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Author: Bandelow, Uwe × Start date: 2010 × Type: Text × Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik ×

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Now showing 1 - 10 of 36
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    Influence of the carrier reservoir dimensionality on electron-electron scattering in quantum dot materials
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Wilms, Alexander; Mathé, Peter; Schulze, Franz; Koprucki, Thomas; Knorr, Andreas; Bandelow, Uwe
    We calculated Coulomb scattering rates from quantum dots (QDs) coupled to a 2D carrier reservoir and QDs coupled to a 3D reservoir. For this purpose, we used a microscopic theory in the limit of Born-Markov approximation, in which the numerical evaluation of high dimensional integrals is done via a quasi-Monte Carlo method. Via a comparison of the so determined scattering rates, we investigated the question whether scattering from 2D is generally more efficient than scattering from 3D. In agreement with experimental findings, we did not observe a significant reduction of the scattering efficiency of a QD directly coupled to a 3D reservoir. In turn, we found that 3D scattering benefits from it’s additional degree of freedom in the momentum space
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    Ultrashort optical solitons in transparent nonlinear media with arbitrary dispersion
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Amiranashvili, Shalva; Bandelow, Uwe; Akhmediev, Nail
    We consider the propagation of ultrashort optical pulses in nonlinear fibers and suggest a new theoretical framework for the description of pulse dynamics and exact characterization of solitary solutions. Our approach deals with a proper complex generalization of the nonlinear Maxwell equations and completely avoids the use of the slowly varying envelope approximation. The only essential restriction is that fiber dispersion does not favor both the so-called Cherenkov radiation, as well as the resonant generation of the third harmonics, as these effects destroy ultrashort solitons. Assuming that it is not the case, we derive a continuous family of solitary solutions connecting fundamental solitons to nearly single-cycle ultrashort ones for arbitrary anomalous dispersion and cubic nonlinearity.
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    Calculation 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, Alexander
    Ultrashort 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.
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    Spatio-temporal pulse propagation in nonlinear dispersive optical media
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Brée, Carsten; Amiranashvili, Shalva; Bandelow, Uwe
    We discuss state-of-art approaches to modeling of propagation of ultrashort optical pulses in one and three spatial dimensions.We operate with the analytic signal formulation for the electric field rather than using the slowly varying envelope approximation, because the latter becomes questionable for few-cycle pulses. Suitable propagation models are naturally derived in terms of unidirectional approximation.
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    Cancellation 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, Shalva
    We 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.
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    Sasa-Satsuma equation: Soliton on a background and its limiting cases
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Bandelow, Uwe; Akhmediev, Nail
    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
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    Sasa-Satsuma hierarchy of integrable evolution equations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Bandelow, Uwe; Ankiewicz, Adrian; Amiranashvili, Shalva; Pickartz, Sabrina; Akhmediev, Nail
    We 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.
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    Rotational symmetry breaking in small-area circular vertical cavity surface emitting lasers
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Babushkin, Ihar; Bandelow, Uwe; Vladimirov, Andrei
    We investigate theoretically the dynamics of three low-order transverse modes in a small-area vertical cavity surface emitting laser. We demonstrate the breaking of axial symmetry of the transverse field distribution in such a device. In particular, we show that if the linewidth enhancement factor is sufficiently large dynamical regimes with broken axial symmetry can exist up to very high diffusion coefficients 10 um^2/ns.
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    Unusual ways of four-wave mixing instability
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2022) Amiranashvili, Shalva; Bandelow, Uwe
    A 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.
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    Multi-dimensional modeling and simulation of semiconductor nanophotonic devices
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Kantner, Markus; Höhne, Theresa; Koprucki, Thomas; Burger, Sven; Wünsche, Hans-Jürgen; Schmidt, Frank; Mielke, Alexander; Bandelow, Uwe
    Self-consistent modeling and multi-dimensional simulation of semiconductor nanophotonic devices is an important tool in the development of future integrated light sources and quantum devices. Simulations can guide important technological decisions by revealing performance bottlenecks in new device concepts, contribute to their understanding and help to theoretically explore their optimization potential. The efficient implementation of multi-dimensional numerical simulations for computer-aided design tasks requires sophisticated numerical methods and modeling techniques. We review recent advances in device-scale modeling of quantum dot based single-photon sources and laser diodes by self-consistently coupling the optical Maxwell equations with semiclassical carrier transport models using semi-classical and fully quantum mechanical descriptions of the optically active region, respectively. For the simulation of realistic devices with complex, multi-dimensional geometries, we have developed a novel hp-adaptive finite element approach for the optical Maxwell equations, using mixed meshes adapted to the multi-scale properties of the photonic structures. For electrically driven devices, we introduced novel discretization and parameter-embedding techniques to solve the drift-diffusion system for strongly degenerate semiconductors at cryogenic temperature. Our methodical advances are demonstrated on various applications, including vertical-cavity surface-emitting lasers, grating couplers and single-photon sources.