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Publications

Monographs

  • U.W. Pohl, A. Strittmatter, A. Schliwa, M. Lehmann, T. Niermann, T. Heindel, S. Reitzenstein, M. Kantner, U. Bandelow, Th. Koprucki, H.-J. Wünsche, Stressor-induced site control of quantum dots for single-photon sources, M. Kneissl, A. Knorr, S. Reitzenstein, A. Hoffmann, eds., Semiconductor Nanophotonics, Springer, Heidelberg, 2020, pp. 53--90, (Chapter Published).
    Abstract
    The strain field of selectively oxidized A10x current apertures in an A1GaAs/GaAs mesa is utilized to define the nucleation site of InGaAs/GaAs quantum dots. A design is developed that allows for the self-aligned growth of single quantum dots in the center of a circular mesa. Measurements of the strain tensor applying transmission-electron holography yield excellent agreement with the calculated strain field. Single-dot spectroscopy of site-controlled dots proves narrow excitonic linewidth virtually free of spectral diffusion due to quantum-dot growth in a defect-free matrix. Implementation of such dots in an electrically driven pin structure yields single-dot electroluminescence. Single-photon emission with excellent purity is provided for this device using a Hanbury Brown and Twiss setup. The injection efficiency of the initian pin design is affected by a substantial lateral current spreading close to the oxide aperture. Allpying 3D carier-transport simulation a ppn doping profile is developed achieving a substantial improvement of the current injection.

  • S. Rodt, P.-I. Schneider, L. Zschiedrich, T. Heindel, S. Bounouar, M. Kantner, Th. Koprucki, U. Bandelow, S. Burger, S. Reitzenstein, Deterministic quantum devices for optical quantum communication, M. Kneissl, A. Knorr, S. Reitzenstein, A. Hoffmann, eds., Semiconductor Nanophotonics, Springer, Heidelberg, 2020, pp. 285--359, (Chapter Published).
    Abstract
    Photonic quantum technologies are based on the exchange of information via single photons. The information is typically encoded in the polarization of the photons and security is ensured intrinsically via principles of quantum mechanics such as the no-cloning theorem. Thus, all optical quantum communication networks rely crucially on the availability of suitable quantum-light sources. Such light sources with close to ideal optical and quantum optical properties can be realized by self-assembled semiconductor quantum dots. These high-quality nanocrystals are predestined single-photon emitters due to their quasi zero-dimensional carrier confinement. Still, the development of practical quantum-dot-based sources of single photons and entangled-photon pairs for applications in photonic quantum technology and especially for the quantum-repeater scheme is very demanding and requires highly advanced device concepts and deterministic fabrication technologies. This is mainly explained by their random position and emission energy as well as by the low photon-extraction efficiency in simple planar device configurations.

  • M. Kantner, Th. Hóhne, Th. Koprucki, S. Burger, H.-J. Wünsche, F. Schmidt, A. Mielke, U. Bandelow, Multi-dimensional modeling and simulation of semiconductor nanophotonic devices, M. Kneissl, A. Knorr, S. Reitzenstein, A. Hoffmann, eds., Semiconductor Nanophotonics, Springer, Heidelberg, 2020, pp. 241--283, (Chapter Published).
    Abstract
    Self-consistent modeling and multi-dimensional simulation of semiconductor nanophotonicdevices is an important tool in the development of future integrated light sources and quantumdevices. Simulations can guide important technological decisions by revealing performance bottle-necks in new device concepts, contribute to their understanding and help to theoretically exploretheir optimization potential. The efficient implementation of multi-dimensional numerical simulationsfor computer-aided design tasks requires sophisticated numerical methods and modeling tech-niques. We review recent advances in device-scale modeling of quantum dot based single-photonsources and laser diodes by self-consistently coupling the optical Maxwell equations with semi-classical carrier transport models using semi-classical and fully quantum mechanical descriptionsof 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 approachfor the optical Maxwell equations, using mixed meshes adapted to the multi-scale properties ofthe photonic structures. For electrically driven devices, we introduced novel discretization andparameter-embedding techniques to solve the drift-diffusion system for strongly degenerate semi-conductors at cryogenic temperature. Our methodical advances are demonstrated on variousapplications, including vertical-cavity surface-emitting lasers, grating couplers and single-photonsources.

Articles in Refereed Journals

  • I. Franović, S. Yanchuk, S. Eydam, I. Bačić, M. Wolfrum, Dynamics of a stochastic excitable system with slowly adapting feedback, Chaos. An Interdisciplinary Journal of Nonlinear Science, 30 (2020), published online on 03.08.2020, DOI 10.1063/1.5145176 .
    Abstract
    We study an excitable active rotator with slowly adapting nonlinear feedback and noise. Depending on the adaptation and the noise level, this system may display noise-induced spiking, noise-perturbed oscillations, or stochastic busting. We show how the system exhibits transitions between these dynamical regimes, as well as how one can enhance or suppress the coherence resonance, or effectively control the features of the stochastic bursting. The setup can be considered as a paradigmatic model for a neuron with a slow recovery variable or, more generally, as an excitable system under the influence of a nonlinear control mechanism. We employ a multiple timescale approach that combines the classical adiabatic elimination with averaging of rapid oscillations and stochastic averaging of noise-induced fluctuations by a corresponding stationary Fokker-Planck equation. This allows us to perform a numerical bifurcation analysis of a reduced slow system and to determine the parameter regions associated with different types of dynamics. In particular, we demonstrate the existence of a region of bistability, where the noise-induced switching between a stationary and an oscillatory regime gives rise to stochastic bursting.

  • U. Bandelow, S. Amiranashvili, S. Pickartz, Stabilization of optical pulse transmission by exploiting fiber nonlinearities, Journal of Lightwave Technology, 38 (2020), pp. 5743--5747, DOI 10.1109/JLT.2020.3003447 .
    Abstract
    We 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.

  • M. Kantner, Th. Koprucki, Beyond just ``flattening the curve'': Optimal control of epidemics with purely non-pharmaceutical interventions, Journal of Mathematics in Industry, 10 (2020), published online on 18.08.2020, DOI 10.1186/s13362-020-00091-3 .
    Abstract
    When effective medical treatment and vaccination are not available, non-pharmaceutical interventions such as social distancing, home quarantine and far-reaching shutdown of public life are the only available strategies to prevent the spread of epidemics. Based on an extended SEIR (susceptible-exposed-infectious-recovered) model and continuous-time optimal control theory, we compute the optimal non-pharmaceutical intervention strategy for the case that a vaccine is never found and complete containment (eradication of the epidemic) is impossible. In this case, the optimal control must meet competing requirements: First, the minimization of disease-related deaths, and, second, the establishment of a sufficient degree of natural immunity at the end of the measures, in order to exclude a second wave. Moreover, the socio-economic costs of the intervention shall be kept at a minimum. The numerically computed optimal control strategy is a single-intervention scenario that goes beyond heuristically motivated interventions and simple ?flattening of the curve?. Careful analysis of the computed control strategy reveals, however, that the obtained solution is in fact a tightrope walk close to the stability boundary of the system, where socio-economic costs and the risk of a new outbreak must be constantly balanced against one another. The model system is calibrated to reproduce the initial exponential growth phase of the COVID-19 pandemic in Germany.

  • S. Amiranashvili, E. Tobisch, Extended criterion for the modulation instability, New Journal of Physics, 21 (2019), pp. 033029/1--033029/7, DOI 10.1088/1367-2630/ab0130 .
    Abstract
    Modulation instability, following the classical Lighthill criterion, appears if nonlinearity and dispersion make opposite contributions to the wave frequency, e.g. in the framework of the one-dimensional nonlinear Schrödinger equation (NLSE). Several studies of the wave instabilities in optical fibers revealed four wave mixing instabilities that are not covered by the Lighthill criterion and require use of the generalized NLSE. We derive an extended criterion, which applies to all four wave interactions, covers arbitrary dispersion, and depends neither on the propagation equation nor on the slowly varying envelope approximation.

