Laser Dynamics

Publications

Articles in Refereed Journals

• D. Dolinina, G. Huyet, D. Turaev, A.G. Vladimirov, Desynchronization of temporal solitons in Kerr cavities with pulsed injection, Optics Letters, 49 (2024), pp. 4050--4053, DOI 10.1364/OL.529083 .
  Abstract
  A numerical and analytical study was conducted to investigate the bifurcation mechanisms that cause desynchronization between the soliton repetition frequency and the frequency of external pulsed injection in a Kerr cavity described by the Lugiato--Lefever equation. The results suggest that desynchronization typically occurs through an Andronov--Hopf bifurcation. Additionally, a sim- ple and intuitive criterion for this bifurcation to occur is proposed.

• D.A. Dolinina, A. Vladimirov, Synchronization between Kerr cavity solitons and broad laser pulse injection, Photonics, 11 (2024), pp. 1050/1--1050/10, DOI 10.3390/photonics11111050 .
  Abstract
  The synchronization of a soliton frequency comb in a Kerr cavity with pulsed laser injection is studied numerically. A neutral delay differential equation is used to model the light dynamics in the cavity. This model allows for the investigation of both cases where the pulse repetition period is close to the cavity round-trip time and where the repetition period of the injection pulses is close to a rational fraction M/N of the round-trip time. It is demonstrated that solitons can exist in this latter case, provided that the injection pulses are of a higher amplitude, which is directly proportional to the number M. Furthermore, it is shown that the synchronization range of the solitons is also proportional to the number M . The solitons excited by pulses with a period slightly different from the M : N -resonance can be destabilized by the Andronov--Hopf bifurcation, which occurs when the injection level at the soliton position decreases to M times the injection amplitude corresponding to the saddle-node bifurcation in a model equation with uniform injection.

• E. Kuhn, Simulation of the mode dynamics in broad-ridge laser diodes, IEEE Photonics Journal, 16 (2024), pp. 0601008/1--0601008/8, DOI 10.1109/JPHOT.2024.3374448 .
  Abstract
  In this publication a method to simulate the mode dynamics in broad-ridge laser diode is presented. These devices exhibit rich lateral mode dynamics in addition to longitudinal mode dynamics observed in narrow-ridge laser diodes. The mode dynamics are strongly influenced by higher order effects, which are described by effective interaction terms and can derived from the band structure and the carrier scattering in the quantum well. The spatial dependency of pump current densities plays a crucial role in lateral mode dynamics, and thus, a Drift-Diffusion model is employed to calculate the current densities with an additional capturing term.

• L. Mertenskötter, M. Kantner, Frequency noise characterization of narrow-linewidth lasers: A Bayesian approach, IEEE Photonics Journal, 16 (2024), pp. 0601407/1--0601407/7, DOI 10.1109/JPHOT.2024.3385184 .
  Abstract
  We describe a Bayesian estimation approach to infer on the frequency noise characteristics of narrow-linewidth semiconductor lasers from delayed self-heterodyne beat note measurements. Our technique is grounded in a statistical model of the measurement process that accounts for both the impact of the interferometer and the detector noise. The approach yields accurate results, even in scenarios where the intrinsic linewidth plateau is obscured by detector noise. The analysis is carried out using a Markov-chain Monte Carlo method in the frequency domain and exploits prior knowledge about the statistical distribution of the data. The method is validated using simulated time series data from a stochastic laser rate equation model incorporating 1/f -type non-Markovian noise.

• K. Panajotov, A.G. Vladimirov, M. Tlidi, Polarized frequency combs in a mode-locked VECSEL, IEEE Journal of Selected Topics in Quantum Electronics, 30 (2024), pp. 1100200/1--1100200/10, DOI 10.1109/JSTQE.2024.3470227 .
  Abstract
  In this paper, we present a detailed and rigorous derivation of the delay differential equations of the spin-flip model for vertical external cavity lasers with a semiconductor saturable absorption mirror. This model describe mode-locked semiconductor lasers in the ring-resonator geometry with unidirectional lasing. This contribution completes a previous communication [Vladimirov et al. Opt. Lett., 45, 252 (2020)], and we further complete the analytical derivation by taking into account phase and amplitude anisotropies and the resulting different delay times for orthogonal linear polarizations. We show evidence of the coexistence of two linearly polarized frequency combs generation with slightly different repetition rates due to the birefringence-induced time-of-flight difference.

