Mapping the energy density of shaped waves in scattering media onto a complete set of diffusion modes

Abstract

Abstract:We show that the spatial distribution of the energy density of optimally shaped waves inside a scattering medium can be described by considering only a few of the lowest eigenfunctions of the diffusion equation. Taking into account only the fundamental eigenfunction, the total internal energy inside the sample is underestimated by only 2%. The spatial distribution of the shaped energy density is very similar to the fundamental eigenfunction, up to a cosine distance of about 0.01. We obtained the energy density inside a quasi-1D disordered waveguide by numerical calculation of the joined scattering matrix. Computing the transmission-averaged energy density over all transmission channels yields the ensemble averaged energy density of shaped waves. From the averaged energy density obtained, we reconstruct its spatial distribution using the eigenfunctions of the diffusion equation. The results from our study have exciting applications in controlled biomedical imaging, efficient light harvesting in solar cells, enhanced energy conversion in solid-state lighting, and low threshold random lasers.

Universality of eigenchannel structures in dimensional crossover

“…An unprecedented degree of control reached in experiments on classical waves is turning the dream of understanding and controlling wave propagation in complex media into reality 1 . Central to many ongoing research activities is the concept of transmission eigenchannel [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] (abbreviated as eigenchannel herefater). Loosely speaking, the eigenchannel refers to a specific wave field, which is excited by the input waveform corresponding to the right-singular vector [17][18][19] of the transmission matrix (TM) t. When a wave is launched into a complex medium it is decomposed into a number of "partial waves", each of which propagates along an eigenchannel and whose superposition gives the field distribution excited by the incoming wave.…”

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].…”

Angular Memory Effect of Transmission Eigenchannels

“…A recent breakthrough in coherent control of light in diffusive media is the selective excitation of transmission eigenchannels by wavefront shaping [39][40][41][42]. In this way not only the transmittance can be varied from near zero to the order of unity, but also the spatial distribution of energy density inside the medium is changed drastically [42][43][44][45][46][47][48]. Moreover, it has very recently been discovered that in a wide diffusive slab, the transmission eigen- * hui.cao@yale.edu channels are localized in transverse directions with the same transverse width at the front and the back surfaces of the slab (i.e.…”