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.

Figure 1

(a) Conventionally, first, the scattering matrix $S$ of a given complex medium is measured; second, the desired WFS protocol is applied to $S$; third, the obtained ${\psi }_{\mathrm{WFS}}$ (illustrated as phasors) is injected into the system. Each channel requires independent control of amplitude and phase to inject ${\psi }_{\mathrm{WFS}}$. (b) In our proposal, the complex medium is doped with programmable meta-atoms, here 1-bit programmable meta-atoms with two possible digitalized states “0” and “1”. By judiciously programming the meta-atoms, the system’s scattering matrix can be tweaked (from $S$ to $S^{\prime }$) such that the required wavefront for a desired WFS protocol coincides with a fixed arbitrary wavefront: ${\psi }_{\mathrm{WFS}}(S^{\prime })={\psi }_{\mathrm{arb}}$.

Figure 2

(a) Experimental setup: multiport irregularly shaped cavity equipped with two arrays of 152 programmable meta-atoms. The inset shows one meta-atom. For our GWS experiments, the eighth port is switched between OC and ML terminations. (b) Example iterative optimization maximizing ${\mathcal{C}}_{\mathrm{GWS}}=|q_1^{\prime }{\psi }_{\mathrm{arb}}^{†}|$ (colored). Throughout the optimization, $C=|q_1^{\prime }{\psi }_{\mathrm{PC}}(S^{\prime })|$ is very close to unity (black-dashed line). (c) Variations of intensity $T(S^{\prime },{\psi }_{\mathrm{arb}})$ (colored) and optimal value $T(S^{\prime },q_1^{\prime })$ (black) over the course of the optimization.

Figure 3

(a) Distribution of intensity transmitted to the target on a logarithmic scale for an arbitrary impinging wavefront on a random system [$T(S_{\mathrm{rand}},{\psi }_{\mathrm{arb}})$, blue], the optimal wavefront impinging on a random system $[T\mathbf{(}{S}_{\mathrm{rand}},{\psi }_{\mathrm{PC}}(S_{\mathrm{rand}})\mathbf{)},\text{black}]$, and an arbitrary wavefront impinging on a system optimized for that arbitrary wavefront [$T(S_{\mathrm{opt}},{\psi }_{\mathrm{arb}})$, red]. (b) Visualization in the complex plane of the transmission coefficients from five ports to the targeted port for 100 random configurations of the meta-atoms. (c) Dependence of $T(S_{\mathrm{opt}},{\psi }_{\mathrm{arb}})$ on the degree of correlation between ${\psi }_{\mathrm{arb}}$ and $t_0^{*}$.

Figure 4

(a) Spectrum corresponding to CPA (blue) and anti-CPA condition (red) within the 5.135–5.159 GHz range. (b) Comparison of these two scattering anomalies with the distribution of $R^{\prime }$ in our system (black).