Browsing by Author "Bandelow, Uwe"
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- ItemAdditive splitting methods for parallel solution of evolution problems(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Amiranashvili, Shalva; Radziunas, Mindaugas; Bandelow, Uwe; Busch, Kurt; Čiegis, RaimondasWe demonstrate how a multiplicative splitting method of order P can be used to construct an additive splitting method of order P + 3. The weight coefficients of the additive method depend only on P, which must be an odd number. Specifically we discuss a fourth-order additive method, which is yielded by the Lie-Trotter splitting. We provide error estimates, stability analysis, and numerical examples with the special discussion of the parallelization properties and applications to nonlinear optics.
- ItemAdiabatic theory of champion solitons(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Pickartz, Sabrina; Bandelow, Uwe; Amiranashvili, ShalvaWe consider scattering of small-amplitude dispersive waves at an intense optical soliton which constitutes a nonlinear perturbation of the refractive index. Specifically, we consider a single-mode optical fiber and a group velocity matched pair: an optical soliton and a nearly perfectly reflected dispersive wave, a fiber-optical analogue of the event horizon. By combining (i) an adiabatic approach that is used in soliton perturbation theory and (ii) scattering theory from Quantum Mechanics, we give a quantitative account for the evolution of all soliton parameters. In particular, we quantify the increase in the soliton peak power that may result in spontaneous appearance of an extremely large, so-called champion soliton. The presented adiabatic theory agrees well with the numerical solutions of the pulse propagation equation. Moreover, for the first time we predict the full frequency band of the scattered dispersive waves and explain an emerging caustic structure in the space-time domain.
- ItemAmplifications of picosecond laser pulses in tapered semiconductor amplifiers : numerical simulations versus experiments(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Tronciu, Vasile; Schwertfeger, Sven; Radziunas, Mindaugas; Klehr, Andreas; Bandelow, Uwe; Wenzel, HansWe 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.
- ItemAnalysis of the interplay between soliton fission and modulation instability in supercontinuum generation(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Demircan, Ayhan; Bandelow, UweWe investigate the generation mechanisms for ultrawide spectra in nonlinear optical fibers. Soliton fission and modulation instability represent fundamental mechanisms for the generation process. The primary origin of the spectral broadening changes with the pump-pulse duration. Soliton fission dominates for low input power and short pulses. Its efficiency for supercontinuum generation and especially the extend to the blue side can be increased by proper design of the dispersion profile. The modulation instability has a strong impact for high input powers and greatly enhances the generation process, but leads to a degradation of the coherence properties. Also for short pulses with durations of 60 fs the modulation instability is present and can hardly be suppressed. The interplay between these two effects leads to various characteristics of the resulting spectra, which are modified by to the relative impact of the modulation instability.
- ItemAsymptotically stable compensation of soliton self-frequency shift(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Pickartz, Sabrina; Bandelow, Uwe; Amiranashvili, ShalvaWe report the cancellation of the soliton self-frequency shift in nonlinear optical fibers. A soliton which interacts with a group velocity matched low intensity dispersive pump pulse, experiences a continuous blue-shift in frequency, which counteracts the soliton selffrequency shift due to Raman scattering. The soliton self-frequency shift can be fully compensated by a suitably prepared dispersive wave. We quantify this kind of soliton-dispersive wave interaction by an adiabatic approach and demonstrate that the compensation is stable in agreement with numerical simulations.
- ItemBeam combining scheme for high-power broad-area semiconductor lasers with Lyot-filtered reinjection: Modeling, simulations, and experiments(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Brée, Carsten; Raab, Volker; Montiel-Ponsoda, Joan; Garre-Werner, Guillermo; Staliunas, Kestutis; Bandelow, Uwe; Radziunas, MindaugasA brightness- and power-scalable polarization beam combining scheme for high-power, broadarea semiconductor laser diodes is investigated numerically and experimentally. To achieve the beam combining, we employ Lyot-filtered optical reinjection from an external cavity, which forces lasing of the individual diodes on interleaved frequency combs with overlapping envelopes and enables a high optical coupling efficiency. Unlike conventional spectral beam combining schemes with diffraction gratings, the optical coupling efficiency is insensitive to thermal drifts of laser wavelengths. This scheme can be used for efficient coupling of a large number of laser diodes and paves the way towards using broad-area laser diode arrays for cost-efficient material processing, which requires high-brilliance emission and optical powers in the kW-regime.
- ItemCalculation of ultrashort pulse propagation based on rational approximations for medium dispersion(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Amiranashvili, Shalva; Bandelow, Uwe; Mielke, AlexanderUltrashort optical pulses contain only a few optical 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 numerical treatment of pulse propagation along nonlinear and dispersive optical media.