• D. Röhlig, E. Kuhn, F. Teichert, A. Tränhardt, Th. Blaudeck, Function phononic crystals, Europhysics Letters, 145 (2024), pp. 26001/p1--26001/p6, DOI 10.1209/0295-5075/ad1de9 .
  Abstract
  We propose a novel type of phononic crystal for which the materials parameters are continuous functions of space coordinates without discontinuities corresponding to a seamless fusion of the constituent materials within the crystal lattice. With the help of an adaptation of this fundamental approach, we extend the well-established concept of phononic crystals, allowing an investigation of the transition from conventional phononic crystals with a regulated step-like parameter function to the realm of so-called function phononic crystals. Our study is based on a first-principle theory assisted by high-performance computer simulations and focuses on an understanding of the effects of a deviation from the typical parameter step function on the phononic density of states (DOS). Our exploration of the DOS reveals a characteristic rapid convergence: even a slight deviation from an ideal step function has the potential to induce radical changes in the band structure leading to the emergence of desirable features, especially multiple complete phononic band gaps.

• B. King, H. Wenzel, E. Kuhn, M. Radziunas, P. Crump, Design of very-large area photonic crystal surface emitting lasers with an all-semiconductor photonic crystal, Optics Express, 32 (2024), pp. 44945--44957, DOI 10.1364/OE.537452 .
  Abstract
  We report on the design of a photonic crystal surface emitting laser (PCSEL) with an all-semiconductor (InGaP/GaAs) photonic crystal suitable for very-large-area emission and high-power operation. Using coupled-wave theory for PCSELs we model infinite- and finite-size cavity PCSELs and show that a photonic crystal unit cell with square lattice periodicity and a rotated and stretched triangular feature is suitable for the realization of PCSELs with very large areas (1 mm< L < 3 mm for a square cavity of size L X L) while maintaining high mode discrimination between the fundamental laser mode and higher order cavity modes as well as high external efficiency. This was achieved by exploiting a single-lattice photonic crystal unit cell design that minimizes one-dimensional coupling in the photonic crystal, providing a promising alternative to double-lattice PCSELs.

• J. Yan, M. Majumdar, S. Ruffo, Y. Sato, Ch. Beck, R. Klages, Transition to anomalous dynamics in a simple random map, Chaos. An Interdisciplinary Journal of Nonlinear Science, 34 (2024), pp. 023128/1--023128/18, DOI 10.1063/5.0176310 .

• J. Yan, R. Moessner, H. Zhao, Prethermalization in aperiodically kicked many-body dynamics, Phys. Rev. B., 109 (2024), pp. 064305/1--064305/14, DOI 10.1103/PhysRevB.109.064305 .

• S. Amiranashvili, R. Čiegis, Stability of the higher-order splitting methods for the generalized nonlinear Schrödinger equation, Mathematical Modelling and Analysis, 29 (2024), pp. 560--574, DOI 10.3846/mma.2024.20905 .
  Abstract
  The numerical solution of the generalized nonlinear Schrödinger equation by explicit splitting methods can be disturbed by so-called spurious instabilities. They are manifested by the appearance of extraneous spectral peaks which change their position in the frequency domain and disappear with decreasing integration step. The spurious instabilities can coexist with the true physical ones, like modulation instability, in which case they are particularly difficult to detect. We consider an arbitrary multiplicative splitting method and discuss conditions necessary for the absence of spurious instabilities.

• M. Radziunas, E. Kuhn, H. Wenzel, B. King, P. Crump, Optical mode calculation in large-area photonic crystal surface-emitting lasers, IEEE Photonics Journal, 16 (2024), pp. 0601209/1--0601209/9, DOI 10.1109/JPHOT.2024.3380532 .
  Abstract
  We discuss algorithms and numerical challenges in constructing and resolving spectral prob- lems for photonic crystal surface-emitting lasers (PCSELs) with photonic crystal layers and large (up to several tens of mm2) emission areas. We show that finite difference schemes created using coarse numerical meshes provide sufficient accuracy for several major (lowest-threshold) modes of particular device designs. Our technique is applied to the example of large-area all- semiconductor PCSELs, showing how it can be used to optimize device performance.

