Statistical Treatment of Light-Ray Propagation in Beam-Waveguides

Hirano, Fukatsu and Rowe1 have studied the behavior of a light beam in a beam-waveguide whose lenses are randomly displaced from a perfectly straight line. The first two authors considered also a waveguide with sinusoidal axis displacements. The behavior of light beams in bent lens-waveguides was studied in Ref. 2. These two papers represent two extreme cases of completely uncorrelated departures of the waveguide axis from perfect straightness on the one hand and perfectly correlated departures from a straight line on the other hand. 2065 2066 THE B E L L SYSTEM TECHNICAL JOURNAL, NOVEMBER 1965 This paper describes the statistics of a light ray by introducing a correlation function connecting different points on the waveguide axis.7 We show how the ray position at the nth lens depends on one Fourier component of the curvature function of the waveguide axis, while the rms value of the beam displacement depends on one frequency component of the "power spectrum" of the curvature function. The dependence of the ray position on the Fourier component of the curvature function of the waveguide axis is analogous to the mode conversion loss of multimode waveguides.3 The description of the beam deflection in terms of the correlation function of the guide axis is used to draw some general conclusions. It is found that the rms value of the light beam deflection depends on the square root of the number of lenses in the guide provided that the correlation length is much less than the length of the guide.