We address the problem of optical propagation in random lattices. This can be relevant in characterizing, among other phenomena, the urban shortwave channels such as those involved in cellular communications. We consider an ensemble of optical rays, generated by an isotropic source, that propagates in a two-dimensional disordered medium whose characteristic parameter is the density of inner square reflectors. The statistical characterization of the propagation mechanism is our aim. In a previous work [G. Franceschetti <i>et al</i>., IEEE Trans. Antennas Propag. <b>47</b>(7) (1999)], a quite similar scenario has been considered, with a ray impinging on a semi-infinite layer of reflectors and with a Markov chain formulation. We report the extension of such an approach to the internal-source scenario and point out how the independence assumption of the ray characterization may not lead to particularly accurate results. Therefore we propose a different approach, based solely on the geometry of the random lattice. We exploit the intuition that the relevant geometry in such a propagation problem should be based on the city-block distance rather than on the usual Euclidean distance. This allows us to obtain a simple analytical solution in the form of a parametric family of distribution functions. This basic result is validated by means of computer simulations.
© 1999 Optical Society of America
(000.5490) General : Probability theory, stochastic processes, and statistics
(070.6020) Fourier optics and signal processing : Continuous optical signal processing
(080.2720) Geometric optics : Mathematical methods (general)
(350.5500) Other areas of optics : Propagation
Stefano Marano, Francesco Palmieri, and Giorgio Franceschetti, "Statistical characterization of ray propagation in a random lattice," J. Opt. Soc. Am. A 16, 2459-2464 (1999)