CC BY
5ALT'22
PLENARY SESSION
P-II
Nonlinear singular polarization optics of wave beams and pulses
V.A. Makarov
M.V Lomonosov Moscow State University, Faculty of Physics, Leninskie Gory, Moscow 119991
vamakarov@phys.msu.ru
In the middle of 70's the first experimental evidence of the nonlinear optical activity came to light, giving the impulse to the development of nonlinear polarization optics. The subsequent theoretical and experimental investigations assure that the polarization self-action and interaction of waves are fine and widespread phenomena in nonlinear optics. Despite the popularity and wide range of the considered problems, investigations of the origin and dynamics of the polarization singularities in nonlinear optical processes are virtually absent. The present report focuses on the study of formation of L-type C-type polarization singularities in the signal beam cross section generated in various nonlinear optical processes.
The conditions of appearance and the behavior of polarization singularities 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. The ranges of the parameters of an elliptically polarized Gaussian beam and a medium with local and nonlocal nonlinearity are determined, at which the lines of circular polarization singularity appear in cross sections of propagated beam. The specific features of nonlinear optics with laser beams containing polarization singularities are also discussed.
Analytically found expressions, which relate the values of two parameters characterizing the topological type of linear and circular polarization singularities in nonparaxial light fields to the values of the complex amplitude components of the electric field and their first spatial derivatives are also discussed.
The numerically investigate the interaction of a plane elliptically polarized monochromatic wave on a spherical nanoparticle. In the resulting light field near the particle, the topology of strips, formed by the axes of the polarization ellipses and the normal vectors to their planes, is studied. The strips may have one half-twist only if they enclose a circular polarization singularity line, while almost all other strips, even enclosing the linear polarization singularity lines, are trivial. The correlation between the twisting indices of different strips is found, and their relation to the topological features of points of the singular lines is analyzed.
The found laws of transformation of the total topological indices allow one to get an idea of the fine details of these nonlinear optical processes and may be of interest for creating light beams and pulses with an inhomogeneous distribution of the electric field containing polarisation singularities of a given type by methods of nonlinear optics. The latter are promising for use in quantum information optical systems and can be used in problems of nonlinear bulk and surface spectroscopy of nonlinear media.
I take this opportunity to acknowledge many key contributions to this report by former students and postgraduate students of M.V. Lomonosov Moscow State University. I am indeed grateful to Prof. Dr. A.A. Golubkov, Dr. K.S. Grigoriev, Dr. I.A. Perezhogin, Dr. N.N. Potravkin, andM.P.S. N.Yu. Kuznetsov, G.M. Shishkov, P.S. Ryzhikov, andG.A. Gryaznov.
