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Vortex beams are a type of structured light characterized by phase rotationaround the propagation axis, resulting in orbital angular momentum. Theirproperties make them useful in various applications such as high-resolutionmicroscopy, optical tweezing, and telecommunications. This has led to acomprehensive development of methods for their generation, ranging from usingsingle-purpose glass elements to utilizing computer-generated holograms usingspatial light modulators. One of the most commonly used elements for vortextransformation is a vortex half-wave retarder called a q-plate, which cantransform a Gaussian beam into a scalar vortex or vector beam depending on theinput polarization. Although the commercially available ones are limited in therange of possible output topological charges, they can be stacked to performarithmetic operations to expand them. However, changing the output or workingwavelength requires rearranging the elements. We present an improvement to thismethod that solves these problems by introducing Q-modules, easy-to-fabricate,electrically tunable liquid crystal devices that combine the features ofq-plates and half-wave plates and can be used as building blocks in modularassemblies. Electrical tuning makes it possible to change the workingwavelength as well as the topological output charge or polarization orderwithout the need to interact mechanically with the setup.

Multi-wavelength Q-plate Arithmetic in an All-Liquid-Crystal Modular Setup