OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • 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)

View Full Text Article

Enhanced HTML    Acrobat PDF (786 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



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

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

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)

Sort:  Author  |  Year  |  Journal  |  Reset  


  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]

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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited