Linear Beam Position Control in Optical Waveguides

The ability of a beam waveguide to guide optical frequency electromagnetic energy is severely limited by the tolerances held on the transverse positions of the lenses. Hirano and Fukatsu 1 have shown that uncorrelated transverse lens displacements will cause the expected deviation of the beam from the guide axis to grow as the square root of the number of lenses through which it has passed. Steier 2 has shown that random longitudinal lens displacements and variations in the focal lengths of the lenses couple with random 783 784 THE BELL SYSTEM TECHNICAL JOURNAL, M A Y - J U N E 1968 transverse lens displacements to cause the expected value of the rms beam displacement to grow exponentially with the number of lenses through which it has passed. This paper describes the performance of linear self-aligning beam waveguides that are subjected to transverse disturbances of the lens and sensor positions. It is quite likely t h a t nonlinear control systems may turn out to be more effective or practical in practice but an understanding of linear systems will facilitate the more involved analysis of nonlinear control systems. The idea of using active guiding media for optical communications was proposed long ago by R. Kompfner 3 and L. U. Kibler, 4 and has been discussed by E. A. J. Marcatili. 5 The improvement that can be obtained with self-aligning beam waveguides has been demonstrated experimentally and with computer simulations by Christian, Goubau, and Mink. 6 In the guiding systems considered in this paper, the lenses are physically moved an amount that is determined by sensing the position of the beam in the guide.