Magnet-less gyrotropy using time-periodic modulation of permittivity

Time-varying (TV) media in electromagnetics have unlocked new paths to important electromagnetic effects such as non-reciprocity, frequency conversion, and parametric amplification. In light of such advances over the past decade, a curious question arises as to whether chirality or/and gyrotropy, may also be achieved using TV dielectrics. In this paper, we propose a suitable time-modulation of the permittivity tensor in a static achiral and non-gyrotropic crystal and thereby <i>emulate</i> gyrotropy without the need of magnetic materials and external magnetic bias field. The <i>emulated</i> gyrotropy is owed to the temporal rotation of the principal axes of the permittivity tensor, which sustains only circularly/elliptically polarized eigenmodes. A possible realization using modulated electro-optic effects in a nonlinear crystal is proposed, showing a feasible approach to realize gyrotropy by time variation in non-magnetic achiral media.