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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.
- 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.
- 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.
- ItemTraveling wave analysis of non-thermal far-field blooming in high-power broad-area lasers(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Zeghuzi, Anissa; Radziunas, Mindaugas; Wünsche, Hans-Jürgen; Koester, Jan-Philipp; Wenzel, Hans; Bandelow, Uwe; Knigge, AndreaWith rising current the lateral far-field angle of high-power broad-area lasers widens (far-field blooming) which can be partly attributed to non-thermal effects due to carrier induced refractive index and gain changes that become the dominant mechanism under pulsed operation. To analyze the non-thermal contribution to far-field blooming we use a traveling wave based model that properly describes the injection of the current into and the diffusion of the carriers within the active region. Although no pre-assumptions regarding the modal composition of the field is made and filamentation is automatically accounted for, the highly dynamic time-dependent optical field distribution can be very well represented by only few modes of the corresponding stationary waveguide equation obtained by a temporal average of the carrier density and field intensity. The reduction of current spreading and spatial holeburning by selecting proper design parameters can substantially improve the beam quality of the laser.
- ItemUnusual ways of four-wave mixing instability(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2022) Amiranashvili, Shalva; Bandelow, UweA pump carrier wave in a dispersive system may decay by giving birth to blue- and red-shifted satellite waves due to modulation or four-wave mixing instability. We analyse situations where the satellites are so different from the carrier wave, that the red-shifted satellite either changes its propagation direction (k < 0, ω > 0) or even gets a negative frequency (k, ω < 0). Both situations are beyond the envelope approach and require application of Maxwell equations.
- 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.