Geometrical Representation of Gaussian Beam Propagation

The propagation of a Gaussian beam and its transformation through a lens has been well treated in previous literature. 1,2 3 4 This paper will show that a single, formally identical equation governs three properties of Gaussian beam propagation: (i) the phase front curvature and the beam radius in terms of the distance from the beam waist and the minimum beam radius; (ii) the propagation of a Gaussian beam in free space; {Hi) the transformation of a Gaussian beam through a lens. Geometrical representations of these characteristics highlight the relationship between Gaussian beam propagation and geometrical optics. Several recent papers5'6,7,8 have been devoted to graphical solutions of Gaussian mode problems. One recalls that the Smith chart is a geometrical representation of complex reflection coefficient in transmission line theory. It seems logical, therefore, to look for the counterpart of a complex reflection coefficient in Gaussian mode theory in order that the full potential of the Smith chart may be realized in graphical solutions of Gaussian mode problems. In this paper, a complex mismatch coefficient will be defined such that the geometrical representation of this 287