Discrete spatial solitons in a diffraction-managed nonlinear waveguide array: a unified approach

Localized, stable nonlinear waves, often referred to as solitons, are of broad interest in mathematics and physics. They are found in both continuous and discrete media. In this paper, a unified method is presented which is used to describe the propagation of linearly polarized light as well as two polarization modes in a diffraction-managed nonlinear waveguide array. In the regime of normal diffraction, both stationary and moving discrete solitons are analyzed using the Fourier transform method. The numerical results based on a modified Neumann iteration scheme as well as renormalization techniques, indicate that traveling wave solutions are unlikely to exist. An asymptotic equation is derived from first principles which governs the propagation of electromagnetic waves in a waveguide array in the presence of both normal and anomalous diffraction. This is termed diffraction management. The theory is then extended to the vector case of coupled polarization modes.