Abstract-In this paper, ray propagation in stratified semi-infinite percolation lattices consisting of a succession of uniform density layers is considered. Two different mathematical approaches for analytically evaluating the penetration depth are presented. In order to compare performances and to assess the range of validity of the two approaches, an exhaustive set of numerical Monte-Carlo-like experiments is presented.
2. Marano, S. and M. Franceschetti, "Ray propagation in a random lattice: a maximum entropy, anomalous diffusion process," IEEE Trans. Antennas Propag., Vol. 53, No. 6, 1888-1896, 2005.
3. Ishimaru, A. Wave Propagation and Scattering in Random Media, IEEE Press, 1997., 1997.
4. Gong, S. H. and J. Y. Huang, "Accurate analytical model for equivalent dielectric constant for rain medium," J. Electromagn. Wave Appl., Vol. 20, No. 13, 1775-1783, 2006.
5. Huang, X. E. and A. K. Fung, "Electromagnetic wave scattering from vegetation with odd-pinnate compound leaves," J. Electromagn. Wave Appl., Vol. 19, No. 2, 231-244, 2005.
6. El-Ocla, H. and M. Tateiba, "Numerical analysis of some scattering problems in continuous random medium," Progress In Electromagnetics Research, Vol. 42, 107-130, 2003.
7. Mudaliar, S., "On the application of the radiative transfer approach to scattering from a random medium layer with rough boundaries," J. Electromagn. Wave Appl., Vol. 20, No. 13, 1739-1749, 2006.
8. Blaustein, N., "Theoretical aspects of wave propagation in random media based on quanty and statistical field theory," Progress In Electromagnetics Research, Vol. 47, 135-191, 2004.
9. Matsuoka, T. and M. Tateiba, "Numerical analysis of scattered power from a layer of random medium containing many particles of high dielectric constantâ€”Applications to the detection of a water content of soil," Progress In Electromagnetics Research, Vol. 33, 199-218, 2001.
10. Franceschetti, G., S. Marano, and F. Palmieri, "Propagation without wave equation toward an urban area model," IEEE Trans. Antennas Propag., Vol. 47, No. 9, 1393-1404, 1999.
11. Grimmett, G., Percolation, Springer-Verlag, New York, 1989.
12. Norris, J. R., Markov Chains, Cambridge University Press, 1998.
13. Ross, R. M., Stochastic Processes, J. Wiley, New York, 1983.
14. Martini, A., M. Franceschetti, and A. Massa, Percolation-based approaches for ray-optical propagation in inhomogeneous random distributions of discrete scatterers, 1st European Conference on Antennas and Propagation (EuCAP 2006), 6-10, 2006.
15. Martini, A., M. Franceschetti, and A. Massa, A percolation model for the wave propagation in non-uniform random media, 9th International Conference on Electromagnetics in Advanced Applications (ICEAA 05), 12-16, 2005.
16. Martini, A., M. Franceschetti, and A. Massa, "Ray propagation in a nonuniform random lattice," J. Opt. Soc. Am. A, Vol. 23, No. 9, 2251-2261, 2006.