Determining triple half-twist of optical Möbius strips in electromagnetic fields with a non-planar structure.

Polarization ellipses in a nonparaxial field form twisted strips when traced along closed contours around a circular polarization singularity line. We found an analytical expression for the twist number of the strip when the contour is coplanar with the polarization ellipse in its center. Necessary and sufficient conditions for strips having one or three half-twists are found. A set of five parameters of electromagnetic field at the polarization singularity point is found which definitely determines the value of the twist number of the strip.

Indices of polarization Möbius strips surrounding lines of circular polarization in nonparaxial optical fields.

Detailed analysis of polarization ellipse strips constructed on small circular contours surrounding a single polarization singularity line of an electromagnetic field is carried out. It is shown that the strips formed by major and minor axes of polarization ellipses are nonorientable Möbius strips with opposite directions of twist. Explicit analytical expressions relating the direction of the strip twist to the orientation of its construction contour and the parameters of the electromagnetic field at the polarization singularity point are found.

Transformation of spin and orbital angular momentum in second-harmonic generation process by the near-surface layer of isotropic nonlinear medium.

We investigate the conversion between orbital and spin components of the angular momentum of light beams in the second-harmonic generation process from the near-surface layer of the nonlinear isotropic medium without spatial dispersion at oblique incidence of the elliptically polarized fundamental beam. The conservation of the projection of both spin and orbital angular momenta onto the normal to the surface of the medium during the transformation of the incident wave into a reflected double frequency wave has been demonstrated.

Interconversion between OAM and SAM in five-wave mixing process in medium with the fourth-order optical susceptibility.

We investigate the interconversion between spin components of the angular momentum (SAM) and orbital components of the angular momentum (OAM) of collinear elliptically polarized monochromatic fundamental beams with frequencies ω1 and ω2 in the five-wave mixing process in homogeneous isotropic nonracemic mixtures of chiral molecules with nonlinear fourth-order susceptibility. Fundamental beams have helicoidal wavefronts and arbitrary radial distributions of intensity. The discovered non-conservation of the total SAM and OAM projections on the direction of propagation of the interacting waves during the generation of radiation at the frequency 3ω1 - ω2 compensate each other, ensuring the conservation of the total angular momentum projection. A straightforward classical and quantum interpretation of the results is given.

Transformation of spin and orbital angular momentum in second-harmonic generation process at oblique incidence of light from the surface of an isotropic medium with spatial dispersion of quadratic nonlinearity.

We discuss key features of the conversion of spin and orbital angular momentum of electromagnetic waves in the process of second-harmonic generation from the surface of the isotropic medium at oblique incidence. Conservation of the projections of spin and orbital parts of angular momentum of interacting waves onto the normal to the surface is shown for an arbitrary case of polarization and mode structure of the incident light beam.

Three-dimensional structure of polarization singularities of a light field near a dielectric spherical nanoparticle.

We numerically study the structure of polarization singularity lines in a near-field of the sub-wavelength dielectric particle when it is irradiated by a monochromatic elliptically polarized plane wave. For the various values of the ellipticity degree of the incident radiation, we trace the CT and LT-lines on which the polarization ellipse turns into a circle or a line, respectively. The continuous variation of the isotropy parameters of the singularities is visualized along the lines. The main rules of CT and LT-lines deformation, emergence, and vanishing are revealed.

Interconversion between the orbital and spin angular momentum of light beams in three-wave mixing processes in the bulk of an isotropic chiral medium.

A phenomenological description of nondegenerate and degenerate three-wave mixing in the bulk of an isotropic chiral medium is given for the wide class of fundamental light beams with nonuniform polarization distribution and multimode transverse structure. Special attention is paid to the classical and quantum interpretation of interconversion between spin and orbital parts of the angular momentum of the input and output beams.

Structure of polarization singularities of a light beam at triple frequency generated in isotropic medium by singularly polarized beam.

The components of electric field of the third harmonic beam, generated in isotropic medium with cubic nonlinearity by a monochromatic light beam carrying polarization singularity of an arbitrary type, are found analytically. The relation between C-points characteristics in the fundamental and signal beams are determined, as well as the impact of the phase mismatch on the shape of the C-lines.

Second harmonic generation in isotropic chiral medium with nonlocality of nonlinear optical response by heterogeneously polarized pulsed beams.

The second harmonic generation in the bulk of an isotropic chiral liquid with spatial or temporal nonlocality of its quadratic response is studied analytically. The fundamental pulsed beam has Gaussian time envelope and carries a polarization singularity at its axis. The influence of the topological charge and the handedness of the polarization singularity on the polarization state of the signal beam is revealed.