  • S. Amiranashvili, M. Radziunas, U. Bandelow, R. Čiegis, Numerical methods for accurate description of ultrashort pulses in optical fibers, Communications in Nonlinear Science and Numerical Simulation, 67 (2019), pp. 391--402, DOI 10.1016/j.cnsns.2018.07.031 .
    Abstract
    We consider a one-dimensional first-order nonlinear wave equation (the so-called forward Maxwell equation, FME) that applies to a few-cycle optical pulse propagating along a preferred direction in a nonlinear medium, e.g., ultrashort pulses in nonlinear fibers. The model is a good approximation to the standard second-order wave equation under assumption of weak nonlinearity. We compare FME to the commonly accepted generalized nonlinear Schrödinger equation, which quantifies the envelope of a quickly oscillating wave field based on the slowly varying envelope approximation. In our numerical example, we demonstrate that FME, in contrast to the envelope model, reveals new spectral lines when applied to few-cycle pulses. We analyze and compare pseudo-spectral numerical schemes employing symmetric splitting for both models. Finally, we adopt these schemes to a parallel computation and discuss scalability of the parallelization.

  • C. Brée, V. Raab, J. Montiel-Ponsoda, G. Garre-Werner, K. Staliunas, U. Bandelow, M. Radziunas, Beam-combining scheme of high-power broad-area semiconductor lasers with Lyot-filtered reinjection: Modeling, simulations, and experiments, Journal of the Optical Society of America. B, 36 (2019), pp. 1721--1730, DOI 10.1364/JOSAB.36.001721 .
    Abstract
    A 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.

  • S. Eydam, I. Franović, M. Wolfrum, Leap-frog patterns in systems of two coupled FitzHugh--Nagumo units, Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 99 (2019), pp. 042207/1--042207/9, DOI 10.1103/PhysRevE.99.042207 .
    Abstract
    We study a system of two identical FitzHugh-Nagumo units with a mutual linear coupling in the fast variables. While an attractive coupling always leads to synchronous behavior, a repulsive coupling can give rise to dynamical regimes with alternating spiking order, called leap-frogging. We analyze various types of periodic and chaotic leap-frogging regimes, using numerical pathfollowing methods to investigate their emergence and stability, as well as to obtain the complex bifurcation scenario which organizes their appearance in parameter space. In particular, we show that the stability region of the simplest periodic leap-frog pattern has the shape of a locking cone pointing to the canard transition of the uncoupled system. We also discuss the role of the timescale separation in the coupled FitzHugh-Nagumo system and the relation of the leap-frog solutions to the theory of mixed-mode oscillations in multiple timescale systems.

  • S. Eydam, M. Wolfrum, The link between coherence echoes and mode locking, Chaos. An Interdisciplinary Journal of Nonlinear Science, 29 (2019), pp. 103114/1--103114/10, DOI 10.1063/1.5114699 .
    Abstract
    We investigate the appearance of sharp pulses in the mean field of Kuramoto-type globally- coupled phase oscillator systems. In systems with exactly equidistant natural frequencies self- organized periodic pulsations of the mean field, called mode locking, have been described re- cently as a new collective dynamics below the synchronization threshold. We show here that mode locking can appear also for frequency combs with modes of finite width, where the natu- ral frequencies are randomly chosen from equidistant frequency intervals. In contrast to that, so called coherence echoes, which manifest themselves also as pulses in the mean field, have been found in systems with completely disordered natural frequencies as the result of two consecutive stimulations applied to the system. We show that such echo pulses can be explained by a stimula- tion induced mode locking of a subpopulation representing a frequency comb. Moreover, we find that the presence of a second harmonic in the interaction function, which can lead to the global stability of the mode-locking regime for equidistant natural frequencies, can enhance the echo phenomenon significantly. The non-monotonous behavior of echo amplitudes can be explained as a result of the linear dispersion within the self-organized mode-locked frequency comb. Fi- nally we investigate the effect of small periodic stimulations on oscillator systems with disordered natural frequencies and show how the global coupling can support the stimulated pulsation by increasing the width of locking plateaus.

  • M. Kantner, Generalized Scharfetter--Gummel schemes for electro-thermal transport in degenerate semiconductors using the Kelvin formula for the Seebeck coefficient, Journal of Computational Physics, published online on 07.11.2019, urlhttps://doi.org/10.1016/j.jcp.2019.109091, DOI 10.1016/j.jcp.2019.109091 .
    Abstract
    Many challenges faced in today's semiconductor devices are related to self-heating phenomena. The optimization of device designs can be assisted by numerical simulations using the non-isothermal drift-diffusion system, where the magnitude of the thermoelectric cross effects is controlled by the Seebeck coefficient. We show that the model equations take a remarkably simple form when assuming the so-called Kelvin formula for the Seebeck coefficient. The corresponding heat generation rate involves exactly the three classically known self-heating effects, namely Joule, recombination and Thomson--Peltier heating, without any further (transient) contributions. Moreover, the thermal driving force in the electrical current density expressions can be entirely absorbed in the (nonlinear) diffusion coefficient via a generalized Einstein relation. The efficient numerical simulation relies on an accurate and robust discretization technique for the fluxes (finite volume Scharfetter--Gummel method), which allows to cope with the typically stiff solutions of the semiconductor device equations. We derive two non-isothermal generalizations of the Scharfetter--Gummel scheme for degenerate semiconductors (Fermi--Dirac statistics) obeying the Kelvin formula. The approaches differ in the treatment of degeneration effects: The first is based on an approximation of the discrete generalized Einstein relation implying a specifically modified thermal voltage, whereas the second scheme follows the conventionally used approach employing a modified electric field. We present a detailed analysis and comparison of both schemes, indicating a superior performance of the modified thermal voltage scheme.

  • A. Pimenov, A.G. Vladimirov, Dynamics of an inhomogeneously broadened passively mode-locked laser, The European Physical Journal B. Condensed Matter and Complex Systems, 92 (2019), pp. 114/1--114/12, DOI 10.1140/epjb/e2019-90642-8 .
    Abstract
    We study theoretically the effect of inhomogeneous broadening of the gain and absorption lines on the dynamics of a passively mode-locked laser. We demonstrate numerically using travelling wave equations the formation of a Lamb-dip instability and suppression of Q-switching in a laser with large inhomogeneous broadening. We derive simplified delay-differential equation model for a mode-locked laser with inhomogeneously broadened gain and absorption lines and perform numerical bifurcation analysis of this model.

  • S. Slepneva, B. O'Shaughnessy, A.G. Vladimirov, S. Rica, E.A. Viktorov, G. Huyet, Convective Nozaki--Bekki holes in a long cavity OCT laser, Optics Express, 27 (2019), pp. 16395--16404, DOI 10.1364/OE.27.016395 .
    Abstract
    We show, both experimentally and theoretically, that the loss of coherence of a long cavity optical coherence tomography (OCT) laser can be described as a transition from laminar to turbulent flows. We demonstrate that in this strongly dissipative system, the transition happens either via an absolute or a convective instability depending on the laser parameters. In the latter case, the transition occurs via formation of localised structures in the laminar regime, which trigger the formation of growing and drifting puffs of turbulence. Experimentally, we demonstrate that these turbulent bursts are seeded by appearance of Nozaki-Bekki holes, characterised by the zero field amplitude and ? phase jumps. Our experimental results are supported with numerical simulations based on the delay differential equations model.

  • P. Kravetc, D. Rachinskii, A.G. Vladimirov, Periodic pulsating dynamics of slow-fast delayed systems with a periodic close to the delay, European Journal of Applied Mathematics, 30 (2019), pp. 39--62, DOI 10.1017/S0956792517000377 .
    Abstract
    We consider slow?fast delayed systems and discuss pulsating periodic solutions, which are characterised by specific properties that (a) the period of the periodic solution is close to the delay, and (b) these solutions are formed close to a bifurcation threshold. Such solutions were previously found in models of mode-locked lasers. Through a case study of population models, this work demonstrates the existence of similar solutions for a rather wide class of delayed systems. The periodic dynamics originates from the Hopf bifurcation on the positive equilibrium. We show that the continuous transformation of the periodic orbit to the pulsating regime is simultaneous with multiple secondary almost resonant Hopf bifurcations, which the equilibrium undergoes over a short interval of parameter values. We derive asymptotic approximations for the pulsating periodic solution and consider scaling of the solution and its period with the small parameter that measures the ratio of the time scales. The role of competition for the realisation of the bifurcation scenario is highlighted.