• M. Radziunas, E. Kuhn, H. Wenzel, Solving a spectral problem for large-area photonic crystal surface-emitting lasers, Mathematical Modelling and Analysis, 29 (2024), pp. 575--599, DOI 10.3846/mma.2024.20496 .
  Abstract
  We present algorithms for constructing and resolving spectral problems for novel photonic crystal surface-emitting lasers with large emission areas, given by first-order PDEs with two spatial dimensions. These algorithms include methods to overcome computer-arithmetic-related challenges when dealing with huge and small numbers. We show that the finite difference schemes, constructed using relatively coarse numerical meshes enable accurate estimation of several major, optical modes, which are essential in practical applications.

• M. Radziunas, D.M. Kane, Traveling wave mode analysis of a coherence collapse regime semiconductor laser with optical feedback, Journal of the Optical Society of America. B, 41 (2024), pp. 2638--2647, DOI 10.1364/JOSAB.537153 .
  Abstract
  A highly developed traveling wave model for a semiconductor laser system supports sophisticated mode analysis of the coherence collapse regime in semiconductor lasers with delayed optical feedback. The concept of instantaneous optical modes is used. Time-frequency representations of chaotic trajectories are constructed and interpreted from synthesizing the calculated optical modes with their corresponding steady states, analysis of the mode driving and coupling sources, and field expansion into modal components. The results support detailed physical interpretation of the optical and radiofrequency spectra in the coherence collapse regime.

• M. Radziunas, V. Raab, Modeling and simulation of the cascaded polarization-coupled system of broad-area semiconductor lasers, IEEE Journal of Selected Topics in Quantum Electronics, 31 (2025), pp. 1501108/1--1501108/8, DOI 10.1109/JSTQE.2024.3442429 .
  Abstract
  We consider a brightness- and power-scalable rectified polarization beam combining scheme for high-power, broad-area edge-emitting semiconductor laser diodes. The coupling of 2m emitters is achieved through Lyot-filtered optical reinjection from a specially designed multi-stage external cavity, which forces individual diodes to lase on interleaved frequency combs with overlapping envelopes. Simulations of up to sixteen coupled emitters and analysis of the calculated beams suggest that, under ideal conditions, a beam coupling efficiency of approximately 90% can be expected. Reducing optical losses within the external cavity is crucial for improving this efficiency in experimental systems.

• A.G. Vladimirov, D. Dolinina, Neutral delay differential equation model of an optically injected Kerr cavity, Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 109 (2024), pp. 024206/1--024206/10, DOI 10.1103/PhysRevE.109.024206 .
  Abstract
  A neutral delay differential equation (NDDE) model of a Kerr cavity with external coherent injection is developed that can be considered as a generalization of the Ikeda map with second- and higher-order dispersion being taken into account. It is shown that this model has solutions in the form of dissipative solitons both in the low dissipation limit, where the model can be reduced to the Lugiato-Lefever equation (LLE), and beyond this limit, where the soliton is eventually destroyed by the Cherenkov radiation. Unlike the standard LLE, the NDDE model is able to describe the overlap of multiple resonances associated with different cavity modes.

Contributions to Collected Editions

• L. Mertenskötter, M. Kantner, Bayesian estimation of laser linewidth from delayed self-heterodyne measurements, Conference on Structural Nonlinear Dynamics and Diagnosis (CSNDD 2023), Marrakesh, Morocco, May 15 - 17, 2024, M. Belhaq, ed., 301 of Springer Proceedings in Physics, Springer, Singapur, 2024, pp. 269--279, DOI 10.1007/978-981-99-7958-5_21 .
  Abstract
  We present a statistical inference approach to estimate the frequency noise characteristics of ultra-narrow linewidth lasers from delayed self-heterodyne beat note measurements using Bayesian inference. Particular emphasis is on estimation of the intrinsic (Lorentzian) laser linewidth. The approach is based on a statistical model of the measurement process, taking into account the effects of the interferometer as well as the detector noise. Our method therefore yields accurate results even when the intrinsic linewidth plateau is obscured by detector noise. The regression is performed on periodogram data in the frequency domain using a Markov-chain Monte Carlo method. By using explicit knowledge about the statistical distribution of the observed data, the method yields good results already from a single time series and does not rely on averaging over many realizations, since the information in the available data is evaluated very thoroughly. The approach is demonstrated for simulated time series data from a stochastic laser rate equation model with 1 / f-type non-Markovian noise.

