Properties
An optical singularity is a zero of an optical field. The phase in the field circulates around these points of zero intensity (giving rise to the name vortex). Vortices are points in 2D fields and lines in 3D fields (as they have codimension two). Integrating the phase of the field around a path enclosing a vortex yields an integer multiple of . This integer is known as the topological charge, or strength, of the vortex.
A hypergeometric-Gaussian mode (HyGG) has an optical vortex in its center. The beam, which has the form
is a solution to the paraxial wave equation (see paraxial approximation, and the Fourier optics article for the actual equation) consisting of the Bessel function. Photons in a hypergeometric-Gaussian beam have an orbital angular momentum of mħ. The integer m also gives the strength of the vortex at the beam's centre. Spin angular momentum of circularly polarized light can be converted into orbital angular momentum.
Read more about this topic: Optical Vortex
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