Nonreciprocity-Enabled Chiral Stability of Nonlinear Waves

TL;DR

This work reveals a chiral stability mechanism in a dissipative, nonreciprocal sine-Gordon model, showing that nonlinear waves propagate with direction-dependent stability. By deriving exact traveling-wave solutions and performing a thorough spectral analysis using Floquet theory, the authors demonstrate that nonreciprocity acts as a master switch that stabilizes waves in one direction while destabilizing their mirror images. The findings apply to both periodic waves and kink solitons and are corroborated by nonlinear simulations, emphasizing how nonreciprocity fundamentally shapes the dynamical landscape in active materials. The results offer a principled route to control wave propagation in nonreciprocal media and point to modulational instability as a future area of exploration.

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.

Figures (8)

• Figure 1: The stability spectrum for the subluminal, rotational wave. The parameters are: $A=-1$, $B=2$, $\eta=0.5$, $E=-0.75$, $\Gamma=1$ (left), and $\Gamma=-1$ (right).
• Figure 2: The stability spectrum for the subluminal kink solution (\ref{['k1']}). The parameters are: $\eta=0.5$, $\Gamma=1$ (left), and $\Gamma=-1$ (right).
• Figure 3: The stability spectrum for the superluminal, rotational wave. The parameters are: $A=1$, $B=-2$, $\eta=0.5$, $E=3.1$, $\Gamma=0.4$ (left), and $\Gamma=-0.4$ (right).
• Figure 4: The stability spectrum for the superluminal kink solution (\ref{['k2']}). The parameters are: $\eta=0.5$, $\Gamma=0.4$ (left), and $\Gamma=-0.4$ (right).
• Figure 5: (Top panels) Spatiotemporal evolution of $\cos(\varphi(x,t))$ for the subluminal rotational waves analysed in Fig. \ref{['figg1']}. Left (right) panel corresponds to the solution with $c>0$ ($c<0$). Bottom left panel shows the initial condition $\varphi(x,0)$ for the simulation whereas right panel shows the profile at the end of the simulation for the $c>0$ (top) and the $c<0$ (bottom) case.