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

Three-loop contribution of the Faddeev-Popov ghosts to the β\beta-function of N=1{\cal N}=1 supersymmetric gauge theories and the NSVZ relation

We find the three-loop contribution to the $\beta$-function of ${\cal N}=1$ supersymmetric gauge theories regularized by higher covariant derivatives produced by the supergraphs containing loops of the Faddeev--Popov ghosts. This is done using a recently proposed algorithm, which essentially simplifies such multiloop calculations. The result is presented in the form of an integral of double total derivatives in the momentum space. The considered contribution to the $\beta$-function is compared with the two-loop anomalous dimension of the Faddeev--Popov ghosts. This allows verifying the validity of the NSVZ equation written as a relation between the $\beta$-function and the anomalous dimensions of the quantum superfields. It is demonstrated that in the considered approximation the NSVZ equation is satisfied for the renormalization group functions defined in terms of the bare couplings. The necessity of the nonlinear renormalization for the quantum gauge superfield is also confirmed.Comment: 20 pages, 4 figures, minor corrections, the final version to appear in Eur.Phys.J.

Spectral sidebands of solitons in passive mode-locked lasers

Date du colloque : 06/2010International audienc

Dissipative solitons in passive mode-locked fiber lasers with nonlinear polarization rotation technique

Date du colloque : 06/2010International audienc

Dispersive-wave mechanism of interaction between ultrashort pulses in passive mode-locked fiber lasers

On the basis of numerical simulation, it is found that powerful long-distance soliton wings can be formed by dispersive waves which are emitted by solitons because of lumped elements in a laser cavity. We analyze peculiarities of the interaction of two solitons through such wings in lasers with lumped saturable absorbers. Various sets of bound steady states of a two-soliton molecule are demonstrated. The relation between the spectral sidebands and the dispersive-wave wings of a soliton is found. The periodic changes in a soliton\u27s profile during its pass through the laser cavity are studied

Three-loop verification of a new algorithm for the calculation of a β\beta-function in supersymmetric theories regularized by higher derivatives for the case of N=1{\cal N}=1 SQED

We verify a recently proposed method for obtaining a $\beta$-function of ${\cal N}=1$ supersymmetric gauge theories regularized by higher derivatives by an explicit calculation. According to this method, a $\beta$-function can be found by calculating specially modified vacuum supergraphs instead of a much larger number of the two-point superdiagrams. The result is produced in the form of a certain integral of double total derivatives with respect to the loop momenta. Here we compare the results obtained for the three-loop $\beta$-function of ${\cal N}=1$ SQED in the general $\xi$-gauge with the help of this method and with the help of the standard calculation. Their coincidence confirms the correctness of the new method and the general argumentation used for its derivation. Also we verify that in the considered approximation the NSVZ relation is valid for the renormalization group functions defined in terms of the bare coupling constant and for the ones defined in terms of the renormalized coupling constant in the HD+MSL scheme, both its sides being gauge-independent.Comment: 19 pages, 8 figures; title changed, minor corrections; the final version to appear in Nuclear Physics