Inverse design of perfectly transmitting eigenchannels in scattering media

Abstract

Light-matter interactions inside turbid medium can be controlled by tailoring the spatial distribution of energy density throughout the system. Wavefront shaping allows selective coupling of incident light to different transmission eigenchannels, producing dramatically different spatial intensity profiles. In contrast to the density of transmission eigenvalues that is dictated by the universal bimodal distribution, the spatial structures of the eigenchannels are not universal and depend on the confinement geometry of the system. Here, we develop and verify a model for the transmission eigenchannel with the corresponding eigenvalue close to unity. By projecting the original problem of two-dimensional diffusion in a homogeneous scattering medium onto a one-dimensional inhomogeneous diffusion, we obtain an analytical expression relating the intensity profile to the shape of the confining waveguide. Inverting this relationship enables the inverse design of the waveguide shape to achieve the desired energy distribution for the perfectly transmitting eigenchannel. Our approach also allows to predict the intensity profile of such channel in a disordered slab with open boundaries, pointing to the possibility of controllable delivery of light to different depths with local illumination.PACS numbers: 42.25. Dd,42.25.Hz, Interference of scattered waves in random media gives rise to well-known phenomena such as enhanced backscattering, Anderson localization and universal conductance fluctuation. These phenomena are general and occur not only for electromagnetic waves, but also for acoustic, electronic and other kinds of waves [1, 2]. Recently, there has been a growing interest in another interference effect -formation of perfectly transmitting channels [3, 4], which can greatly enhance the total transmission through opaque media [5][6][7][8]. In addition, the perfectly transmitting channels have energy density buildup deep inside the medium [7,[9][10][11], opening the possibility of enhancing linear and non-linear light-matter interactions inside turbid media. Recent advances of optical wavefront shaping techniques [12][13][14][15][16] enabled direct coupling of incident light to perfectly transmitting channels [11], making the depth profile of energy density dramatically different from the typical decay in a diffusive medium. To unlock the full potential of this approach for tailoring light-matter interactions in turbid media, it becomes imperative to understand what determines the spatial structure of the perfectly transmitting channels.Recently two theoretical models have been put forward to describe the spatial profile of the perfectly transmitting channels in lossless diffusive media. Davy et al [9] applied the supersymmetry theory to wave propagation in a quasi-one-dimensional random system and related the intensity profile to the return probability (RP) of diffusive waves. Ojambati et all [10,17] proposed that the perfectly transmitting channel in a disordered slab is related to the fundamental mode (FM) of the onedi...

Inverse design of long-range intensity correlation in scattering media

“…We consider a two-dimensional waveguide where A(z) = W (z), and use the following parameters: N 0 = 125, L/ 30, W (0)/ 5, W min /W (0) = 1/3, z c = L/3, and g 7. The simulations were performed using the method described in detail in our previous works [23,32,61]. The cross-section averaged intensity was obtained numerically by solving the wave equation and then was used to compute C(z 1 , z 2 ) using Eq.…”

“…In this work, we derive expressions for the Green's function in the two-and three-dimensional disordered waveguides with an arbitrary shape in order to obtain the nonlocal long-range mesoscopic correlations [9,[14][15][16][17][18][19][20][21]. We adapt the projection technique, developed in physical chemistry for the particle diffusion in confined geometries [22,23], to describe wave diffusion. We reduce the problem to one dimension and obtain analytical solution.…”

“…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].…”

Enhanced deep detection of Raman scattered light by wavefront shaping

“…On the contrary, the mode with the highest transmission is also one that accumulates a large amount of energy inside the sample [22,23], and the energy distribution takes an approximately cosine shape (green curve in Fig. 1a), with a maximum at the center [24].…”

Transverse localization of transmission eigenchannels

“…In recent years, spatial light modulators (SLMs) have been used to excite the open channels [5][6][7][8][9][10][11][12][13][14] to enhance light transmission through diffusive media. Selective excitation of individual channels can dramatically change the total energy stored inside the random media as well as the spatial distribution of energy density [14][15][16][17][18][19][20].However, some important questions regarding the transmission eigenchannels remain open. What are the transverse spatial profiles for coupling light into such channels?…”