No abstract

We derive model equations for optical pulse propagation in a medium described by a two-level Hamiltonian, without the use of the slowly varying envelope approximation. Assuming that the resonance frequency of the twolevel atoms is either well above or well below the inverse of the characteristic duration of the pulse, we reduce the propagation problem to a modified Korteweg-de Vries or a sine-Gordon equation. We exhibit analytical solutions of these equations which are rather close in shape and spectrum to pulses in the two-cycle regime produced experimentally, which shows that soliton-type propagation of the latter can be envisaged.

No abstract

No abstract

Using Maxwell-Bloch equations, we analyze the response of a two-component medium of two-level atoms driven by a two-cycle optical pulse beyond the traditional approach of slowly varying amplitudes and phases. We show that the notions of carrier, envelope, phase, and group velocities can be generalized to this situation. For optical pulses of a given duration, we show that the optical field can form a temporal soliton.

The dynamics of a fiber ring laser mode locked by nonlinear polarization rotation is reduced to a quintic complex Ginzburg-Landau (CGLQ) equation. The coefficients of the equation are explicitly given as functions of the physical parameters of the laser, especially the orientation of the phase plates. Then known results about analytic solutions, stability of pulse-like solutions, and bound states of the CGLQ equation are examined from the point of view of their dependence with regard to the physical parameters.

No abstract

We give a detailed theoretical analysis of spontaneous periodic pattern formation in fiber lasers. The pattern consists of a bound state of hundreds of pulses in a ring fiber laser passively mode locked by nonlinear rotation of the polarization. The phenomenon is described theoretically using a multiscale approach to the gain dynamics: the fast evolution of a small excess of gain is responsible for the stabilization of a periodic pattern, while the slow evolution of the mean value of gain explains the finite length of the quasiperiodic soliton train. The resulting model is well adapted to experimental observations in a Er:Yb-doped double-clad fiber laser.