  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.
