Novel nonlinear optical phenomena in nematic liquid crystals

In normal materials, the nonlinear optical effects arise from nonlinearities in the polarisabilities of the constituent atoms or molecules. On the other hand the nonlinear optical effects in liquid crystals arise from totally different processes. Also they occur at relatively low laser intensities. In a laser field a liquid crystal exhibits many novel and interesting nonlinear optical effects. In addition we also find laser field induced effects that are peculiar to liquid crystals, like structural transformations, orientational transitions, modulated structures and phase transitions, to name a few. Here we dwell upon a few of these interesting and important nonlinear optical phenomena that exist in nematic liquid crystals

Piezooptics of crystals

In this paper the effects of mechanical stress on the refractive, absorptive and the rotatory properties of crystals have been considered with particular emphasis on the role of crystal symmetry. Stress-induced optical activity and the photoelastic behaviour of transparent, weakly absorbing and metallic crystals have been discussed. Piezooptia of polycrystalline media has also been briefly dealt with

On some elastic instabilities in biaxial nematics

Within the framework of the continuum elastic theory of biaxial nematic liquid crystals, we have addressed ourselves to the structure, stability and energetics of some singular and non-singular topological defects, and certain director configurations. We find that certain non-singular hybrid disclinations could be energetically favourable relative to certain half-strength disclinations. The interaction between singular hybrids depends strongly on the biaxial elastic anisotropy. We suggest possible defect structures that can exist in spherical droplets of biaxial nematics. Further we find structural instabilities, in confined geometries, arising due to the inherent biaxiality of the system

On the optics of twist grain boundary smectics

We have studied theoretically the optical properties of twist grain boundary smectics. We find many reflection bands even at normal incidence. In some of the reflection bands an incident light in any state of polarization gets strongly reflected while in some others the strongly reflected state is of a circular polarization with the same or the opposite handedness as that of the structure. At oblique incidence, depending upon the screw symmetry, a reflection band either has three sub-bands of different polarizations or is a single band of a particular polarization. We find optical diffraction for light incident perpendicular to the twist axis. The diffraction pattern is completely different for TGBA and TGBC. In addition in absorbing TGBC the pattern can even become asymmetric. From a Fourier inversion of the complex diffracted amplitudes we can evaluate in some cases the sizes of the smectic blocks and the grain boundaries

Nematic kink states in a laser field

We have investigated the nonlinear optical interaction of uniform and kink states of a nematic and a ferrofluid-doped nematic (ferronematic) liquid crystal with an incident laser field. We find that the transition between the permitted uniform oreintational states of these systems is of first order in the case of nematics, and of second order in the case of ferronematics. In the latter case we also find the phenomenon of reentrance. We find new kink states in a magnetic field with topological winding different from p in the case of nematics, and 2π in the case of ferronematics. In ferronematics, due to grain segregation the phase diagrams for uniform and kink states are entirely different. In these systems we find a first or second order structural transformation from a single kink into a pair of kinks. Further, we obtain a rich variety of kink states as the intensity of the laser field is varied

A hardware implementation of a relaxation algorithm to segment images

Relaxation labelling is a mathematical technique frequently applied in image processing algorithms. In particular, it is extensively used for the purpose of segmenting images. The paper presents a hardware implementation of a segmentation algorithm, for images consisting of two regions, based on relaxation labelling. The algorithm determines, for each pixel, the probability that it should be labelled as belonging to a particular region, for all regions in the image. The label probabilities (labellings) of every pixel are iteratively updated, based on those of the pixel's neighbors, until they converge. The pixel is then assigned to the region correspondent to the maximum label probability. The system consists of a control unit and of a pipeline of segmentation stages. Each segmentation stage emulates in the hardware an iteration of the relaxation algorithm. The design of the segmentation stage is based on commercially available digital signal processing integrated circuits. Multiple iterations are accomplished by stringing stages together or by looping the output of a stage, or string of stages, to its input. The system interfaces with a generic host computer. Given the modularity of the architecture, performance can be enhanced by merely adding segmentation stages

Defects in liquid crystals

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Control dependence for extended finite state machines

Though there has been nearly three decades of work on program slicing, there has been comparatively little work on slicing for state machines. One of the primary challenges that currently presents a barrier to wider application of state machine slicing is the problem of determining control dependence. We survey existing related definitions, introducing a new definition that subsumes one and extends another. We illustrate that by using this new definition our slices respect Weiser slicing’s termination behaviour. We prove results that clarify the relationships between our definition and older ones, following this up with examples to motivate the need for these differences

Optics of absorbing anisotropic media

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Defects in smectic C<SUP>&#8727;</SUP> liquid crystals

We consider the structure and properties of various topological defects that can occur in smectic C∗ liquid crystals. The polarization field associated with disclinations, the effect of incornmensuration on the structure of dispirations, some interesting situations in the interaction between dispiration and disclination and between dispirations themselves have been discussed in detail. The properties of cholesteric type disclinations and a possible model for the core structure of a wedge disclination have also been dealt with