Transmission of Light in Crystals with different homogeneity: Using Shannon Index in Photonic Media

Light transmission in inhomogeneous photonic media is strongly influenced by the distribution of the diffractive elements in the medium. Here it is shown theoretically that, in a pillar photonic crystal structure, light transmission and homogeneity of the pillar distribution are correlated by a simple linear law once the grade of homogeneity of the photonic structure is measured by the Shannon index, widely employed in statistics, ecology and information entropy. The statistical analysis shows that the transmission of light in such media depends linearly from their homogeneity: the more is homogeneous the structure, the more is the light transmitted. With the found linear relationship it is possible to predict the transmission of light in random photonic structures. The result can be useful for the study of electron transport in solids, since the similarity with light in photonic media, but also for the engineering of scattering layers for the entrapping of light to be coupled with photovoltaic devices.