Non-Local Phononic Crystals for Dispersion Customization and Undulation-point Dynamics

TL;DR

This paper introduces a method for inverse designing phononic dispersion relations in one-dimensional spring-mass chains using non-local interactions, enabling precise customization of wave behaviors and the creation of complex critical points.

Contribution

It presents an analytical inverse design approach for phononic dispersion, allowing for exact customization of wave properties and the engineering of complex critical points in phononic crystals.

Findings

Achieved precise control of dispersion curves in single and double-band cases.

Designed phononic crystals with multiple critical points including roton, maxon, and undulation.

Analyzed wave packet dynamics in the engineered phononic structures.

Abstract

Dispersion relations govern wave behaviors, and tailoring them is a grand challenge in wave manipulation. We demonstrate inverse design of phononic dispersion using non-local interactions on one-dimensional spring-mass chains. For both single-band and double-band cases, we can achieve any valid dispersion curves with analytical precision. We further employ our method to design phononic crystals with multiple ordinary (roton/maxon) and higher-order (undulation) critical points and investigate their wave packet dynamics.