Universality of eigenchannel structures in dimensional crossover

Abstract

The propagation of waves through transmission eigenchannels in complex media is emerging as a new frontier of condensed matter and wave physics. A crucial step towards constructing a complete theory of eigenchannels is to demonstrate their spatial structure in any dimension and their wavecoherence nature. Here, we show a surprising result in this direction. Specifically, we find that as the width of diffusive samples increases transforming from quasi one-dimensional (1D) to twodimensional (2D) geometry, notwithstanding the dramatic changes in the transverse (with respect to the direction of propagation) intensity distribution of waves propagating in such channels, the dependence of intensity on the longitudinal coordinate does not change and is given by the same analytical expression as that for quasi-1D. Furthermore, with a minimal modification, the expression describes also the spatial structures of localized resonances in strictly 1D random systems. It is thus suggested that the key ingredients of eigenchannels are not only universal with respect to the disorder ensemble and the dimension, but also of 1D nature and closely related to the resonances. Our findings open up a way to tailor the spatial energy density distribution in opaque materials.

Optical transmission matrix measurement sampled on a dense hexagonal lattice

“…These channels are useful in imaging and communication [5,10] and are an important building block of quantum transport theory in scattering samples [11][12][13][14][15]. The predicted theoretical distribution of the singular values in a multiple scattering waveguide is a bimodal distribution known as the Dorokhov-Mello-Pereyra-Kumar curve [16,17] and the properties of transmission channels are a subject of recent intense research [7,10,[18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. In an open optical system, the finite field of view and finite numerical aperture of the optics and the escape of energy parallel to the surface of the sample make it impossible to measure the complete matrix.…”

Anderson localization of two-dimensional massless pseudospin-1 Dirac particles in a correlated random one-dimensional scalar potential

“…Since the wave equation obtained from the Dirac equation is of a substantially different type from the Schrödinger equation and the electromagnetic wave equation, we expect conceptually new localization phenomena to arise in Dirac materials. Anderson localization in pseudospin-1/2 systems in a random one-dimensional (1D) scalar potential has been studied theoretically by several authors [38][39][40][41][42][43]. It has been shown that localization is destroyed at normal incidence due to the Klein tunneling effect.…”

“…Anderson localization of pseudospin-1 Dirac particles in a random 1D scalar potential was studied theoretically in two recent papers [42,43]. In Ref.…”

“…In Ref. [43], the localization length was calculated as a function of the wavelength in the long wavelength limit using the same method as in Ref. [42] for three different types of random multilayer models.…”

“…We point out that the random multilayer structures considered in Refs. [42] and [43] have short-range disorder correlations imbedded in them. However, the influence of these correlations on localization phenomena was not studied explicitly.…”