The Statistical Effects of Random Variations in the Components of a Beam Waveguide

Abstract

The effects of variations in the components of a beam waveguide are considered. These variations statistically cause the Gaussian beam spot size of the light propagating down the waveguide to grow and cause the beam center to oscillate about the waveguide axis with ever-increasing amplitude. Random variations in lens focal length and spacing and random lateral lens displacements are considered. It is also shown how random variations in focal length and spacing can be included in the published analyses for short random bends in the waveguide axis. When the number of lenses is large, it is shown that the beam displacement and beam spot size both grow exponentially with distance. As an example, a confocal waveguide with lenses spaced one meter apart and built to somewhat optimistic tolerances will require a beam redirector every 2.5 kilometers to prevent the beam oscillations from exceeding an rms value of 2 millimeters.