Controlling transmission eigenchannels in random media by edge reflection

Abstract

Transmission eigenchannels and associated eigenvalues, that give a full account of wave propagation in random media, have recently emerged as a major theme in theoretical and applied optics. Here we demonstrate, both analytically and numerically, that in quasi one-dimensional (1D) diffusive samples, their behavior is governed mostly by the asymmetry in the reflections of the sample edges rather than by the absolute values of the reflection coefficients themselves. We show that there exists a threshold value of the asymmetry parameter, below which high transmission eigenchannels exist, giving rise to a singularity in the distribution of the transmission eigenvalues, ρ(T → 1) ∼ (1−T )At the threshold, ρ(T ) exhibits critical statistics with a distinct singularity ∼ (1 − T ) − 1 3 ; above it the high transmission eigenchannels disappear and ρ(T ) vanishes for T exceeding a maximal transmission eigenvalue. We show that such statistical behavior of the transmission eigenvalues can be explained in terms of effective cavities (resonators), analogous to those in which the states are trapped in 1D strong Anderson localization. In particular, the ρ(T )-transition can be mapped onto the shuffling of the resonator with perfect transmittance from the sample center to the edge with stronger reflection. We also find a similar transition in the distribution of resonant transmittances in 1D layered samples. These results reveal a physical connection between high transmission eigenchannels in diffusive systems and 1D strong Anderson localization. They open up a fresh opportunity for practically useful application: controlling the transparency of opaque media by tuning their coupling to the environment.

Probing nonorthogonality of eigenfunctions and its impact on transport through open systems

“…. Assuming a uniform distribution of x 0 between 0 and L leads to a bimodal distribution of C n [50]. The bimodal distribution of C n and hence T n is in agreement with the formula proposed for isolated peaks in the transmission spectrum of one-dimensional (1D) samples using a resonator model associated with effective cavities of length ξ [50,51].…”

Optical transmission matrix as a probe of the photonic strength

“…We investigate the effect of interface reflections at this surface on the statistics of the TM. In some earlier studies, numerical and analytical results have been obtained on the effect of boundary reflections on transmission matrices [30,39,40]. In these studies it was shown that the distribution of transmission eigenvalues of the fully controlled TM is not very sensitive to surface reflection for moderate surface reflectivity.…”

Inverse design of long-range intensity correlation in scattering media

“…Spatial light modulator and related technologies have enabled manipulation of light propagation in scattering media via shaping the incident wave-front field to tailor it to the specific configuration of scatters in the sample [8,24,25]. This * yamilov@mst.edu brought renewed attention to the nonlocal correlations as they were found to be related to such transport parameters as focusing contrast inside the medium [26] and energy deposition [20,23,[27][28][29][30][31][32][33][34][35]. The long-range correlation also affects total transmission via an optimized wave front with a limited degree of input control [21]; it is also a key factor determining the broadband transmission achievable in wave-front shaping [36].…”