The representation of 3D gaussian beams by means of inhomogeneous waves

Abstract

There are different methods to mathematically represent a bounded beam. Perhaps the most famous method is the classical Fourier method that consists of the superposition of pure homogeneous plane waves all traveling in different directions and having an amplitude that can be found by the Fourier transform of the required profile. This method works perfectly for 2D as well as for 3D bounded beams. However, some researchers prefer the inhomogeneous wave theory to represent a bounded beam because some phenomena, e.g. the Schoch effect, are explained by this method by means of concepts that agree better with intuition. There are several papers dealing with this method for 2D gaussian beams. Until now, it has never been considered possible to represent 3D gaussian beams as well. The present paper shows a method to overcome this shortcoming and presents different sorts of 3D gaussian beams that are built up by means of inhomogeneous plane waves.