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

TL;DR

This paper investigates how time-reversal symmetry affects the unidirectional behavior of nonlinear optical devices, revealing that apparent paradoxes are resolved by the failure of the adiabatic approximation in the time-reversed scenario.

Contribution

It provides a theoretical explanation for the compatibility of time-reversal invariance with one-way nonlinear devices, highlighting the role of the adiabatic approximation's limitations.

Findings

Lossless nonlinear materials are generally time-reversal invariant.

Time-reversal invariance does not necessarily imply bidirectionality in nonlinear systems.

Failure of the adiabatic approximation explains the unidirectional behavior in practice.

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 bi-directional. 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. Due to this reason the adiabatic approximation fails to predict the bi-directional nature of nonlinear system. We discuss the implications of this finding in the performance of practical nonlinear "one-way" devices.