Density of states in 1D disordered photonic crystals: Analytical solution

Greshnov, A. A.; Kaliteevski, M. A.; Abram, R. A.; Brand, S.; Zegrya, G. G.

doi:10.1016/j.ssc.2008.01.037

Cited by 10 publications

(11 citation statements)

References 15 publications

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“…For instance, in ref. 20, this term has not been taken into account, so our Fano result (4) cannot be reproduced. The analytical results of ref.…”

Section: Methodsmentioning

confidence: 94%

“…Our general conclusions are supported by both numerical studies and analytical theory. As an example, not restricting generality of our analysis, we study the light propagation in a one-dimensional (1D) photonic crystal described by a simple binary structure ABAB .... Properties of such 1D superlattices have been discussed in many theoretical and experimental studies,15 including the analysis of the degradation of the photonic bandgaps and enhanced localization in the presence of disorder 161718192021. However, a complete understanding of an interplay between periodicity and Bragg scattering in disordered photonic crystals is still missing.…”

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confidence: 99%

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Fano interference governs wave transport in disordered systems

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Light localization in disordered systems and Bragg scattering in regular periodic structures are considered traditionally as two entirely opposite phenomena: disorder leads to degradation of coherent Bragg scattering whereas Anderson localization is suppressed by periodicity. Here we reveal a non-trivial link between these two phenomena, through the Fano interference between Bragg scattering and disorder-induced scattering, that triggers both localization and de-localization in random systems. We find unexpected transmission enhancement and spectrum inversion when the Bragg stop-bands are transformed into the Bragg pass-bands solely owing to disorder. Fano resonances are always associated with coherent scattering in regular systems, but our discovery of disorder-induced Fano resonances may provide novel insights into many features of the transport phenomena of photons, phonons, and electrons. Owning to ergodicity, the Fano resonance is a fingerprint feature for any realization of the structure with a certain degree of disorder.

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“…For instance, in ref. 20, this term has not been taken into account, so our Fano result (4) cannot be reproduced. The analytical results of ref.…”

Section: Methodsmentioning

confidence: 94%

mentioning

confidence: 99%

Fano interference governs wave transport in disordered systems

et al. 2012

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“…[48]- [56]. While some problems, like coherent backscattering of light from disordered photonic crystals, can be treated perturbatively using Green function technique [48]- [50], the problem of localization of light by such structures requires summation of all the diagrams or application of the different approaches as done in Refs.…”

Section: Introductionmentioning

confidence: 99%

“…Recently the problem of light localization in the one-dimensional case has been considered in more strict manner using the Fokker-Planck equation [54] similar to considered in Ref. [55], however some aspects have not been treated absolutely accurately. Namely, the authors considered a second-order term "η 2 " using a system of differential equations of the first order (Eq.…”

Section: Introductionmentioning

confidence: 99%

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Analytical theory of light localization in one-dimensional disordered photonic crystals

Greshnov

Kaliteevski

Abram

2013

Solid State Communications

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Publisher's copyright statement: NOTICE: this is the author's version of a work that was accepted for publication in Solid State Communications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be re ected in this document. Changes may have been made to this work since it was submitted for publication. A de nitive version was subsequently published in Solid State Communications, 158, 2013Communications, 158, , 10.1016Communications, 158, /j.ssc.2013.01.009. Additional information:Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractInfluence of the various types of disorder on propagation of light in onedimensional periodic structures is studied analytically using statistical approach based on a Fokker-Planck type equation. It is shown that light localization length behaves non-monotonically as a function of disorder amplitude in all the examined models except for purely geometric disorder. This feature is explained by crossover between weak disorder regime corresponding to gradual destruction of the reflecting properties of a photonic crystal and strong disorder regime, when periodic component of the refractive index can be treated as a perturbation. The region of small disorder is shown to be universal provided that a disorder parameter is properly introduced.

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