Effects of nonlinearity and a new nonlinear resonance in two-path phonon transmittance in lattices with two-dimensional arrays of atomic defects

Abstract

The paper is devoted to analytical and numerical studies of the effects of nonlinearity on the two-path phonon interference in the transmission through two-dimensional arrays of atomic defects embedded in a lattice. The emergence of transmission antiresonance (transmission node) in the two-path system is demonstrated for the few-particle nanostructures, which allow to model both linear and nonlinear phonon transmissioantiresonances. Universality of destructive-interference origin of transmission antiresonances of waves of different nature, such as phonons, photons and electrons, in two-path nanostructures and metamaterials is emphasized. Generation of the higher harmonics in result of the interaction of lattice wave with nonlinear two-path atomic defects is considered, and the full system of nonlinear algebraic equations is obtained to describe the transmission through nonlinear two-path atomic defects with an account for the generation of second and third harmonics. Expressions for the coefficients of lattice energy transmission through and reflection from the embedded nonlinear atomic systems are derived. It is shown that the quartic the interference and nonlinearity in phonon propagation through and scattering in two-dimensional arrays of two-path anharmonic atomic defects with different topology.