Focused Gaussian beam in the paraxial approximation

A focused Gaussian beam represents a case of highly practical importance in many areas of optics and photonics. We derive analytical expressions for a focused Gaussian beam in the paraxial approximation, considering an arbitrary lens filling factor. We discuss the role of higher-order Bessel functions of the first kind in defining the electric field in the focal region. (C) 2020 Optical Society of America