Low-Complexity 3D InISAR Imaging Using a Compressive Hardware Device and a Single Receiver.

An Interferometric Inverse SAR system is able to perform 3D imaging of non-cooperative targets by measuring their responses over time and through several receiving antennas. Phase differences between signals acquired with a spatial diversity in vertical or horizontal directions are used to localize moving scatterers in 3D. The use of several receiving channels generally results into a costly and complex hardware solution, and this paper proposes performing this multichannel acquisition using a single receiver and a hardware compressive device, based on a chaotic cavity which simultaneously multiplexes in the spectral domain signals acquired over different antennas. The radar responses of the scene are encoded in the spectral domain onto the single output of a leaky chaotic cavity, and can be retrieved by solving an inverse problem involving the random transfer matrix of the cavity. The applicability of this compressed sensing approach for the 3D imaging of a non-cooperative target using low-complexity hardware is demonstrated using both simulations and measurements. This study opens up new perspectives to reduce the hardware complexity of high-resolution ISAR systems.

Anti-reflection structure for perfect transmission through complex media.

The scattering of waves when they propagate through disordered media is an important limitation for a range of applications, including telecommunications1, biomedical imaging2, seismology3 and material engineering4,5. Wavefront shaping techniques can reduce the effect of wave scattering, even in opaque media, by engineering specific modes-termed open transmission eigenchannels-through which waves are funnelled across a disordered medium without any back reflection6-9. However, with such channels being very scarce, one cannot use them to render an opaque sample perfectly transmitting for any incident light field. Here we show that a randomly disordered medium becomes translucent to all incoming light waves when placing a tailored complementary medium in front of it. To this end, the reflection matrices of the two media surfaces facing each other need to satisfy a matrix generalization of the condition for critical coupling. We implement this protocol both numerically and experimentally for the design of electromagnetic waveguides with several dozen scattering elements placed inside them. The translucent scattering media we introduce here also have the promising property of being able to store incident radiation in their interior for remarkably long times.

Exceptional Points of PT-Symmetric Reflectionless States in Complex Scattering Systems.

We investigate experimentally and analytically the coalescence of reflectionless (RL) states in symmetric complex wave-scattering systems. We observe RL exceptional points (EPs), first with a conventional Fabry-Perot system for which the scattering strength within the system is tuned symmetrically and then with single- and multichannel symmetric disordered systems. We confirm that an EP of the parity-time (PT)-symmetric RL operator is obtained for two isolated quasinormal modes when the spacing between central frequencies is equal to the decay rate into incoming and outgoing channels. Finally, we leverage the transfer functions associated with RL and RL-EP states to implement first- and second-order analog differentiation.

Diffuse field cross-correlations: Scattering theory and electromagnetic experiments.

The passive estimation of impulse responses from ambient noise correlations arouses increasing interest in seismology, acoustics, optics, and electromagnetism. Assuming the equipartition of the noise field, the cross-correlation function measured with noninvasive receiving probes converges towards the difference of the causal and anticausal Green's functions. Here, we consider the case when the receiving field probes are antennas which are well coupled to a complex medium-a scenario of practical relevance in electromagnetism. We propose a general approach based on the scattering matrix formalism to explore the convergence of the cross-correlation function. The analytically derived theoretical results for chaotic systems are confirmed in microwave measurements within a mode-stirred reverberation chamber. This study provides fundamental insight into the Green's function retrieval technique and paves the way for a new technique to characterize electromagnetic antennas.

Coherent Wave Control in Complex Media with Arbitrary Wavefronts.

Wavefront shaping (WFS) has emerged as a powerful tool to control the propagation of diverse wave phenomena (light, sound, microwaves, etc.) in disordered matter for applications including imaging, communication, energy transfer, micromanipulation, and scattering anomalies. Nonetheless, in practice the necessary coherent control of multiple input channels remains a vexing problem. Here, we overcome this difficulty by doping the disordered medium with programmable meta-atoms in order to adapt it to an imposed arbitrary incoming wavefront. Besides lifting the need for carefully shaped incident wavefronts, our approach also unlocks new opportunities such as sequentially achieving different functionalities with the same arbitrary wavefront. We demonstrate our concept experimentally for electromagnetic waves using programmable metasurfaces in a chaotic cavity, with applications to focusing with the generalized Wigner-Smith operator as well as coherent perfect absorption. We expect our fundamentally new perspective on coherent wave control to facilitate the transition of intricate WFS protocols into real applications for various wave phenomena.

Selectively exciting quasi-normal modes in open disordered systems.

Transmission through disordered samples can be controlled by illuminating a sample with waveforms corresponding to the eigenchannels of the transmission matrix (TM). But can the TM be exploited to selectively excite quasi-normal modes and so control the spatial profile and dwell time inside the medium? We show in microwave and numerical studies that spectra of the TM can be analyzed into modal transmission matrices of rank unity. This makes it possible to enhance the energy within a sample by a factor equal to the number of channels. Limits to modal selectivity arise, however, from correlation in the speckle patterns of neighboring modes. In accord with an effective Hamiltonian model, the degree of modal speckle correlation grows with increasing modal spectral overlap and non-orthogonality of the modes of non-Hermitian systems. This is observed when the coupling of a sample to its surroundings increases, as in the crossover from localized to diffusive waves.

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 Green's functions between two points. This property has paved the way to passive imaging using ambient noise sources. In this Letter, we investigate Green's 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 Green's function can be retrieved with a matched antenna. Finally, we interpret this result as an equivalent time-reversal experiment with an electromagnetic sink.

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.

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 eigenchannels and the densities of states of random media.

We show in microwave measurements and computer simulations that the contribution of each eigenchannel of the transmission matrix to the density of states (DOS) is the derivative with angular frequency of a composite phase shift. The accuracy of the measurement of the DOS determined from transmission eigenchannels is confirmed by the agreement with the DOS found from the decomposition of the field into modes. The distribution of the DOS, which underlies the Thouless number, is substantially broadened in the Anderson localization transition. We find a crossover from constant to exponential scaling of fluctuations of the DOS normalized by its average value. These results illuminate the relationships between scattering, stored energy, and dynamics in complex media.

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.

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.

Green's function retrieval and passive imaging from correlations of wideband thermal radiations.

We present an experimental demonstration of electromagnetic Green's function retrieval from thermal radiations in anechoic and reverberant cavities. The Green's function between two antennas is estimated by cross correlating milliseconds of decimeter noise. We show that the temperature dependence of the cross-correlation amplitude is well predicted by the blackbody theory in the Rayleigh-Jeans limit. The effect of a nonuniform temperature distribution on the cross-correlation time symmetry is also explored. Finally, we open a new way to image scatterers using ambient thermal radiations.