Modulated-nonlinearity in phononic crystals: From extremely linear to effective cubic nonlinear media

Abstract

[EN] In solids, the constitutive relations between strain and stress lead in most cases to a dominant quadratic nonlinear response. However, there exist some solid materials that exhibit negative quadratic nonlinearity, as occurs in common glasses as borosilicate glass or fused silica. In this work, we present the dynamical response of a phononic crystal with modulated nonlinearity. In particular, we analyze a 1D phononic crystal composed of layers of alternating properties with quadratic nonlinearity, each layer presenting an alternating (positive and negative) nonlinear parameter value. First, we observe that the common distortion produced by the nonlinear steepening can be almost compensated. Thus, the propagation through the phononic crystal can be extended far beyond the shock formation distance, avoiding common saturation effects. Second, we show that in the absence of dispersion the artificial material exhibits weakly-cubic nonlinear effective properties. The structure presented here can be employed to avoid nonlinear distortion in waveguides, or to design metamaterials with effective cubic nonlinear properties using quadratic nonlinear building blocks.