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- ItemModeling of quantum dot lasers with microscopic treatment of Coulomb effects(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Koprucki, Thomas; Wilms, Alexander; Knorr, Andreas; Bandelow, UweWe present a spatially resolved semiclassical model for the simulation of semiconductor quantum-dot lasers including a multi-species description for the carriers along the optical active region. The model links microscopic determined quantities like scattering rates and dephasing times, that essentially depend via Coulomb interaction on the carrier densities, with macroscopic transport equations and equations for the optical field.78A60 68U2078A60 68U20
- ItemTime-dependent simulation of thermal lensing in high-power broad-area semiconductor lasers(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Zeghuzi, Anissa; Wünsche, Hans-Jürgen; Wenzel, Hans; Radziunas, Mindaugas; Fuhrmann, Jürgen; Klehr, Andreas; Bandelow, Uwe; Knigge, AndreaWe propose a physically realistic and yet numerically applicable thermal model to account for short and long term self-heating within broad-area lasers. Although the temperature increase is small under pulsed operation, a waveguide that is formed within a few-ns-long pulse can result in a transition from a gain-guided to an index-guided structure, leading to near and far field narrowing. Under continuous wave operation the longitudinally varying temperature profile is obtained self-consistently. The resulting unfavorable narrowing of the near field can be successfully counteracted by etching trenches.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- ItemStabilization of optical pulse transmission by exploiting fiber nonlinearities(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Bandelow, Uwe; Amiranashvili, Shalva; Pickartz, SabrinaWe prove theoretically, that the evolution of optical solitons can be dramatically influenced in the course of nonlinear interaction with much smaller group velocity matched pulses. Even weak pump pulses can be used to control the solitons, e.g., to compensate their degradation caused by Raman-scattering.