Nonreciprocal microresonators for the miniaturization of optical waveguide isolators.

By introducing nonreciprocal phase shifts into microresonators, we propose new designs for the miniaturization of optical waveguide isolators and circulators. We present detailed design procedures, and numerically demonstrate the operation of these magneto-optical devices. The device sizes can be reduced down to several tens of micrometers. The nonreciprocal function of these devices is due to nonreciprocal resonance shifts. Next, the operation bandwidth can be expanded by increasing the number of resonators (the filter order). This is demonstrated by comparing the characteristics of a single-resonator structure with those of a three-resonator structure. This paper furthermore presents the nonreciprocal characteristics of three-dimensional resonators with finite heights, leading to a guideline for the design of nonreciprocal optical circuits. This involves a demonstration of how the resonators with selected parameters are practical for miniaturized nonreciprocal circuits.