Non-reciprocity using quadrature-phase time-varying slab resonators

In this paper, it is shown that non-reciprocity can be observed in time-varying media without employing spatio-temporal modulated permittivities. We show that by using only two one dimensional Fabry-Perot slabs with time-periodic permittivities having quadrature phase difference, it is possible to achieve considerable non-reciprocity in transmission at the incidence frequency. To analyze such scenario,generalized transfer matrices are introduced to find the wave amplitudes of all harmonics in all space. The results are verified by in-house FDTD simulations. Moreover, in order to have a simple model of such time-varying slab resonators, a time-perturbed coupled mode theory is developed for multiple resonances, and it is shown that the results obtained by this method and the analytical method are in excellent agreement.