Implementing digital holograms to create and measure complex-plane optical fields

Abstract

The coherent superposition of a Gaussian beam with an optical vortex can be mathematically described to occupy the complex plane. The authors provide a simple analogy between the mathematics, in the form of the complex plane, and the visual representation of these two superimposed optical fields. They provide detailed instructions as to how one can experimentally produce, measure, and control these fields with the use of digital holograms encoded on a spatial light modulator.