Geometrical Representation of Gaussian Beam Propagation

A single equation governing the various properties encountered in propagation of Gaussian beams is discussed. These characteristics may be graphically presented on an impedance chart such as a Smith chart or in the form of normalized curves. The geometrical representations highlight the relation between Gaussian mode theory and geometrical optics formulas. The power coupling coefficient between two Gaussian modes suggests a complex mismatch coefficient whose geometrical representation is essentially the same as that of a complex reflection coefficient in transmission-line theory. Application of the Smith chart in determining a complex mismatch coefficient is illustrated by graphical solution of a beam-matching problem.