A one-dimensional model of random scattering is considered for a totally refracting random multilayer that has two separated spatial scales, i.e., deterministic macroscale and random microscale. The interplay of internal refraction and random multiple scattering for a turning point problem is analyzed with an intermediate scale of the wavelength. Two extended limit theorems for stochastic differential equations with a small parameter provide the characterization of the diffusion processes above and below the turning point. Both results are combined, and a global limit law for the phenomenon of the random phase is obtained.
All Science Journal Classification (ASJC) codes
- Applied Mathematics