Nonlinear Phononics and Coupled Mode Theory

Abstract

Understanding phononic wave propagation in nonlinear and coupled media is inevitable in designing devices to harness phonons. In photonics, the nonlinear Schrodinger equation (NSE) and coupled mode theory (CMT) are extensively used to manipulate the propagation of electromagnetic (EM) waves. Since phonons as the quasi-particles related to mechanical vibrations are similar to their photonic counterparts (photons), inspired by EM, the NSE and CMT are developed for elastic or phononic waves. In the first section, from the novel point of view, the nonlinearity is dealt with and consequently applied to the equation of motion to derive the NSE. In the following, a hard limiter is introduced as an application of nonlinear wave propagation. The coupled-mode equations are obtained for the elastic slab waveguides in the second section. These equations are applied to explain the wave propagation in two parallel and nonparallel waveguides.