Some Spacetimes with Higher Rank Killing-Stackel Tensors

By applying the lightlike Eisenhart lift to several known examples of low-dimensional integrable systems admitting integrals of motion of higher-order in momenta, we obtain four- and higher-dimensional Lorentzian spacetimes with irreducible higher-rank Killing tensors. Such metrics, we believe, are first examples of spacetimes admitting higher-rank Killing tensors. Included in our examples is a four-dimensional supersymmetric pp-wave spacetime, whose geodesic flow is superintegrable. The Killing tensors satisfy a non-trivial Poisson-Schouten-Nijenhuis algebra. We discuss the extension to the quantum regime

Wave Functions and Energy Terms of the SCHR\"Odinger Equation with Two-Center Coulomb Plus Harmonic Oscillator Potential

Schr\"odinger equation for two center Coulomb plus harmonic oscillator potential is solved by the method of ethalon equation at large intercenter separations. Asymptotical expansions for energy term and wave function are obtained in the analytical form.Comment: 4 pages, no figures, LaTeX, submitted to PR

Polarization dynamics in nonlinear anisotropic fibers

We give an extensive study of polarization dynamics in anisotropic fibers exhibiting a third-order index nonlinearity. The study is performed in the framework of the Stokes parameters with the help of the Poincaré sphere. Stationary states are determined, and their stability is investigated. The number of fixed points and their stability depend on the respective magnitude of the linear and nonlinear birefringence. A conservation relation analogous to the energy conservation in mechanics allows evidencing a close analogy between the movement of the polarization in the Poincaré sphere and the motion of a particle in a potential well. Two distinct potentials are found, leading to the existence of two families of solutions, according to the sign of the total energy of the equivalent mechanical system. The mechanical analogy allows us to fully characterize the solutions and also to determine analytically the associated beat lengths. General analytical solutions are given for the two families in terms of Jacobi’s functions. The intensity-dependent transmission of a fiber placed between two crossed polarizers is calculated. Optimal conditions for efficient nonlinear switching compatible with mode-locking applications are determined. The general case of a nonlinear fiber ring with an intracavity polarizer placed between two polarization controllers is also considered

Spectral-doublet rectangular pulses in passive mode-locked fiber lasers with anomalous dispersion

It has been found by numerical simulation that dissipative soliton resonance in passive mode-locked fiber lasers with anomalous dispersion can result in the formation of rectangular pulses with a spectral doublet. With an increase in the pump power and hence in the length of the pulses, the width of the peaks of the spectral doublet decreases, and their position remains unchanged. As a consequence, the generation of a single pulse in the laser resonator turns out to be stable, and the regime of a high-energy rectangular pulse with a doublet spectral structure is observed. The mechanisms involved in this regime are analyzed

Mechanism of dispersive-wave soliton interaction in fiber lasers

Date du colloque : 06/2012International audienc

Dispersive Wave Interaction between Solitons in Fiber Lasers with Saturable Absorbers

On basis of numerical simulation it is found that the long-distance soliton wings can be formed by dispersive waves emitted by ultrashort pulses due to of various lumped elements in passive mode-locked fiber lasers. Peculiarities of the interaction of two solitons through such wings in lasers with lumped saturable absorbers (SA) are analyzed. Different sets of bound steady-states of two-soliton molecule are obtained. Among them there are sets with and without an alternation of parity of neighboring quantum steady-states. It is shown that the investigated interaction can result in mechanisms of both attraction and repulsion of loosely bound solitons. It is demonstrated a coding of an information by highly-stable bound soliton sequences

Theory of passively-mode-locked fiber lasers with phase-modulated square pulses

We present results of the analysis of square pulses generated in passively-mode-locked lasers under dissipative-soliton-resonance conditions. The master equation used in this work takes into account the gain saturation, the quadratic frequency dispersion of the gain and the refractive index, and the cubic-quintic nonlinearity of the losses and refractive index. The phase modulation effects are defined as a perturbation to the solution of this equation that has the form of a square pulse without phase modulation. An analytical dependence of the change in the carrier frequency of the radiation along the pulse is found. Conditions for the occurrence of the singlet and doublet spectra of the square pulse are determined. The mechanisms responsible for the occurrence of this regime are analyzed. The obtained analytical dependencies are in good agreement with the results of numerical simulation

Spectra of Doubly Heavy Quark Baryons

Baryons containing two heavy quarks are treated in the Born-Oppenheimer approximation. Schr\"odinger equation for two center Coulomb plus harmonic oscillator potential is solved by the method of ethalon equation at large intercenter separations. Asymptotical expansions for energy term and wave function are obtained in the analytical form. Using those formulas, the energy spectra of doubly heavy baryons with various quark compositions are calculated analytically.Comment: 19 pages, latex2e, published at PRC61(2000)04520