- ItemCancellation of Raman self-frequency shift for compression of optical pulses(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Pickartz, Sabrina; Brée, Carsten; Bandelow, Uwe; Amiranashvili, ShalvaWe study to which extent a fiber soliton can be manipulated by a specially chosen continuous pump wave. A group velocity matched pump scatters at the soliton, which is compressed due to the energy/momentum transfer. As the pump scattering is very sensitive to the velocity matching condition, soliton compression is quickly destroyed by the soliton self-frequency shift (SSFS). This is especially true for ultrashort pulses: SSFS inevitably impairs the degree of compression. We demonstrate numerically that soliton enhancement can be restored to some extent and the compressed soliton can be stabilized, provided that SSFS is canceled by a second pump wave. Still the available compression degree is considerably smaller than that in the Raman-free nonlinear fibers.
- ItemCompression limit by third-order dispersion in the normal dispersion regime(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Demircan, Ayhan; Kroh, Marcel; Bandelow, Uwe; Hüttl, Bernd; Weber, Hans-GeorgBroad-band continua at gigahertz rates generated in high-nonlinear dispersion flattened fibers in the normal dispersion regime near the zero-dispersion wavelength can be used for a subsequent efficient pulse compression, leading to stable high-repetition-rate trains of femtosecond pulses. We show experimentally and theoretically that third-order dispersion defines a critical power, where beyond further compression is inhibited. This fundamental limit is caused by a pulse-breakup.
- ItemDispersion of nonlinear group velocity determines shortest envelope solitons(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Amiranashvili, Shalva; Bandelow, Uwe; Akhmediev, Nail N.We demonstrate that a generalized nonlinear Schrödinger equation (NSE), that includes dispersion of the intensity-dependent group velocity, allows for exact solitary solutions. In the limit of a long pulse duration, these solutions naturally converge to a fundamental soliton of the standard NSE. In particular, the peak pulse intensity times squared pulse duration is constant. For short durations this scaling gets violated and a cusp of the envelope may be formed. The limiting singular solution determines then the shortest possible pulse duration and the largest possible peak power. We obtain these parameters explicitly in terms of the parameters of the generalized NSE.
- ItemDynamical regimes in a monolithic passively mode-locked quantum dot laser(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Vladimirov, Andrei; Bandelow, Uwe; Fiol, Gerrit; Arsenijevi´c, Dejan; Kleinert, Moritz; Bimberg, Dieter; Pimenov, Alexander; Rachinskii, DmitriiOperation regimes of a two section monolithic quantum dot (QD) mode-locked laser are studied experimentally and theoretically, using a model that takes into account carrier exchange between QD ground state and 2D reservoir of a QD-in-a-well structure, and experimentally. It is shown analytically and numerically that, when the absorber section is long enough, the laser exhibits bistability between laser off state and different mode-locking regimes. The Q-switching instability leading to slow modulation of the mode-locked pulse peak intensity is completely eliminated in this case. When, on the contrary, the absorber length is rather short, in addition to usual Q-switched mode-locking, pure Q-switching regimes are predicted theoretically and observed experimentally.
- ItemDynamical regimes of multi-stripe laser array with external off-axis feedback(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Pimenov, Alexander; Trpmciu, Vasile Z.; Bandelow, Uwe; Vladimirov, Andrei G.We study theoretically the dynamics of a multistripe laser array with an external cavity formed by either a single or two off-axis feedback mirrors, which allow to select a single lateral mode with transversely modulated intensity distribution. We derive and analyze a reduced model of such an array based on a set of delay differential equations taking into account transverse carrier grating in the semiconductor medium. With the help of the bifurcation analysis of the reduced model we show the existence of single and multimode instabilities leading to periodic and irregular pulsations of the output intensity. In particular, we observe a multimode instability leading to a periodic regime with anti-phase oscillating intensities of the two counter-propagating waves in the external cavity. This is in agreement with the result obtained earlier with the help of a 2+1 dimensional traveling wave model
- ItemDynamics in high-power diode lasers(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Bandelow, Uwe; Radziunas, Mindaugas; Zeghuzi, Anissa; Wünsche, Hans-Jürgen; Wenzel, HansHigh-power broad-area diode lasers (BALs) exhibit chaotic spatio-temporal dynamics above threshold. Under high power operation, where they emit tens of watts output, large amounts of heat are generated, with significant impact on the laser operation. We incorporate heating effects into a dynamical electro-optical (EO) model for the optical field and carrier dynamics along the quantum-well active zone of the laser. Thereby we effectively couple the EO and heat-transport (HT) solvers. Thermal lensing is included by a thermally-induced contribution to the index profile. The heat sources obtained with the dynamic EO-solver exhibit strong variations on short time scales, which however have only a marginal impact on the temperature distribution. We consider two limits: First, the static HT-problem, with time-averaged heat sources, which is solved iteratively together with the EO solver. Second, under short pulse operation the thermally induced index distribution can be obtained by neglecting heat flow. Although the temperature increase is small, a waveguide is introduced here within a few-ns-long pulse resulting in significant near field narrowing. We further show that a beam propagating in a waveguide structure utilized for BA lasers does not undergo filamentation due to spatial holeburning. Moreover, our results indicate that in BALs a clear optical mode structure is visible which is neither destroyed by the dynamics nor by longitudinal effects.
