Spiral light fields in the form of closed curves as generalization of Laguerre-Gaussian beams

Spiral beams as the generalization of the known Laguerre-Gaussian beams are researched in the work. It is demonstrated that similar to the Laguerre-Gaussian beams, this generalization can also be described with the operation of a certain differentiation operator. A number of these beams parameters are estimated, such as quantization conditions, amplitude, scalar product and angular momentum, as well as the result of their astigmatic transformation. The results obtained could also be of interest in the sphere of laser technologies and laser micromanipulation.