Optical vortices in dispersive nonlinear Kerr type media

The applied method of slowly varying amplitudes of the electrical and magnet vector fields give us the possibility to reduce the nonlinear vector integro-differential wave equation to the amplitude vector nonlinear differential equations. It can be estimated different orders of dispersion of the linear and nonlinear susceptibility using this approximation. The critical values of parameters to observe different linear and nonlinear effects are determinate. The obtained amplitude equation is a vector version of 3D+1 Nonlinear Schredinger Equation (VNSE) describing the evolution of slowly varying amplitudes of electrical and magnet fields in dispersive nonlinear Kerr type media. We show that VNSE admit exact vortex solutions with classical orbital momentum $\ell=1$ and finite energy. Dispersion region and medium parameters necessary for experimental observation of these vortices, are determinate. PACS 42.81.Dp;05.45.Yv;42.65.TgComment: 24 page

The light filament as vector solitary wave

We present an analytical approach to the theory of nonlinear propagation of femtosecond optical pulses with broad-band spectrum in gases. The vector character of the nonlinear third-order polarization is investigated in details, taking into account the carrier to envelope phase. The corresponding system of vector amplitude equations is written by using left-hand and right-hand circular components of the electrical field. We found that this system nonlinear equations admits $3D+1$ vector soliton solution with Lorentz shape. The solution presents relatively stable propagation and rotation with GHz frequency of the vector of the electrical field in plane, orthogonal to the direction of propagation. The evolution of the intensity profile demonstrate weak self-compression and week spherical wave in the first milliseconds of propagation.Comment: 5 pages, 1 figur