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- ItemInfinite hierarchy of nonlinear Schrödinger equations and Infinite hierarchy of nonlinear Schrödinger equations and(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Ankiewicz, Adrian; Kedziora, David Jacob; Chowdury, Amdad; Bandelow, Uwe; Nail Akhmediev, NailWe study the infinite integrable nonlinear Schrödinger equation (NLSE) hierarchy beyond the Lakshmanan-Porsezian-Daniel equation which is a particular (fourth-order) case of the hierarchy. In particular, we present the generalized Lax pair and generalized soliton solutions, plane wave solutions, AB breathers, Kuznetsov-Ma breathers, periodic solutions and rogue wave solutions for this infinite order hierarchy. We find that even order equations in the set affect phase and stretching factors in the solutions, while odd order equations affect the velocities. Hence odd order equation solutions can be real functions, while even order equation solutions are always complex.
- ItemA model for mode-locking in quantum dot lasers(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Viktorov, Evgeny; Mandel, Paul; Vladimirov, Andrei; Bandelow, UweWe propose a model for passive mode-locking in quantum dot laser and report on specific dynamical properties of the regime which is characterized by a fast gain recovery. No Q-switching instability has been found accompanying the mode-locking. Bistability can occur between the mode-locking regime and zero intensity steady state.
- ItemModeling and simulation of strained quantum wells in semiconductorlasers(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2000) Bandelow, Uwe; Kaiser, Hans-Christoph; Koprucki, Thomas; Rehberg, JoachimA model allowing for efficiently obtaining band structure information on semiconductor Quantum Well structures will be demonstrated which is based on matrix-valued kp-Schrödinger operators. Effects such as confinement, band mixing, spin-orbit interaction and strain can be treated consistently. The impact of prominent Coulomb effects can be calculated by including the Hartree interaction via the Poisson equation and the bandgap renormalization via exchange-correlation potentials, resulting in generalized (matrix-valued) Schrödinger-Poisson systems. Band structure information enters via densities and the optical response function into comprehensive simulations of Multi Quantum Well lasers. These device simulations yield valuable information on device characteristics, including effects of carrier transport, waveguiding and heating and can be used for optimization.
- ItemOn the propagation of vector ultra-short pulses(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Pietrzyk, Monika; Kanattsikov, I.; Bandelow, UweA two component vector generalization of the Schäfer-Wayne short pulse equation which describes propagation of ultra-short pulses in optical fibers with Kerr nonlinearity beyond the slowly varying envelope approximation and takes into account the effects of anisotropy and polarization is presented. As a special case, the integrable two-component short pulse equations are constructed which represent the counterpart of the Manakov system in the case of ultra-short pulses.
- 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.
- ItemModeling of current spreading in high-power broad-area lasers and its impact on the lateral far field divergence(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Zeghuzi, Anissa; Radziunas, Mindaugas; Wenzel, Hans; Wünsche, Hans-Jürgen; Bandelow, Uwe; Knigge, AndreaThe effect of current spreading on the lateral farfield divergence of highpower broadarea lasers is investigated with a timedependent model using different descriptions for the injection of carriers into the active region. Most simulation tools simply assume a spatially constant injection current density below the contact stripe and a vanishing current density beside. Within the driftdiffusion approach, however, the injected current density is obtained from the gradient of the quasiFermi potential of the holes, which solves a Laplace equation in the pdoped region if recombination is neglected. We compare an approximate solution of the Laplace equation with the exact solution and show that for the exact solution the highest farfield divergence is obtained. We conclude that an advanced modeling of the profiles of the injection current densities is necessary for a correct description of farfield blooming in broadarea lasers.
- ItemSasa-Satsuma hierarchy of integrable evolution equations(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Bandelow, Uwe; Ankiewicz, Adrian; Amiranashvili, Shalva; Pickartz, Sabrina; Akhmediev, NailWe present the infinite hierarchy of Sasa-Satsuma evolution equations. The corresponding Lax pairs are given, thus proving its integrability. The lowest order member of this hierarchy is the nonlinear Schrödinger equation, while the next one is the Sasa-Satsuma equation that includes third-order terms. Up to sixthorder terms of the hierarchy are given in explicit form, while the provided recurrence relation allows one to explicitly write all higher-order terms. The whole hierarchy can be combined into a single general equation. Each term in this equation contains a real independent coefficient that provides the possibility of adapting the equation to practical needs. A few examples of exact solutions of this general equation with an infinite number of terms are also given explicitly.
- 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.
- ItemMode transitions in distributed-feedback tapered master-oscillator power-amplifier(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Radziunas, Mindaugas; Tronciu, Vasile Z.; Bandelow, Uwe; Lichtner, Mark; Spreemann, Martin; Wenzel, HansTheoretical and experimental investigations have been carried out to study the spectral and spatial behavior of monolithically integrated distributed-feedback tapered master-oscillators power-amplifiers emitting around 973 nm. Introduction of self and cross heating effects and the analysis of longitudinal optical modes allows us to explain experimental results. The results show a good qualitative agreement between measured and calculated characteristics.
- ItemPersistence of rouge waves in extended nonlinear Schrödinger equations : integrable Sasa-Satsuma case(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Bandelow, Uwe; Akhmediev, Nail N.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.