We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Department of Physics

Staff profile

Publication details for Dr Stuart Brand

Kaliteevski, M. A., Beggs, D. M, Brand, S., Abram, R. A. & Nikolaev, V. V. (2006). Stability of the photonic band gap in the presence of disorder. Physical Review B 73(3): 033106.

Author(s) from Durham


The photonic eigenmodes near a band gap of a type of one-dimensional disordered photonic crystal have been investigated statistically. For the system considered, it is found that the tail of the density of states entering the band gap is characterized by a certain penetration depth, which is proportional to the disorder parameter. A quantitative relation between the relative penetration depth, the relative width of the photonic band gap, and the disorder has been found. It is apparent that there is a certain level of disorder below which the probability of the appearance of photonic eigenstates at the center of the photonic band gap essentially vanishes. Below the threshold, the ensemble-averaged transmission at the center of the photonic band gap does not change significantly with increasing disorder, but above threshold it increases much more rapidly. A simple empirical formula has been obtained which describes how the logarithm of the transmission relates to the periodic refractive index modulation and the disorder


1Y. A. Vlasov et al., Phys. Rev. E 61, 5784 2000.
2T. F. Krauss et al., Nature 383, 699 1996.
3Z.-Y. Li and Z.-Q. Zhang, Phys. Rev. B 62, 1516 2000.
4Photonic Band Gap and Localization, edited by C. M. Soukoulis,
NATO ASI Series B, vol. 308 Plenum, New York, 1993.
5A. P. Vinogradov et al., Phys. Rev. E 70, 026610 2004.
6D. J. Thouless, Phys. Rep., Phys. Lett. 13, 142 1974.
7P. Cheng, Introduction to Wave Scattering Localization and Mesoscopic
Academic, London, 1995.
8A. R. McGurn et al., Phys. Rev. B 47, 13120 1993.
9M. Y. Azbel and P. Soven, Phys. Rev. B 27, 831 1983.
10Y. A. Vlasov et al., Phys. Rev. B 60, 1555 1999.
11 E. Abrahams et al., Phys. Rev. Lett. 42, 673 1979.
12 L. I. Deych et al., Phys. Rev. Lett. 81, 5390 1998.
13 S. John, Phys. Rev. Lett. 58, 2486 1987.
14D. J. Thouless, Phys. Rev. Lett. 39, 1167 1977.
15H. Kogelnick and C. V. Shank, J. Appl. Phys. 43, 2327 1972,
the coupled wave theory developed in this paper is a rather
rough approximation the authors neglect the second derivative
of the amplitude of the waves on the spatial coordinate, and
therefore it cannot be applied to the analysis of disordered systems.
16M. A. Kaliteevski et al., Phys. Rev. B 66, 113101 2002.
17M. A. Kaliteevski et al., Phys. Status Solidi A 195, 612 2003.