Faraday rotation in nonreciprocal photonic time-crystals

Faraday rotation is one of the most classical ways to realize nonreciprocal photonic devices like optical isolators. Recently, the temporal analog of Faraday rotation, achieved through time-interfaces, was introduced [Li et al., Phys. Rev. Lett. 128, 173901 (2022)]. Here, we extend this concept to the periodic switching regime by introducing nonreciprocal photonic time-crystals (NPTC), formed by switching material properties of a spatially homogeneous magnetoplasma medium periodically in time. Based on a temporal transfer matrix formalism, we study the NPTC band structure and show that temporal Faraday rotation can be achieved in both momentum bands and (partial) bandgaps. When combined with the bandgaps of the NPTCs, the temporal Faraday effect can enable a unidirectional wave amplifier by extracting energy from the modulation. Our study expands the catalog of photonic time-crystals (PTCs), forging a link between photonic nonreciprocity and parametric gain and shedding light on unexplored functionalities of PTCs in wave engineering.