Warped embeddings between Einstein manifolds

Warped embeddings from a lower dimensional Einstein manifold into a higher dimensional one are analyzed. Explicit solutions for the embedding metrics are obtained for all cases of codimension 1 embeddings and some of the codimension n>1 cases. Some of the interesting features of the embedding metrics are pointed out and potential applications of the embeddings are discussed.Comment: 12 pages, to appear in Mod. Phys. Lett.

Models for optical solitons in the two-cycle regime

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 two-level 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

Passive harmonic mode-locking in a fiber laser with nonlinear polarization rotation

On basis of numerical simulation and analytical treatment, we investigate the multiple pulse passive mode-locking of a fiber laser with nonlinear loss due to the nonlinear polarization rotation technique. Various additional mechanisms resulting in the ordering of ultrashort pulses inside the laser resonator and in the realization of harmonic passive mode-locking are analyzed. Among which are the active harmonic modulation of the intracavity loss or of the refractive index, the passive modulation of the index due to the inertial properties of intracavity elements, and the amplification modulation due to the depletion and the relaxation of the gain. The velocity of pulses relative to each other is determined, it results in attractive or repulsive pulse–pulse interaction, and allows to evaluate the conditions of ordering of the pulses inside the cavity

Theoretical study of the erbium-doped fiber laser passively mode-locked by nonlinear polarization rotation

We investigate theoretically the mode-locking properties of an erbium-doped birefringent fiber laser in a unidirectional cavity containing an optical isolator. The mode-locking is achieved through nonlinear polarization rotation. The approach is based on a master equation which takes explicitly into account the angles between the eigen axis of the fiber at each side of the polarizer. The stability conditions of both the stationary and localized solutions are determined. This allows to establish a stability diagram versus the angles which gives the domains where the laser operates in continuous, mode-locked or unstable regime. The model also allows to calculate the pulse duration together with the pulse energy as a function of the orientation of the eigen axis of the fiber with respect to the polarizer

Modelling of figure-eight all-fiber laser

The figure-eight fiber laser is considered in two configurations, with either a unidirectional active ring cavity coupled with a nonlinear optical loop mirror (NOLM) or a unidirectional passive cavity and a nonlinear amplifying loop mirror (NALM). In each case, we derive a master equation of cubic complex Ginzburg Landau (CGL) type, in which the coefficients explicitly depend on the characteristics of the cavity. Single-pulse and continuous wave (cw) solutions in both normal and anomalous dispersion are discussed analytically

Auto-organisation d’un grand nombre d’impulsions dans un laser à fibre dope Er:Yb

Nous proposons une étude inédite de l’interaction d’un grand nombre d’impulsions dans un laser à fibre double gaine dopée à l\u27Er :Yb fonctionnant par rotation non linéaire de la polarisation. A cause des phénomènes d\u27attractions et de répulsions entre solitons, des régimes auto-organisés peuvent être générés. Par analogie avec les états de la matière, nous nous sommes intéressés aux régimes "gaz de solitons", "jet supersonique de solitons", "polycristal de solitons", "liquide de solitons" et "cristal de solitons"

Comparative study of soliton complexes in different laser configurations

We investigate the formation of self-organized and disorganized soliton structures in passively mode-locked Er:Yb doped double-clad fiber laser. Two laser configurations are studied. The first one is based on mode-locking through nonlinear polarization rotation while the second geometry is a figure-eight cavity in which the mode-locking is obtained with a nonlinear optical loop mirror. Although the physical mechanisms of mode-locking are different, we demonstrate that collective behaviours and soliton complexes are similar in both configurations. That demonstrates the universality of the solitonic structures

Laser à fibre verrouillé en phase à haute cadence

We investigate different ways to considerably increase the repetition-rate of passively mode-locked fiber lasers. We first report the harmonic mode-locking of a double-clad fiber laser passively mode-locked through nonlinear polarization rotation. We then consider the theoretical possibility to generate a bound-state filling the optical cavity thus resulting in ultra-high repetition rate with a remarkable stability

Spectral-selective management of dissipative solitons in passive mode-locked fibre lasers

We study properties of dissipative solitons in passive mode-locked fibre lasers due to additional intracavity narrow spectral selection. Such selection allows us to control the soliton velocity, the nature of the interaction between solitons (attraction or repulsion), to create a bistable state in which the velocity of a single soliton can have two different values, to realize an elastic particle-like collision between single solitons. In the investigated laser system, the soliton interaction distance can be considerably larger than the soliton duration, which allows the realization of passive harmonic mode-locking