Well known approaches for inducing topological defects in nematics include geometric confinement of the liquid crystalline material into spherical droplets and also the use of colloidal microspheres dispersed in the bulk of a uniformly aligned liquid crystal. In both cases, topological defects appear to assure the topological charge conservation while compensating for the topological charges due well-defined boundary conditions at the surfaces of droplets and particles. This lecture will discuss the topology-dictated generation of defects in liquid crystals confined into topologically nontrivial handlebody-shaped pores and droplets as well as when topologically nontrivial colloidal microparticles are introduced into an aligned liquid crystal. Furthermore, it will be shown that stable hierarchical arrays of defects in confined chiral nematic liquid crystals can be generated and controlled using optical vortex laser beams. Experimental studies will be compared with the results of numerical modeling.
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