Preprints, Reports, Technical Reports

• A. Thayil, L. Ermoneit, M. Kantner, Theory of valley-splitting in Si/SiGe spin-qubits: Interplay of strain, resonances and random alloy disorder, Preprint no. 3158, WIAS, Berlin, 2024, DOI 10.20347/WIAS.PREPRINT.3158 .
  PDF (5807 kByte)

• M. Radziunas, H. Wenzel, B. King, P. Crump, E. Kuhn, Dynamical simulations of single-mode lasing in large-area all-semiconductor PCSELs, Preprint no. 3156, WIAS, Berlin, 2024, DOI 10.20347/WIAS.PREPRINT.3156 .
  Abstract, PDF (1864 kByte)
  We perform modeling and dynamic simulations of all-semiconductor photonic crystal surface- emitting lasers (PCSELs). A two-dimensional photonic crystal consists of a GaAs layer with InGaP features, repeating periodically in both lateral directions. In our dynamic simulations, we demon- strate for the first time that photonic crystals with large isosceles triangular features, having a base angle close to 71.5°, enable suppression of higher-order modes and achieve single-mode, high-quality lasing in large-area all-semiconductor PCSELs under moderate and even high pump levels.

• S. Amiranashvili, U. Bandelow, R. Čiegis, Additive splitting methods for the generalized nonlinear Schrödinger equation, Preprint no. 3144, WIAS, Berlin, 2024, DOI 10.20347/WIAS.PREPRINT.3144 .
  Abstract, PDF (23 MByte)
  Splitting methods provide an efficient approach to solving evolutionary wave equations, especially in situations where dispersive and nonlinear effects on wave propagation can be separated, as in the generalized nonlinear Schrödinger equation (GNLSE). However, such methods are explicit and can lead to numerical instabilities. We study these instabilities in the context of the GNLSE. Results previously obtained for multiplicative splitting methods are extended to additive splittings. An easy-to-use estimate of the largest possible integration step is derived and confirmed by numerical experiments.

• O. Burylko, M. Wolfrum, S. Yanchuk, Reversible saddle-node separatrix-loop bifurcation, Preprint no. 3133, WIAS, Berlin, 2024, DOI 10.20347/WIAS.PREPRINT.3133 .
  Abstract, PDF (1167 kByte)
  We describe the unfolding of a special variant of the codimension-two Saddle-Node Separatrix-Loop (SNSL) bifurcation that occurs in systems with time-reversibility. While the classical SNSL bifurcation can be characterized as the collision of a saddle-node equilibrium with a limit cycle, the reversible variant (R-SNSL) is characterised by as the collision of a saddle-node equilibrium with a boundary separating a dissipative and a conservative region in phase space. Moreover, we present several reversible versions of the SNIC (Saddle-Node on Invariant Circle) bifurcation and discuss the role of an additional reversible saddle equilibrium in all these scenarios. As an example, we provide a detailed bifurcation scenario for a reversible system of two coupled phase rotators (a system on a 2D torus) involving a R-SNSL bifurcation.

Talks, Poster

• D. Dolinina, Neutral delay differential equation model of an optically injected Kerr cavity, Working with continuation methods, WIAS Berlin, May 21, 2024.

• L. Ermoneit, B. Schmidt, A. Sala, N. Ciroth, L. Schreiber, T. Breiten, Th. Koprucki, M. Kantner, Simulation and optimal control of single-electron shuttling in a SiGe quantum bus, Applied Mathematics and Simulation for Semiconductor Devices (AMaSiS 2024), September 10 - 13, 2024.

