Forschungsgruppe "Laserdynamik"

Publikationen

Autor:
Jahre:	-
Topic:
Typ:
Liste:	BibTeX:

Artikel in Referierten Journalen

S. Amiranashvili, C. Brée, From optical rogue waves to optical transistors, Nonlin. Phenom. Complex Syst., 1 (2013) pp. .
Abstract

We study the propagation of few-cycle optical solitons in nonlinear media with an anomalous, but otherwise arbitrary, dispersion and a cubic nonlinearity. Our approach does not derive from the slowly varying envelope approximation. The optical field is derived directly from Maxwell's equations under the assumption that generation of the third harmonic is a nonresonant process or at least cannot destroy the pulse prior to inevitable linear damping. The solitary wave solutions are obtained numerically up to nearly single-cycle duration using the spectral renormalization method originally developed for the envelope solitons. The theory explicitly distinguishes contributions between the essential physical effects such as higher-order dispersion, self-steepening, and backscattering, as well as quantifies their influence on ultrashort optical solitons.
S. Amiranashvili, U. Bandelow, N. Akhmediev, Few-cycle optical solitary waves in nonlinear dispersive media, Phys. Rev. A, 87 (2013) pp. 013805/1--013805/8.
Abstract

We study the propagation of few-cycle optical solitons in nonlinear media with an anomalous, but otherwise arbitrary, dispersion and a cubic nonlinearity. Our approach does not derive from the slowly varying envelope approximation. The optical field is derived directly from Maxwell's equations under the assumption that generation of the third harmonic is a nonresonant process or at least cannot destroy the pulse prior to inevitable linear damping. The solitary wave solutions are obtained numerically up to nearly single-cycle duration using the spectral renormalization method originally developed for the envelope solitons. The theory explicitly distinguishes contributions between the essential physical effects such as higher-order dispersion, self-steepening, and backscattering, as well as quantifies their influence on ultrashort optical solitons.
A. Pérez-Serrano, J. Javaloyes, S. Balle, Multi-channel wavelength conversion using four-wave mixing in semiconductor ring lasers, IEEE Phot. Tech. Letter, 25 (2013) pp. 476--479.
Abstract

We theoretically study all-optical simultaneous wavelength conversion of multiple channels by four-wave mixing in semiconductor ring lasers. Locking the semiconductor ring laser to a holding beam allows to achieve large conversion efficiencies with good signal-tonoise ratio in several channels at multi-Gb/s bit rates. Cross-talk between signals, arising from the peculiar four-wave mixing cascade of modes in semiconductor ring lasers and their cross-gain saturation, is studied in detail. We show that it can be controlled by adjusting the intensity of the holding beam, the bias current of the laser and the number, intensity and wavelength of signals that one wants to convert.
S. Amiranashvili, U. Bandelow, A. Mielke, Calculation of ultrashort pulse propagation based on rational approximations for medium dispersion, Opt. Quantum Electron., 44 (2012) pp. 241--246.
Abstract

Ultrashort optical pulses contain only a fewoptical cycles and exhibit broad spectra. Their carrier frequency is therefore not well defined and their description in terms of the standard slowly varying envelope approximation becomes questionable. Existing modeling approaches can be divided in two classes, namely generalized envelope equations, that stem from the nonlinear Schrödinger equation, and non-envelope equations which treat the field directly. Based on fundamental physical rules we will present an approach that effectively interpolates between these classes and provides a suitable setting for accurate and highly efficient
A. Pimenov, T.C. Kelly, A. Korobeinikov, M.J.A. O'Callaghan, A.V. Pokrovskii, D. Rachinskii, Memory effects in population dynamics: Spread of infectious disease as a case study, Math. Model. Nat. Phenom., 7 (2012) pp. 204--226.
A. Wilms, D. Breddermann, P. Mathé, Theory of direct capture from two- and three-dimensional reservoirs to quantum dot states, Phys. Status Solidi C, 9 (2012) pp. 1278--1281.
B. Fiedler, C. Rocha, M. Wolfrum, A permutation characterization of Sturm global attractors of Hamiltonian type, J. Differential Equations, 252 (2012) pp. 588--623.
Abstract

We consider Neumann boundary value problems of the form $u_t = u_xx + f $ on the interval $0 leq x leq pi$ for dissipative nonlinearities $f = f (u)$. A permutation characterization for the global attractors of the semiflows generated by these equations is well known, even in the general case $f = f (x, u, u_x )$. We present a permutation characterization for the global attractors in the restrictive class of nonlinearities $f = f (u)$. In this class the stationary solutions of the parabolic equation satisfy the second order ODE $v^primeprime + f (v) = 0$ and we obtain the permutation characterization from a characterization of the set of $2pi$-periodic orbits of this planar Hamiltonian system. Our results are based on a diligent discussion of this mere pendulum equation.
B. Fiedler, C. Rocha, M. Wolfrum, Sturm global attractors for S$^1$-equivariant parabolic equations, Networks Heterogeneous Media, 7 (2012) pp. 617--659.
Abstract

