Brewster anomalies: A polarization-induced delocalization effect.

The demonstration that almost all stationary states in a one-dimensional disordered system are localized proceeds by the construction of a product of the transfer matrices of the system and application of Furstenberg's theorem on the product of random matrices. The proof of that theorem begins with the supposition that the matrices are irreducible; that is, in the simple case of twodimensional matrices, they cannot all be diagonalized by the same transformation. It is easy to see why this assumption is ultimately crucial in establishing the localization of stationary states: If all the random transfer matrices were diagonal, the inhomogeneities in the system could not mix the state represented by one of the eigenvectors of those matrices with the state represented by the other. If those states corresponded to waves propagating to the right and left, the absence of scattering from one to the other would allow each to survive as a delocalized stationary state of the system. In this Letter we show that, under certain special circumstances, precisely this situation (or a situation close to it) can occur for the transport of light through disordered one-dimensional structures. The light is then no longer localized and the localization length diverges (or is at least enhanced orders of magnitude over its usual value). The effect is shown to have its origin in the inherent vector nature of the electromagnetic radiation and therefore is without analogy for the scalar waves. To see physically how a beam of light might pass through a one-dimensional disordered structure without scattering, consider first the simple case of small inhomogeneities. For a dielectric constant e(z) = f + f ( z ) , with | i(z) | <̂ C6, we initially neglect i(z) and imagine a beam i propagating at some angle 6 with respect to the direction of inhomogeneity towards + z [see Fig. 1(a)]; we consider light polarized in the plane of incidence as shown (/? -polarized light). Energy can be removed from i by backscattering into a beam s; such a beam must make an angle 0 from — z, since the system is translationally invariant in the (xy) plane. An inhomogeneity i(z) that could lead to such scattering would do so by generating a polarization P(z) that, for \i \ <^e, would be given by P(z) =[6(z) — e]E/4;r, where E is the electric field in beam /. If 0=45°, P(z) points in the direction that beam s must propagate. Since dipoles cannot radiate in the direction they point, no backscattered wave can be generated. If there is no dissipation in the system, the beam / can then continue to propagate without extinction. The effect is closely analogous to the zero in reflectivity from a homogeneous medium at Brewster's angle, where the dipoles in the refracted beam point in the direction that the reflected beam would have to propagate, forbidding its generation. We shall see in the following that at 0=45° in a random medium with | i\ <£e, as well as at a special angle in the particular case of a randomly layered binary medium with arbitrary | e | , the localization length indeed diverges. More generally, the localization length is enhanced in the neighborhood of a certain angle