Fig. 3: Physical-model-based coherent wave control with phaseless calibration data. | Nature Communications

Fig. 3: Physical-model-based coherent wave control with phaseless calibration data.

From: Experimentally realized physical-model-based frugal wave control in metasurface-programmable complex media

Fig. 3

a–d Measured ground truth and phase-retrieval physical-model (PR-Model) predictions for four selected scattering coefficients (for ten random unseen metasurface configurations). The PR-Model was calibrated for the \(4\times 4\). scattering matrix without any phase information. e Deposited energy at port 1 upon injecting a coherent wavefront through the remaining three ports (for 50 random unseen metasurface configurations). \({{{{{{\boldsymbol{\psi }}}}}}}_{{{{{{\rm{in}}}}}}}^{{{{{{\rm{opt}}}}}}}\) (blue) is the benchmark (and provably optimal) wavefront obtained via phase conjugation given perfect knowledge of the relevant scattering coefficients, \({{{{{{\boldsymbol{\psi }}}}}}}_{{{{{{\rm{in}}}}}}}^{{{{{{\rm{mod}}}}}}}\) (red) is obtained with the same approach but using the PR-Model, and \({{{{{{\boldsymbol{\psi }}}}}}}_{{{{{{\rm{in}}}}}}}^{{{{{{\rm{uni}}}}}}}\) (yellow) is a uniform wavefront (see Methods for details). f Reflected power upon injecting a coherent wavefront through all four ports (for 50 random unseen metasurface configurations). High absorption corresponds to low reflected power. \({{{{{{\boldsymbol{\psi }}}}}}}_{{{{{{\rm{in}}}}}}}^{{{{{{\rm{opt}}}}}}}\) (blue) is the benchmark (and provably optimal) wavefront obtained via an eigendecomposition of \({{{{{{\bf{S}}}}}}}^{{{\dagger}} }{{{{{\bf{S}}}}}}\) assuming perfect knowledge of \({{{{{\bf{S}}}}}}\), \({{{{{{\boldsymbol{\psi }}}}}}}_{{{{{{\rm{in}}}}}}}^{{{{{{\rm{mod}}}}}}}\) (red) is obtained with the same approach but using the PR-Model, and \({{{{{{\boldsymbol{\psi }}}}}}}_{{{{{{\rm{in}}}}}}}^{{{{{{\rm{uni}}}}}}}\) (yellow) is a uniform wavefront (see “Methods” for details). g Identification using the PR-Model of four metasurface configurations (shown as insets) that enable quadrature-phase-shift-keying (QPSK) backscatter communications when port 2 radiates a continuous-wave signal and port 4 detects the received phase (or vice versa) (see “Methods” for details).

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