Transients in beam position control systems for optical waveguides

Beam position transients in self-aligning beam waveguides are studied. The control system senses the beam position, rn, at each lens and introduces a corrective term to the transverse position of the preceding lens. The Laplace transform of the beam position at the th lens, for the case of a general control function , relating rnand , is found. The special case of a confocal guide, where the control function is an integrator with gain , results in a time dependence of the beam positions at the lenses, equal to the product of a decaying exponential and Laguerre polynomials. The case where the control function represents a second-order system has been simulated on a digital computer. The results show that overshoot can be controlled by increasing the damping term in .