Nonparaxial hypergeometric modes

We derive an analytical expression to describe the exact solution of Helmholtz equation in the cylindrical coordinates as a product of two Kummer's functions. The solution is presented as a sum of two terms that describe the non-paraxial hypergeometric light beams propagated along the optical axis in the positive and negative directions. With the distance from the initial plane becoming much larger than the wavelength of light, the expression derived for the non-paraxial hypergeometric beam coincides with that for a paraxial hypergeometric mode.