On the problem of homogenizing one-dimensional systems

The possibility of introducing effective one-dimensional medium parameters in the long-wave approximation is considered. A layered system was used as a model of one-dimensional medium. The effective parameters were shown to be functions of sample thickness. Both periodic and random media were studied; the thicknesses of random samples were assumed to be much smaller than the localization length, which allowed us to ignore the localization effect. The results are compared with the Rytov solution. The wave vector was found to tend to the Rytov value as the thickness of the sample increased, whereas the characteristic impedance had no limit in the long-wave approximation. What is more, the characteristic impedance could differ from the Rytov value by 100%. The results were obtained by computer simulation of the propagation of electromagnetic waves in a layered system. (C) 2002 MAIK Nauka/Interperiodica.