- ItemEffect of higher-order dispersion on modulation instability, soliton propagation and pulse splitting(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Demircan, Ayhan; Pietrzyk, Monika; Bandelow, UweBy solving numerically the extended nonlinear Schrödinger equation we investigate the influence of higher-order dispersion effects on the propagation of optical pulses in highly nonlinear fibers. In the anomalous dispersion regime third-order dispersion can, in general, induce soliton fission and yields asymmetric spectra, whereas modulation instability can be slightly suppressed. In the normal dispersion regime we demonstrate pulse splitting by third-order dispersion, as well as its later suppression by fourth-order dispersion.
- ItemEfficient all-optical control of solitons(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Pickartz, Sabrina; Bandelow, Uwe; Amiranashvili, ShalvaWe consider the phenomenon of an optical soliton controlled (e.g. amplified) by a much weaker second pulse which is efficiently scattered at the soliton. An important problem in this context is to quantify the small range of parameters at which the interaction takes place. This has been achieved by using adiabatic ODEs for the soliton characteristics, which is much faster than an empirical scan of the full propagation equations for all parameters in question.
- ItemEfficient coupling of electro-optical and heat-transport models for broad-area semiconductor lasers(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Radziunas, Mindaugas; Fuhrmann, Jürgen; Zeghuzi, Anissa; Wünsche, Hans-Jürgen; Koprucki, Thomas; Brée, Carsten; Wenzel, Hans; Bandelow, UweIn this work, we discuss the modeling of edge-emitting high-power broad-area semiconductor lasers. We demonstrate an efficient iterative coupling of a slow heat transport (HT) model defined on multiple vertical-lateral laser cross-sections with a fast dynamic electro-optical (EO) model determined on the longitudinal-lateral domain that is a projection of the device to the active region of the laser. Whereas the HT-solver calculates temperature and thermally-induced refractive index changes, the EO-solver exploits these distributions and provides time-averaged field intensities, quasi-Fermi potentials, and carrier densities. All these time-averaged distributions are used repetitively by the HT-solver for the generation of the heat sources entering the HT problem solved in the next iteration step.
- ItemEfficient coupling of inhomogeneous current spreading and dynamic electro-optical models for broad-area edge-emitting semiconductor devices(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Radziunas, Mindaugas; Zeghuzi, Anissa; Fuhrmann, Jürgen; Koprucki, Thomas; Wünsche, Hans-Jürgen; Wenzel, Hans; Bandelow, UweWe extend a 2 (space) + 1 (time)-dimensional traveling wave model for broad-area edgeemitting semiconductor lasers by a model for inhomogeneous current spreading from the contact to the active zone of the laser. To speedup the performance of the device simulations, we suggest and discuss several approximations of the inhomogeneous current density in the active zone.
- ItemEfficient Current Injection Into Single Quantum Dots Through Oxide-Confined p-n-Diodes(New York, NY : IEEE, 2016) Kantner, Markus; Bandelow, Uwe; Koprucki, Thomas; Schulze, Jan-Hindrik; Strittmatter, Andre; Wunsche, Hans-JurgenCurrent injection into single quantum dots embedded in vertical p-n-diodes featuring oxide apertures is analyzed in the low-injection regime suitable for single-photon emitters. The experimental and theoretical evidence is found for a rapid lateral spreading of the carriers after passing the oxide aperture in the conventional p-i-n-design. By an alternative design employing p-doping up to the oxide aperture, the current spreading can be suppressed resulting in an enhanced current confinement and increased injection efficiencies, both, in the continuous wave and under pulsed excitation.
- ItemFew-cycle optical solitons in dispersive media beyond the envelope approximation(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Amiranashvili, Shalva; Bandelow, Uwe; Akhmediev, NailWe study the propagation of few-cycle optical solitons in nonlinear media with an anomalous, but otherwise arbitrary, dispersion and a cubic nonlinearity. Our theory extends beyond the slowly varying envelope approximation. The optical field is derived directly from the Maxwell equations under the assumption that generation of the third harmonic is a non-resonant 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 a modification of the spectral renormalisation method originally developed for the envelope solitons.
- ItemGeneralized integrable evolution equations with an infinite number of free parameters(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Akhmediev, Nail; Ankiewicz, Adrian; Amiranashvili, Shalva; Bandelow, UweEvolution equations such as the nonlinear Schrödinger equation (NLSE) can be extended to include an infinite number of free parameters. The extensions are not unique. We give two examples that contain the NLSE as the lowest-order PDE of each set. Such representations provide the advantage of modelling a larger variety of physical problems due to the presence of an infinite number of higher-order terms in this equation with an infinite number of arbitrary parameters. An example of a rogue wave solution for one of these cases is presented, demonstrating the power of the technique.
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