Statistical characterization of ray propagation in a random lattice

We address the problem of optical propagation in random lattices. This can be relevant in characterizing, among other phenomena, the urban shortwave c hannels such as those involved in cellular communications. We consider an e nsemble of optical rays, generated by an isotropic source, that propagates in a two-dimensional disordered medium whose characteristic parameter is th e density of inner square reflectors. The statistical characterization of t he propagation mechanism is our aim. In a previous work [G. Franceschetti e t al., IEEE Trans. Antennas Propag. 47(7) (1999)], a quite similar scenario has been considered, with a ray impinging on a semi-infinite layer of refl ectors and with a Markov chain formulation. We report the extension of such an approach to the internal-source scenario and point out how the independ ence assumption of the ray characterization may not lead to particularly ac curate results. Therefore we propose a different approach, based solely on the geometry of the random lattice. We exploit the intuition that the relev ant geometry in such a propagation problem should be based on the city-bloc k distance rather than on the usual Euclidean distance. This allows us to o btain a simple analytical solution in the form of a parametric family of di stribution functions. This basic result is validated by means of computer s imulations. (C) 1999 Optical Society of America [S0740-3232(99)00510-4].