Nonlinear Schrödinger equations with mean terms in nonresonant multidimensional quadratic materials

We derive the asymptotic equations governing the evolution of a quasi-monochromatic optical pulse in a nonresonant quadratic material starting from Maxwell equations. Under rather general assumptions, equations of nonlinear Schrödinger (NLS) type with coupling to mean fields result (here called NLSM). In particular, if the incident pulse is polarized along one of the principal axes of the material, scalar NLSM equations are obtained. For a generic input, however, coupled vector NLSM systems result. Special reductions of these equations include the usual scalar and vector NLS equations. Based on results known for similar systems which arise in other physical contexts, we expect the behavior of the solutions to be characterized by a rather large variety of phenomena. In particular, we show that the presence of the coupling to the dc fields can have a dramatic effect on the dynamics of the optical pulse, and stable localized multidimensional pulses can arise through interaction with boundary terms associated to the mean fields.