Publikationen

Monografien

  • U.W. Pohl, A. Strittmatter, A. Schliwa, M. Lehmann, T. Niermann, T. Heindel, S. Reitzenstein, M. Kantner, U. Bandelow, Th. Koprucki, H.-J. Wünsche, Chapter 3: 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, Heidelberg, 2020, pp. 53--90, (Chapter Published), DOI 10.1007/978-3-030-35656-9_3 .
    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, Chapter 8: 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, Heidelberg, 2020, pp. 285--359, (Chapter Published), DOI 10.1007/978-3-030-35656-9_8 .
    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. Höhne, Th. Koprucki, S. Burger, H.-J. Wünsche, F. Schmidt, A. Mielke, U. Bandelow, Chapter 7: 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, Heidelberg, 2020, pp. 241--283, (Chapter Published), DOI 10.1007/978-3-030-35656-9_7 .
    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.

  • M. Kantner, Electrically Driven Quantum Dot Based Single-Photon Sources: Modeling and Simulation, Springer Theses, Springer, Cham, 2020, XVII, 180 pages, (Monograph Published), DOI 10.1007/978-3-030-39543-8 .
    Abstract
    Semiconductor quantum optics is on the verge of moving from the lab to real world applications. When stepping from basic research to new technologies, device engineers will need new simulation tools for the design and optimization of quantum light sources, which combine classical device physics with cavity quantum electrodynamics. This thesis aims to provide a holistic description of single-photon emitting diodes by bridging the gap between microscopic and macroscopic modeling approaches. The central result is a novel hybrid quantum-classical model system that self-consistently couples semi-classical carrier transport theory with open quantum many-body systems. This allows for a comprehensive description of quantum light emitting diodes on multiple scales: It enables the calculation of the quantum optical figures of merit together with the simulation of the spatially resolved current flow in complex, multi-dimensional semiconductor device geometries out of one box. The hybrid system is shown to be consistent with fundamental laws of (non-)equilibrium thermodynamics and is demonstrated by numerical simulations of realistic devices.

Artikel in Referierten Journalen

  • H. Wenzel, M. Kantner, M. Radziunas, U. Bandelow, Semiconductor laser linewidth theory revisited, APPS. Applied Sciences, 11 (2021), pp. 1--29, DOI 10.3390/app11136004 .
    Abstract
    More and more applications require semiconductor lasers distinguished not only by large modulation bandwidths or high output powers, but also by small spectral linewidths. The theoretical understanding of the root causes limiting the linewidth is therefore of great practical relevance. In this paper, we derive a general expression for the calculation of the spectral linewidth step by step in a self-contained manner. We build on the linewidth theory developed in the 1980s and 1990s but look from a modern perspective, in the sense that we choose as our starting points the time-dependent coupled-wave equations for the forward and backward propagating fields and an expansion of the fields in terms of the stationary longitudinal modes of the open cavity. As a result, we obtain rather general expressions for the longitudinal excess factor of spontaneous emission (K-factor) and the effective Alpha-factor including the effects of nonlinear gain (gain compression) and refractive index (Kerr effect), gain dispersion and longitudinal spatial hole burning in multi-section cavity structures. The effect of linewidth narrowing due to feedback from an external cavity often described by the so-called chirp reduction factor is also automatically included. We propose a new analytical formula for the dependence of the spontaneous emission on the carrier density avoiding the use of the population inversion factor. The presented theoretical framework is applied to a numerical study of a two-section distributed Bragg reflector laser.

  • S. Amiranashvili, M. Radziunas, U. Bandelow, K. Busch, R. Čiegis, Additive splitting methods for parallel solutions of evolution problems, Journal of Computational Physics, 436 (2021), pp. 110320/1--110320/14, DOI 10.1016/j.jcp.2021.110320 .
    Abstract
    We demonstrate how a multiplicative splitting method of order Pcan be utilized 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 of a test problem, and numerical examples with special discussion of the parallelization properties and applications to nonlinear optics.

  • A. Pimenov, S. Amiranashvili, A. Vladimirov, Temporal cavity solitons in a delayed model of a dispersive cavity ring laser, Mathematical Modelling of Natural Phenomena, 15 (2020), pp. 47/1--47/18, DOI 10.1051/mmnp/2019054 .
    Abstract
    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 continuous wave states and temporal cavity solitons.

