A new kind of spatiotemporal systems in optics
C. Szwaj, S. Bielawski and D. Derozier
Laboratoire de spectroscopie hertzienne,
Centre d'Etudes et de
Recherches Lasers et Applications,
Université de Lille I, F-59655 Villeneuve d'Ascq Cedex
France
Multimode lasers have been the subject of numerous investigation because they are prototypes of high dimensional systems. In the limit case of homogeneous broadening, multimode class-B lasers can be considered as globally coupled systems [1], but in the general case of both homogeneous and inhomogeneous broadenings, the conceptual frame is not so developed.
Here, we propose an original approach which consists in considering the set of longitudinal modes of a class-B laser as a propagation medium. The discrete spatial variable is the index of each mode and the information which propagates is the deviation of the mode intensities from their steady state values. Propagation of linear waves is demonstrated theoretically and experimentally in the case of a Nd-doped fiber laser. The dispersion curves are extracted and we show that the group and phase velocities always have opposite signs [2]. This result is a direct consequence of the mode coupling nature and does not depend on the model details.
As the representation of the laser in terms of spatiotemporal system is shown to be valid, the nonlinear dynamics could be investigated. Under strong pump modulation, the laser dynamics exhibits different spatiotemporal behaviors depending on the control parameters (amplitude or frequency modulation). We observe regular dynamics (travelling or stationnary waves) as well as irregular regimes both in space and time. A bifurcation between stationnary and travelling waves could be pointed up and other phenomena predicted for nonlinear chains [3] are also expected.
In conclusion, we have shown up theoretically and experimentally the existence of a new kind of spatiotemporal system in optics. The multimode class-B laser can be considered as a one-dimensional chain of nonlinear oscillators.