Graph-based analysis of nonreciprocity in coupled-mode systems

TL;DR

This paper develops a graph-based framework to analyze and design nonreciprocal behavior in multi-mode coupled systems, applicable across various physical platforms, and demonstrates its utility with a new amplifier design and analysis of a SQUID system.

Contribution

It introduces a novel graph-based methodology to derive conditions for nonreciprocity in multi-mode systems, enabling systematic device design and optimization.

Findings

Nonreciprocity arises from multi-path interference and dissipation.

A new three-mode unilateral amplifier was synthesized.

Analysis of isolation in a DC-SQUID system was performed.

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.