He-Ne laser (0.63 mkm) initiates developing singular speckle-fields due to «optical damage» in photorefractive LiNbO<sub>3</sub>: Fe crystal. They were investigated by techniques of dynamic stocks-polarimetry, monstardom and polarization characteristics of optical vortices combined with morphology of polarization singularities. Ergodicity of dynamic speckle-fields was found. It was shown that sign of C points coincides with speckle handedness they are nested; stars/monstar, lemon are underlined by negative/positive OVs. General regularities of dynamic elliptic speckle-fields development were established.
Dynamics of polarization optical singularities chain reactions in generic elliptically polarized speckle fields created in photorefractive
crystal LiNbO3 was investigated in details Induced speckle field develops in the tens of minutes scale due to photorefractive 'optical
damage effect' induced by incident beam of He-Ne laser. It was shown that polarization singularities develop through topological
chain reactions of developing speckle fields driven by photorefractive nonlinearities induced by incident laser beam. All optical
singularities (C points, optical vortices, optical diabolos,) are defined by instantaneous topological structure of the output wavefront
and are tangled by singular optics lows. Therefore, they have develop in tangled way by six topological chain reactions driven by
nonlinear processes in used nonlinear medium (photorefractive LiNbO3:Fe in our case): C-points and optical diabolos for right (left)
polarized components domains with orthogonally left (right) polarized optical vortices underlying them. All elements of chain
reactions consist from loop and chain links when nucleated singularities annihilated directly or with alien singularities in 1:9 ratio. The
topological reason of statistics was established by low probability of far enough separation of born singularities pair from existing
neighbor singularities during loop trajectories. Topology of developing speckle field was measured and analyzed by dynamic stokes
polarimetry with few seconds' resolution. The hierarchy of singularities govern scenario of tangled chain reactions was defined. The
useful space-time data about peculiarities of optical damage evolution were obtained from existence and parameters of 'islands of
stability' in developing speckle fields.
By using an unconventional holography, referred to as coherence holography, developed recently, we will explore the
whole phase field in an optical coherence function and present the direct experimental investigation to the coherence
critical points, including coherence phase saddles, coherence phase extrema and coherence phase singularities. We have
observed the local phase structures around the coherence critical points, and studied the relationship between the saddles
and the extrema in the optical coherence function. Some topological rules associated with the coherence critical points,
such as topological sign rule governing the coherence vortices and topological index conservation during the reaction of
the coherence vortices, are also investigated by experiments.
It is shown the space-time dynamics of optical singularities is fully described by singularities trajectories in space-time
domain, or evolution of transverse coordinates(x, y) in some fixed plane z<sub>0</sub>. The dynamics of generic developing speckle
fields was realized experimentally by laser induced scattering in LiNbO<sub>3</sub>:Fe photorefractive crystal. The space-time
trajectories of singularities can be divided topologically on two classes with essentially different scenario and duration.
Some of them (direct topological reactions) consist from nucleation of singularities pair at some (x, y, z<sub>0</sub>, t) point, their
movement and annihilation. They possess form of closed loops with relatively short time of existence. Another much
more probable class of trajectories are chain topological reactions. Each of them consists from sequence of links, i.e. of
singularities nucleation in various points (x<sub>i</sub> y<sub>i</sub>, t<sub>i</sub>) and following annihilation of both singularities in other space-time
points with alien singularities of opposite topological indices. Their topology and properties are established. Chain
topological reactions can stop on the borders of a developing speckle field or go to infinity. Examples of measured both
types of topological reactions for optical vortices (polarization C points) in scalar (elliptically polarized) natural
developing speckle fields are presented.
Optical and electrical conductivity properties of multi-walled carbon nanotubes (MWCNTs) and nematic liquid crystal
(LC) composites are investigated. The MWCNTs with high aspect ratio L/d ≈ 300 ÷ 1000 and nematic LC 5CB (4-
pentyl-4-cyanobiphenyl) are used. The composites are prepared by introduction of MWCNTs (0.0001÷0.1 % wt) into LC
solvent with subsequent sonication. The increase of MWCNT concentration (between 0.0025÷0.05 % wt) results in selfaggregation
of MWCNTs and formation of up to 200 micron-sized 3d aggregates with fractal boundaies. The visually
observed formation of spanning MWCNT networks near the percolation threshold at ~0.025 % wt is accompanied with
transition from non-conductive to conductive state and generation of optical singularities. The observed effects are
explained by the strong interactions between MWCNTs and LC medium and planar orientation of 5CB molecules on the
lateral surface of MWCNTs. As a result, an interfacial 5CB micro size shell with inhomogeneous structure appears
around each nanotube cluster. Diffraction of laser beam on clusters fractal boundaries creates speckle field with
multitude of optical vortices. The irregular birefringence of interfacial shells induces polarization singularities in
propagating laser beam. Growth of the LC interfacial shell thickness in external electric field and its disappearance
during transition of the nematic to isotropic liquid are measured and discussed. It is shown that the formation of 5CB
interfacial shell allows fixing existence of nanostructures beyond space resolution of microscope.
It was investigated development of singular generic elliptic speckle patterns generated and driven by laser beam in
LiNbO<sub>3</sub>:Fe crystal by quick-action stokes polarimetry. It is realized through totality of local topological transitions in
random space-time point governed by smoothly varying control parameter (amplitude of funnel bottom in the place of
forthcoming vortices pair nucleation). Vortices pair nucleates when zero amplitude value is reached. Total development
of singular light fields proceeds through the direct and chain topological reactions. Direct reactions possess short spacetime
loop trajectories. Chain reaction trajectory consists from sequence of singularities pair nucleation and annihilation
with singularities from other pairs. They can finish generically on field borders only, don't touch and intersect. Existing
wave front singularities are arranged in the topological network which plays role of its skeleton and keeps integrity
during field development. Its genesis was realized in the speckle field appeared after PDLC cell with variable applied
constant electric field. Nucleation of first optical vortices pairs was observed firstly.
Time-dependent elliptic light fields were realized and investigated first. They were created by the dynamic system 'laser
light>LiNbO<sub>3</sub>:Fe crystal' and measured by the elaborated acquit-action (1s) real-time Stokes polarimetry what insures
measurements of all Stokes components at practically the same state of dynamic system and investigated field. The
interval between cloze-ups (15s) was two orders less then full topological 'life story' of an individual C point pair.
Regularities of singularities topological space-time dynamics of azimuth networks, optical diabolos pairs and handedness
areas were established. It was found that macroscopic (total) development of singular elliptic speckle patterns is
irreversible contrary to fully reversible microscopic (local) transformations of field smooth parts to singular states and
back which occur independent in space and time. Their scenarios contain obligatory pre-nucleation ('embryo') and after-annihilation
('decay') states. Elaborated approach and presented results start dynamic singular optics of time-dependent
elliptic light fields. It has established topological scenario of singularities nucleation/annihilation processes in developing
generic elliptic light fields.
This work started the dynamic singular optics, or real-time topological dynamics of developing singular light fields. We
have used the system "laser beam → photorefractive crystal LiNbO<sub>3</sub>: Fe" which generates slowly developing scalar or
vector random scattered singular light field (speckle patterns). It was investigated by elaborated technique of phase
reconstruction for a scalar field or real-time Stokes-polarimetry for reconstruction of a vector field ellipticity and
azimuth. It was shown the "life-story" of pair singularities from pre-nucleation up to after-annihilation states is realized
as 'local topological transition' with fully reversible scenarios. Applications of dynamic singular optics are discussed.