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Physics of the Solid State

, Volume 49, Issue 10, pp 1999–2003 | Cite as

Density of states of a one-dimensional disordered photonic crystal

  • A. A. GreshnovEmail author
  • M. A. Kaliteevskiĭ
  • R. A. Abram
  • S. Brand
  • G. G. Zegrya
Low-Dimensional Systems and Surface Physics

Abstract

An analytic theory of the density of states in one-dimensional disordered photonic crystals is proposed. It is shown that the problem of the density of optical modes can be reduced in the small dielectric contrast approximation to solving a generalized Fokker-Planck equation for the distribution function of the logarithmic derivative of the electric field (the wave phase). The exact analytic solution and density-of-states asymptotics deep in the band gap of the photonic crystal and close to the band gap edge are derived. The results obtained agree well with the empirical relations derived earlier from numerical experiments.

PACS numbers

42.70.Qs 78.67.-n 

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References

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    M. A. Kaliteevski, D. M. Beggs, S. Brand, R. A. Abram, and V. V. Nikolaev, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 73, 056616 (2006).Google Scholar
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    I. M. Lifshitz, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Nauka, Moscow, 1982; Wiley, New York, 1988), Chap. 6.Google Scholar
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    M. A. Leontovich, Introduction to Thermodynamics: Statistical Physics (Nauka, Moscow, 1983), Chap. 6 [in Russian].Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2007

Authors and Affiliations

  • A. A. Greshnov
    • 1
    Email author
  • M. A. Kaliteevskiĭ
    • 1
    • 2
  • R. A. Abram
    • 2
  • S. Brand
    • 2
  • G. G. Zegrya
    • 1
  1. 1.Ioffe Physicotechnical InstituteRussian Academy of SciencesSt. PetersburgRussia
  2. 2.Department of PhysicsDurham UniversityDurhamUK

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