Piezoelectric phononic-crystal plates, structured on their surface with metallic strips introducing electric-circuit loads, exhibit a tunable frequency-dispersion behaviour, nondestructively controlled in real time. Under an appropriate choice of boundary conditions through these loads, obeying a space-time propagation rule, it is demonstrated experimentally that these systems support nonreciprocal propagation of Lamb-like guided modes in their interior. The observations combined with numerical calculations confirm a broadband translation of the dispersion curves in the frequency-wavenumber space depending on the modulation speed. A careful analysis reveals a simple vector-rule relationship between the static bands and those induced by the time modulation of the external loads in the dispersion diagram. The device proposed in this study, offering dynamic changes in the electric boundary conditions by making use of switches driven by a microcontroller, thus, becomes an efficient tool not only for the realization of real-time control of elastic waves but also, and more importantly, a versatile platform for a robust generation of nonreciprocity effects in tunable, low-dimensional systems.

Complex-frequency excitations have recently attracted a lot of attention owing to their ability to solve a number of extraordinary challenges in photonics, such as overcoming losses without gain in metalenses and plasmonic waveguides and achieving virtual absorption. However, the totality of the works so far has been mainly computational or experimental, and a full theory of the complex dynamics enabled by these excitations is still missing. Here, we develop a fully analytical, exact time-domain theory for the dynamical scattering of these excitations by both sides of dielectric plates, which have been used to achieve virtual absorption. Our precise theoretical analysis confirms previous observations and, in addition, reveals a number of intriguing phenomena that were previously missed, such as discontinuities in the scattering of the outgoing electromagnetic field and release of the stored energy in distinct packets.