COUPLED-WAVE METHOD IN THE THEORY OF A DIATOMIC ANHARMONIC LATTICE

We use the coupled wave method to investigate a one-dimensional nonlin ear diatomic lattice. We consider the case where the two different lat tice atoms have similar masses. This narrows the forbidden frequency g ap between the longitudinal acoustic and optic phonon branches. As a r esult, the nonlinear shift of the gap's borders becomes comparable wit h the width of the gap itself. We find the exact solution, in the form of only two waves propagating towards each other. This is an importan t first step towards a full three-dimensional solution. We calculate t he ratio of the two waves' amplitudes, and analyse the dispersive prop erties of the diatomic chain. Of special interest is how stable locali zed modes emerge in the forbidden frequency gap, both stationary and s lowly propagating along the chain. We show that the envelope of their amplitudes has the form of solitary waves. What is crucial for such lo calized modes to appear is the spatial phase modulation of the particl es' vibrations. This is because it makes the chain transparent at the margins of the forbidden gap, due to the self-action of the wave (opti cal switching).