  • CH. Schelte, A. Pimenov, A.G. Vladimirov, J. Javaloyes, S.V. Gurevich, Tunable Kerr frequency combs and temporal localized states in time-delayed Gires--Tournois interferometers, Optics Letters, 44 (2019), pp. 4925--4928, DOI 10.1364/OL.44.004925 .
    Abstract
    In this Letter, we study theoretically a new setup allowing for the generation of temporal localized states (TLSs) and frequency combs. The setup is compact (a few centimeters) and can be implemented using established technologies, while offering tunable repetition rates and potentially high power operation. It consists of a vertically emitting micro-cavity, operated in the Gires?Tournois regime, containing a Kerr medium strong time-delayed optical feedback, and detuned optical injection. We disclose sets of multistable dark and bright TLSs coexisting on their respective bistable homogeneous backgrounds.

  • K.R. Schneider, The point charge oscillator: Qualitative and analytical investigations, Mathematical Modelling and Analysis. Matematinis Modeliavimis ir Analize. The Baltic Journal on Mathematical Applications, Numerical Analysis and Differential Equations, 24 (2019), pp. 372--384, DOI 10.3846/mma.2019.023 .
    Abstract
    We determine the global phase portrait of a mathematical model describing the point charge oscillator. It shows that the family of closed orbits describing the point charge oscillations has two envelopes: an equilibrium point and a homoclinic orbit to an equilibrium point at infinity. We derive an expression for the growth rate of the primitive perod Τα of the oscillation with the amplitude α as α tends to infinity. Finally, we determine an exact relation between period and amplitude by means of the Jacobi elliptic function cn.

  • S. Yanchuk, S. Ruschel, J. Sieber, M. Wolfrum, Temporal dissipative solitons in time-delay feedback systems, Physical Review Letters, 123 (2019), pp. 053901/1--053901/6, DOI 10.1103/PhysRevLett.123.053901 .
    Abstract
    Localized states are a universal phenomenon observed in spatially distributed dissipative nonlinear systems. Known as dissipative solitons, auto-solitons, spot or pulse solitons, these states play an important role in data transmission using optical pulses, neural signal propagation, and other processes. While this phenomenon was thoroughly studied in spatially extended systems, temporally localized states are gaining attention only recently, driven primarily by applications from fiber or semiconductor lasers. Here we present a theory for temporal dissipative solitons (TDS) in systems with time-delayed feedback. In particular, we derive a system with an advanced argument, which determines the profile of the TDS. We also provide a complete classification of the spectrum of TDS into interface and pseudo-continuous spectrum. We illustrate our theory with two examples: a generic delayed phase oscillator, which is a reduced model for an injected laser with feedback, and the FitzHugh--Nagumo neuron with delayed feedback. Finally, we discuss possible destabilization mechanisms of TDS and show an example where the TDS delocalizes and its pseudo-continuous spectrum develops a modulational instability.

  • M. Krüger, V.Z. Tronciu, A. Bawamia, Ch. Kürbis, M. Radziunas, H. Wenzel, A. Wicht, A. Peters, G. Tränkle, Improving the spectral performance of extended cavity diode lasers using angled-facet laser diode chips, Applied Physics B: Lasers and Optics, 66 (2019), pp. 125/1--125/12, DOI 10.1007/s00340-019-7178-z .
    Abstract
    We present and compare theoretical and experimental results on the electro-optical performance of extended cavity diode lasers (ECDLs) that employ two ridge waveguide designs for the single-transverse mode GaAs laser diode chip. One facet of the laser diode chips serves as a partially reflective output coupler for the laser cavity. The other facet constitutes an intra-cavity interface which introduces spurious optical feedback to the laser diode chip. The waveguide designs differ with respect to the suppression of this spurious feedback. The first design employs a straight ridge waveguide intersecting both facets at normal incidence. The intra-cavity facet is anti-reflection coated and features a residual intensity reflectivity of the order 10?4. The second design employs a bent ridge waveguide intersecting the anti-reflection-coated intra-cavity facet at an appropriate angle. This provides an additional suppression of the spurious intensity reflection to a value estimated to be less than 10?6 . We compare the electro-optical performance of both designs theoretically and experimentally. The utilization of a bent waveguide results in an improved spectral stability and purity, specifically a higher side mode suppression and a small intrinsic spectral linewidth over the whole investigated current range, of the external cavity diode laser without sacrificing other parameters such as the output power. The external cavity diode lasers under study exhibit no degradation of the measured frequency noise power spectra and intrinsic linewidths even if there is a drop of the side mode suppression ratio provided that it is not reduced to a very small value. Thus, the usage of a more readily accessible straight waveguide chip in an ECDL could be sufficient if only a limited tuning range and a particularly compact assembly are needed. For spectroscopic applications requiring a small intrinsic spectral linewidth over a large frequency range a bent waveguide chip could be the better choice.

  • A. Zeghuzi, M. Radziunas, H.-J. Wünsche, J.-P. Koester, H. Wenzel, U. Bandelow, A. Knigge, Traveling wave analysis of non-thermal far-field blooming in high-power broad-area lasers, IEEE J. Quantum Electron., 55 (2019), pp. 2000207/1--2000201/7, DOI 10.1109/JQE.2019.2893352 .
    Abstract
    With 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 nonthermal 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.

  • J.-P. Koester, M. Radziunas, A. Zeghuzi, H. Wenzel, A. Knigge, Simulation and design of a compact GaAs based tunable dual-wavelength diode laser system, Optical and Quantum Electronics, 51 (2019), pp. 334/1--334/12, DOI 10.1007/s11082-019-2050-2 .
    Abstract
    We present our design of a compact, integrated and tunable dual-wavelength diode laser system emitting around 785 nm, which is of interest for several applications like Raman spectroscopy and the generation of THz radiation. To achieve a more compact device compared to previous GaAs based designs two etch depths are realized, leading to shallowly etched ridge waveguides in regions were optical gain is applied and deeply etched waveguides used to enable compact integrated waveguide components. The device parameters are optimized using a numerically efficient simulation tool for passive waveguides. Subsequently, the entire laser system is further analyzed applying a sophisticated traveling-wave equation based model for active devices giving access to internal intensity and carrier density distributions. It is shown that active laser simulations are crucial to deduce critical and performance limiting design aspects not accessible via an all-passive simulation.

  • A. Zeghuzi, H.-J. Wünsche, H. Wenzel, M. Radziunas, J. Fuhrmann, A. Klehr, U. Bandelow, A. Knigge, Time-dependent simulation of thermal lensing in high-power broad-area semiconductor lasers, IEEE J. Select. Topics Quantum Electron., 25 (2019), pp. 1502310/1--1502310/10, DOI 10.1109/JSTQE.2019.2925926 .
    Abstract
    We 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.

  • M. Radziunas, D.J. Little, D.M. Kane, Numerical study of optical feedback coherence in semiconductor laser dynamics, Optics Letters, 44 (2019), pp. 4207--4210, DOI 10.1364/OL.44.004207 .
    Abstract
    The nonlinear dynamics of semiconductor laser with coherent, as compared to incoherent, delayed optical feedback systems have been discussed and contrasted in prior research literature. Here, we report simulations of how the dynamics change as the coherence of the optical feedback is systematically varied from being coherent to incoherent. An increasing rate of phase disturbance is used to vary the coherence. An edge emitting, 830nm, Fabry Perot semiconductor laser with a long external cavity is simulated. Following this study, consideration of prior and future experimental studies should include evaluation of where on the continuum of partial coherence the delayed optical feedback sits. Partial coherence is a parameter that will affect the dynamics.

  • M. Radziunas, J. Fuhrmann, A. Zeghuzi, H.-J. Wünsche, Th. Koprucki, C. Brée, H. Wenzel, U. Bandelow, Efficient coupling of dynamic electro-optical and heat-transport models for high-power broad-area semiconductor lasers, Optical and Quantum Electronics, 51 (2019), pp. 69/1--69/10, DOI 10.1007/s11082-019-1792-1 .
    Abstract
    In 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.

