What is Nonreciprocity?

TL;DR

This paper provides a comprehensive overview of electromagnetic nonreciprocity, clarifying definitions, classifications, and fundamental principles, while addressing misconceptions and highlighting the characteristics and applications of various nonreciprocal systems.

Contribution

It offers a unified theoretical framework for nonreciprocal systems, clarifies misconceptions, and derives a generalized Lorentz reciprocity theorem for LTI systems.

Findings

General definition and classification of nonreciprocal systems.

Derivation of a generalized Lorentz reciprocity theorem for LTI systems.

Clarification of the role of loss and energy conservation in nonreciprocity.

Abstract

This paper aims at providing a global perspective on electromagnetic nonreciprocity and clarifying confusions that arose in the recent developments of the field. It provides a general definition of nonreciprocity and classifies nonreciprocal systems according to their linear time-invariant (LTI), linear time-variant (LTV) or nonlinear nonreciprocal natures. The theory of nonlinear systems is established on the foundation of the concepts of time reversal, time-reversal symmetry, time-reversal symmetry breaking and related Onsager- Casimir relations. Special attention is given to LTI systems, as the most common nonreciprocal systems, for which a generalized form of the Lorentz reciprocity theorem is derived. The delicate issue of loss in nonreciprocal systems is demystified and the so-called thermodynamics paradox is resolved from energy conservation considerations. The fundamental characteristics and applications of LTI, LTV and nonlinear nonreciprocal systems are overviewed with the help of pedagogical examples. Finally, asymmetric structures with fallacious nonreciprocal appearances are debunked.