Abstract

Beginning with the Maxwell’s equations for an isotropic nonlinear medium, we have obtained vector slowly varying amplitude equations. The equations are a nonparaxial vector generalization of the well-known scalar $3\mathrm{D}+1$ nonlinear Schrodinger equation. We have determined the dispersion region and medium parameters necessary for experimental observation of wave propagation described by these equations. We show that these equations admit exact vortex solutions with spin $l=1.$ For the case of two vortices, we also obtain exact analytical expressions describing their interaction. Stability and interaction properties of these vortices are also investigated numerically by a split-step Fourier method. Finally, we discuss applications of these vortices in the area of nuclear fusion and the stabilization of laser pulses.

© 2002 Optical Society of America

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