Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

A geometric description of nonreciprocity in coupled two-mode systems



Leonardo M. Ranzani, Jose A. Aumentado


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.
Physical Review X


reciprocity, parametric devices, isolators


Ranzani, L. and Aumentado, J. (2014), A geometric description of nonreciprocity in coupled two-mode systems, Physical Review X, [online], (Accessed July 18, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created October 16, 2014, Updated February 19, 2017