Cholesteric dislocations in mica wedges

Optical vortices generated by dislocations in a cholesteric liquid crystal.

We report the observation of optical vortices in a laser beam propagating through the stripe pattern of a cholesteric liquid crystal. The liquid crystal is confined in a cell with homogeneous boundary conditions and forms a diffraction phase grating. Optical vortices are produced by edge dislocations of the cholesteric grating. The vortices show up as spots of zero light intensity in the diffra...

Anchoring-mediated interaction of edge dislocations with bounding surfaces in confined cholesteric liquid crystals.

We employ the fluorescent confocal polarizing microscopy to image edge dislocations in cholesteric liquid crystals. Surface anchoring at the bounding plates determines the structure and behavior of defects. Two types of plates set in-plane director orientation but differ in the type of associated anchoring potentials. Plates with strong polar anchoring and nonzero azimuthal anchoring repel the ...

Three-dimensional director structures of defects in Grandjean-Cano wedges of cholesteric liquid crystals studied by fluorescence confocal polarizing microscopy.

We use a nondestructive technique of fluorescence confocal polarizing microscopy to visualize three-dimensional director patterns of defects in Grandjean-Cano wedges filled with a cholesteric liquid crystal of pitch p=5 microm. Strong surface anchoring of the director causes a stable lattice of dislocations in the bulk. Optical slicing in the vertical cross sections of the wedges allows us to e...

Cholesteric to cholesteric phase transitions in liquid crystals

Centerpoint Theorems for Wedges

The Centerpoint Theorem states that, for any set S of n points in R, there exists a point p in R such that every closed halfspace containing p contains at least dn/(d+ 1)e points of S. We consider generalizations of the Centerpoint Theorem in which halfspaces are replaced with wedges (cones) of angle α. In R, we give bounds that are tight for all values of α and give an O(n) time algorithm to f...