Abstract
Anderson localization of p-polarized waves and the Brewster anomaly phenomenon, which is the delocalization of p-polarized waves at a special incident angle, in randomly-stratified anisotropic media are studied theoretically for two different random models. In the first model, the random parts of the transverse and longitudinal components of the dielectric tensor, between which the longitudinal component is the one in the stratification direction, are assumed to be uncorrelated, while, in the second model, they are proportional to each other. We calculate the localization length in a precise way using the invariant imbedding method. From analytical considerations, we provide an interpretation of the Brewster anomaly as a phenomenon arising when the wave impedance is effectively uniform. Similarly, the ordinary Brewster effect is interpreted as an impedance matching phenomenon. We derive the existence condition for the Brewster anomaly and concise analytical expressions for the localization length, which are accurate in the weak disorder regime. We find that the Brewster anomaly can arise only when disorder is sufficiently weak and only in the second model with a positive ratio of the random parts. The incident angle at which the anomaly occurs depends sensitively on the ratio of the random parts and the average values of the tensor components. In the cases where the critical angle of total reflection exists, the angle at which the anomaly occurs can be either bigger or smaller than the critical angle. When the transverse and longitudinal components are uncorrelated, localization is dominated by the the transverse component at small incident angles. When only the longitudinal component is random, the localization length diverges as θ−4 as the incident angle θ goes to zero and is also argued to diverge for all θ in the strong disorder limit.
Highlights
Even though it has been studied extensively for over half a century, Anderson localization of quantum particles and classical waves continues to attract the interest of many researchers [1, 2, 3, 4, 5, 6, 7, 8]
We focus especially on the unique phenomenon called Brewster anomaly (BA), which is the delocalization of p-polarized electromagnetic waves in randomly-stratified media at a special incident angle [9, 10, 11, 12, 13, 14, 15]
Using an analytical method based on the invariant imbedding theory [24, 25], we will derive precise conditions for the occurrence of the BA in randomly-stratified anisotropic media and derive concise analytical expressions for the localization length in the weak disorder regime for two different random models
Summary
Even though it has been studied extensively for over half a century, Anderson localization of quantum particles and classical waves continues to attract the interest of many researchers [1, 2, 3, 4, 5, 6, 7, 8]. Jordan et al have studied the BA occurring in randomly-layered anisotropic media consisting of alternating isotropic-uniaxial media using numerical calculations based on the transfer matrix method [17]. Using an analytical method based on the invariant imbedding theory [24, 25], we will derive precise conditions for the occurrence of the BA in randomly-stratified anisotropic media and derive concise analytical expressions for the localization length in the weak disorder regime for two different random models. These results will be compared with more accurate numerical results obtained using the invariant imbedding method and with the previous results obtained for randomly-layered anisotropic media [17, 19].
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