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

Abstract

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.

Interplay between evanescence and disorder in deep subwavelength photonic structures

“…From the transfer matrices, we find the average rate of transmission decay using the Hamiltonian mapping method, which maps the transfer matrix problem to a trajectory in the E y , B x plane (the y and x components of the electric and magnetic fields, respectively), as a function of the number of layers. Alternative methods include transfer matrix theory 33 , Green function-based approaches 34 and mapping the problem to the Fokker–Planck equation 35 36 . These alternative methods are very rigorous and accurate, but are less suited to the case at hand than the Hamiltonian mapping technique, which we use here, based on the methods of ref.…”

Effect of thickness disorder on the performance of photonic crystal surface wave sensors

“…Therefore the RI relative uncertainty is an order of magnitude below that of the thickness variations. For a reflectivity simulation within a narrow angular range (4 deg), the small disorder of the optical length of single layers can be well modeled by the layer thickness disorder only [23].…”

A study of a phase formalism for calculating the cumulative density of states of one-dimensional photonic crystals

“…With the aid of some judicious approximations they were able to derive a Fokker-Planck equation (9 ) for the distribution function of the phase and then solve that equation to predict the density of states at frequencies in and close to the lowestfrequency bandgap of the structure. In later work (10 ) the light localization length was studied using similar techniques.…”