Theoretical investigation of a nonreciprocal micro-ring resonator with nonreciprocity provided by its magneto-optical input–output coupler

The simplest Micro-Ring Resonator consists of an input–output directional coupler connected into itself through a feedback loop. We show that a magneto-optical coupler exhibiting a nonreciprocal phase shift is enough to render the whole structure nonreciprocal, even with an otherwise reciprocal loop. We illustrate this effect by considering a planar (slab) coupler made of bigyrotropic waveguides submitted to a suitable external magnetization; its scattering parameters are derived analytically in the frame of Coupled Mode Theory. Including the modal dispersion, it is possible to adjust the dimensions and/or the operating wavelength in order to design very specific regimes, either in absorption, amplification or emission, from a rather trivial unidirectional behavior to the subtler case of well-balanced interdigitated frequency combs—circulating both ways, but separated by exactly one half of a Free Spectral Range.