Light Transmission Properties and Shannon Index in One-Dimensional Photonic Media With Disorder Introduced by Permuting the Refractive Index Layers

Abstract

In this paper, we have studied, with a numerical method, how introducing disorder affects the light transmission properties of 1-D photonic structures over a wide range of wavelengths. A new type of disorder is introduced by permuting the refractive index layers in the optical medium. We compared the light transmission properties of ideal photonic crystals and of disordered media with the same kind and number of scattering elements for different sample lengths. We have calculated the transmission properties, by the transfer matrix method, of thousands of different disordered structures in order to perform a statistical analysis. We found that, below a certain sample length, disorder induces less average light reflection than ordered structures, whereas above the threshold length, disordered structures show more average reflection. Moreover, we have quantified the disorder of the structures with the Shannon index. We have found a decrease in the average light transmission as a function of the Shannon index. Furthermore, the sample length affects the trend of the average transmission as a function of the Shannon index.

Optical properties of periodic, quasi-periodic, and disordered one-dimensional photonic structures

“…'We'discuss'the'optical'response,'the' fabrication'methods,'and'the'most'significant'applications'of'1D'periodic,'quasiperiodic,'and' disordered' photonic' structures.' Concerning' 1D' disordered' photonic' structures,' we' particularly' focus' on' 1D' photonic' structures' in' which' the' disorder' is' obtained' in' different' ways:' i)' with' a' random' sequence' of' high' and' low' refractive' index' layers' [45];' ii)' with' a' random'arrangement'of'a'fixed'number'of'high'refractive'layers'between'a'fixed'number'of' low'refractive'index'layers' [59,60];'iii)'with'a'random'variation'of'the'thickness'of'the'layers' in'a'periodic'structure' [61][62][63].' ' 2.…”

One dimensional disordered photonic structures characterized by uniform distributions of clusters

“…In 2005, Bertolotti et al experimentally observed optical necklaces [22], while in 2007 Ghulinyan observed periodic oscillations in the average transmission as a function of the sample length [23]. Recently, the Shannon index, a diversity index used in information theory and statistics [24], has been used to quantify the evenness in one dimensional photonic crystals [25,26].…”

The Influence of a Power Law Distribution of Cluster Size on the Light Transmission of Disordered 1-D Photonic Structures

“…It is well known that the light transport depends on the dimensionality of the material structure [9]. One--dimensional systems are realized by modulating the dielectric constant in a linear arrangement, as, for example, a random multilayer [3,10,11]. For sake of clarity, a periodic alternation of the dielectric constant results in a one--dimensional photonic crystal [12--15], while a modulation of the dielectric constant that follow a deterministic generation rule gives rise to a quasicrystal [16--20].…”