Digital programming of reciprocity breaking in resonant piezoelectric metamaterials

We demonstrate a digitally controlled piezoelectric metamaterial waveguide leveraging resonant, spatiotemporally modulated synthetic impedance circuits for programmable reciprocity breaking. Piezoelectric metamaterials have effective stiffness that depends on the shunt circuitry connected to each unit cell, offering greatly increased design freedom over their purely mechanical counterparts. By connecting a digitally controlled synthetic impedance shunt circuit to each unit cell of the metamaterial domain, the effective stiffness is externally programmed according to a desired profile in space and time. Specifically, we present threefold capabilities in this electromechanical system: (1) smooth parameter modulation (no abrupt switching) through synthetic impedance circuits that eliminate cumbersome analog electrical components, (2) resonant electromechanical modulation in space and time so that one does not have to operate near the Bragg band gap, and (3) precise digital programming by numerically entering the space and time properties of the domain. We also demonstrate the frequency conversion in narrow-band excitation centered at a directional band gap. The experimental results are compared against high-fidelity multiphysics finite-element simulations, yielding excellent agreement for this class of digitally programmable nonreciprocal elastic metamaterials.