  • 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), pp. 083109/1--083109/11, 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. 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, Optics Letters, 45 (2020), pp. 4903--4906, DOI 10.1364/OL.397840 .
    Abstract
    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 roundtrip 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, Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 101 (2020), pp. 012212/1--012212/5, DOI 10.1103/PhysRevE.101.012212 .
    Abstract
    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 narrow-band filter, there exist two bursting cycles determined by different parts of a continuous-wave solutions branch.

  • O. Melchert, C. Brée, A. Tajalli, A. Pape, R. Arkhipov, S. Willms, I. Babushkin, D. Skryabin, G. Steinmeyer, U. Morgner, A. Demircan, All-optical supercontinuum switching, Nature Photonics, 3 (2020), pp. 146/1--146/8, DOI 10.1038/s42005-020-00414-1 .
    Abstract
    Efficient all-optical switching is a challenging task as photons are bosons and cannot immediately interact with each other. Consequently, one has to resort to nonlinear optical interactions, with the Kerr gate being the classical example. However, the latter requires strong pulses to switch weaker ones. Numerous approaches have been investigated to overcome the resulting lack of fan-out capability of all-optical switches, most of which relied on types of resonant enhancement of light-matter interaction. Here we experimentally demonstrate a novel approach that utilizes switching between different portions of soliton fission induced supercontinua, exploiting an optical event horizon. This concept enables a high switching efficiency and contrast in a dissipation free setting. Our approach enables fan-out, does not require critical biasing, and is at least partially cascadable. Controlling complex soliton dynamics paves the way towards building all-optical logic gates with advanced functionalities.

  • M. Tlidi, E. Berríos-Caro , D. Pinto-Ramo, A.G. Vladimirov, M.G. Clerc, Interaction between vegetation patches and gaps: A self-organized response to water scarcity, Physica D. Nonlinear Phenomena, 414 (2020), pp. 132708/1--132708/12, DOI 10.1016/j.physd.2020.132708 .
    Abstract
    The dynamics of ecological systems are often described by integrodifferential equations that incorporate nonlocal interactions associated with facilitative, competitive interactions between plants, and seed dispersion. In the weak-gradient limit, these models can be reduced to a simple partial-differential equation in the form of a nonvariational Swift?Hohenberg equation. In this contribution, we perform this reduction for any type of kernels provided that their Taylor series converge. Some parameters such as linear and nonlinear diffusion coefficients are affected by the spatial form of the kernel. In particular, Gaussian and exponential kernels are used to evaluate all coefficients of the reduced model. This weak gradient approximation is greatly useful for the investigation of periodic and localized vegetation patches, and gaps. Based on this simple model, we investigate the interaction between two-well separated patches and gaps. In the case of patches, the interaction is always repulsive. As a consequence, bounded states of patches are excluded. However, when two gaps are close to one another, they start to interact through their oscillatory tails. The interaction alternates between attractive and repulsive depending on the distance separating them. This allows for the stabilization of bounded gaps and clusters of them. The analytical formula of the interaction potential is derived for both patches and gaps interactions and checked by numerical investigation of the model equation.

  • A. Boni, H.-J. Wünsche, H. Wenzel, P. Crump, Impact of the capture time on the series resistance of quantum-well diode lasers, Semiconductor Science and Technology, 35 (2020), pp. 085032/1--085032/9, DOI 10.1088/1361-6641/ab9723 .
    Abstract
    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.

  • 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, Semiconductor Science and Technology, 36 (2020), pp. 015014/1--015014/12, DOI 10.1088/1361-6641/abc6e7 .
    Abstract
    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

  • 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), pp. 23/1--23/23, 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.

  • 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, 402 (2020), pp. 109091/1--109091/24, 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 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.G. Vladimirov, K. Panajotov, M. Tlidi, Orthogonally polarized frequency combs in a mode-locked VECSEL, Optics Letters, 45 (2020), pp. 252--255, DOI 10.1364/OL.45.000252 .
    Abstract
    We introduce a spin?flip model for a vertical-external-cavity surface-emitting laser (VECSEL) with a saturable absorber. We demonstrate the possibility, due to the spin?flip dynamics, to generate two orthogonally linearly polarized frequency combs in the mode-locked regime. The two combs are shifted in wavelength due to the birefringence in the VECSEL gain and/or saturable absorption mirror. We show that the polarization degree of freedom may also lead to several pulses being generated per roundtrip in the two orthogonal linear polarizations and to more complicated dynamics with both linear polarizations excited.

