Electromagnetic Nonreciprocity

Research output: Contribution to journalArticle


  • Christophe Caloz
  • Andrea Alù
  • Sergei Tretyakov

  • Dimitrios Sounas
  • Karim Achouri
  • Zoé Lise Deck-Léger

Research units

  • Polytechnique Montreal
  • City University of New York
  • University of Texas at Austin
  • Swiss Federal Institute of Technology Lausanne


We aim at providing a global perspective on electromagnetic nonreciprocity and clarifying confusions that arose in recent developments of the field. We provide a general definition of nonreciprocity and classify nonreciprocal systems according to their linear time-invariant (LTI), linear time-variant (LTV), or nonlinear natures. The theory of nonreciprocal systems is established on the foundation formed by the concepts of time reversal, time-reversal symmetry, time-reversal symmetry breaking, and related Onsager-Casimir relations. Special attention is given to LTI systems, 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. An overview of the fundamental characteristics and applications of LTI, LTV, and nonlinear nonreciprocal systems is given with the help of pedagogical examples. Finally, asymmetric structures with fallacious nonreciprocal appearances are debunked.


Original languageEnglish
Article number047001
JournalPhysical Review Applied
Issue number4
Publication statusPublished - 1 Oct 2018
MoE publication typeA1 Journal article-refereed

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