Geometry and transport in a model of two coupled quadratic nonlinear waveguides

This paper applies geometric methods developed to understand chaos and transport in Hamiltonian systems to the study of power distribution in nonlinear waveguide arrays. The specific case of two linearly coupled chi((2)) waveguides is modeled and analyzed in terms of transport and geometry in the phase space. This gives us a transport problem in the phase space resulting from the coupling of the two Hamiltonian systems for each waveguide. In particular, the effect of the presence of partial and complete barriers in the phase space on the transfer of intensity between the waveguides is studied, given a specific input and range of material properties. We show how these barriers break down as the coupling between the waveguides is increased and what the role of resonances in the phase space has in this. We also show how an increase in the coupling can lead to chaos and global transport and what effect this has on the intensity.