# Nonlinear Optics with Elliptically Polarized Singular Beams and Short Pulses in Media with Spatial Dispersion

## Abstract

The conditions of appearance and the behavior of polarization singularities (*C*-points) in the cross-section of light beam arising due to nonlinear interaction of elliptically polarized laser beams with a medium with nonlocality of quadratic and cubic optical responses are discussed. The formation dynamics and propagation features of *C*-points, including pairwise creation and annihilation, for sum-frequency and second harmonic generation, beams self-action and interaction and other nonlinear optical processes are presented. We also discuss the effects accompanying the propagation of ultrashort (several oscillations) elliptically polarized light pulses in nonlinear isotropic gyrotropic medium with frequency dispersion.

## Notes

### Acknowledgements

The author takes this opportunity to acknowledge many key contributions to this field of nonlinear polarization optics made by his former students and postgraduate students at M.V. Lomonosov Moscow State University. I am indeed grateful to Prof. Dr. A.A. Golubkov, Dr. S.N. Volkov, Dr. I.A. Perezhogin, Dr. N.N. Potravkin, Dr. K.S Grigoriev, and M.P.S G.A. Gryaznov. Some results of common work are observe in this chapter. I have endeavored to provide within the practical limitations of a chapter as comprehensive a review of theoretical problems of singular nonlinear polarization optics.

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