Simulation of optical Bloch oscillations and breathing modes in the waveguide arrays

A plain array of parallel optical wave guides is studied. A special case is considered, for which the refractive index of the waveguides changes linearly with the number of the waveguide. Thus far, such optical waveguide array (OWA) was described by a set of coupled mode equations introduced by a postulate manner and the parameters entering these equations were taken as a result of comparison with an experiment. In this paper, for the first time, these equations are derived based on the multiple scattering approach for electromagnetic waves by the OWA. In the approach proposed, the parameters entering the set of equations are expressed in terms of the geometry and the refractive index of the OWA. As an example of the application of the results obtained we describe the experiments on optical Bloch oscillation and breathing modes. Surprisingly, not only qualitative but also a good quantitative agreement with these experiments is found.