Peter J. Collings

Undergraduate courses in optics generally include a discussion of polarized light, covering the types of polarized light, linear polarizers, and phase retarders. Jones calculus, with its two component state vectors and two-by-two operational matrices, is often introduced so that students can efficiently determine the effects of various optical devices on different types of polarized light. However, this treatment may not show that Jones calculus can also describe the optical properties of various materials and the devices that use them. Students simply need to combine Jones calculus with a simple computational algorithm. Liquid crystals provide an excellent arena to investigate this. The Jones calculus taught in undergraduate optics courses allows instructors and students to understand the behavior of a liquid crystal display (LCD), the optics of a patterned liquid crystal sample, and a polarized light microscopic image of a liquid crystal drop. If the refractive index ellipsoid is introduced, then more complex systems can be examined. Multiple examples from the liquid crystal field are explored to provide instructors and students with new course-related activities, including reviewing basic optics, writing code to implement a calculation, testing their knowledge by working out examples, analyzing liquid crystal laboratory experiments, and bridging the gap between course material and current research.

The three adjacent drop geometries for (a) sessile–sessile merging, (b) sessile–suspended or mixed merging, and (c) suspended–suspended merging.

We observe the formation of stable, magnetic field induced, alignment inversion walls, also called Helfrich walls, in nematic liquid crystals (NLCs) confined to a toroidal droplet with tangential anchoring at the boundaries. Walls are rare in NLCs due to their high energy compared to lower-dimensional defect structures. However, we find that Helfrich walls naturally form, transform, and migrate in this unconventional toroidal setting, generating intricate director-field configurations due to the interplay of confining geometry and external fields. Interestingly, the presence and number of point defects in the zero field nematic configuration of the toroid influences the types of walls that arise. In the absence of point defects, splay-bend walls emerge. By contrast, when a point defect pair exists on the toroidal surface, a wall not previously classified by Helfrich, and that involves both twist and splay-bend distortions, forms, and transforms. Our experiments and numerical simulations enable the quantification and elucidation of the physics behind the formation and transformation of these wall structures, extending the class of walls that were believed to occur in NLCs.

We deploy optical microscopy with and without an applied magnetic field to characterize the three-dimensional morphology and measure the line tension of twist disclinations in twisted nematic liquid crystal (LC) sample cells. Twist disclinations are generated by quenching the LC, 5CB (4-cyano-4’-pentylbiphenyl), into the nematic phase; 5CB is confined between substrates with in-plane anchoring directions perpendicular to one another. The disclinations form loops separating domains of opposite twist handedness. Many segments of these loops are pinned to the substrates, and the ends of some pinned segments connect to free disclination segments that penetrate into the bulk nematic. We use confocal microscopy to measure the profiles of these free disclinations and test theoretical predictions about their shape, yielding a lower bound of $\sim$32 nm for the disclination core radius. We then use an applied magnetic field to deform the free disclinations into circular arcs whose curvature increases with magnetic field strength and depends on the field-induced energy difference between opposite twist domains. The line tension of the disclinations is derived from an energy-balance equation that relates disclination curvature to magnetic field. The measured line tension increases logarithmically with sample cell thickness; it ranges from 75 to 200 pN in samples with thickness spanning from 6 to 27 $\mu$m. In total, the investigation introduces new non-invasive methodologies for studies of defects in LCs, and it provides new information about the line tension and character of isolated twist disclinations, thereby testing theory and laying experimental foundation for the study of ensembles of disclinations.

The absorption spectrum and orientational order of a dye molecule dissolved in a lyotropic chromonic liquid crystal depends on whether it is free in solution, externally bound to a chromonic assembly, or intercalated in a chromonic assembly.

Stable and metastable smectic liquid crystal textures, including focal conic domains, dislocations, and undulations, arise within liquid crystal Janus drops. The different textures can be created and controlled via different fabrication pathways.