Stochastic differential equation approach for waves in a random medium.
نویسندگان
چکیده
We present a mathematical approach that simplifies the theoretical treatment of electromagnetic localization in random media and leads to closed-form analytical solutions. Starting with the assumption that the dielectric permittivity of the medium has delta-correlated spatial fluctuations, and using Ito's lemma, we derive a linear stochastic differential equation for a one-dimensional random medium. The equation leads to localized wave solutions. The localized wave solutions have a localization length that scales as L approximately omega(-2) for low frequencies whereas in the high-frequency regime this length behaves as L approximately omega(-2/3) .
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عنوان ژورنال:
- Physical review. E, Statistical, nonlinear, and soft matter physics
دوره 79 3 Pt 2 شماره
صفحات -
تاریخ انتشار 2009