Monte Carlo computer technique for one-dimensional random media

Hochstim and Martens were the first to use Monte Carlo computations to study scattering characteristics of scalar waves from randomly fluctuating slabs with an exponential spatial correlation. This paper describes an alternative procedure which overcomes some of the difficiencies in their treatment and extends the study to physical circumstances which their treatment excludes (e.g., background inhomogeneity, crossover into cutoff regions, etc.). The two-point correlation function characterizing the medium fluctuations (more directly the spectral density) may be arbitrarily selected and is no longer restricted to an exponential. The correlation properties of the medium are virtually independent of the length of the elementary slabs comprising the overall slab region, whence the medium may be structured by equal sized slab realizations-a major advantage whenever a background profile is superimposed. Furthermore, the statistics associated with the reflection and transmission of both the coherent as well as the incoherent waves are calculated separately. The results so obtained yield solutions with which appropriate analytical theories can be conveniently compared and they provide information additional to that found in previous studies. As examples, the syntheses of Gaussian and exponential correlation functions are shown. For the exponential, propagation calculations for a homogeneous random slab were made using the new technique and compared with results using Hochstim and Martens' approach.