Beiträge zu Sammelwerken

  • A. Roche, U. Gowda, A. Pimenov, A.V. Kovalev, M. Marconi, M. Giudici, E.A. Viktorov, A.G. Vladimirov, G. Huyet, S. Slepneva, Turn on transient in a long cavity laser, in: Physics and Simulation of Optoelectronic Devices XXVII, B. Witzigmann, M. Osiński, Y. Arakawa, eds., 11274 of Proceedings of SPIE, SPIE Digital Library, 2020, pp. 112740L/1--112740L/6, DOI 10.1117/12.2545965 .
    Abstract
    In this paper we study, both experimentally and theoretically, the turn on transient dynamics observed in a long (20m) cavity laser. The laser consists of a ring cavity based on a single mode fiber with unidirectional propagation of light. The gain is provided by a semiconductor optical amplifier (SOA) centered around 1300nm and wavelength selection is provided by a tunable narrow transmission bandwidth Fabry-Perot filter. At high bias current and when the filter transmission sets the laser to operate in an anomalous dispersion regime, the laser exhibits only chaotic oscillations, while in a normal dispersion regime, the laser can exhibit stable operation. At a bias current close to the threshold the laser always exhibits multiple dropouts. In order to record the lasing build up dynamics, the bias current driven to the SOA is periodically switched from the off-state to a high current level. The lasing build up occurs at each roundtrip via a step-wise increase of the laser intensity. The laser intensity is widely oscillating during the first steps and approaches a stationary state after a large number of roundtrips. Recording of the phase evolution of the electric field during each step demonstrates the linewidth narrowing at each subsequent roundtrip. Theoretically, we describe the system by a set of delay differential equations and observe similar behavior. While typically a semiconductor laser exhibits relaxation oscillations before reaching the stable lasing regime, which is associated with class B lasers, our study shows that the long cavity laser demonstrates a different mechanism of lasing build up.

  • 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: High-Power Diode Laser Technology XVIII, M.S. Zediker, ed., 11262 of Proceedings of SPIE, 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.

  • U. Gowda, A. Roche, S. Slepneva, A. Pimenov, E.A. Viktorov, A.G. Vladimirov, G. Huyet, Stability of a long cavity laser, in: Real-time Measurements, Rogue Phenomena, and Single-Shot Applications V, D.R. Solli, G. Herink, S. Bielawski, eds., 11265 of Proceedings of SPIE, SPIE Digital Library, 2020, pp. 112650F/1--112650F/6, DOI 10.1117/12.2545916 .
    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 a rich variety of dynamical regimes including the formation of localised structures and transition to turbulence. The interest to frequency sweeping long cavity lasers has 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, the quality of the obtained images.1 Our laser consists of a fiber based ring cavity resonator including a semiconductor optical amplifier as a gain medium and a Fabry-Perot tunable filter. Experimentally, we considered different laser configurations which has allowed us to study the influence of the cavity length, frequency sweeping speed and the detuning. We considered the dynamical regimes of the laser operating at a static (fixed output frequency) and quasi static regimes. The study shows that the laser can be stable or unstable and demonstrate localised structures stable over multiple roundtrips. We also show the connection of the dynamics observed in the static, quasi-static and synchronisation regimes of long cavity lasers. Numerically, we used a model based on a system of delayed differential equations. The numerical simulation showed excellent agreement with the experimental data. We also show the formation of dark pulses, both periodic and nonperiodic, and showed that they are closely connected to Nozaki-Bekki holes previously predicted in the complex Ginzburg-Landau equation.

  • M. Kolarczik, F. Böhm, U. Woggon, N. Owschimikow, A. Pimenov, M. Wolfrum, A.G. 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. 91--133, 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.