  • A.G. Vladimirov, A.V. Kovalev, E.A. Viktorov, N. Rebrova, G. Huyet, Dynamics of a class-A nonlinear mirror mode-locked laser, Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 100 (2019), pp. 012216/1--012216/7, DOI 10.1103/PhysRevE.100.012216 .
    Abstract
    Using a simple delay differential equation model we study theoretically the dynamics of a unidirectional class-A ring laser with a nonlinear amplifying loop mirror. We perform analytical linear stability analysis of the CW regimes in the large delay limit and demonstrate that these regimes can be destabilized via modulational and Turing-type instabilities, as well as by a bifurcation leading to the appearance of square-waves. We investigate the formation of square-waves and mode-locked pulses in the system. We show that mode-locked pulses are very asymmetric with exponential decay of the trailing and superexponential growth of the leading edge. We discuss asymmetric interaction of these pulses leading to a formation of harmonic mode-locked regimes.

Contributions to Collected Editions

  • G. Garre--Werner, J.J. Montiel--Ponsoda, V. Raab, G. Safont, C. Brée, M. Radziunas, C. Cojocaru, K. Staliunas, 1 kW cw fiber-coupled diode laser with enhanced brightness, in: Proceedings SPIE 11262, High-Power Diode Laser Technology XVIII, M.S. Zediker, ed., 11262 of SPIE Proceedings Series, SPIE, San Francisco, 2020, pp. 1126202/1--1126202/9, DOI 10.1117/12.2546086 .
    Abstract
    We developed a 1kW cw fiber-coupled diode laser at 9XX nm by using beam combining of eight high power diode laser bars. To achieve beam combining, we employ Lyot-filtered optical reinjection from an external cavity, which forces lasing of the individual diode laser bars on intertwined frequency combs with overlapping envelopes and enables a high optical coupling efficiency. Unlike other spectral beam combining techniques that are based on the use of grating elements, this technique is insensitive to the thermal drift of the laser diodes. In addition to this, the FWHM spectral width at 1 kW output power is only around 7 nm, which is convenient for wavelength sensitive applications such as pumping.

  • M. Kolarczik, F. Böhm, U. Woggon, N. Owschimikow, A. Pimenov, M. Wolfrum, A. Vladimirov, S. Meinecke, B. Lingnau, L. Jaurigue, K. Lüdge, Coherent and incoherent dynamics in quantum dots and nanophotonic devices, in: Semiconductor Nanophotonics, M. Kneissl, A. Knorr, S. Reitzenstein, A. Hoffmann, eds., 194 of Springer Series in Solid-State Sciences, Springer, Cham, 2020, pp. published online on 11.03.2020, DOI 10.1007/978-3-030-35656-9_4 .
    Abstract
    The interest in coherent and incoherent dynamics in novel semiconductor gain media and nanophotonic devices is driven by the wish to understand the optical gain spectrally, dynamically, and energetically for applications in optical amplifiers, lasers or specially designed multi-section devices. This chapter is devoted to the investigation of carrier dynamics inside nanostructured gain media as well as to the dynamics of the resulting light output. It is structured into two parts. The first part deals with the characterization of ultrafast and complex carrier dynamics via the optical response of the gain medium with pump-probe methods, two-color four-wave mixing setups and quantum-state tomography. We discuss the optical nonlinearities resulting from light-matter coupling and charge carrier interactions using microscopically motivated rate-equation models. In the second part, nanostructured mode-locked lasers are investigated, with a focus on analytic insights about the regularity of the pulsed light emission. A method for efficiently predicting the timing fluctuations is presented and used to optimize the device properties. Finally, one specific design of a mode-locked laser with tapered gain section is discussed which draws the attention to alternative ways of producing very stable and high intensity laser pulses.

  • U.W. Pohl, A. Strittmatter, A. Schliwa, M. Lehmann, T. Niermann, T. Heindel, S. Reitzenstein, M. Kantner, U. Bandelow, Th. Koprucki, H.-J. Wünsche, Stressor-induced site control of quantum dots for single-photon sources, in: Semiconductor Nanophotonics, M. Kneissl, A. Knorr, S. Reitzenstein, A. Hoffmann, eds., 194 of Springer Series in Solid-State Sciences, Springer, Cham, 2020, pp. published online on 11.03.2020, DOI 10.1007/978-3-030-35656-9_3 .
    Abstract
    The strain field of selectively oxidized AlOx current apertures in an AlGaAs/GaAs mesa is utilized to define the nucleation site of InGaAs/GaAs quantum dots. A design is developed that allows for the self-aligned growth of single quantum dots in the center of a circular mesa. Measurements of the strain tensor applying transmission-electron holography yield excellent agreement with the calculated strain field. Single-dot spectroscopy of site-controlled dots proves narrow excitonic linewidth virtually free of spectral diffusion due to quantum-dot growth in a defect-free matrix. Implementation of such dots in an electrically driven pin structure yields single-dot electroluminescence. Single-photon emission with excellent purity is proved for this device using a Hanbury Brown and Twiss setup. The injection efficiency of the initial pin design is affected by a substantial lateral current spreading close to the oxide aperture. Applying 3D carrier-transport simulation a ppn doping profile is developed achieving a substantial improvement of the current injection.

  • S. Rodt, P.-I. Schneider, L. Zschiedrich, T. Heindel, S. Bounouar, M. Kantner, Th. Koprucki, U. Bandelow, S. Burger, S. Reitzenstein, Deterministic quantum devices for optical quantum communication, in: Semiconductor Nanophotonics, M. Kneissl, A. Knorr, S. Reitzenstein, A. Hoffmann, eds., 194 of Springer Series in Solid-State Sciences, Springer, Cham, 2020, pp. published online on 11.03.2020, DOI 10.1007/978-3-030-35656-9 .
    Abstract
    Photonic quantum technologies are based on the exchange of information via single photons. The information is typically encoded in the polarization of the photons and security is ensured intrinsically via principles of quantum mechanics such as the no-cloning theorem. Thus, all optical quantum communication networks rely crucially on the availability of suitable quantum-light sources. Such light sources with close to ideal optical and quantum optical properties can be realized by self-assembled semiconductor quantum dots. These high-quality nanocrystals are predestined single-photon emitters due to their quasi zero-dimensional carrier confinement. Still, the development of practical quantum-dot-based sources of single photons and entangled-photon pairs for applications in photonic quantum technology and especially for the quantum-repeater scheme is very demanding and requires highly advanced device concepts and deterministic fabrication technologies. This is mainly explained by their random position and emission energy as well as by the low photon-extraction efficiency in simple planar device configurations.

  • J.--P. Köster, M. Radziunas, A. Zeghuzi, H. Wenzel, A. Knigge, Traveling wave model-based analysis of tapered broad-area lasers, in: Proceedings SPIE 11274, Physics and Simulation of Optoelectronic Devices XXVIII, B. Witzigmann, M. Osiński, Y. Arakawa, eds., 11274 of SPIE Proceedings Series, SPIE, San Francisco, 2020, pp. 112740I/1--112740I/10, DOI 10.1117/12.2537015 .
    Abstract
    We present simulation results showing the impact of a longitudinal linearly varying electrical contact width on intra-cavity intensity, carrier density and temperature distributions of broad-area lasers. In addition, the impact of index guiding trenches on these internal distributions is investigated. The simulations were performed using a time-dependent traveling wave model which takes all relevant physical effects into account. We show that a tapered contact area results in a reduced longitudinal intensity inhomogeneity as well as longitudinal spatial hole burning, at the cost of an increased temperature towards the front facet. Index guiding trenches were found to effectively prevent lateral intensity modulation as well as lateral carrier accumulation near the contact edges at the front facet.

  • U. Bandelow, M. Radziunas, A. Zeghuzi, H.-J. Wünsche, H. Wenzel, Dynamics in high-power diode lasers, in: Proceedings of SPIE, M. Sciamanna, R. Michalzik, K. Panajotov, S. Höfling, eds., 11356, 2020, pp. 113560W/1--113560W/14, DOI 10.1117/12.2559175 .
    Abstract
    High-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.

