A New Mechanism of Passive Mode Locking in A Soliton Fiber Laser

The propagation of pulses and beam profiles under the action of two-photon absorption (TPA) has great interest nowadays, because the potential action of TPA as a limitation factor in switching devices using high nonlinearitiesll]. Variational approaches have been applied successfully to the problem of temporal dispersion andlor spatial diffraction in nonlinear propagation which is described by a nonlinear Schrodinger equation[2]. These approaches am usually limited to conservative optical systems, due to mathematical difficulties that the dissipation term brings about. The purpose of this study is lo apply a variational technique to investigate dissipative nonlinear propagation. By means of the generalization of the Kantorovich method, suitable for non-conservative systems, we are able to deal with the problem of soliton propagation under the influence of TPA. Based on the characteristics of the exact solution in the absence of TPA. and supposing an adiabatic process we propose a family of soliton solutions as trial functions. This procedure results in analytical expressions that illustrate the changes during propagation of the soliton’s parameters such as amplitude, width and phase. The rate at which energy is dissipated is also obtained and, as expected, from a TPA process. is proportional to 1’. Comparison of the behavior predicted by our approximate solutions with numerical results available in the literature show very good agreement[3]. The dissipative variational approach can be extended to deal with more dimensions in the NLSE and to different kinds of dissipative nonlinearities as €?+-doped fiber amplifiers. In conclusion, a variational approach for non-conservative propagation has been used to provide a suggestive description for soliton propagation under TPA effect. As the problem of non-conservative propagation is shared by many areas of physics other than light pulse propagation, we emphasize that the present approach may be useful for a quite wide range of areas and different kinds of dissipative terms.