From Photonic Time Interfaces to Smooth Temporal Modulations

Recently, time has been introduced as an additional degree of freedom to manipulate wave-matter interactions in both space and time [1].In this context, time interfaces are considered the temporal analogue of spatial interfaces [2].This has inspired the proposal and development of exotic applications including temporal coherence, temporal anisotropy, filters and effective medium concepts, to name a few [3][4][5][6][7][8][9][10][11][12][13].Recent ground-breaking works have experimentally demonstrated time interfaces in scenarios ranging from water waves, microwaves up to optical frequencies [14][15].In this work, we will discuss our recent efforts in studying wave propagation in time modulated media using time interfaces.It is well known that a fundamental requirement to create time interfaces in an unbounded medium is to rapidly modulate the permittivity/permeability/refractive index of the medium where the wave travels.Interestingly, recent works have shown the potential of tapered temporal switching as the temporal analogue of spatial tapering in, for instance, waveguides to reduce reflections.However, one may ask: would it be possible to fully mimic the time refracted signal produced by a time interface using smooth modulations of the refractive index of the medium?Here, we will discuss our recent efforts to answer this question by considering a cavity filled with a time-dependent material where its refractive index is adiabatically modulated from 1 to 2 .A full theoretical and numerical analysis will be presented showing that there are some values of rising/falling time of () where the smooth transition has the same solution as that of the time interface [16].