Formation of "windows" of transparency in a layered samplewith an inhomogeneous distribution of inclusions in the layers; special case

In this work we studied the formation of transparency "windows" in a layered sample with the layers consisting of a basic, opaque material with transparent inclusions, in the case when islands of the transparent material are distributed inhomogeneously in the layer. The distribution densities of the "windows" over the area were obtained for inhomogeneities of various types and different values of "thickening" of the islands toward the center or edge of the layer. The special solutions for the case of a single island in a layer in a two-layer sample are considered.