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

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.