Analysis of Endless Tuning of Polarization Controllers

Polarization control (PC) is an important issue in modern fiber-optical transmission systems and opto-electronic hardware in general, and drives the ongoing search for low-cost, high-speed, and robust PC devices. This paper revisits the problem of endless, reset free PC from a mathematical point of view, and gives precise definitions, explicit analytic control algorithms, and quantitative proofs for endless, reset free operation of a PC architecture consisting of generalized waveplates (WP). The control algorithms lead to a restricted range of WP parameters which allows us to implement them using planar lightwave circuits as a sequence of alternating phase shifters (PS) and directional couplers (DC) with values that stay within prescribed bounds. The final results are provable solutions for endless, reset free PC of fixed into arbitrary state of polarization (SOP) and of arbitrary into arbitrary SOP. For input to the analytic control algorithms, we assume measured input SOP vectors which are changing in time.