Step Correction of Misaligned Beam Waveguides

This paper studies the steady-state performance of a system that stabilizes the beam position in optical waveguides. We have constrained the system to make only a single fixed amount of correction in the beam position at any given lens. We consider a symmetric corrector capable of correcting both positive and negative errors at any given lens and an unsymmetric corrector capable of correcting only positive errors at any given lens. We give the results from our studies of the performance of these systems when the lens misalignment forms a wave at the guide resonant spatial frequency, ωo, and from our simulation of 5,000 confocal guides which were subjected to uncorrelated lens misalignment. We also derive an approximate sťatistical theory relating the root mean square beam displacement to the root mean square lens misalignment. We relate systems where correction occurs at every lens to systems where correction can occur only at every nth lens.