Percolation-based approaches for ray-optical propagation in inhomogeneous random distribution of discrete scatterers

We address the problem of optical ray propagation in an inhomogeneous half-plane lattice, where each cell can be occupied according to a known one-dimensional obstacles density distribution. A monochromatic plane wave impinges on the random grid with a known angle and undergoes specular reflections on the occupied cells. We present two different approaches for evaluating the propagation depth inside the lattice. The former is based on the theory of the Martingale random processes, while in the latter ray propagation is modelled in terms of a Markov chain. A numerical validation assesses the proposed solutions, while validation through experimental data shows that the percolation model, in spite of its simplicity, can be applied to model real propagation problems.