?
Effects of nonlinearity and a new nonlinear resonance in two-path phonon transmittance in lattices with two-dimensional arrays of atomic defects
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 us to model both linear and nonlinear phonon transmissioantiresonances.
The 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 as a result of the interaction of lattice waves 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 interatomic nonlinearity shifts the antiresonance
frequency in the direction determined by the sign of the nonlinear coefficient and enhances in general the
transmission of high-frequency phonons due to third harmonic generation and propagation. The effects of the
quartic nonlinearity on phonon transmission are described for the two-path atomic defects with a different
topology. Transmission through the nonlinear two-path atomic defects is also modeled with the simulation of
the phonon wave packet, for which the proper amplitude normalization is proposed and implemented. It is
shown that the cubic interatomic nonlinearity red shifts in general the antiresonance frequency for longitudinal
phonons independently of the sign of the nonlinear coefficient, and the equilibrium interatomic distances (bond
lengths) in the atomic defects are changed by the incident phonon due to cubic interatomic nonlinearity. For
longitudinal phonons incident on a system with the cubic nonlinearity, the new narrow transmission resonance on
the background of a broad antiresonance is predicted to emerge, which we relate to the opening of the additional
transmission channel for the phonon second harmonic through the nonlinear defect atoms. Conditions of the
existence of the new nonlinear transmission resonance are determined and demonstrated for different two-path
nonlinear atomic defects. A two-dimensional array of embedded three-path defects with an additional weak
transmission channel, in which a linear analog of the nonlinear narrow transmission resonance on the background
of a broad antiresonance is realized, is proposed and modeled. The presented results provide better understanding
and detailed description of the interplay between the interference and nonlinearity in phonon propagation through
and scattering in two-dimensional arrays of two-path anharmonic atomic defects with a different topology.