Localized multi-dimensional optical pulses in non-resonant quadratic materials

The propagation of an optical pulse in a non-resonant multi-dimensional quadratic material is studied. In a number of relevant cases, the evolution of the pulse is governed by equations of non-linear Schrödinger type with coupling to mean (i.e. low frequency) fields. The presence of this coupling can have a dramatic effect on the dynamics of the optical pulse. In particular, we show that stable localized multi-dimensional pulses can arise through interaction with boundary terms associated to the mean fields.