Statistical Treatment of Light-Ray Propagation in Beam-Waveguides

Abstract

It is well known that uncorrelated, transverse displacements of the lenses of a beam-waveguide cause the light beam to deviate from its axis and that the tolerance requirements on the accuracy of the transverse lens positions are very stringent. This paper extends the statistics of beam waveguides to include correlations between displacements of different lenses and studies the effects of a succession of uncorrelated bends. It can be concluded from this work that the rms deviation of the light beam is proportional to the square root of the length of the waveguide if the correlation between lens displacements extends only over a limited range. The amplitude of the Fourier component of the waveguide axis whose period equals the oscillation period of the ray has to be less than 0.2 micron if the deviation of a light beam passing through 10,000 lenses of a confocal waveguide is to be kept less than 2 mm. This requirement means that the average radius of curvature of a waveguide composed of independent circular sections of an average length of 20 m with lenses spaced 1 m apart has to be more than 10 km. The comparison between two model guides, one composed of circular section and the other of sections shaped like sin2 sin2 βx, indicates that the beam deflection depends only on the average radius of curvature and average length of the sections but not on their particular shape.