ABSTRACT
The Helmholtz equation that describes the propagation of a non-paraxial monochromatic light wave in uniform space admits of solutions with separable variables in 11 different coordinate systems. This implies that there are electromagnetic fields that can propagate without changing their structure. This chapter deals with another family of laser modes that form an orthonormalized basis and are defined by a separable-variable-based solution of the paraxial parabolic equation in the cylindrical coordinate system. In the cylindrical coordinate system, in addition to solutions in the form of Bessel and Laguerre-Gauss modes, the solution of Schroedinger's equation can be found as degenerate hypergeometric (HyG) functions. The cutting-edge research has lately shown a significant increase of interest in various types of laser beams. Studies of the well-known Laguerre-Gauss modes have been under way.
