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Graph-based analysis of nonreciprocity in coupled-mode systems



Leonardo M. Ranzani, Jose A. Aumentado


In this work we derive the general conditions for obtaining nonreciprocity in multi-mode parametrically- coupled systems. The results can be applied to a broad variety of optical, microwave, and hybrid systems including recent electro- and opto-mechanical devices. In deriving these results, we use a graph-based methodology to derive the scattering matrix. This approach naturally expresses the terms in the scattering coefficients as separate graphs corresponding to distinct coupling paths between modes such that it is evident that nonreciprocity arises as a consequence of multi-path interference and dissipation in key ancillary modes. These concepts facilitate the construction of new devices in which several other characteristics might also be simultaneously optimized. As an example, we synthesize a novel three-mode unilateral amplifier design by use of graphs. Finally, we analyze the isolation generated in a common parametric multi-mode system, the dc-SQUID.
Physical Review A


microwave devices, Josephson devices, optical devices, nonreciprocity


Ranzani, L. and Aumentado, J. (2015), Graph-based analysis of nonreciprocity in coupled-mode systems, Physical Review A, [online], (Accessed July 20, 2024)


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Created February 10, 2015, Updated February 19, 2017