A theoretical approach to feedback control of optical soliton propagation

Feedback control is applied to the problem of propagating ultra-short pulse width solitons in optical fibers. Assuming that fiber dispersion can be tuned quickly and continuously, a full-state feedback control law is derived, which achieves propagation of Gaussian solitons of any desired width and chirp. This is in contrast with traditional, open-loop, dispersion management. In this paper, a variational model is used for control design, and two cases - zero and non-zero chirp - are considered. In the first case, a stable fixed point is created in closed-loop; in the second, a controlled Hopf bifurcation creates a stable limit cycle. These control laws are simulated and compared to other existing methods.