Abstract
This paper reports on the waveform shaped by a finite duration photonic time-crystal with its permittivity and permeability periodically varying in time. A Gaussian-modulated sinusoidal pulse is incident onto this photonic time-crystal to evaluate the backward- and forward-scattering waveforms. An analytical formulation, utilizing a cascade of temporal transfer matrices and the inverse fast Fourier transform, was employed to conduct time-domain waveform computations. Interestingly, the dispersion diagram of the temporal unit cell, which displays a momentum gap characterized by a complex effective angular frequency, plays a crucial role in shaping the incident waveform. Specifically, the presence of momentum gaps in the spectrum of the incident pulse determines the frequencies of the generated oscillation modes.