Shape dependence of transmission, reflection, and absorption eigenvalue densities in disordered waveguides with dissipation

Abstract

The universal bimodal distribution of transmission eigenvalues in lossless diffusive systems underpins such celebrated phenomena as universal conductance fluctuations, quantum shot noise in condensed matter physics and enhanced transmission in optics and acoustics. Here, we show that in the presence of absorption, density of the transmission eigenvalues depends on the confinement geometry of scattering media. Furthermore, in an asymmetric waveguide, densities of the reflection and absorption eigenvalues also depend of the side from which the waves are incident. With increasing absorpotion, the density of absorption eigenvalues transforms from single-peak to double-peak function. Our findings open a new avenue for coherent control of wave transmission, reflection and absorption in random media.PACS numbers: 42.25. Dd, 42.25.Bs, Mesoscopic electronic transport through a disordered conductor can be described by a N × N transmission matrixt which relates the amplitudes of N incoming and outgoing transverse modes [1]. Dimensionless conductance is g = Tr t †t = n τ n , where τ n are the eigenvalues of the matrixt †t [2] and ... denotes ensemble average. Therefore, electron transport in a metallic wire can be viewed as parallel transmission over N orthogonal eigenchannels with individual transmissions of τ n . Due to the mesoscopic correlations [3,4], density of the transmission eigenvalues D(τ ) has a bimodal functional form [5][6][7][8][9][10][11] with peaks at τ → 0 and τ → 1. The latter implies the existence of nearly perfect transmission eigenchannels [5,12, 13] that lead to e.g. universal conductance fluctuations [14, 15] and quantum shot noise [16,17]. In Ref.[18], bimodal distribution was proven to be applicable to an arbitrary geometry of the conductor as long as the transport remains diffusive and free of dissipation.The bimodal distribution obtained in the context of mesoscopic physics is also applicable to transport of classical waves in scattering media [19]. In optics, rapid development of spatial light modulators has enabled an experimental access to the transmission eigenchannels [20] that led to experimental demonstration of enhanced transmission [21,22] with applications in focusing and imaging through turbid media [21,[23][24][25][26][27][28][29][30]. Absorption, common in optics, breaks energy conservation and makes the density of transmission eigenvalues [31] as well as reflection [32][33][34] eigenvalues to depend on its strength. However, the questions of whether the geometry of the system could affect the eigenvalue density in dissipative systems and if so, how it would affect it, have not been addressed.In this work we demonstrate that, unlike passive systems, the density of the transmission eigenvalues in absorbing disordered waveguides is geometry dependent, that is beyond predictions of the existing theory [31]. This opens possibility of tuning the functional form of the eigenvalue density by choosing the shape of the boundary. Furthermore, we show that dissipation makes a profound impact o...

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