  • J.--P. Köster, M. Radziunas, A. Zeghuzi, H. Wenzel, A. Knigge, Traveling wave model-based analysis of tapered broad-area lasers, in: Physics and Simulation of Optoelectronic Devices XXVIII, B. Witzigmann, M. Osiński, Y. Arakawa, eds., 11274 of Proceedings of SPIE, 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: Semiconductor Lasers and Laser Dynamics IX, M. Sciamanna, R. Michalzik, K. Panajotov, S. Höfling, eds., 11356 of Proceedings of SPIE, 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. 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 -- FVCA 9, Bergen, June 2020, R. Klöfkorn, E. Keilegavlen, F.A. Radu, J. Fuhrmann, eds., 323 of Springer Proceedings in Mathematics & Statistics, Springer International Publishing, Cham et al., 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. Radziunas, D.M. Kane, Semiconductor laser with delayed optical feedback -- What simulations tell us that we didn't know, in: 14th Pacific Rim Conference on Lasers and Electro-Optics (CLEO PR 2020), OSA Technical Digest, Optical Society of America, Washington, 2020, pp. C4C_4/1--C4C_4/2, DOI 10.1364/CLEOPR.2020.C4C_4 .
    Abstract
    Comprehensive numerical simulations of a semiconductor laser with optical feedback system showing the impact of key laser parameters on dynamical mapping are reported. These raise new opportunities for optimising such systems for their key applications.

  • M. Radziunas, J. Montiel-Ponsoda, G. Garre-Werner, V. Raab, Simulation of cascaded polarization-coupled systems of broad-area semiconductor lasers, in: Proceedings of the 20th International Conference on Numerical Simulation of Optoelectronic Devices -- NUSOD 2020, J. Piprek, K. Hinzer, eds., IEEE Conference Publications Management Group, Piscataway, 2020, pp. 97--98, DOI 10.1109/NUSOD49422.2020.9217764 .
    Abstract
    We present a brightness- and power-scalable polarization beam combining scheme for high-power, broad-area semiconductor lasers. 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. We demonstrate how repeatedly introduced new stages of the external cavity allow efficient coupling of 2 n emitters. We simulate the operation of two-four-eight-sixteen coupled emitters, analyze beam coupling efficiency, and discuss possible limiting factors of this coupling scheme.

Preprints, Reports, Technical Reports

  • A.G. Vladimirov, S. Suchkov, G. Huyet, S.K. Turitsyn, A delay differential equation NOLM--NALM mode-locked laser model, Preprint no. 2858, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2858 .
    Abstract, PDF (2904 kByte)
    Delay differential equation model of a NOLM-NALM mode-locked laser is developed that takes into account finite relaxation rate of the gain medium and asymmetric beam splitting at the entrance of the nonlinear mirror loop. Asymptotic linear stability analysis of the continuous wave solutions performed in the limit of large delay indicates that in a class-B laser flip instability leading to a period doubling cascade and development of square-wave patterns can be suppressed by a short wavelength modulational instability. Numerically it is shown that the model can demonstrate large windows of regular fundamental and harmonic mode-locked regimes with single and multiple pulses per cavity round trip time separated by domains of irregular pulsing.

  • A. Zeghuzi, J.-P. Koester, M. Radziunas, H. Christopher, H. Wenzel, A. Knigge, Spatially modulated broad-area lasers for narrow lateral far-field divergence, Preprint no. 2857, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2857 .
    Abstract, PDF (397 kByte)
    A novel laser design is presented that combines a longitudinal-lateral gain-loss modulation with an additional phase tailoring achieved by etching rectangular trenches. At 100 A pulsed operation, simulations predict a far-field profile with 0.3-degree full width at half maximum where a 0.4-degree-wide main lobe contains 40% of the emitted optical output power. While far-field measurements of these structured lasers emitting 10 ns long pulses with 35 W peak power confirm a substantial enhancement of radiation within the central one-degree angular range, the measured far-field intensity outside of the obtained central peak remains high.

