Nonlinear harmonic generation in two-dimensional lattices of repulsive magnets

TL;DR

This study experimentally demonstrates nonlinear wave propagation and second harmonic generation in a 2D lattice of repulsive magnets, revealing tunable wave modes and directivity patterns driven by amplitude changes.

Contribution

It provides the first experimental evidence of nonlinear wave behavior and SHG in magnetic lattices, with a detailed phonon band analysis explaining the phenomena.

Findings

Confirmation of co-existing spectral components in wave response

Identification of second harmonic generation due to quadratic nonlinearity

Tunable wave modes and directivity patterns via excitation amplitude

Abstract

In this Letter, we provide experimental evidence of nonlinear wave propagation in a triangular lattice of repulsive magnets supported by an elastic foundation of thin pillars and we interpret all the individual features of the nonlinear wavefield through the lens of a phonon band calculation that precisely accounts for the inter-particle repulsive forces. We confirm the co-existence of two spectrally distinct components (homogeneous and forced) in the wave response that is induced via second harmonic generation (SHG), a well-known effect of quadratic nonlinearity (here embedded in the magnetic interaction). We show that the modal and spatial characteristics of the second harmonic components are complementary to those exhibited by the fundamental harmonic. This endows the lattice with a functionality enrichment capability, whereby additional modes and directivity patterns can be triggered and tuned by merely increasing the amplitude of excitation.