Multidimensional optical pulses in non-resonant quadratic materials

The propagation of a light pulse in media with quadratic nonlinearity has attracted significant interest in recent years. In such media the nonlinear response is known to generate DC fields which subsequently play a key role in the evolution of the optical pulse. In a one-dimensional nonresonant quadratic material, the evolution of the slowly-varying envelope of the optical pulse was recently found to be governed by the nonlinear Schrodinger equation (hereafter NLS), as in the more familiar case of Kerr materials. The NLS equation is also a centrally important equation in other areas as well, e.g. fluid dynamics, plasma physics. However, it is well known that (1+1)-dimensional structures propagating in a multidimensional medium may be unstable with respect to transverse modulations. As a consequence, pulse dynamics in a multidimensional medium cannot be reduced to simple one-dimensional systems. When studying the modulation of a wave packet in a multidimensional dispersive medium, generalized NLS systems with coupling to a mean term (hereafter denoted as NLSM) are known to appear in various physical situations. In special cases these systems are known to be integrable. However, even in the non-integrable case these equations exhibit interesting phenomena such as focusing, singularities and a rich structure of solutions