  • A. Hajizadeh, A. Matysiak, M. Wolfrum, P.J.C. May, Auditory cortex modelled as a dynamical network of oscillators: Understanding event-related fields and their adaptation, Preprint no. 2854, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2854 .
    Abstract, PDF (857 kByte)
    Adaptation, the reduction of neuronal responses by repetitive stimulation, is a ubiquitous feature of auditory cortex (AC). It is not clear what causes adaptation, but short-term synaptic depression (STSD) is a potential candidate for the underlying mechanism. We examined this hypothesis via a computational model based on AC anatomy, which includes serially connected core, belt, and parabelt areas. The model replicates the event-related field (ERF) of the magnetoencephalogram as well as ERF adaptation. The model dynamics are described by excitatory and inhibitory state variables of cell populations, with the excitatory connections modulated by STSD. We analysed the system dynamics by linearizing the firing rates and solving the STSD equation using time-scale separation. This allows for characterization of AC dynamics as a superposition of damped harmonic oscillators, so-called normal modes. We show that repetition suppression of the N1m is due to a mixture of causes, with stimulus repetition modifying both the amplitudes and the frequencies of the normal modes. In this view, adaptation results from a complete reorganization of AC dynamics rather than a reduction of activity in discrete sources. Further, both the network structure and the balance between excitation and inhibition contribute significantly to the rate with which AC recovers from adaptation. This lifetime of adaptation is longer in the belt and parabelt than in the core area, despite the time constants of STSD being spatially constant. Finally, we critically evaluate the use of a single exponential function to describe recovery from adaptation.

  • V.V. Klinshov, S.Y. Kirillov, V.I. Nekorkin, M. Wolfrum, Noise-induced dynamical regimes in a system of globally coupled excitable, Preprint no. 2853, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2853 .
    Abstract, PDF (2811 kByte)
    We study the interplay of global attractive coupling and individual noise in a system of identical active rotators in the excitable regime. Performing a numerical bifurcation analysis of the nonlocal nonlinear Fokker-Planck equation for the thermodynamic limit, we identify a complex bifurcation scenario with regions of different dynamical regimes, including collective oscillations and coexistence of states with different levels of activity. In systems of finite size this leads to additional dynamical features, such as collective excitability of different types, noise-induced switching and bursting. Moreover, we show how characteristic quantities such as macroscopic and microscopic variability of inter spike intervals can depend in a non-monotonous way on the noise level.

  • A. Vladmirov, M. Tlidi, M. Taki, Dissipative soliton interaction in Kerr resonators with high-order dispersion, Preprint no. 2843, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2843 .
    Abstract, PDF (1126 kByte)
    We consider an optical resonator containing a photonic crystal fiber and driven coherently by an injected beam. This device is described by a generalized Lugiato--Lefever equation with fourth order dispersion We use an asymptotic approach to derive interaction equations governing the slow time evolution of the coordinates of two interacting dissipative solitons. We show that Cherenkov radiation induced by positive fourth-order dispersion leads to a strong increase of the interaction force between the solitons. As a consequence, large number of equidistant soliton bound states in the phase space of the interaction equations can be stabilized. We show that the presence of even small spectral filtering not only dampens the Cherenkov radiation at the soliton tails and reduces the interaction strength, but can also affect the bound state stability.

  • M. Nizette, A.G. Vladimirov, A generalized Haus master equation model for mode-locked class-B lasers, Preprint no. 2840, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2840 .
    Abstract, PDF (893 kByte)
    Using the multiscale technique we develop a generalized version of the class-B Haus modelocking model that accounts for both the slow gain response to the averaged value of the field intensity and the fast gain dynamics on the scale comparable to the pulse duration. We show that unlike the standard class-B Haus mode-locked model, our model is able to describe not only Q-switched instability of the fundamental mode-locked regime, but also the appearance of harmonic mode-locked regimes with the increase of the pump power.

  • S. Slepneva, A. Pimenov, Nonlinear dynamical properties of frequency swept fiber-based semiconductor lasers, Preprint no. 2839, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2839 .
    Abstract, PDF (3636 kByte)
    We investigate dynamics of semiconductor lasers with fiber-based unidirectional ring cavity that can be used as frequency swept sources. We identify key factors behind the reach dynamical behaviour of such lasers using state-of-the-art experimental and analytical methods. Experimentally, we study the laser in static, quasi-static and synchronisation regimes.We apply experimental methods such as optical heterodyne or electric field reconstruction in order to characterise these regimes or study the mechanisms of transition between them. Using a delay differential equation model, we demonstrate that the presence of chromatic dispersion can lead to destabilisation of the laser modes through modulational instability, which results in undesirable chaotic emission. We characterise the instability threshold both theoretically and experimentally, and demonstrate deterioration of the FDML regime near the threshold.

