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Role of Time-Reversal Symmetry in the Dynamical Response of One-Way Nonlinear Devices

David E. Fernandes1,* and Mário G. Silveirinha2,†

  • 1Department of Electrical Engineering, Instituto de Telecomunicações, University of Coimbra, 3030-290 Coimbra, Portugal
  • 2Instituto Superior Técnico and Instituto de Telecomunicações, University of Lisbon, Avenida Rovisco Pais, 1, 1049-001 Lisboa, Portugal

  • *dfernandes@co.it.pt
  • †mario.silveirinha@co.it.pt
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Phys. Rev. Applied 18, 024002 – Published 1 August, 2022

DOI: https://doi.org/10.1103/PhysRevApplied.18.024002

Abstract

We study the role of time-reversal symmetry on the dynamical response of nonlinear optical systems that behave as unidirectional (one-way) devices. It is shown that lossless nonlinear materials, despite being nonreciprocal, are typically time-reversal invariant. This property raises an apparent paradox because time-reversal-invariant systems are forcibly bidirectional. Here, we present a solution for this conundrum, and theoretically explain why the one-way behavior can indeed be compatible with the time-reversal invariance. It is found that in the time-reversed problem the incident waves have a variation in time that is generally incompatible with the adiabatic approximation. For this reason, the adiabatic approximation fails to predict the bidirectional nature of nonlinear systems. We discuss the implications of this finding on the performance of practical nonlinear one-way devices.

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Phys. Rev. Applied 18, 024002– Published 1 August, 2022
  • Received 15 November 2021
  • Revised 27 May 2022
  • Accepted 13 June 2022
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