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

What is it about?

Consider a homogeneous material whose properties are modulated instantaneously in time. If a pulse propagates in the material when its properties are instantaneously changed in time, then the pulse will split into two pulses going opposite directions. If this process is repeated periodically, then there will be multiple reflected and transmitted pulses. In the one-dimensional case, their interference will be such that the amplitude of the wavefront will increase exponentially in time, thus leading to instability (in the two-dimensional case, the blow up will occur at the source). Instead of working with homogeneous materials, in our paper we propose to apply time modulation to suitably chosen composite materials with a properly designed microstructure. Specifically, we provide design principles so that the interference of the reflected and transmitted pulses due to the time modulation and the space geometry is such that the wavefront propagates without any instability. In other words, we design the microgeometry of the composite to counteract the effects of the time modulation so that the wavefront does not increase exponentially in amplitude. We provide examples of such composites in the one-dimensional and two-dimensional case.

Featured Image

Photo by Pawel Czerwinski on Unsplash

Photo by Pawel Czerwinski on Unsplash

Why is it important?

Time-modulated materials are a new generation of metamaterials that present extreme wave phenomena. However, the experimental realization of sharp time interfaces, by instantaneously switching the material properties, is a challenging task. Furthermore, the instability resulting from the exponential blow up of the amplitude of the wavefront if the time modulation is repeated limits the implementation of such materials. Our paper provides a solution to such a problem by offering a wide range of spatial composites that, if suitably time modulated, will experience wave propagation with no blow up. Note that, in order to apply the time switch, one has to input some energy into the system. For repeated switches, the energy associated with the wave will increase exponentially in time. Our special time-modulated composites will then create the possibility to exploit the stable propagation of the pulse to accumulate energy for harvesting.