We present an analytic random matrix theory for the effect of incomplete channel control on the measured statistical properties of the scattering matrix of a disordered multiple-scattering medium. When the fraction of the controlled input channels, m1, and output channels, m2, is decreased from unity, the density of the transmission eigenvalues is shown to evolve from the bimodal distribution describing coherent diffusion, to the distribution characteristic of uncorrelated Gaussian random matrices, with a rapid loss of access to the open eigenchannels. The loss of correlation is also reflected in an increase in the information capacity per channel of the medium. Our results have strong implications for optical and microwave experiments on diffusive scattering media.

We demonstrate order of magnitude coherent control of total transmission of light through random media by shaping the wavefront of the input light. To understand how the finite illumination area on a wide slab affects the maximum values of total transmission, we develop a model based on random matrix theory that reveals the role of long-range correlations. Its predictions are confirmed by numerical simulations and provide physical insight into the experimental results. PACS numbers: 42.25.Bs, 05.60.Cd, 02.10.Yn A lossless strong scattering medium, that has a thickness L much larger than the elastic mean free path ℓ, is normally opaque to incident beams of light, with only a small fraction, ℓ/L, of the incident photon flux diffusively transmitted. However, it has been known for over two decades that, due to the coherence of elastic scattering, this transmitted flux is not totally random in character, but has subtle correlations that were first discovered in the context of mesoscopic electron transport [1][2][3][4]. One striking implication of these correlations is that an optimally prepared coherent input beam could be transmitted through a strong scattering medium hundreds of mean free paths in thickness with order unity efficiency. These highly transmitting input states are eigenvectors of the matrix t † t, where t is the transmission matrix (TM) of the sample. They were predicted using a random matrix theory approach [1-3] and were termed "open channels".Because the input electron states are not controllable in mesoscopic conductors, the open channel concept was not testable there, except indirectly through other properties such as conductance fluctuations or shot noise [5]. Experimental measurements of the TM through disordered waveguides at microwave frequencies are consistent with the theory developed for this geometry [6][7][8] and imply that open channels should exist, but enhanced transmission has not yet been directly demonstrated in these systems due to the difficulty of imposing an appropriate input waveform. The advent of wavefront shaping methods using a Spatial Light Modulator (SLM) at optical frequencies has reopened the search for this dramatic effect in strong scattering media. It has already been shown that wavefront shaping of input states combined with feedback optimization can enable diverse functions for multiple scattering media in optics [9], causing them to act as lenses [10,11], phase plates [12,13] or spectral filters [14,15]. However coherent control of total transmission, which is a non-local property of the TM, is much more difficult. Some progress in this direction has been made by studying the increase of the total transmission when focusing light through scattering media to wavelength scale spots [16] or by measuring the partial TM and injecting light into calculated singular vectors [17]. In addition, a very recent study highlights effects of the mesoscopic correlation on the transmission properties by measuring a large -but still not complete -TM [18]. We report here a furth...

We study probability distributions of eigenvalues of Hermitian and non-Hermitian Euclidean random matrices that are typically encountered in the problems of wave propagation in random media.

We develop a theory for the eigenvalue density of arbitrary non-Hermitian Euclidean matrices. Closed equations for the resolvent and the eigenvector correlator are derived. The theory is applied to the random Green's matrix relevant to wave propagation in an ensemble of pointlike scattering centers. This opens a new perspective in the study of wave diffusion, Anderson localization, and random lasing.