We consider Neumann boundary value problems of the form $u_t = u_xx + f $ on the interval $0 leq x leq pi$ for dissipative nonlinearities $f = f (u)$. A permutation characterization for the global attractors of the semiflows generated by these equations is well known, even in the general case $f = f (x, u, u_x )$. We present a permutation characterization for the global attractors in the restrictive class of nonlinearities $f = f (u)$. In this class the stationary solutions of the parabolic equation satisfy the second order ODE $v^primeprime + f (v) = 0$ and we obtain the permutation characterization from a characterization of the set of $2pi$-periodic orbits of this planar Hamiltonian system. Our results are based on a diligent discussion of this mere pendulum equation.
T. Habruseva, S.P. Hegarty, A.G. Vladimirov, A. Pimenov, D. Rachinskii, N. Rebrova, E.A. Viktorov, G. Huyet, Bistable regimes in an optically injected mode-locked laser, Opt. Express, 20 (2012) pp. 25572--25583.
A. Demircan, S. Amiranashvili, C. Brée, Ch. Mahnke, F. Mitschke, G. Steinmeyer, Rogue events in the group velocity horizon, Sci. Rep., 2 (2012) pp. 00850/1--00850/6.
R. Driben, I. Babushkin, Accelerated rogue waves generated by soliton fusion at the advanced stage of supercontinuum formation in photonic-crystal fibers, Opt. Lett., 37 (2012) pp. 5157--5159.
R. Herrero, M. Botey, M. Radziunas, K. Staliunas, Beam shaping in spatially modulated broad area semiconductor amplifiers, Opt. Lett., 37 (2012) pp. 5253--5255.
M. Lichtner, V.Z. Tronciu, A.G. Vladimirov, Theoretical investigations of striped and non-striped broad area lasers with off-axis feedback, IEEE J. Quantum Electron., 48 (2012) pp. 353--360.
CH. Otto, K. Lüdge, A.G. Vladimirov, M. Wolfrum, E. Schöll, Delay induced dynamics and jitter reduction of passively mode-locked semiconductor lasers subject to optical feedback, New J. Phys., 14 (2012) pp. 113033/1-113033/29.
U.K. Sapaev, I. Babushkin, J. Herrmann, Quasi-phase-matching for third harmonic generation in noble gases employing ultrasound, Optics Express, 20 (2012) pp. 22753--22762.
M. Tlidi, E. Averlant, A.G. Vladimirov, K. Panajotov, Delay feedback induces a spontaneous motion of two-dimensional cavity solitons in driven semiconductor microcavities, Phys. Rev. A, 86 (2012) pp. 033822/1--033822/8.
V. Tronciu, S. Schwertfeger, M. Radziunas, A. Klehr, U. Bandelow, H. Wenzel, Numerical simulation of the amplification of picosecond laser pulses in tapered semiconductor amplifiers and comparison with experimental results, Opt. Commun., 285 (2012) pp. 2897--2904.
Abstract

We apply a travelling wave model to the simulation of the amplification of laser pulses generated by Q-switched or mode-locked distributed-Bragg reflector lasers. The power amplifier monolithically integrates a ridge-waveguide section acting as pre-amplifier and a flared gain-region amplifier. The diffraction limited and spectral-narrow band pulses injected in to the pre-amplifier have durations between 10 ps and 100 ps and a peak power of typical 1 W. After the amplifier, the pulses reach a peak power of several tens of Watts preserving the spatial, spectral and temporal properties of the input pulse. We report results obtained by a numerical solution of the travelling-wave equations and compare them with experimental investigations. The peak powers obtained experimentally are in good agreement with the theoretical predictions. The performance of the power amplifier is evaluated by considering the dependence of the pulse energy as a function of different device and material parameters.
D. Turaev, A.G. Vladimirov, S. Zelik, Long range interaction and synchronization of oscillating dissipative solitons, Phys. Rev. Lett., 108 (2012) pp. 263906/1--263906/5.
U. Bandelow, N. Akhmediev, Persistence of rogue waves in extended nonlinear Schrödinger equations: Integrable Sasa--Satsuma case, Phys. Lett. A, 376 (2012) pp. 1558--1561.
Abstract

We present the lowest order rogue wave solution of the Sasa-Satsuma equation (SSE) which is one of the integrable extensions of the nonlinear Schrödinger equation (NLSE). In contrast to the Peregrine solution of the NLSE, it is significantly more involved and contains polynomials of fourth order rather than second order in the corresponding expressions. The correct limiting case of Peregrine solution appears when the extension parameter of the SSE is reduced to zero.
U. Bandelow, N. Akhmediev, Sasa--Satsuma equation: Soliton on a background and its limiting cases, Phys. Rev. E (3), 86 (2012) pp. 026606/1--026606/8.
Abstract

We present a multi-parameter family of a soliton on a background solutions to the Sasa-Satsuma equation. The solution is controlled by a set of several free parameters that control the background amplitude as well as the soliton itself. This family of solutions admits a few nontrivial limiting cases that are considered in detail. Among these special cases is the NLSE limit and the limit of rogue wave solutions.
C. Brée, A. Demircan, G. Steinmeyer, Kramers--Kronig relations and high order nonlinear susceptibilities, Phys. Rev. A, 85 (2012) pp. 033806/1--033806/8.
Abstract

