Different kind of vortex structures of laser beam can be created by optical holograms and different optical masks. In the theory these vortices are solutions of the 2D scalar Leontovich equations. These solutions admit amplitude and phase singularities.
The main tack of this work is to investigate the possibility of formation of vortex structures for narrow-band optical pulses, propagating in Kerr-type media. The evolution of such type of laser pulses is governed by nonlinear vector system of amplitude equations in second approximation of the linear dispersion. We found new class of analytical solutions with vortex structures. The nonlinear dispersion relations obtained by these vortex solutions show that their stability is due not only to balance between diffraction and nonlinearity, but also to a balance between non-linearity and angular distribution.
In last two decades actively are studied the phenomena resulting from the evolution of ultrashort optical pulses in nonlinear dispersive media. The well-known (1+1D) nonlinear Schrödinger equation (NSE) describes very well the propagation of narrow-band optical pulses (Δω<<ω0). Nowadays, it is quite easy to obtain broad-band phase-modulated femtosecond laser pulses or to reach the attosecond region where Δω≈ω0. To explore their behavior it is necessary to use the more general nonlinear amplitude equation (NAE). In local time coordinate system it differs from the standard NSE with two additional non-paraxial terms. In present paper, by using the NAE, it is investigated the dynamics of higher order non-paraxial solitons. It is shown that the peak of soliton is linearly shifted in time domain. This temporal shift is observed in the frames of non-paraxial optics, even when the higher order nonlinear and dispersive effects are neglected.
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