We explore the concept of nonreciprocity in coupled two-mode systems using a geometric mapping to the Poincaré sphere. From this perspective, we recast the requirements for nonreciprocity in terms of rotation and inversion symmetry arguments for the vector describing the two-mode state. We provide a few examples (the microwave circulator, parametric up/down converter, and traveling wave frequency converter) to demonstrate how this general geometric picture can provide insight into specific physical systems.
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Ranzani et al. (2014) studied this question.
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