Optimal Multiplexing of Spatially Encoded Information across Custom-Tailored Configurations of a Metasurface-Tunable Chaotic Cavity

Letter

Optimal Multiplexing of Spatially Encoded Information across Custom-Tailored Configurations of a Metasurface-Tunable Chaotic Cavity

Philipp del Hougne, Matthieu Davy, and Ulrich Kuhl

Phys. Rev. Applied 13, 041004 – Published 24 April 2020

Abstract

Tunable disorder-engineered materials offer the opportunity to add functionalities for finely tailored dynamic wave control to applications inevitably or voluntarily based on random materials. Exciting prospects are tailored channel matrices that optimally multiplex information on multiple incoming spatial channels across multiple spatial or configurational channels on the receive side. Here we demonstrate the latter at microwave frequencies based on a chaotic cavity equipped with tunable reflect-array metasurfaces that are configured using a judiciously tailored coding sequence. The results have immediate technological relevance in computational imaging and sensing, since they enable the single-port acquisition of large-aperture spatial information with the lowest possible latency and processing burden. A reduction of the necessary number of measurements by a factor of 2.5 compared with state-of-the-art approaches is found in in situ experiments. The proposed concept and platform set the stage for “on-demand” realizations of desired channel-matrix properties and provide fundamental insights into the role of engineered disorder in the interplay of different types of degrees of freedom in mesoscopic physics. The principle is also expected to inspire novel multimode-fiber-based tailored-multiplexing schemes in the optical domain.

Received 24 January 2020
Revised 29 February 2020
Accepted 20 March 2020

DOI:https://doi.org/10.1103/PhysRevApplied.13.041004

Physics Subject Headings (PhySH)

Optical chaos Optoelectronics Photonics

Metamaterials Random & disordered media Surfaces

Cavity resonators Microwave techniques

Atomic, Molecular & Optical

Authors & Affiliations

Philipp del Hougne ^1,*, Matthieu Davy², and Ulrich Kuhl¹

¹Institut de Physique de Nice, CNRS UMR 7010, Université Côte d’Azur, 06108 Nice, France
²Univ Rennes, CNRS, Institut d’Electronique et de Télécommunications de Rennes (IETR) - UMR 6164, F35000 Rennes, France

^*philipp.delhougne@inphyni.cnrs.fr

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Vol. 13, Iss. 4 — April 2020

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Images

Figure 1
Principle of information multiplexing with different types of measurement diversity. A complex medium scrambles $n$ pieces of spatially ( $r_{TX, i}$ , blue) encoded information. To recover these inputs, the scrambled wave field is probed with $p$ independent measurements, which can be of spatial nature ( $r_{R X, i}$ , blue) or spectral nature ( $f_{i}$ , red) or can correspond to different configurations of the complex medium ( ${PC}_{i}$ , green).
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Figure 2
(a) The programmable coding metacavity (PCM) is an irregular metallic cavity containing scattering objects and two walls are covered by reconfigurable reflect-array metasurfaces. (b) Eight signals, modulated in situ by eight in-phase and quadrature (IQ) modulators, excite the cavity via eight antennas. A ninth antenna probes the resulting cavity wave field for different PCM configurations.
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Figure 3
Dynamics and outcome of tailoring the channel matrix. (a) SV spectra for random channel matrices with $γ = 1$ and $γ = 2.5$ (averaged over 25 realizations), as well as for a channel matrix with $γ = 1$ tailored to maximize $R_{eff}$ or $T$ , respectively. The shaded areas indicate the standard deviations for the cases with random coding sequences. The insets indicate the distribution of the eigenvalues $λ_{i}$ of $H$ in the complex plane for 25 random channel matrices with $γ = 1$ (top left), for the channel matrix tailored to maximize $R_{eff}$ (top right), and for the channel matrix tailored to maximize $T$ (bottom). For reference, an orange circle is indicated, whose radius is the average magnitude of the eigenvalues for the channel matrix tailored to maximize $R_{eff}$ . (b) Evolution of $R_{eff}$ (top row) and $T$ (bottom row) over the course of the iterative optimization of the coding sequence to maximize $R_{eff}$ (left column) or $T$ (right column). The shaded area and the continuous black line indicate the standard deviation and average, respectively, of the values of $R_{eff}$ and T obtained in 100 random realizations. cod. seq., coding sequence; max., maximize.
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Figure 4
Reconstruction quality with a random (purple) versus a tailored (orange) channel matrix. (a)–(f) Sample reconstructions of two injected signals (smiley, circle) at three distinct SNRs: 56.4 dB (left), 50.0 dB (middle), and 40.0 dB (right). $ρ = 56.4 dB$ is the highest realizable SNR in our experiment. The displayed realizations are chosen such that their reconstruction error is closest to the average reconstruction error. (g) Dependence of the average NMSE, $χ$ , on the SNR, $ρ$ . The corresponding curves for a reconstruction based on in situ measurements (continuous lines) are contrasted with the curves dictated by the theory from Eq. (1) (dashed lines). The difference between the two curves for random versus tailored coding sequences is plotted in green. (h) Minimum number of measurements $p_{min}$ necessary to guarantee a given reconstruction quality $χ$ at the SNR at which $p = n$ guarantees this reconstruction quality using the tailored coding sequence. The shaded area indicates the standard deviation when random coding sequences are used. (i) Lowest necessary SNR $ρ_{min}$ that guarantees a given reconstruction quality $χ$ for a system with $γ = 1$ for the case of using a random coding sequence or a tailored coding sequence.
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