Nonlinear Wavepacket Dynamics in Proximity to a Stationary Inflection Point

TL;DR

This paper explores the unique nonlinear dynamics of wavepackets near a stationary inflection point in a periodic waveguide, revealing amplitude-dependent propagation behaviors with potential applications in wave routing.

Contribution

It introduces a theoretical framework for analyzing nonlinear wavepacket evolution at an SIP, highlighting the distinct nonlinear effects on wave propagation.

Findings

Nonlinear interactions lead to predominantly ballistic wavepacket propagation.

Wavepacket speed and direction depend on amplitude in nonlinear regime.

Behavior is unique to wavepackets centered at an SIP.

Abstract

A stationary inflection point (SIP) in the Bloch dispersion relation of a periodic waveguide is an exceptional point degeneracy where three Bloch eigenmodes coalesce forming the so-called frozen mode with a divergent amplitude and vanishing group velocity of its propagating component. We have developed a theoretical framework to study the time evolution of wavepackets centered at an SIP. Analysis of the evolution of statistical moments distribution of linear pulses shows a strong deviation from the conventional ballistic wavepacket dynamics in dispersive media. The presence of nonlinear interactions dramatically changes the situation, resulting in a mostly ballistic propagation of nonlinear wavepackets with the speed and even the direction of propagation essentially dependent on the wavepacket amplitude. Such a behavior is unique to nonlinear wavepackets centered at an SIP and can be used for the realization of a novel family of beam power routers for classical waves.