Statistics of the eigenmodes and optical properties of one-dimensional disordered photonic crystals

Kaliteevski, MA; Beggs, DM; Brand, S; Abram, RA; Nikolaev, VV

Abstract

The eigenmode spectrum and transmission properties of a certain class of one-dimensional disordered photonic crystals have been studied statistically. It is shown that the relative fluctuation of the optical width of the period of the photonic crystal is a universal parameter allowing a quantitative description of the disordered photonic crystal for various models of disorder. It is shown that the tail of the density of states is characterized by a certain penetration depth and a quantitative relation between the penetration depth, the relative band gap width, and the disorder parameter is obtained. It is found that a threshold level of disorder exists, below which the density of states in the center of the photonic band gap vanishes, and the ensemble-averaged transmission coefficient does not change significantly with increasing disorder. Also, the standard deviation of the transmission coefficient is less than its mean value. Above threshold, the ensemble averaged transmission coefficient and density of states increase with the level of disorder rapidly, and the standard deviation of the transmission coefficient exceeds its mean value. A scaling formula is presented, which relates the logarithm of the transmission to the periodic refractive index modulation and the disorder.

Citation

Kaliteevski, M., Beggs, D., Brand, S., Abram, R., & Nikolaev, V. (2006). Statistics of the eigenmodes and optical properties of one-dimensional disordered photonic crystals. Physical review E: Statistical, nonlinear, and soft matter physics, 73(5), https://doi.org/10.1103/physreve.73.056616

• Journal Article Type: Article
• Publication Date: May 1, 2006
• Deposit Date: Dec 7, 2010
• Publicly Available Date: Dec 8, 2010
• Journal: Physical review . E, Statistical, nonlinear, and soft matter physics
• Print ISSN: 1539-3755
• Electronic ISSN: 1550-2376
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 73
• Issue: 5
• DOI: https://doi.org/10.1103/physreve.73.056616
• Keywords: Weak localization, Scaling theory, Light, Diffusion, Absence.
• Public URL: https://durham-repository.worktribe.com/output/1539641