The evolution of optical beams in self-focusing media

The diffraction of intensive electromagnetic waves by a system of N slits in a non-linear medium is studied. The beams, created by the slits, have an arbitrary polarization and are therefore characterized by two orthogonal modes. To describe the dynamics of the modes the set of two coupled non-linear Schrِdinger equations (the Manakov system) is used. The dynamics is analyzed on the basis of the corresponding linear 3×3 scattering problem. The dependence of the number of emerging solitons and their parameters on both the initial conditions and the separating distance is obtained. The important observation is that beams without initial phase modulations can result in beams propagating on some non-zero angle to the initial wave-vector. The case N=2 is analyzed in detail. The influence of the initial intensity and polarization on the mode switching, soliton binding and separating is studied. Numerical calculations of the Manakov equations show good agreement with theoretical predictions.