Abstract

Wavefront dislocations are important topological features of propagating laser beams [1]. We report a scenario of spatio-temporal dynamics of birth, transformations and annihilation of screw dislocations (optical vortices) accompanied with phase saddles and extrema. These topological objects appear on a wave front when initially regular Gaussian beam is corrupted via self-action in a nonlinear medium. A topological map of the phase objects on the wave front is calculated, and the fundamental principles of topological transformations, or topological events are analysed. In the calculations we approximated the lens as Gaussian focusing or defocusing lens. A stigmatic Gaussian lens produces rings of zero field amplitude at certain distances. Even a small amount of astigmatism makes the closed lines of zero amplitude be stretched along the direction of the beam propagation, and in the beam cross-section four points of zero amplitude appear (“quadrupole” of optical vortices). Figure 1 shows the shape of a wave front within one quadrant and the topological objects on it. The total number of phase saddles equal 6, with associated index -6. There are also 4 maxima and 3 phase minima, including the central one, with the total index +7, what makes the whole wave-front topological index equal +1. In all other transformations, including vortices birth and annihilation, this index is constant, corresponding to the value of the initial smooth wave front index +1. This study can be used in the analysis of laser beams generation in optical cavities with phase-conjugated mirrors and propagation in free space and nonlinear media.

© 1998 IEEE