Diffraction of light by topological defects in liquid crystals

Abstract

We study light scattering by a hedgehog-like and linear disclination topological defects in a nematic liquid crystal by a metric approach. Light propagating near such defects feels an effective metric equivalent to the spatial part of the global monopole and cosmic string geometries. We obtain the scattering amplitude and the differential and total scattering cross section for the case of the hedgehog defect, in terms of the characteristic parameters of the liquid crystal. Studying the disclination case, a cylindrical partial wave method is developed. As an application of the previous developments, we also examine the temperature influence on the localization of the diffraction patterns.

Decomposition vs. escape of topological defects in a nematic liquid crystal

“…This observation is in line with our preliminary theoretical analysis 14 , which suggests the first order structural transition between the escaped defect and split defect structure on varying d. Consequently, a bistability regime must exist, giving rise to the observed hysteresis behavior. We note that because of the typically small biaxial correlation length of ~30 -50 nm associated with calamitic nematics 13 , optical observation of the biaxial region is not possible using standard optical microscopy.…”

“…(Note that the tensor nematic order parameter admits the possibility of biaxiality as yet another strain relief mechanism. 11,12,13 .) These configurations are separated by a discontinuous structural transition on increasing the cell thickness.…”

“…Ackerman, Qi, and Smalyukh have used an optical technique to create 3D patterns of electrically erasable "torons", with spacings as small as [10][11][12][13][14][15][16][17][18][19][20]. Guo, et al developed a plasmonic photopatterning technique to create arbitrary patterns for planar liquid crystal alignment on length scales of tens of micrometers 4 .…”

Helical phase of chiral nematic liquid crystals as the Bianchi VII0group manifold

“…[19][20][21]) and where, in addition, the refractive indices n o ,n e vary with position inside the ball r = |x| < 1 according to…”

“…Then one has a model related to Maxwell's fish-eye lens by a coordinate transformation, but whose rays are straight lines. Other examples may be found in [19][20][21]. Optical properties such as (15) may appear unnatural, but modern metamaterials are increasingly able to mimic such refractive indices, at least within a certain range of frequencies for the electromagnetic field.…”