Nail Akhmediev

Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation.

Numerical simulations of the onset phase of continuous wave supercontinuum generation from modulation instability show that the structure of the field as it develops can be interpreted in terms of the properties of Akhmediev Breathers. Numerical and analytical results are compared with experimental measurements of spectral broadening in photonic crystal fiber using nanosecond pulses.

Observation of Kuznetsov-Ma soliton dynamics in optical fibre

The nonlinear Schrödinger equation (NLSE) is a central model of nonlinear science, applying to hydrodynamics, plasma physics, molecular biology and optics. The NLSE admits only few elementary analytic solutions, but one in particular describing a localized soliton on a finite background is of intense current interest in the context of understanding the physics of extreme waves. However, although the first solution of this type was the Kuznetzov-Ma (KM) soliton derived in 1977, there have in fact been no quantitative experiments confirming its validity. We report here novel experiments in optical fibre that confirm the KM soliton theory, completing an important series of experiments that have now observed a complete family of soliton on background solutions to the NLSE. Our results also show that KM dynamics appear more universally than for the specific conditions originally considered, and can be interpreted as an analytic description of Fermi-Pasta-Ulam recurrence in NLSE propagation.

Stability of the pulselike solutions of the quintic complex Ginzburg-Landau equation

We performed a detailed investigation of the stability of analytic pulselike solutions of the quintic complex Ginzburg–Landau equation that describes the dynamics of the field in a passively mode-locked laser. We found that in general they are unstable except in a few special cases. We also obtained regions in the parameter space in which stable pulse solutions exist. These stable solutions do not have analytical expressions and must be calculated numerically. We compared and connected the regions in which stable solitonlike solutions exist with the lines for which we had analytical solutions.

Stable soliton pairs in optical transmission lines and fiber lasers

Optical-fiber transmission of pulses can be modeled with the complex Ginzburg–Landau equation. We find novel stable soliton pairs and trains, which are relevant in this case, and analyze them. We suggest that the distance between the pulses and the phase difference between them is defined by energy and momentum balance equations, rather than by equations of standard perturbation theory. We present a two-dimensional phase plane (interaction plane) for analyzing the stability properties and general dynamics of two-soliton solutions of the Complex Ginzburg–Landau equation.

Multipulse operation of a Ti:sapphire laser mode locked by an ion-implanted semiconductor saturable-absorber mirror

We show results obtained from a semiconductor saturable-absorber mirror mode-locked Ti:sapphire soliton laser that was operated in the multiple-pulse regime. Double, triple, and quadruple pulses were observed when the dispersion was decreased below a critical value. The pulse pairs and triplets were either widely separated or closely coupled, and spectra that resembled those of constant as well as rotating phase differences between pulses were observed. We explain our observations in the framework of the generalized complex Ginzburg‐ Landau equation as the master equation of the laser.

Does the nonlinear Schrodinger equation correctly describe beam propagation

The parabolic equation (nonlinear Schrödinger equation) that appears in problems of stationary nonlinear beam propagation (self-focusing) is reconsidered. It is shown that an additional term, which involves changes of the propagation constant along the propagation direction, should be taken into account. The physical consequences of this departure from the standard approximation, which uses the parabolic equation, are discussed. A numerical simulation showing the difference between the new approach and the standard nonlinear Schrödinger equation is given as an example.

Rogue waves, rational solutions, the patterns of their zeros and integral relations

The focusing nonlinear Schrodinger equation, which describes generic nonlinear phenomena, including waves in the deep ocean and light pulses in optical fibres, supports a whole hierarchy of recently discovered rational solutions. We present recurrence relations for the hierarchy, the pattern of zeros for each solution and a set of integral relations which characterizes them.

Three-dimensional rogue waves in nonstationary parabolic potentials

Using symmetry analysis we systematically present a higher-dimensional similarity transformation reducing the (3+1) -dimensional inhomogeneous nonlinear Schrödinger (NLS) equation with variable coefficients and parabolic potential to the (1+1) -dimensional NLS equation with constant coefficients. This transformation allows us to relate certain class of localized exact solutions of the (3+1) -dimensional case to the variety of solutions of integrable NLS equation of the (1+1) -dimensional case. As an example, we illustrated our technique using two lowest-order rational solutions of the NLS equation as seeding functions to obtain rogue wavelike solutions localized in three dimensions that have complicated evolution in time including interactions between two time-dependent rogue wave solutions. The obtained three-dimensional rogue wavelike solutions may raise the possibility of relative experiments and potential applications in nonlinear optics and Bose-Einstein condensates.

Phase-locked stationary soliton states in birefringent nonlinear optical fibers

We consider stationary soliton states in a birefringent optical fiber with two components locked in phase. Two values of the phase difference between the two components of the soliton states are studied: 0 and π/2. These cases allow us to find composite soliton states in a simple way. The bifurcation diagrams for the coupled soliton states in these two cases are constructed. The stability of these soliton states is examined also.

Quantized separations of phase-locked soliton pairs in fiber lasers

We report the discovery of a quantization of the separation between phase-locked soliton pairs that is related to the radiation waves known as Kelly sidebands, in a passively mode-locked fiber ring laser. Our numerical simulations that predict this phenomenon have been confirmed by our experimental results.