• L. Ermoneit, B. Schmidt, J. Fuhrmann, A. Sala, N. Ciroth, L. Schreiber, T. Breiten, Th. Koprucki, M. Kantner, Optimal control of a Si/SiGe quantum bus for scalable quantum computing architectures, QUANTUM OPTIMAL CONTROL From Mathematical Foundations to Quantum Technologies, Berlin, May 21, 2024.

• L. Ermoneit, B. Schmidt, Th. Koprucki, T. Breiten, M. Kantner, Coherent transport of semiconductor spin-qubits: Modeling, simulation and optimal control, MATH+ Day 2024, Berlin, October 2, 2024.

• L. Ermoneit, Optimal control of a SiGe-Quantum bus for coherent electron shuttling in the presence of material defects, APS March Meeting, March 3 - 8, 2024, Minneapolis, USA, March 7, 2024.

• E. Kuhn, Time-dependent simulation of photonic crystal surface emitting lasers, European Semiconductor Laser Workshop 2024, September 20 - 21, 2024, University of Kassel.

• L. Mertenskötter, M. Kantner, Narrow-linewidth lasers, CLEO Conference, North Carolina, USA, May 5 - 10, 2024.

• M. O'Donovan, Multi-scale simulation of electronic and transport properties in (Al,Ga)N quantum well systems for UV-C emission, Applied Mathematics and Simulation for Semiconductor Devices (AMaSiS 2024), September 10 - 13, 2024, WIAS Berlin, September 11, 2024.

• M. O'Donovan, Simulation of the alloy fluctuations on luminescence and transport in AIGaN-based UV-LEDs, XXXV. Heimbach Workshop, September 23 - 27, 2024, Technische Universität Berlin, Mansfeld, September 26, 2024.

• M. O'Donovan, Theoretical investigations on different scales towards novel III-N materials and devices, Rundgespräch des SPP 2477 ``Nitrides4Future'', Magdeburg, September 24 - 25, 2024.

• A. Thayil, Optimization of valley splitting in Si/SiGe spin qubits, Applied Mathematics and Simulation for Semiconductor Devices (AMaSiS 2024), September 10 - 13, 2024, WIAS Berlin, September 12, 2024.

• N. Ciroth, A. Sala, L. Ermoneit, Th. Koprucki, M. Kantner, L. Schreiber, Numerical simulation of coherent spin-shuttling in silicon devices across dilute charge defects, Silicon Quantum Electronics Workshop 2024, Davos, Switzerland, September 4 - 6, 2024.

• D. Dolinina, Desynchronization of temporal solitons in Kerr cavities with pulsed injection, XLIV Dynamics Days Europe, Bremen, July 29 - August 2, 2024.

• A. Glitzky, Electrothermal models for organic semiconductor devices, Applied Mathematics and Simulation for Semiconductor Devices (AMaSiS 2024), Berlin, September 10 - 13, 2024.

• J. Yan, Dynamics in coupled kicked Rotor systems, Frontiers in Noisy Dynamical Systems, October 25 - 29, 2024, University of Tokyo, Japan, October 25, 2024.

• J. Yan, From deterministic to random dynamical systems, Women in Math - Introduction of the Iris Runge Program, WIAS Berlin, March 18, 2024.

• S. Amiranashvili, Role of modulation instability in numerical analysis, 6th International Conference on Application of Optics and Photonics, July 16 - 19, 2024, University of Aveiro, Portugal, July 16, 2024.

• S. Amiranashvili, Role of modulation instability in numerical analysis, XX Workshop on Instabilities and Nonequilibrium Structures, October 7 - 9, 2024, Institut de Physique de Nice, France, October 8, 2024.

• U. Bandelow, Applied mathematical research in nonlinear photonics at WIAS Berlin, Workshop on ``Nonlinear Photonics and Metasurfaces'', February 8, 2024, Australian National University, Canberra, Australia, February 8, 2024.

• U. Bandelow, Applied mathematical research in photonics at WIAS Berlin, Workshop on ``Optics'', February 5, 2024, Monash University, Melbourne, Australia, February 5, 2024.

• U. Bandelow, Hierarchies of integrable NLS-type equations and selected solutions, Workshop 2411b ``Nonlinear Optics: Physics, Analysis, and Numerics'', March 10 - 15, 2024, Mathematisches Forschungsinstitut Oberwolfach, March 11, 2024.

