Dynamics of wave packets in two-dimensional random systems with anisotropic disorder

Abstract

A theoretical model is proposed to describe narrowband pulse dynamics in two-dimensional systems with arbitrary correlated disorder. In anisotropic systems with elongated cigarlike inhomogeneities, fast propagation is predicted in the direction across the structure where the wave is exponentially localized and tunneling of evanescent modes plays a dominant role in typical realizations. Along the structure, where the wave is channeled as in a waveguide, the motion of the wave energy is relatively slow. Numerical simulations performed for ultra-wide-band pulses show that even at the initial stage of wave evolution, the radiation diffuses predominantly in the direction along the major axis of the correlation ellipse. Spectral analysis of the results relates the long tail of the wave observed in the transverse direction to a number of frequency domain "lucky shots" associated with the long-living resonant modes localized inside the sample.

Diffuse time tomography of strongly scattering random structures†

“…In what follows we show that integral transform (28) can be reduced to a well-known spherical mean problem. To make this evident, we write down explicitly the integral over Kτ…”

“…For a given spectrum ε (K), the final result depends somehow on both the modulus and direction of the wave vector k. The calculations ofτ (k) in two dimensions, including anisotropic structures was carried out in [28]. In particular, it has been found there that in anisotropic structures with a cigar-like correlation function the diffuse time is rather sensitive to the propagation direction.…”

“…Equation (28) shows that for a fixed value of wavenumber k not only spectral components lying in the interior of the limiting sphere (K ≤ 2k) contribute to the diffuse time, but also the higher frequencies (K > 2k). As we have seen in Section 2, in the linearised diffraction tomography where the measurements are performed in the far-field and then only homogeneous modes are available, a low-frequency content of the object function may be recovered, that imposes the classical λ/2 resolution limit for image reconstruction.…”

“…In this case the power spectrum ε (K) depends only on the absolute value of vector K, and Equation (28) can be essentially simplified. The shortest path to show this is to replace the step function in Equation (28) with an auxiliary integral of the form (A.4) and then to integrate over angular variables. For 3D structures this transforms the auxiliary integral into the form of Equation (A.8), and we arrive finally at…”

“…Let us recall that Equation (28) was obtained assuming the scattering potentialε(r) is non-dispersive. The role of dispersion may be two-fold here.…”