  Vortex beams are a type of structured light characterized by phase rotation
around the propagation axis, resulting in orbital angular momentum. Their
properties make them useful in various applications such as high-resolution
microscopy, optical tweezing, and telecommunications. This has led to a
comprehensive development of methods for their generation, ranging from using
single-purpose glass elements to utilizing computer-generated holograms using
spatial light modulators. One of the most commonly used elements for vortex
transformation is a vortex half-wave retarder called a q-plate, which can
transform a Gaussian beam into a scalar vortex or vector beam depending on the
input polarization. Although the commercially available ones are limited in the
range of possible output topological charges, they can be stacked to perform
arithmetic operations to expand them. However, changing the output or working
wavelength requires rearranging the elements. We present an improvement to this
method that solves these problems by introducing Q-modules, easy-to-fabricate,
electrically tunable liquid crystal devices that combine the features of
q-plates and half-wave plates and can be used as building blocks in modular
assemblies. Electrical tuning makes it possible to change the working
wavelength as well as the topological output charge or polarization order
without the need to interact mechanically with the setup.