  • M. Kantner, Th. Höhne, Th. Koprucki, S. Burger, H.-J. Wünsche, F. Schmidt, A. Mielke, U. Bandelow, Multi-dimensional modeling and simulation of semiconductor nanophotonic devices, in: Semiconductor Nanophotonics, M. Kneissl, A. Knorr, S. Reitzenstein, A. Hoffmann, eds., 194 of Springer Series in Solid-State Sciences, Springer, Cham, 2020, pp. 241--283, DOI 10.1007/978-3-030-35656-9_7 .
    Abstract
    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 semi-classical 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 temperatures. Our methodical advances are demonstrated on various applications, including vertical-cavity surface-emitting lasers, grating couplers and single-photon sources.

  • M. Kantner, Th. Koprucki, Non-isothermal Scharfetter--Gummel scheme for electro-thermal transport simulation in degenerate semiconductors, in: Proceedings of ``Finite Volumes for Complex Applications IX'', R. Klöfkorn, E. Keilegavlen, F.A. Radu, J. Fuhrmann, eds., 323 of Springer Proceedings in Mathematics & Statistics, Springer, Cham, 2020, pp. 173--182, DOI 10.1007/978-3-030-43651-3_14 .
    Abstract
    Electro-thermal transport phenomena in semiconductors are described by the non-isothermal drift-diffusion system. The equations take a remarkably simple form when assuming the Kelvin formula for the thermopower. We present a novel, non-isothermal generalization of the Scharfetter--Gummel finite volume discretization for degenerate semiconductors obeying Fermi--Dirac statistics, which preserves numerous structural properties of the continuous model on the discrete level. The approach is demonstrated by 2D simulations of a heterojunction bipolar transistor.

  • M. Kantner, Th. Koprucki, Non-isothermal Scharfetter-Gummel scheme for electro-thermal transport simulation in degenerate semiconductors, in: Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples, R. Klöfkorn, E. Keilegavlen, F.A. Radu, J. Fuhrmann, eds., 323 of Springer Proceedings in Mathematics & Statistics, Springer, Cham, 2020, pp. 173--182, DOI 10.1007/978-3-030-43651-3_14 .
    Abstract
    Electro-thermal transport phenomena in semiconductors are described by the non-isothermal drift-diffusion system. The equations take a remarkably simple form when assuming the Kelvin formula for the thermopower. We present a novel, non-isothermal generalization of the Scharfetter?Gummel finite volume discretization for degenerate semiconductors obeying Fermi?Dirac statistics, which preserves numerous structural properties of the continuous model on the discrete level. The approach is demonstrated by 2D simulations of a heterojunction bipolar transistor.

  • C. Brée, V. Raab, D. Gailevičius, V. Purlys, J. Montiel, G.G. Werner, K. Staliunas, A. Rathsfeld, U. Bandelow, M. Radziunas, Genetically optimized photonic crystal for spatial filtering of reinjection into broad-area diode lasers, in: 2019 Conference on Lasers and Electro-Optics Europe and European Quantum Electronics Conference, OSA Technical Digest, IEEE, Piscataway, 2019, pp. 1--1, DOI 10.1109/CLEO-EQEC.2019.8871622 .
    Abstract
    Modern high-power broad-area semiconductor laser diodes (BASLDs) deliver optical output powers of several ten Watts at high electro-optical conversion efficiencies, which makes them highly relevant for numerous industrial, medical and scientific applications. However, lateral multimode behavior in BASLDs due to thermal lensing turns out highly detrimental, as it results in poor focusability and decreased laser beam brightnesss. Approaches to overcome this issue include improved epitaxial layer design, the optimization of evanescent spatial filtering by tailoring the emitter geometry and facet reflectivity, or Fourier spatially filtered reinjection from an external resonator [1].

  • C. Brée, V. Raab, J. Montiel, G.G. Werner, K. Staliunas, U. Bandelow, M. Radziunas, Lyot spectral filter for polarization beam combining of high-power, broad-area diode lasers: Modeling, simulations, and experiments, in: 2019 Conference on Lasers and Electro-Optics Europe and European Quantum Electronics Conference, OSA Technical Digest, IEEE, Piscataway, 2019, pp. 1--1, DOI 10.1109/CLEOE-EQEC.2019.8871911 .
    Abstract
    Summary form only given. Recent improvements in design and development have significantly increased the relevance of high-power, broad-area laser diodes and laser diode bars in the market for industrial, high-brightness materials processing applications, like welding, soldering and cutting. Here, we present, experimentally [1] and, for the first time, in direct simulations [2], a polarization beam combining scheme, which maintains the linear polarization of the individual sources, and, unlike common wavelength multiplexing schemes, is insensitive to spectral drifts caused by variations of temperature or injection current. In our setup, two laser diodes are operated with optical reinjection from a common external cavity containing a Lyot spectral filter; cf. the setup shown in Fig. 1a). Our time-domain direct numerical simulations take into account both, the lateral, and longitudinal dimensions of the laser emitters [3]. The optical reinjection from the common external resonator was modeled by suitable Fresnel integrals in the paraxial regime, accounting for the different phase- and group retardations of ordinary and extraordinary beam components within the birefringent crystal (calcite) [4]. Using a half-wave plate for polarization rotating the emission of diode 2, the spectrally filtered feedback enforces lasing of both diodes on interleaved frequency combs. The spectrum of each diode is then localized in the respective transmission window of the Lyot filter, determined by cos 2 ??nL/? (diode 1) and sin 2 ??nL/? (diode 2), where ?? is the phase birefringence of the crystal. In consequence, both beams can be combined with maintained linear polarization and high optical coupling efficiency. Simulated and experimental results for two coupled laser diodes are shown in Figs. 1b) and c). Indeed, simulations and experiments show that the usable output power in the combined beam is 86% (simulations) and 80% (experiment).

  • M. Kantner, A. Mielke, M. Mittnenzweig, N. Rotundo, Mathematical modeling of semiconductors: From quantum mechanics to devices, in: Topics in Applied Analysis and Optimisation, M. Hintermüller, J.F. Rodrigues, eds., CIM Series in Mathematical Sciences, Springer Nature Switzerland AG, Cham, 2019, pp. 269--293, DOI 10.1007/978-3-030-33116-0 .
    Abstract
    We discuss recent progress in the mathematical modeling of semiconductor devices. The central result of this paper is a combined quantum-classical model that self-consistently couples van Roosbroeck's drift-diffusion system for classical charge transport with a Lindblad-type quantum master equation. The coupling is shown to obey fundamental principles of non-equilibrium thermodynamics. The appealing thermodynamic properties are shown to arise from the underlying mathematical structure of a damped Hamitlonian system, which is an isothermal version of socalled GENERIC systems. The evolution is governed by a Hamiltonian part and a gradient part involving a Poisson operator and an Onsager operator as geoemtric structures, respectively. Both parts are driven by the conjugate forces given in terms of the derivatives of a suitable free energy.

  • M. Kantner, Th. Koprucki, H.-J. Wünsche, U. Bandelow, Simulation of quantum dot based single-photon sources using the Schrödinger--Poisson-Drift-Diffusion-Lindblad system, in: Proceedings of the 24th International Conference on Simulation of Semiconductor Processes and Devices (SISPAD 2019), F. Driussi, ed., 2019, pp. 355--358, DOI 10.1007/978-3-030-22116-0_11 .

  • M. Kantner, A generalized Scharfetter--Gummel scheme for degenerate and non-isothermal semiconductors, in: Proceedings of the 19th International Conference on Numerical Simulation of Optoelectronic Devices -- NUSOD 2019, J. Piprek, K. Hinzer, eds., IEEE Conference Publications Management Group, Piscataway, 2019, pp. 7--8, DOI 10.1109/NUSOD.2019.8806839 .
    Abstract
    We present a highly accurate generalization of the Scharfetter--Gummel scheme for the discretization of the currentdensities in degenerate semiconductors under non-isothermalconditions. The underlying model relies on the Kelvin formula forthe Seebeck coefficient, which has the intriguing property that the?T-term in the electrical current density expressions vanishesexactly when passing to the drift-diffusion form ? even thoughthe thermoelectric cross-coupling is fully taken into account.

