Matthieu Davy

Universal structure of transmission eigenchannels inside opaque media

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.

Transmission statistics and focusing in single disordered samples

We show in microwave experiments and random matrix calculations that in samples with a large number of channels the statistics of transmission for different incident channels relative to the average transmission is determined by a single parameter, the participation number of the eigenvalues of the transmission matrix, M. Its inverse, M(-1), is equal to the variance of relative total transmission of the sample, while the contrast in maximal focusing is equal to M. The distribution of relative total transmission changes from Gaussian to negative exponential over the range in which M(-1) changes from 0 to 1. This provides a framework for transmission and imaging in single samples.

Focusing through random media in space and time: a transmission matrix approach.

We exploit the evolution in time of the transmission matrix following pulse excitation of a random medium to focus radiation at a selected time delay t and position r. The temporal profile of a focused microwave pulse is the same as the incident Gaussian pulse. The contrast in space at time t of the focused wave is determined by the participation number of transmission eigenvalues M and the size N of the measured transmission matrix. The initial rise and subsequent decay of the contrast observed reflect the distribution of decay rates of the quasi-normal modes within the sample.

3D SAR imaging of the snowpack in presence of propagation velocity changes: Results from the AlpSAR campaign

In this paper we present results relative to the 3D GBSAR surveys acquired in february 2013 on the Austrian Alps as a part of the ESA campaign AlpSAR. The GBSAR was operated at X- and Ku-Band with a bandwidth of 4 GHz and employing a 2D synthetic aperture, resulting in 3D resolution capabilities at a resolution of few centimeters. Images produced at two different sites reveal the presence of multiple layers within the snowpack. The strongest backscatter contributions have been observed to correspond to bottom layers, that dominate the ones from the snow/air interface and the near subsurface. GBSAR data are observed to provide sensitivity to the propagation velocity into the snowpack, as revealed by the apparent depth variation with respect to the incidence angle.

Statistics and control of waves in disordered media.

Fundamental concepts in the quasi-one-dimensional geometry of disordered wires and random waveguides in which ideas of scaling and the transmission matrix were first introduced are reviewed. We discuss the use of the transmission matrix to describe the scaling, fluctuations, delay time, density of states, and control of waves propagating through and within disordered systems. Microwave measurements, random matrix theory calculations, and computer simulations are employed to study the statistics of transmission and focusing in single samples and the scaling of the probability distribution of transmission and transmittance in random ensembles. Finally, we explore the disposition of the energy density of transmission eigenchannels inside random media.

Green's function retrieval and fluctuations of cross density of states in multiple-scattering media

In this work we derive the average and the variance of the cross-correlation of a noise wavefield. The noise cross-correlation function (NCF) is widely used to passively estimate the Greens function between two probes and is proportional to the cross density of states (CDOS) in photonic and plasmonic systems. We first explain from the ladder approximation how the diffusion halo plays the role of secondary sources to reconstruct the mean Greens function. We then show that fluctuations of NCF are governed by several non-Gaussian correlations. An infinite-range correlation term dominates fluctuations of NCF-CDOS and proves that NCF is not a self-averaging quantity with respect to the plurality of noise sources. The link between these correlations and the intensity ones is highlighted. These results are supported by numerical simulations and are of importance for passive imaging applications and material science.

Spatial structure and density of states of transmission eigenchannels

We explore the spatial profile of the ensemble average of the energy density of eigenchannels of the transmission matrix within random diffusive media using computer simulations and nonperturbative diagrammatic technique. A symmetrical profile with a peak in the middle of the sample is found for the fully transmitting eigenchannel and is shown to be closely related to a position dependent diffusion coefficient of the open media. We show that the average spatial profile of each transmission eigenchannel when normalized by the profile of the completely transmitting eigenchannel depends only upon the value of transmission through the corresponding eigenchannel. A universal expression for the average spatial profile is given in terms of the auxiliary localization lengths determined from transmission eigenvalues and position dependent diffusion coefficient. These lengths were first introduced by Dorokhov to describe the scaling of transmission and conductance through disordered media. Though direct measurement of energy distribution within a scattering medium is generally difficult, we demonstrate in microwave measurements that the integrated energy density stored in the media of each eigenchannel can be determined from the measurements of spectra of the transmission matrix. The derivative of the composite phase of the eigenchannels with respect to the angular frequency yields the contribution to the density of states (DOS) from the individual transmission eigenchannels. This is proportional to integrated energy stored and the dwell time of the transmission eigenchannel. The DOS determined from the transmission eigenchannel is shown to be in good agreement with DOS obtained by analyzing the field spectra into quasi-normal modes of the open medium. These results provide a path towards controlling the energy deposition within a scattering medium.

Green’s Function Retrieval with Absorbing Probes in Reverberating Cavities

The cross-correlation of a diffuse wave field converges toward the difference between the anticausal and causal Greens functions between two points. This property has paved the way to passive imaging using ambient noise sources. In this Letter, we investigate Greens function retrieval in electromagnetism. Using a model based on the fluctuation dissipation theorem, we demonstrate theoretically that the cross-correlation function strongly depends on the absorption properties of the receivers. This is confirmed in measurements within a reverberation chamber. In contrast to measurements with noninvasive probes, we show that only the anticausal Greens function can be retrieved with a matched antenna. Finally, we interpret this result as an equivalent time-reversal experiment with an electromagnetic sink.

Densities of states, dynamics and intensity profiles of transmission eigenchannels of opaque media

We determine the frequency derivative of the composite phase of transmission eigenchannels and relate this to their contribution to the density of states, their dwell time and their intensity profile within the random medium.

Statistics of the Density of States in Random Media

We have found the continuous density of states for microwave radiation localized in quasi-one-dimensional samples and studied the statistics of the density of states for three sample lengths.