• U. Bandelow, Modeling and simulation of semiconductor devices at WIAS: From lasers to quantum technologies, Workshop on ``Quantum Technology'', February 6, 2024, University of Melbourne, Australia, February 6, 2024.

• U. Bandelow, Modeling of pulse propagation in nonlinear dispersive media at WIAS Berlin, Workshop on ``Integrability for Higher-Order Optical Pulse Propagation'' associated with the meeting of the Australian and New Zeeland Association of Mathematical Physics (ANZAMP), February 6 - 9, 2024, Katoomba, Australia, February 9, 2024.

• M. Kantner, L. Ermoneit, B. Schmidt, A. Sala, N. Ciroth, L. Schreiber, Th. Koprucki, Optimal control of conveyor-mode electron shuttling in a Si/SiGe quantum bus in the presence of charged defects, Silicon Quantum Electronics Workshop 2024, Davos, Switzerland, September 4 - 6, 2024.

• M. Kantner, Conveyor-mode electron shuttling in a Si/SiGe quantum bus: modeling, simulation, optimization, Focus Workshop on Theory of Spin-Qubit Shuttling, RWTH Aachen, September 18, 2024.

• M. Radziunas, Mode analysis in dynamical semiconductor laser models, 25th congress of the Australian Institute of Physics (AIP), Conference``Microelectronic Materials and Devices (COMMAD) 2024'', December 2 - 6, 2024, Melbourne, Australia, December 2, 2024.

• M. Radziunas, Modeling, simulation, and analysis of all-semiconductor photonic crystal surface-emitting lasers, International Symposium on Semiconductor Optoelectronics and Nanotechnology (ISSON), December 8 - 11, 2024, Canberra, Australia, December 10, 2024.

• A. Thayil, L. Ermoneit, M. Kantner, Towards optimization of valley splitting in Si/SiGe quantum wells, Silicon Quantum Electronics Workshop 2024, Davos, Switzerland, September 4 - 6, 2024.

• A.G. Vladimirov , Dynamics of neutral delay differential equation model of a dispersive Kerr cavity, Dynamics day in Shangai, China, September 8, 2024.

• A.G. Vladimirov , Modeling dispersive nonlinear optical cavities using delay differential equations, XX Workshop on Instabilities and Nonequilibrium Structures, October 7 - 9, 2024, Institut de Physique de Nice, France, October 8, 2024.

• A.G. Vladimirov , Short pulse interaction in delay differential equation models of mode-locked lasers, Dynamics days in Jinhua, September 10 - 15, 2024, China, September 11, 2024.

• M. Wolfrum, Localized structures in delay-differential equations with large delay, XLIV Dynamics Days Europe, Minisymposium ``Current topics in delay equations", July 29 - August 2, 2024, Constructor University, Bremen.

• M. Wolfrum, Synchronization patterns induced by short range attraction and long range repulsion, XLIV Dynamics Days Europe, Minisymposium ``Patterns of synchrony in complex networks", July 29 - August 2, 2024, Constructor University, Bremen.

External Preprints

• H. Wenzel, E. Kuhn, B. King, P. Crump, M. Radziunas, Theory of the linewidth-power product of photonic-crystal surface-emitting lasers, Preprint no. 11246, Cornell University, 2024, DOI 10.48550/arXiv.2402.11246 .
  Abstract
  A general theory for the intrinsic (Lorentzian) linewidth of photonic-crystal surface-emitting lasers (PCSELs) is presented. The effect of spontaneous emission is modeled by a classical Langevin force entering the equation for the slowly varying waves. The solution of the coupled-wave equations, describing the propagation of four basic waves within the plane of the photonic crystal, is expanded in terms of the solutions of the associated spectral problem, i.e. the laser modes. Expressions are given for photon number, rate of spontaneous emission into the laser mode, Petermann factor and effective Henry factor entering the general formula for the linewidth. The theoretical framework is applied to the calculation of the linewidth-power product of air-hole and all-semiconductor PCSELs. For output powers in the Watt range, intrinsic linewidths of a few tens of Hertz are predicted if stable single mode operation is ensured.