Singularities in Computational Optics

Phase singularities in optical fields are associated with a non-vanishing curl component of phase gradients. Huygen’s diverging spherical wavefronts that primary/secondary point sources emit, during propagation, a have zero curl component. Therefore, the propagation of waves that contain phase singularities exhibits new exciting features. Their effect is also felt in computational optics. These singularities provide orbital angular momentum and robustness to beams and remove degeneracies in interferometry and diffractive optics. Recently, the improvisations in a variety of computation algorithms have resulted in the vortices leaving their footprint in fast-expanding realms such as diffractive optics design, multiplexing, signal processing, communication, imaging and microscopy, holography, biological fields, deep learning, and ptychography. This review aims at giving a gist of the advancements that have been reported in multiple fields to enable readers to understand the significance of the singularities in computation optics.