Abstract
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.
Highlights
Reciprocity is the symmetry of a physical system with respect to the exchange of a source and detector
In the superconducting quantum information and microwave engineering fields, this has motivated a push to understand how nonreciprocity can be generated using alternative methods [7, 8, 9, 10, 11] and this general pursuit has been paralleled by similar efforts in optics [12, 13, 14, 15, 16, 17]
These different ideas are embodied in different physical implementations, they all share a common mathematical description based in coupled-mode theory
Summary
Reciprocity is the symmetry of a physical system with respect to the exchange of a source and detector. With the approach we describe in this work, the synthesis of a multi-mode device is translated into the process of building a directed graph whose edges are subject to specific conditions Since this approach is agnostic to physical implementation, it may benefit similar efforts based on optical, mechanical, and hybrid systems. We use this picture to discuss the mechanism for nonreciprocity in general parametrically-coupled systems. We conclude the paper with a discussion of how this graphical approach might be effectively applied in future work
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