As previous theoretical results recently revealed, a Kramers-Kronig transform of multiphoton absorption rates allows for a precise prediction on the dispersion of the nonlinear refractive index $n_2$ in the near IR. It was shown that this method allows to reproduce recent experimental results on the importance of the higher-order Kerr effect. Extending these results, the current manuscript provides the dispersion of $n_2$ for all noble gases in excellent agreement with reference data. It is furthermore established that the saturation and inversion of the nonlinear refractive index is highly dispersive with wavelength, which indicates the existence of different filamentation regimes. While shorter laser wavelengths favor the well-established plasma clamping regime, the influence of the higher-order Kerr effect dominates in the long wavelength regime.
T. Girnyk, M. Hasler, Y. Maistrenko, Multistability of twisted states in non-locally coupled Kuramoto-type models, Chaos Solitons Fractals, 22 (2012) pp. 013114/1--013114/10.
Abstract

A ring of N identical phase oscillators with interactions between L-nearest neighbors is considered, where L ranges from 1 (local coupling) to N/2 (global coupling). The coupling function is a simple sinusoid, as in the Kuramoto model, but with a minus sign which has a profound influence on its behavior. Without limitation of the generality the frequency of the free-running oscillators can be set to zero. The resulting system is of gradient type and therefore all its solutions converge to an equilibrium point. All so-called q-twisted states, where the phase difference between neighboring oscillators on the ring is 2 pi q/N are equilibrium points, where q is an integer. Their stability in the limit N -> inf. is discussed along the line of1. In addition we prove that when a twisted state is asymptotically stable for the infinite system, it is also asymptotically stable for sufficiently large N. Note that for smaller N, the same q-twisted states may become unstable and other q-twisted states may become stable. Finally, the existence of additional equilibrium states, called here multi-twisted states, is shown by numerical simulation. The phase difference between neighboring oscillators is approximately 2 pi q/N in one sector of the ring, -2 pi q/N in another sector, and it has intermediate values between the two sectors. Our numerical investigation suggests that the number of different stable multi-twisted states grows exponentially as N -> inf. It is possible to interpret the equilibrium points of the coupled phase oscillator network as trajectories of a discrete-time translational dynamical system where the space-variable (position on the ring) plays the role of time. The q-twisted states are then fixed points and the multi-twisted states are periodic solutions of period N that are close to a heteroclinic cycle. Due to the apparently exponentially fast growing number of such stable periodic solutions, the system shows spatial chaos as N -> 1.
O. Omel'chenko, M. Wolfrum, Nonuniversal transitions to synchrony in the Sakaguchi--Kuramoto model, Phys. Rev. Lett., 109 (2012) pp. 164101/1--164101/4.
Abstract

We investigate the transition to synchrony in a system of phase oscillators that are globally coupled with a phase lag (Sakaguchi-Kuramoto model). We show that for certain unimodal frequency distributions there appear unusual types of synchronization transitions, where synchrony can decay with increasing coupling, incoherence can regain stability for increasing coupling, or multistability between partially synchronized states and/or the incoherent state can appear. Our method is a bifurcation analysis based on a frequency dependent version of the Ott-Antonsen method and allows for a universal description of possible synchronization transition scenarios for any given distribution of natural frequencies.
O. Omel'chenko, M. Wolfrum, S. Yanchuk, Y. Maistrenko, O. Sudakov, Stationary patterns of coherence and incoherence in two-dimensional arrays of non-locally coupled phase oscillators, Phys. Rev. E (3), 85 (2012) pp. 036210/1--036210/5.
Abstract

Recently it has been shown that large arrays of identical oscillators with non-local coupling can have a remarkable type of solutions that display a stationary macroscopic pattern of coexisting regions with coherent and incoherent motion, often caled chimera states. We present here a detailed numerical study of the appearance of such solutions in two-dimensional arrays of coupled phase oscillators. We discover a variety of stationary patterns, including circular spots, stripe patterns, and patterns of multiple spirals. Here, the stationarity means that for increasing system size the locally averaged phase distributions tend to the stationary profile given by the corresponding thermodynamic limit equation.
M. Wolfrum, The Turing bifurcation in network systems: Collective patterns and single differentiated nodes, Phys. D, 241 (2012) pp. 1351--1357.
Abstract

We study the emergence of patterns in a diffusively coupled network that undergoes a Turing instability. Our main focus is the emergence of stable solutions with a single differentiated node in systems with large and possibly irregular network topology. Based on a mean-field approach, we study the bifurcations of such solutions for varying system parameters and varying degree of the differentiated node. Such solutions appear typically before the onset of Turing instability and provide the basis for the complex scenario of multistability and hysteresis that can be observed in such systems. Moreover, we discuss the appearance of stable collective patterns and present a codimension-two bifurcation that organizes the interplay between collective patterns and patterns with single differentiated nodes.