  • M. Kantner, Hybrid modeling of quantum light emitting diodes: Self-consistent coupling of drift-diffusion, Schrödinger--Poisson, and quantum master equations, in: Proc. SPIE 10912, B. Witzigmann, M. Osiński, Y. Arakawa, eds., Physics and Simulation of Optoelectronic Devices XXVII, SPIE Digital Library, Bellingham, 2019, pp. 10912OU/1--10912OU/8, DOI 10.1117/12.2515209 .
    Abstract
    The device-scale simulation of electrically driven solid state quantum light emitters, such as single-photon sources and nanolasers based on semiconductor quantum dots, requires a comprehensive modeling approach, that combines classical device physics with cavity quantum electrodynamics. In a previous work, we have self-consistently coupled the semi-classical drift-diffusion system with a Markovian quantum master equation in Lindblad form to describe (i) the spatially resolved current injection into a quantum dot embedded within a semiconductor device and (ii) the fully quantum mechanical light-matter interaction in the coupled quantum dot-photon system out of one box. In this paper, we extend our hybrid quantum-classical modeling approach by including a Schroedinger?Poisson problem to account for energy shifts of the quantum dot carriers in response to modifications of its macroscopic environment (e.g., quantum confined Stark effect due to the diode's internal electric field and plasma screening). The approach is demonstrated by simulations of a single-photon emitting diode.

  • M. Kantner, Simulation of quantum light sources using the self-consistently coupled Schrödinger--Poisson-Drift-Diffusion-Lindblad system, in: Proceedings of the 19th International Conference on Numerical Simulation of Optoelectronic Devices -- NUSOD 2019, J. Piprek, K. Hinzer, eds., IEEE Conference Publications Management Group, Piscataway, 2019, pp. 15--16, DOI 10.1109/NUSOD.2019.8806839 .
    Abstract
    The device-scale simulation of electrically drivenquantum light sources based on semiconductor quantum dotsrequires a combination of the (classical) semiconductor deviceequations with cavity quantum electrodynamics. In this paper, weextend our previously developed hybrid quantum-classical modelsystem ? where we have coupled the drift-diffusion system witha Lindblad-type quantum master equation ? by including a self-consistent Schrödinger?Poisson problem. The latter describes the(quasi-)bound states of the quantum dot carriers. The extendedmodel allows to describe the bias-dependency of the emissionspectrum due to the quantum confined Stark effect

  • A. Pimenov, A.G. Vladimirov, S. Amiranashvili, Analysis of temporal dissipative solitons in a delayed model of a ring semiconductor laser, in: Extended Abstracts Spring 2018, A. Korobeinikov, M. Caubergh, T. Lázaro, J. Sardanyés, eds., 11 of Trends in Mathematics, Birkhäuser, Cham, 2019, pp. 7--12, DOI 10.1007/978-3-030-25261-8_2 .
    Abstract
    Temporal dissipative solitons are short pulses observed in periodic time traces of the electric field envelope in active and passive optical cavities. They sit on a stable background, so that their trajectory comes close to a stable steady state solution between the pulses. A common approach to predict and study these solitons theoretically is based on the use of Ginzburg?Landau-type partial differential equations, which, however, cannot adequately describe the dynamics of many realistic laser systems. Here, for the first time, we demonstrate the formation of temporal dissipative soliton solutions in a time-delay model of a ring semiconductor cavity with coherent optical injection, operating in anomalous dispersion regime, and perform bifurcation analysis of these solutions.

  • S. Slepneva, U. Gowda, A. Pimenov, A.G. Vladimirov, E. Viktorov, G. Huyet, Complex dynamics of long cavity lasers, in: 2019 21st International Conference on Transparent Optical Networks (ICTON), Angers, France, M. Jaworski, M. Marciniak, eds., IEEE, Piscataway, 2019, pp. 1--4, DOI 10.1109/ICTON.2019.8839990 .
    Abstract
    In this paper, we will discuss the properties of long cavity frequency sweeping lasers and demonstrate various scenarios of coherence deterioration in such lasers. The long cavity lasers are known to demonstrate rich variety of dynamical regimes including formation of localised structures and transition to turbulence. The interest to frequency sweeping long cavity lasers has also recently increased due to their application for imaging and sensing. For these applications, the stability of the laser is an important parameter as it directly influences its coherence and therefore, for example, the quality of the obtained images. We investigated static, quasi static and synchronisation regimes of such lasers and analysed possible instabilities in such system. Experimentally, we considered different laser configurations which has allowed us to study the influence of the cavity length, frequency sweeping speed and the detuning. Numerically, we used a model based on a system of delayed differential equations. The numerical simulation of our model showed excellent agreement with the experimental data. In particularly, we studied the formation of dark pulses, both periodic and non-periodic, and showed that they are closely connected to Nozaki-Bekki holes previously predicted in the complex Ginzburg-Landau equation.

  • N. Akhmediev, A. Ankiewicz, S. Amiranashvili, U. Bandelow, Generalized integrable evolution equations with an infinite number of free parameters, in: Workshop on Nonlinear Water Waves, S. Murashige, ed., 2109 of RIMS Kôkyûroku Bessatsu, RIMS, Kyoto, 2019, pp. 33--46.
    Abstract
    Evolution equations such as the nonliear 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.

  • U. Gowda, S. Slepneva, A. Pimenov, A.G. Vladimirov, E. Viktorov, G. Huyet, Stable and unstable Nozaki--Bekki holes in a long laser, in: Proc. SPIE 10912, B. Witzigmann, M. Osiński, Y. Arakawa, eds., Physics and Simulation of Optoelectronic Devices XXVII, SPIE Digital Library, Bellingham, 2019, pp. 109120M/1--109120M/6, DOI 10.1117/12.2510300 .
    Abstract
    Long cavity fibre-based wavelength sweeping lasers are promising devices with a wide range of potential applications ranging from communications to life sciences. For example, Fourier Domain Mode-Locked (FDML) lasers, which are commonly used for Optical Coherence Tomography (OCT) imaging applications are long cavity lasers incorporating an intra-cavity resonator driven in resonance with the cavity round trip time. The coherence properties of such swept sources are of major importance as they define the image quality. The purpose of this work is to analyze the mechanism that deteriorates the coherence of long lasers. In our experiment, the laser included a 100nm wide semiconductor optical amplifier at 1310nm and a fibre cavity that could vary from 20m to 20km. the laser emission wavelength was controlled using a fibre based intra-cavity filter with a bandwidth of 10GHz. Near the lasing threshold and/or for fast carrier decay rate, we observed the appearance of periodic power dropouts with stable Nozaki-Bekki holes (NBH) that circulate in the laser cavity. As a function of the injection current, the laser could operate in various regimes including bi-stability between NBH and stable (cw) operation, unstable NBH or chaotic operation. Such behavior indicates that the interplay between the injection current and carrier decay rate can lead to highly coherent emission of a long cavity laser.

  • J.-P. Köster, M. Radziunas, A. Zeghuzi, H. Wenzel, A. Knigge, Traveling wave model based simulation of tunable multi-wavelength diode laser systems, in: Proceedings of the 19th International Conference on Numerical Simulation of Optoelectronic Devices -- NUSOD 2019, J. Piprek, K. Hinzer, eds., IEEE Conference Publications Management Group, Piscataway, 2019, pp. 75--76.
    Abstract
    We show simulation results of a compact, inte-grated and tunable multi-wavelength diode laser emitting around785 nm. The presented design was optimized using passivewaveguide simulations and then further analyzed by performingactive laser simulations. The latter enables deducing criticaldesign parameters not accessible via an all-passive simulation.

  • U. Bandelow, S. Amiranashvili, S. Pickartz, Control of solitons in the regime of event horizons in nonlinear dispersive optical media, in: Proceedings of the 19th International Conference on Numerical Simulation of Optoelectronic Devices -- NUSOD 2019, J. Piprek, K. Hinzer, eds., IEEE Conference Publications Management Group, Piscataway, 2019, pp. 141--142.
    Abstract
    We describe the propagation of nonlinear pulses indispersive optical media on base of our generalized approach [1].It is known, that intense pulses, such as solitons, can mimic eventhorizons for smaller optical waves. We prove that such strongpulses can be dramatically influenced in the course of nonlinearinteraction with the proper dispersive waves. Moreover, it will bedemonstrated, both numerically and more efficiently by a newanalytic theory [2], that small optical waves can be used to controlsuch solitons [3], [4]. In particular, the typical pulse degradationcaused by Raman-scattering can be completely compensated bythese means [4], which is supported by recent experiments [5].

