Linear Beam Position Control in Optical Waveguides

This paper studies the effect of an active control system that introduces corrective transverse lens displacements on the propagation of beams in optical waveguides. The induced displacement of the nth lens is a linear function of the beam displacement at the (n + 1)th lens. Beam displacements from the ideal design position are caused by transverse displacements of the lenses and sensors from their design positions. Expressions have been obtained for: (i) The conditions for spatial and temporal stability. (ii) The rms beam displacement resulting from uncorrelated displacements of the lenses and sensors. (iii) The beam displacement caused by sinusoidal displacements of the lenses and sensors of arbitrary spatial frequency. (iv) The spatial rate of return to the guide axis of a beam injected into the guide off axis. We also show that the positions of beams, other than the sensed beam, are controlled by the system and that the system can simultaneously guide many different sensed beams. We calculate an upper limit on the probability that the beam will not be contained within a given aperture.