Nonreciprocity-Enabled Chiral Stability of Nonlinear Waves

TL;DR

This paper reveals that nonreciprocity in nonlinear wave systems induces a chiral stability, where waves traveling in one direction are stable and their mirror images are unstable, advancing control in nonreciprocal photonic media.

Contribution

It introduces a fundamental stability criterion for nonlinear waves in nonreciprocal media, supported by exact solutions and stability analysis of a sine-Gordon model.

Findings

Direction-dependent wave stability confirmed by simulations

Nonreciprocity causes symmetry-breaking in wave stability

Chiral stability criterion established for nonlinear waves

Abstract

The control of wave propagation, particularly the quest for unidirectional transport, plays an important role in photonics and metamaterial science. While nonreciprocity is known to enable unidirectional amplification and stabilize complex solitons, its fundamental impact on the intrinsic stability of the nonlinear waves remains an open frontier. By obtaining exact analytical solutions for a dissipative, nonreciprocal sine-Gordon model (that was proposed in [\emph{Nature} 627, 528-533, 2024] and captures all essential physics of active materials) and performing a comprehensive stability analysis, we discover a chiral stability criterion: waves propagating in one direction exhibit robust stability, while their mirror-image counterparts are intrinsically unstable. This direction-dependent stability is confirmed by full nonlinear simulations. Our findings identify the symmetry-breaking role of nonreciprocity in defining the stability of nonlinear waves, a key step toward controlling wave propagation in nonreciprocal media.