Preprints, Reports, Technical Reports

  • S. Amiranashvili, M. Radziunas, U. Bandelow, K. Busch, R. Čiegis, Additive splitting methods for parallel solution of evolution problems, Preprint no. 2767, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2767 .
    Abstract, PDF (312 kByte)
    We 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.

  • J.-P. Köster, A. Putz, H. Wenzel, H.-J. Wünsche, M. Radziunas, H. Stephan, M. Wilkens, A. Zeghuzi, A. Knigge, Mode competition in broad-ridge-waveguide lasers, Preprint no. 2764, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2764 .
    Abstract, PDF (1616 kByte)
    The lateral brightness achievable with high-power GaAs-based laser diodes having long and broad waveguides is commonly regarded to be limited by the onset of higher-order lateral modes. For the study of the lateral-mode competition two complementary simulation tools are applied, representing different classes of approximations. The first tool bases on a completely incoherent superposition of mode intensities and disregards longitudinal effects like spatial hole burning, whereas the second tool relies on a simplified carrier transport and current flow. Both tools yield agreeing power-current characteristics that fit the data measured for 5 to 23 µm wide ridges. Also, a similarly good qualitative conformance of the near and far fields is found. However, the threshold of individual modes, the partition of power between them at a given current, and details of the near and far fields show differences. These differences are the consequence of a high sensitivity of the mode competition to details of the models and of the device structure. Nevertheless, it can be concluded concordantly that the brightness rises with increasing ridge width irrespective of the onset of more and more lateral modes. The lateral brightness 2W · mm¯¹ 1mrad¯¹ at 10MW · cm¯²2 power density on the front facet of the investigated laser with widest ridge (23 µm) is comparable with best values known from much wider broad-area lasers. In addition, we show that one of the simulation tools is able to predict beam steering and coherent beam

  • M. Kantner, Th. Koprucki, Beyond just "flattening the curve": Optimal control of epidemics with purely non-pharmaceutical interventions, Preprint no. 2748, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2748 .
    Abstract, PDF (3116 kByte)
    When effective medical treatment and vaccination are not available, non-pharmaceutical interventions such as social distancing, home quarantine and far-reaching shutdown of public life are the only available strategies to prevent the spread of epidemics. Based on an extended SEIR (susceptible-exposed-infectious-recovered) model and continuous-time optimal control theory, we compute the optimal non-pharmaceutical intervention strategy for the case that a vaccine is never found and complete containment (eradication of the epidemic) is impossible. In this case, the optimal control must meet competing requirements: First, the minimization of disease-related deaths, and, second, the establishment of a sufficient degree of natural immunity at the end of the measures, in order to exclude a second wave. Moreover, the socio-economic costs of the intervention shall be kept at a minimum. The numerically computed optimal control strategy is a single-intervention scenario that goes beyond heuristically motivated interventions and simple "flattening of the curve". Careful analysis of the computed control strategy reveals, however, that the obtained solution is in fact a tightrope walk close to the stability boundary of the system, where socio-economic costs and the risk of a new outbreak must be constantly balanced against one another. The model system is calibrated to reproduce the initial exponential growth phase of the COVID-19 pandemic in Germany.

  • A. Boni, H.-J. Wünsche, H. Wenzel, P. Crump, Impact of the capture time on the series resistance of quantum-well diode lasers, Preprint no. 2735, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2735 .
    Abstract, PDF (4164 kByte)
    Electrons and holes injected into a semiconductor heterostructure containing quantum wellsare captured with a finite time. We show theoretically that this very fact can cause a considerableexcess contribution to the series resistivity and this is one of the main limiting factors to higherefficiency for GaAs based high-power lasers. The theory combines a standard microscopic-basedmodel for the capture-escape processes in the quantum well with a drift-diffusion description ofcurrent flow outside the quantum well. Simulations of five GaAs-based devices differing in theirAl-content reveal the root-cause of the unexpected and until now unexplained increase of theseries resistance with decreasing heat sink temperature measured recently. The finite capturetime results in resistances in excess of the bulk layer resistances (decreasing with increasingtemperature) from 1 mΩ up to 30 mΩ in good agreement with experiment.

  • U. Gowda, A. Roche, A. Pimenov, A.G. Vladimirov, S. Slepneva, E.A. Viktorov, G. Huyet, Turbulent coherent structures in a long cavity semiconductor laser near the lasing threshold, Preprint no. 2724, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2724 .
    Abstract, PDF (2735 kByte)
    We report on the formation of novel turbulent coherent structures in a long cavity semiconductor laser near the lasing threshold. Experimentally, the laser emits a series of power dropouts within a roundtrip and the number of dropouts per series depends on a set of parameters including the bias current. At fixed parameters, the drops remain dynamically stable, repeating over many roundtrips. By reconstructing the laser electric field in the case where the laser emits one dropout per round trip and simulating its dynamics using a time-delayed model, we discuss the reasons for long-term sustainability of these solutions. We suggest that the observed dropouts are closely related to the coherent structures of the cubic complex Ginzburg-Landau equation.

  • A.V. Kovalev, P.S. Dmitriev, A.G. Vladimirov, A. Pimenov, G. Huyet, E.A. Viktorov, Bifurcation structure of a swept source laser, Preprint no. 2681, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2681 .
    Abstract, PDF (602 kByte)
    We numerically analyze a delay differential equation model of a short-cavity semiconductor laser with an intracavity frequency swept filter and reveal a complex bifurcation structure responsible for the asymmetry of the output characteristics of this laser. We show that depending on the direction of the frequency sweep of a narrowband filter, there exist two bursting cycles determined by different parts of a continuous-wave solutions branch.

  • K.R. Schneider, A. Grin, Global bifurcation analysis of limit cycles for a generalized van der Pol system, Preprint no. 2639, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2639 .
    Abstract, PDF (189 kByte)
    We present a new approach for the global bifurcation analysis of limit cycles for a generalized van der Pol system. It is based on the existence of a Dulac-Cherkas function and on applying two topologically equivalent systems: one of them is a rotated vector field, the other one is a singularly perturbed system.

  • K.R. Schneider, A. Grin, Lower and upper bounds for the number of limit cycles on a cylinder, Preprint no. 2638, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2638 .
    Abstract, PDF (295 kByte)
    We consider autonomous systems with cylindrical phase space. Lower and upper bounds for the number of limit cycles surrounding the cylinder can be obtained by means of an appropriate Dulac-Cherkas function. We present different possibilities to improve these bounds including the case that the exact number of limit cycles can be determined. These approaches are based on the use of several Dulac-Cherkas functions or on applying some factorized Dulac function.

  • S. Pickartz, The role of the self-steepening effect in soliton compression due to cross-phase modulation by dispersive waves, Preprint no. 2585, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2585 .
    Abstract, PDF (33 MByte)
    We consider the compression and amplification of an ultrashort soliton pulse through the interaction with a weaker velocity-matched dispersive wave, in the so-called optical event horizon regime. We demonstrate that in this interaction scheme the self-steepening effect plays the key role in producing a strong soliton compression. While the interaction between the two pulses is mediated through cross phase modulation, the self-steepening effect produces an energy exchange, which enhances soliton compression. We provide numerical results and an analytical expression for energy transfer and compression rate.

  • A. Pimenov, S. Amiranashvili, A.G. Vladimirov, Temporal cavity solitons in a delayed model of a dispersive cavity ring laser, Preprint no. 2581, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2581 .
    Abstract, PDF (1614 kByte)
    Nonlinear localised structures appear as solitary states in systems with multistability and hysteresis. In particular, localised structures of light known as temporal cavity solitons were observed recently experimentally in driven Kerr-cavities operating in the anomalous dispersion regime when one of the two bistable spatially homogeneous steady states exhibits a modulational instability. We use a distributed delay system to study theoretically the formation of temporal cavity solitons in an optically injected ring semiconductor-based fiber laser, and propose an approach to derive reduced delay-differential equation models taking into account the dispersion of the intracavity fiber delay line. Using these equations we perform the stability and bifurcation analysis of injection-locked CW states and temporal cavity solitons.

