Dissipative Light Bullets in Passively Mode-Locked Semiconductor Lasers

We demonstrate the existence of stable three dimensional dissipative localized structures in the output of a laser coupled to a distant saturable absorber. These phase invariant light bullets are individually addressable and can be envisioned for three dimensional optical information storage. An effective theory provides for an intuitive picture and allows to relate their formation to the morphogenesis of static auto-solitons and cellular patterns. The complexity incurred by the widely different time scales present in the problem as well as by non-local couplings that stem from the material degrees of freedom is circumvented by the use of a multiple time-scale analysis. This provides a powerful model enabling to tackle effectively the three dimensional case.Comment: 5 pages, 5 figure

Spectral flow and iteration of closed semi-Riemannian geodesics

We introduce the notion of spectral flow along a periodic semi-Riemannian geodesic, as a suitable substitute of the Morse index in the Riemannian case. We study the growth of the spectral flow along a closed geodesic under iteration, determining its asymptotic behavior.Comment: LaTeX2e, 21 page

Finsler metrics and relativistic spacetimes

Recent links between Finsler Geometry and the geometry of spacetimes are briefly revisited, and prospective ideas and results are explained. Special attention is paid to geometric problems with a direct motivation in Relativity and other parts of Physics.Comment: 15 pages, v2: Final version with a new last section of conclusions and minor modifications, to appear in International Journal of Geometric Methods in Modern Physics, in the Special Issue for the XXII IFWGP Evora DOI: 10.1142/S021988781460032