Universal structure of transmission eigenchannels inside opaque media

Abstract

As the desire to explore opaque materials is ordinarily frustrated by multiple scattering of waves, attention has focused on the transmission matrix of the wave field. This matrix gives the fullest account of transmission and conductance and enables the control of the transmitted flux; however, it cannot address the fundamental issue of the spatial profile of eigenchannels of the transmission matrix inside the sample. Here we obtain a universal expression for the average disposition of energy of transmission eigenchannels within random diffusive systems in terms of auxiliary localization lengths determined by the corresponding transmission eigenvalues. The spatial profile of each eigenchannel is shown to be a solution of a generalized diffusion equation. These results reveal the rich structure of transmission eigenchannels and enable the control of the energy distribution inside random media.

Control of Energy Density inside a Disordered Medium by Coupling to Open or Closed Channels

“…Since the energy density determines the light-matter interactions inside a scattering system, manipulating its spatial distribution opens the door to tailoring optical excitations as well as linear and nonlinear optical processes such as absorption, emission, amplification, and frequency mixing inside turbid media. The potential applications range from photovoltaics [7,8] In recent years there have been numerous theoretical and experimental studies on transmission eigenchannels [5,[13][14][15][16][17]. While they can be deduced from the measured transmission matrix [18][19][20][21], it is difficult to directly probe their spatial profiles inside three-dimensional (3D) random media.…”

“…In general, the penetration depth and energy density distribution of multiply scattered waves inside a disordered medium are determined by the spatial profiles of the transmission eigenchannels that are excited by the incident light. The distinct spatial profiles of open and closed channels suggest that selective coupling of incident light to these channels enables an effective control of total transmission and energy distribution inside the random medium [5,6]. Since the energy density determines the light-matter interactions inside a scattering system, manipulating its spatial distribution opens the door to tailoring optical excitations as well as linear and nonlinear optical processes such as absorption, emission, amplification, and frequency mixing inside turbid media.…”

Diffusion in Translucent Media

“…Since the similarity in the scaling of transmission in translucent and diffusive samples is related to the similarity in the statistics of the x n , and so the τ n , it is interesting to explore whether there is a similarity in form between energy densities of the transmission eigenchannels in translucent and diffusive media. This will determine the energy density inside the sample, and ultimately the delay time in transmission [35][36][37][38][39][40] (Supplementary Eq. 10).…”

“…] is a solution of the diffusion equation with boundary conditions appropriate for perfect transmission 40 . A(L/ℓ) is the peak value of F 1 (x/L) at x/L = 1/2.…”

Minimum reflection channel in amplifying random media

“…However, wave interference effects may diminish the reflectance by creating highly transmitting open channels [1][2][3][4] . Recent developments of wavefront shaping and phase recording techniques in optics have enabled the coupling of incident light to these open channels [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] . The open channels can greatly enhance light transmission through scattering media, having a profound impact in a wide range of applications from deep tissue imaging and laser surgery, to spectroscopy [20][21][22][23][24][25][26][27][28][29][30] and opto-genetics 31 .…”