Communications in Mathematical Sciences

Volume 13 (2015)

Number 3

Special Issue in Honor of George Papanicolaou’s 70th Birthday

Guest Editors: Liliana Borcea, Jean-Pierre Fouque, Shi Jin, Lenya Ryzhik, and Jack Xin

Transmission and reflection of electromagnetic waves in randomly layered media

Pages: 707 – 728



Josselin Garnier (Laboratoire de Probabilités et Modèles Aléatoires & Laboratoire Jacques-Louis Lions, Université Paris Diderot, Paris, France)

Knut Sølna (Department of Mathematics, University of California at Irvine)


In this paper, the reflection of an obliquely incident electromagnetic wave on a randomly layered multiscale half-space is analyzed. By using homogenization and diffusion approximation theorems, it is possible to get a complete description of the reflectivity of the random half-space that depends on the effective reflectivity of the interface and on the random reflectivity of the bulk medium. Particular attention is devoted to the characterization of the Brewster anomalies that correspond to small or even zero reflectivity. It turns out that the interface reflectivity and the random medium reflectivity as functions of the incidence angle may both possess Brewster angles that minimize or even cancel them, but these two angles are in general different.


electromagnetic waves, random media, homogenization, diffusion approximation

2010 Mathematics Subject Classification

35Q61, 35R60, 60F05, 78A48

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