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

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

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Authors

MA Kaliteevski

DM Beggs

S Brand

RA Abram

VV Nikolaev



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 Mar 28, 2024
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.

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Copyright Statement
© 2006 by The American Physical Society. All rights reserved.





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