Jones calculus and polarized optical microscopy research

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.