Anderson localization and the Brewster anomaly phenomenon, which is thedelocalization of $p$-polarized waves at a special incident angle, inrandomly-stratified anisotropic media are studied theoretically for twodifferent random models. In the first case, the random parts of the transverseand longitudinal components of the dielectric tensor are assumed to beuncorrelated, while, in the second case, they are proportional to each other.The longitudinal component is the one in the stratification direction. Wecalculate the localization length numerically using the invariant imbeddingmethod. In addition, we derive the existence condition for the Brewster anomalyand concise analytical expressions for the localization length, which areaccurate in the weak disorder limit. We find that the Brewster anomaly canoccur only in the second case with positive ratio of the random parts. Theincident angle at which the anomaly occurs depends sensitively on the ratio ofthe random parts and the average values of the tensor components. In the caseswhere the critical angle of total reflection exists, the angle at which theanomaly occurs can be either bigger or smaller than the critical angle. Whenthe transverse and longitudinal components are uncorrelated, localization isdominated by the the transverse component at small incident angles and by thelongitudinal component at large incident angles.
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