  • L. Mertenskötter, K. Busch, R. DE J. León-Montiel, Entangled two-photon absorption spectroscopy with varying pump wavelength, Preprint no. 2837, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2837 .
    Abstract, PDF (647 kByte)
    In virtual-state spectroscopy, information about the energy-level structure of an arbitrary sample is retrieved by Fourier transforming sets of measured two-photon absorption probabilities of entangled photon pairs where the degree of entanglement and the delay time between the photons have been varied. This works well for simple systems but quickly becomes rather difficult when many intermediate states are involved. We propose and discuss an extension of entangled two-photon absorption spectroscopy that solves this problem by means of repeated measurements at different pump wavelengths. Specifically, we demonstrate that our extension works well for a variety of realistic experimental setups.

  • S. Yanchuk, M. Wolfrum, T. Pereira, D. Turaev, Absolute stability and absolute hyperbolicity in systems with discrete time-delays, Preprint no. 2824, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2824 .
    Abstract, PDF (425 kByte)
    An equilibrium of a delay differential equation (DDE) is absolutely stable, if it is locally asymptotically stable for all delays. We present criteria for absolute stability of DDEs with discrete timedelays. In the case of a single delay, the absolute stability is shown to be equivalent to asymptotic stability for sufficiently large delays. Similarly, for multiple delays, the absolute stability is equivalent to asymptotic stability for hierarchically large delays. Additionally, we give necessary and sufficient conditions for a linear DDE to be hyperbolic for all delays. The latter conditions are crucial for determining whether a system can have stabilizing or destabilizing bifurcations by varying time delays.

  • 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.

  • 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.

  • 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.

Vorträge, Poster

  • M. Kantner, Mathematical modeling and optimal control of the COVID-19 pandemic (online talk), Mathematisches Kolloquium, Bergische Universität Wuppertal, April 27, 2021.

  • M. Kantner, Noise in semiconductor lasers (online talk), MATH+ Spotlight Seminar, MATH+, July 14, 2021.

  • W. Matthias, Temporal dissipative solitons in systems of delay-differential equations, SIAM Conference on Dynamical Systems (Online Event), Minisymposium 184 ``Traveling Pulses in Delay and Lattice Differential Equations'', May 27, 2021, Portland, Oregon, USA, May 27, 2021.

  • U. Bandelow, Applied mathematical research in photonics at WIAS Berlin, Workshop ''Dynamics in Lasers, Photonics and Quantum Light sources'', Macquarie University, Sidney, Australia, February 18, 2020.

  • U. Bandelow, Applied mathematical research in photonics at WIAS Berlin, Workshop ''Photonics and Optoelectronics'', University of New South Wales, Sydney, Australia, February 17, 2020.

  • U. Bandelow, Applied mathematical research in photonics at WIAS Berlin, Workshop ''Nanoscience, Nano-technology, Fibre optics'', University of Sydney, Australia, February 17, 2020.

  • U. Bandelow, Applied mathematical research in photonics at WIAS Berlin, Workshop ''Optical fiber technology, glass development, nonlinear fibers, biophotonics'', University of South Australia, Adelaide, Australia, February 12, 2020.

  • U. Bandelow, Applied mathematical research in photonics at WIAS Berlin, Workshop ``Biomedical engineering, light-matter interactions'', Australian National University, Canberra, Australia, February 14, 2020.

  • U. Bandelow, Dynamics of high-power diode lasers (online talk), SPIE Photonics Europe (Online Event), April 3 - 7, 2020, April 6, 2020.

  • U. Bandelow, Modeling of nonlinear dynamical effects in photonics, Colloquium of the School of Mathematics and Physics, University of West Australia, Perth, Australia, February 19, 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. Kantner, Non-isothermal Scharfetter--Gummel scheme for electro-thermal transport simulation in degenerate semiconductors (online talk), Finite Volumes for Complex Applications IX (Online Event), June 15 - 19, 2020, NORCE - Norwegian Research Centre, Bergen, Norway, June 16, 2020.

  • 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.