Talks, Poster

  • U. Bandelow, Dynamics of high-power diode lasers, SPIE Photonics Europe (Online Only), April 1, 2020.

  • M. Kantner, Non-isothermal Scharfetter--Gummel scheme for electro-thermal transport simulation in degenerate semiconductors, Finite Volumes for Complex Applications IX (Online Event), June 15 - 19, 2020, University of Bergen, Bergen, Norway, June 16, 2020, DOI 10.1007/978-3-030-43651-3_14 .

  • M. Radziunas, Efficient modeling and simulation of dynamics in high-power broad-area semiconductor lasers, final EffiLas/HoTLas project meeting, Jenoptik Berlin, March 4, 2020.

  • M. Radziunas, Simulation of cascaded polarization-coupled systems of broad-area semiconductor lasers, 20th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2020), September 14 - 25, 2020, Politecnico di Torino, Italy.

  • M. Wolfrum, Dynamics of a stochastic excitable system with slowly adapting feedback, Workshop on Control of Self-Organizing Nonlinear Systems 2020, September 2 - 3, 2020, TU Berlin, September 3, 2020.

  • M. Wolfrum, Temporal dissipative solitons in systems with time delay, Séminaire Orléans, Institut Denis Poisson, Orléans, France, January 23, 2020.

  • S. Amiranashvili, Controlling light by light, Waves Côte d'Azur, June 4 - 7, 2019, Université Côte d'Azur, Nice, France, June 4, 2019.

  • S. Amiranashvili, Controlling light by light, Seminar for Theoretical Physics, Technische Universität Wien, Austria, January 23, 2019.

  • C. Brée, V. Raab, D. Gailevičius, V. Purlys, J. Montiel, G.G. Werner, K. Staliunas, A. Rathsfeld, U. Bandelow, M. Radziunas, Genetically optimized photonic crystal for spatial filtering of reinjection into broad-area diode lasers, CLEO/Europe-EQEC 2019, Munich, June 23 - 27, 2019.

  • C. Brée, V. Raab, J. Montiel, G.G. Werner, K. Staliunas, U. Bandelow, M. Radziunas, Lyot spectral filter for polarization beam combining of high-power, broad-area diode lasers: Modeling, simulations, and experiments, CLEO/Europe-EQEC 2019, Munich, June 23 - 27, 2019.

  • S. Eydam, A. Gerdes, Extensive chaos, cluster and chimera states in globally-coupled Stuart--Landau systems, SFB 910: Workshop on ''Control of Self-Organizing Nonlinear Systems'', Lutherstadt Wittenberg, August 20 - 22, 2019.

  • S. Eydam, Mode-locked solutions in systems of globally-coupled phase oscillators, XXXIX. Dynamics Days Europe, September 2 - 6, 2019, University of Rostock, September 6, 2019.

  • S. Eydam, Mode-locked solutions in systems of globally-coupled phase oscillators, WIAS Workshop ,,Optical Solitons and Frequency Comb Generation'', September 18 - 20, 2019, WIAS Berlin, September 18, 2019.

  • M. Kantner, A generalized Scharfetter--Gummel scheme for degenerate and non-isothermal semiconductors, 19th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD), July 8 - 12, 2019, University of Ottawa, Canada, July 8, 2019.

  • M. Kantner, Device-scale simulation of quantum light emitting diodes, International Symposium ,,Semiconductor Nanophotonics'', November 4 - 5, 2019, Technische Universität Berlin, November 4, 2019.

  • M. Kantner, Hybrid modeling of quantum light emitting diodes: Self-consistent coupling of drift-diffusion, Schrödinger--Poisson, and quantum master equations, SPIE Photonics West, February 5 - 7, 2019, San Francisco, USA, February 6, 2019, DOI 10.1117/12.2515209 .

  • M. Kantner, Simulation of quantum dot based single-photon sources using the Schrödinger--Poisson-Drift-Diffusion-Lindblad system, International Conference on Simulation of Semiconductor Processes and Devices (SISPAD 2019), September 4 - 6, 2019, Università degli Studi di Udine, Italy, September 6, 2019.

  • M. Kantner, Simulation of quantum light sources using the self-consistently coupled Schrödinger--Poisson-Drift-Diffusion-Lindblad system, 19th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD), July 8 - 12, 2019, University of Ottawa, Canada, July 8, 2019.

  • A. Pimenov, Temporal solitons in a delayed model of a semiconductor laser, Waves Côte d'Azur, Nice, France, June 4 - 7, 2019.

  • U. Bandelow, Control of solitons in the regime of event horizons in nonlinear dispersive optical media, 19th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD), July 8 - 12, 2019, University of Ottawa, Canada, July 11, 2019.

  • U. Bandelow, Hybrid modeling and simulation of electrically driven quantum light sources, 12th Annual Meeting Photonic Devices, Zuse-Institut Berlin, February 15, 2019.

  • U. Bandelow, Modeling and simulation of electrically driven quantum dot based single-photon sources, Seminar NATEC II, Technical University of Denmark, Kgs. Lyngby, Denmark, June 7, 2019.

  • U. Bandelow, Self-consistent thermal-opto-electronic model for the dynamics in high-power semiconductor lasers, European Semiconductor Laser Workshop (ESLW), September 27 - 28, 2019, University College Cork, Ireland, September 28, 2019.

  • U. Bandelow, Ultrashort solitons and their interaction with dispersive waves in the regime of event horizons in nonlinear optical media, 2nd International Conference on Photonics Research, November 4 - 9, 2019, Kocaeli University, Antalya, Turkey, November 8, 2019.

  • M. Radziunas, Efficient modeling and simulation of dynamics in high-power semiconductor lasers, 24th International Conference on Mathematical Modelling and Analysis (MMA2019), May 28 - 31, 2019, Tallinn University of Technology, Estonia, May 31, 2019.

  • M. Radziunas, Modeling of thermal effects in BALs, HoTLas project meeting, WIAS Berlin, February 20, 2019.

  • M. Radziunas, Modeling parameter dependence on temperature in high-power broad-area semiconductor lasers, Hotlas/Effilas project meeting, Ferdinand-Braun-Institut, Berlin, September 4, 2019.

  • A.G. Vladimirov, Nonlinear wave phenomena in delay differential models of multimode lasers, Waves Côte d'Azur 2019, June 4 - 7, 2019, Faculté des Sciences de l'Université de Nice, France, June 6, 2019.

  • M. Wolfrum, Patterns in discrete media, Fundamentals and Methods of Design and Control of Complex Systems -- Introductory Lectures 2019/20 of CRC 910, Technische Universität Berlin, December 2, 2019.

  • M. Wolfrum, Phase-sensitive excitability of a limit cycle, SFB 910: Workshop on ''Control of Self-Organizing Nonlinear Systems'', August 20 - 22, 2019, SFB 910, Lutherstadt Wittenberg, August 21, 2019.

  • M. Wolfrum, Phase-sensitive excitability of a limit cycle, XXXIX Dynamics Days Europe, September 2 - 6, 2019, University of Rostock, September 3, 2019.

  • M. Wolfrum, Temporal dissipative solitons in a DDE model of a ring laser with optical injection, Equadiff 2019, July 8 - 12, 2019, Leiden University, Netherlands, July 9, 2019.

  • M. Wolfrum, Temporal dissipative solitons in systems with time delay, 11th Colloquium on the Qualitative Theory of Differential Equations, University of Szeged, Bolyai Institute, Hungary, June 20, 2019.

  • M. Wolfrum, The relation of Chimeras, bump states, and Turing patterns in arrays of coupled oscillators, School and Workshop on Patterns of Synchrony: Chimera States and Beyond, May 6 - 17, 2019, International Centre for Theoretical Physics, Trieste, Italy, May 16, 2019.

Research Groups