Photonic Modal Circulator Using Temporal Refractive-Index Modulation with Spatial Inversion Symmetry

It has been demonstrated that dynamic refractive-index modulation, which breaks time-reversal symmetry, can be used to create on-chip nonreciprocal photonic devices. In order to achieve amplitude nonreciprocity, all such devices moreover require modulations that break spatial symmetries, which adds complexity in implementations. Here we introduce a modal circulator, which achieves amplitude nonreciprocity through a circulation motion among three modes. We show that such a circulator can be achieved in a dynamically modulated structure that preserves mirror symmetry, and as a result can be implemented using only a single standing-wave modulator, which significantly simplifies the implementation of dynamically modulated nonreciprocal devices. We also prove that in terms of the number of modes involved in the transport process, the modal circulator represents the minimum configuration in which complete amplitude nonreciprocity can be achieved while preserving spatial symmetry.