown how to construct two independent Floquet–Bloch waves for TM-polarized light in a lossless one-dimensional periodic structure. Particular attention is given to those special situations where either one Bloch wave and a hybrid Floquet mode develop inside the structure (instead of two Bloch waves) or both developed Bloch waves become periodic functions.

© 2012 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(260.2110) Physical optics : Electromagnetic optics
(050.5298) Diffraction and gratings : Photonic crystals

ToC Category:
Diffraction and Gratings

History
Original Manuscript: August 24, 2012
Revised Manuscript: October 5, 2012
Manuscript Accepted: October 6, 2012
Published: November 6, 2012

Citation
G. V. Morozov and D. W. L. Sprung, "Transverse-magnetic-polarized Floquet–Bloch waves in one-dimensional photonic crystals," J. Opt. Soc. Am. B 29, 3231-3239 (2012)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-29-12-3231


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References

  1. G. V. Morozov and D. W. L. Sprung, “Floquet–Bloch waves in one-dimensional photonic crystals,” Europhys. Lett. 96, 54005 (2011). [CrossRef]
  2. G. V. Morozov, R. G. Maev, and G. W. F. Drake, “Switching electromagnetic waves by two-layered periodic dielectric structures,” Phys. Rev. E 60, 4860–4867 (1999). [CrossRef]
  3. I. Nusinsky and A. A. Hardy, “Band-gap analysis of one-dimensional photonic crystals and conditions for gap closing,” Phys. Rev. B 73, 125104 (2006). [CrossRef]
  4. J. K. Nurligareev and V. A. Sychugov, “Propagation of light in a one-dimensional photonic crystal: analysis by the floquet-bloch function method,” Quantum Electron. 38, 452–461 (2008). [CrossRef]
  5. J. K. Nurligareev, “Floquet–Bloch waves in bound one-dimensional photonic crystals,” J. Surf. Invest. 5, 193–208 (2011). [CrossRef]
  6. J. J. Stoker, Nonlinear Vibrations (Waverly, 1950).
  7. V. A. Yakubovich and V. M. Starzhinskii, Linear Differential Equations with Periodic Coefficients (Wiley, 1975).
  8. M. S. P. Eastham, The Spectral Theory of Periodic Differential Equations (Scottish Academic, 1975).
  9. W. Magnus and S. Winkler, Hill’s Equation (Dover, 2004).
  10. G. V. Morozov and F. Placido, “High-order bandgaps in one-dimensional photonic crystals,” J. Opt. 12, 045101 (2010). [CrossRef]
  11. Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998). [CrossRef]
  12. B. G. Bovard, “Rugate filter theory: an overview,” Appl. Opt. 32, 5427–5442 (1993). [CrossRef]
  13. W. H. Southwell, “Spectral response calculations of rugate filters using coupled-wave theory,” J. Opt. Soc. Am. A 5, 1558–1564 (1988). [CrossRef]
  14. N. Perelman and I. Averbukh, “Rugate filter design: an analytical approach using uniform WKB solutions,” J. Appl. Phys. 79, 2839–2845 (1996). [CrossRef]
  15. M. Brack and R. K. Bhaduri, Semiclassical Physics (Addison-Wesley, 1997).
  16. L. W. Casperson, “Solvable Hill equation,” Phys. Rev. A 30, 2749–2751 (1984). [CrossRef]
  17. L. W. Casperson, “Erratum: solvable Hill equation [Phys. Rev. A 30, 2749 (1984)],” Phys. Rev. A 31, 2743(E) (1985). [CrossRef]
  18. S. M. Wu and C. C. Shin, “Construction of solvable Hill equations,” Phys. Rev. A 32, 3736–3738 (1985). [CrossRef]
  19. V. Urumov, “Solvable Hill-Harper equations,” Phys. Rev. A 38, 4863–4865 (1988). [CrossRef]

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