Angular-Momentum Biased Circulators and Their Power Consumption

Angular-momentum biasing has been recently introduced as a robust technique to realize magnetless linear nonreciprocal elements within a subwavelength footprint. By imparting a synthetic angular momentum to a resonant ring, it is possible to break the degeneracy of its counter-rotating states and induce nonreciprocity. Angular momentum is efficiently synthesized by modulating the resonator in space and time via appropriate electrical signals. A question that naturally arises is whether such a modulation approach results in power exchange between the modulation and operation signals; thus, making the device active, as the majority of parametric devices. Here, we theoretically and numerically show that power exchange in this system is generally very small, and it can be made identically zero for perfectly symmetrical differential circulators in absence of parasitic loss. This fact shows that, from a practical point of view, angular-momentum circulators are passive systems, in contrast to several other magnetless nonreciprocal techniques, and as such they are very attractive for low-power and wireless applications.