Slaven Peles

Model for high-gain fiber laser arrays

Recent experiments have shown that a small number of fiber lasers can spontaneously form coherent states when suitably coupled. The observed synchrony persisted for a long time without any active control. In this paper, we develop a dynamical model for fiber laser arrays that is valid in the high gain regime. In the limiting case of a single laser analysis and simulations are presented that agree with physical expectations. Using simulations to examine array behavior we report results that are in qualitative agreement with laboratory observations.

On design of continuous Lyapunov's feedback control

A common approach to Lyapunovs stability control is to design a controller such that a Lyapunov function can be derived for the control system to ensure stability. This procedure often leads to a discontinuous controller. When the controller is implemented, the discontinuous terms are replaced with continuous functions to avoid chattering of the control signal. Two associated problems have been overlooked during this procedure. One is that discontinuous control systems are non-smooth, which violates the fundamental assumptions of solution theories and the applicability of Lyapunovs stability theory is questionable. Another problem is that the replacement of discontinuous terms may weaken stability, which can be critical. In this paper, we discuss proper stability analysis of discontinuous control systems using the extended Lyapunovs second method based on Filippovs solution concept for non-smooth systems. We further propose to utilize the concept of Lyapunov exponents to quantitatively analyze the stability of continuous control systems obtained by replacing the discontinuous terms in the discontinuous controllers. An example involving the stabilization of a two-link non-fixed-base robotic manipulator is presented for demonstration. This research fills the gap in designing continuous Lyapunovs stability controllers regarding limited available Lyapunov functions.

Effect of Gain-Dependent Phase Shift on Fiber Laser Synchronization

Recent experiments have demonstrated synchronization of fiber laser arrays at low and moderate pump levels. It has been suggested that a key dynamical process leading to synchronized behavior is the differential phase shift induced by the gain media. We explore theoretically the role of this effect in generating inphase dynamics. We find that its presence can substantially enhance the degree of inphase stability to an extent that could be practically important. At the same time, our analysis shows that a gain-dependent phase shift is not a necessary ingredient in the dynamical selection of the inphase state, thus, leading us to reconsider the essential mechanism behind inphase selection in fiber laser arrays.

Synchronization in fiber laser arrays: theoretical study

Fiber lasers have small size, high conversion rates and excellent thermal properties. On the other hand they generally produce smaller output intensity than semiconductor lasers. Recent experiments reported that a small number of fiber lasers can be synchronized simply by coupling them with an optical waveguide coupler near the output end. As a result the output peak intensity increases as a square of the number of coupled lasers, and well focused beams of high intensities can be produced, while preserving all other properties of fiber lasers. Synchronous behavior arises spontaneously, at constant pumping levels and without any active control. We investigate synchronization properties using a theoretical model, based on an iterated map with a particular symmetry. Our model captures key qualitative features seen in the experiments. We illustrate our results in a simple fiber laser configuration.

An improved design procedure of Lyapunov feedback control

An improved procedure of Lyapunov feedback control is developed. The procedure includes two parts. First, a discontinuous controller is designed. The extended Lyapunov stability theory is used for the stability analysis of the resulting non-smooth control system. Next, the discontinuous terms in the controller are replaced with continuous functions. This weakens the stability but avoids the chattering of the controller. The trade-off in the stability is analyzed using the concept of Lyapunov exponents. We demonstrate the effectiveness of the design procedure by stabilizing a two-link base-excited inverted pendulum system around the upright position. We believe that our improved design procedure makes the Lyapunov feedback control more applicable.