Temporal waveguiding in modulated 2D lattices

In this work we investigate the transient dynamics of time modulated 2D spring-mass lattices. We show that a suitable temporal modulation of the stiffness parameters can be employed to functionally steer waves in the 2D space. This is accomplished by tailoring the group velocity profile associated with the unit lattice. We firstly derive the necessary modulation conditions to establish an adiabatic variation of the propagation direction for a wave packet, which allows for a reflection-free waveguiding. Then, we show a number of numerical examples to illustrate the limitations of such a strategy and how the performances are affected by non-adiabatic temporal modulations.