Observation of genuine wave vector (k or β) gap in a dynamic transmission line and temporal photonic crystals

By definition, a temporal photonic crystal (TPC) has a permittivity ε(t) that varies periodically with time. We prove that, in the long wavelength limit, a TPC is accurately mimicked by a dynamic transmission line (DTL) having a capacitance (inductance) per unit length equal to ε(t) (μ). Employing a DTL in the microwave region, we measured the photonic band structure, which results to display a genuine wave vector (k or β) gap, in very good agreement with our theoretical model and the equivalent TPC.