Networks of possible topological gratings of complex light fields with polarization singularities were established
and measured first. All allowed morphological forms of optical isotropic points were measured first in optics and discussed.
Strong and weak transformations of topological networks and induced topological reactions under controllable field
perturbations were realized and investigated.
It was investigated basic features of inhomogeneous polarized vector light fields. It was shown both theoretically and experimentally, how the actual topological elements, namely singular points and lines, saddles and traversing them bifurcation lines, are jointed in the structural units (quadruples, dipoles, etc.). In turn, these units are jointed in unified polarization patterns, or topological networks. It was investigated transformations of polarization pattern under guided perturbations. Arrangement of polarization ellipses of all other points of field, i.e. morphology, is defined by polarization pattern topology.
Polarimetry is effective technique for polarized light fields characterization. It was shown recently that most full “finger-print” of light fields with arbitrary complexity is network of polarization singularities: C points with circular polarization and L lines with variable azimuth. The new singular Stokes-polarimetry was elaborated for such measurements. It allows define azimuth, eccentricity and handedness of elliptical vibrations in each pixel of receiving CCD camera in the range of mega-pixels. It is based on precise measurement of full set of Stokes parameters by the help of high quality analyzers and quarter-wave plates with λ/500 preciseness and 4’ adjustment. The matrices of obtained data are processed in PC by special programs to find positions of polarization singularities and other needed topological features. The developed SSP technique was proved successfully by measurements of topology of polarized speckle-fields produced by multimode “photonic-crystal” fibers, double side rubbed polymer films, biomedical samples. Each singularity is localized with preciseness up to ± 1 pixel in comparison with 500 pixels dimensions of typical speckle. It was confirmed that network of topological features appeared in polarized light field after its interaction with specimen under inspection is exact individual “passport” for its characterization. Therefore, SSP can be used for smart materials characterization. The presented data show that SSP technique is promising for local analysis of properties and defects of thin films, liquid crystal cells, optical elements, biological samples, etc. It is able discover heterogeneities and defects, which define essentially merits of specimens under inspection and can’t be checked by usual polarimetry methods. The detected extra high sensitivity of polarization singularities position and network to any changes of samples position and deformation opens quite new possibilities for sensing of deformations and displacement of checked elements in the sub-micron range.
We elaborate new technique of singular Stokes polarimetry for investigation full set of elliptical field characteristics. Full set of topological structures were discussed and measured for complicated elliptical field at first. Total confirmation of sign and loop rules and "networks" with all topological structures were obtained. The different statistics of topological features for fibers and diffusers were obtained and discussed. Possible applications of Stokes-polarimetry for singular optics are discussed.