On the effects of suitably designed space microstructures in the propagation of waves in time modulated composites

In the one-dimensional case, the amplitude of a pulse that propagates in a homogeneous material whose properties are instantaneously changed in time will undergo an exponential increase due to the interference between the reflected and transmitted pulses generated at each sudden switch. Here, we resolve the issue by designing suitable reciprocal PT-symmetric space-time microstructures so that the interference between the scattered waves is such that the overall amplitude of the wave will be constant in time in each constituent material. Remarkably, for the geometries proposed here, a pulse will propagate with constant amplitude regardless of the impedance between the constituent materials, and for some, regardless of the wave speed mismatch. We extend, then, these results to the two-dimensional case, by proposing suitable geometries that avoid the blow up of the wave amplitude at the source point due to the scattering associated with time modulation. Given that the energy associated with the wave will increase exponentially in time, this creates the possibility to exploit the stable propagation of the pulse to accumulate energy for harvesting.