Dynamics of Fermi resonance solitary waves propagating along two interfaces

Abstract

The dynamics of Fermi resonance solitary waves propagating along two parallel interfaces in a layered organic semiconductor system is investigated both analytically and numerically. It is shown that the interaction between solitary waves leads to their attraction or repulsion, depending on their initial phase difference. In the case of attraction the solitary waves create a bound state, and their centers oscillate in time with respect to their common mass center. The corresponding period of oscillations is calculated. It is found that the amplitudes and widths of the solitary waves also oscillate in time. @S0163-1829~98!01604-X# The search for organic materials for nonlinear optics, photonics, and electronics promoted the development of methods for the preparation of a class of organic structures, namely, organic crystalline superlattices ~OCS!. The latest achievements in this field were demonstrated in a number of publications. 1‐5 At present, investigations in this direction are developing further, therefore the analysis of qualitatively new properties of OCS is very topical and important. The interaction of OCS with light is a fundamental physical problem, as well as of importance for future applications. Papers 6‐10 have been devoted to just such an analysis of these properties of OCS. In particular, different kinds of nonlinear excitations propagating through the superlattice have been discussed ~Fermi resonance interface modes, 7 Fermi resonance interface solitary waves 9,10 !. Here we want to consider the dynamics of two Fermi resonance solitary waves located on two different interfaces of a three-layer system. For convenience, instead of the term ‘‘solitary waves’’ in the following we use the shorter term ‘‘solitons,’’ as frequently done in the literature. These solitons interact with each other due to the penetration of the vibrational field of one of them into the location region of the other one. As we shall see, such ‘‘tunnel’’ coupling results in a considerable change of the dynamics of the solitons as compared to a single soliton. Let us consider a system consisting of three layers of organic semiconductors with two interfaces. We suppose that a film withN11 b-molecular layers lies between two ‘‘halfinfinite’’ crystals made of c molecules. The molecules are labeled as follows: sites ( nx ,n y ,nz<21) are occupied by c molecules, sites ( nx ,n y,0<nz<N) are occupied by b molecules, and sites ( nx ,n y ,N11<nz) are occupied by c molecules again. As in Refs. 7‐10, we assume Fermi resonance between c and b harmonic vibrations, i.e., v c .2v b . For this case the main anharmonic interaction occurs across the interfaces, and has the form