Publikationsliste des Fachgebietes Theoretische Physik 2

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Jaurigue, Lina; Robertson, Elizabeth; Wolters, Janik; Lüdge, Kathy
Photonic reservoir computing with non-linear memory cells: interplay between topology, delay and delayed input. - In: Emerging Topics in Artificial Intelligence (ETAI) 2022, (2022), S. 1220408-1-1220408-7

Photonic reservoir computing is an emerging topic due to the possibility to realize very fast devices with minimal training effort. We will discuss the reservoir computing performance of memory cells with a focus on the impact of delay lines and the interplay between coupling topology and performance for various benchmark tasks. We will further show that additional delayed input can be beneficial for reservoir computing setups in general, as it provides an easy tuning parameter, which can improve the performance of a reservoir on a range of tasks.



https://doi.org/10.1117/12.2633339
Meinecke, Stefan; Lüdge, Kathy
Optimizing the cavity-arm ratio of V-shaped semiconductor disk lasers. - In: Physical review applied, ISSN 2331-7019, Bd. 18 (2022), 6, S. 064070

Passively mode-locked semiconductor disk lasers have received tremendous attention from both science and industry. Their relatively inexpensive production combined with excellent pulse performance and great emission-wavelength flexibility make them suitable laser candidates for applications ranging from frequency-comb tomography to spectroscopy. However, due to the interaction of the active medium dynamics and the device geometry, emission instabilities occur at high pump powers and thereby limit their performance potential. Hence, understanding those instabilities becomes critical for an optimal laser design. Using a delay-differential equation model, we are able to detect, understand, and classify three distinct instabilities that limit the maximum achievable pump power for the fundamental mode-locking state and link them to characteristic positive-net-gain windows. We furthermore derive a simple analytic approximation in order to quantitatively describe the stability boundary. Our results enable us to predict the optimal laser-cavity configuration with respect to positive-net-gain instabilities and therefore may be of great relevance for the future development of passively mode-locking semiconductor disk lasers.



https://doi.org/10.1103/PhysRevApplied.18.064070
Köster, Felix; Yanchuk, Serhiy; Lüdge, Kathy
Master memory function for delay-based reservoir computers with single-variable dynamics. - In: IEEE transactions on neural networks and learning systems, ISSN 2162-237X, Bd. 0 (2022), 0, S. 1-14

We show that many delay-based reservoir computers considered in the literature can be characterized by a universal master memory function (MMF). Once computed for two independent parameters, this function provides linear memory capacity for any delay-based single-variable reservoir with small inputs. Moreover, we propose an analytical description of the MMF that enables its efficient and fast computation. Our approach can be applied not only to single-variable delay-based reservoirs governed by known dynamical rules, such as the Mackey-Glass or Stuart-Landau-like systems, but also to reservoirs whose dynamical model is not available.



https://doi.org/10.1109/TNNLS.2022.3220532
Hülser, Tobias; Köster, Felix; Lüdge, Kathy; Jaurigue, Lina
Deriving task specific performance from the information processing capacity of a reservoir computer. - In: Nanophotonics, ISSN 2192-8614, (2022), S. 1-11

In the reservoir computing literature, the information processing capacity is frequently used to characterize the computing capabilities of a reservoir. However, it remains unclear how the information processing capacity connects to the performance on specific tasks. We demonstrate on a set of standard benchmark tasks that the total information processing capacity correlates poorly with task specific performance. Further, we derive an expression for the normalized mean square error of a task as a weighted function of the individual information processing capacities. Mathematically, the derivation requires the task to have the same input distribution as used to calculate the information processing capacities. We test our method on a range of tasks that violate this requirement and find good qualitative agreement between the predicted and the actual errors as long as the task input sequences do not have long autocorrelation times. Our method offers deeper insight into the principles governing reservoir computing performance. It also increases the utility of the evaluation of information processing capacities, which are typically defined on i.i.d. input, even if specific tasks deliver inputs stemming from different distributions. Moreover, it offers the possibility of reducing the experimental cost of optimizing physical reservoirs, such as those implemented in photonic systems.



https://doi.org/10.1515/nanoph-2022-0415
Hülser, Tobias; Köster, Felix; Jaurigue, Lina; Lüdge, Kathy
Role of delay-times in delay-based photonic reservoir computing. - In: Optical materials express, ISSN 2159-3930, Bd. 12 (2022), 3, S. 1214-1231

Delay-based reservoir computing has gained a lot of attention due to the relative simplicity with which this concept can be implemented in hardware. However, unnecessary constraints are commonly placed on the relationship between the delay-time and the input clock-cycle, which can have a detrimental effect on the performance. We review the existing literature on this subject and introduce the concept of delay-based reservoir computing in a manner that demonstrates that no predefined relationship between the delay-time and the input clock-cycle is required for this computing concept to work. Choosing the delay-times independent of the input clock-cycle, one gains an important degree of freedom. Consequently, we discuss ways to improve the computing performance of a reservoir formed by delay-coupled oscillators and show the impact of delay-time tuning in such systems.



https://doi.org/10.1364/OME.451016
Jaurigue, Lina; Lüdge, Kathy
Connecting reservoir computing with statistical forecasting and deep neural networks. - In: Nature Communications, ISSN 2041-1723, Bd. 13 (2022), 227, S. 1-3

Among the existing machine learning frameworks, reservoir computing demonstrates fast and low-cost training, and its suitability for implementation in various physical systems. This Comment reports on how aspects of reservoir computing can be applied to classical forecasting methods to accelerate the learning process, and highlights a new approach that makes the hardware implementation of traditional machine learning algorithms practicable in electronic and photonic systems.



https://doi.org/10.1038/s41467-021-27715-5
Kreismann, Jakob;
Three-dimensional optical microcavities: from geometric phases to tailored far-field emission. - Ilmenau : Universitätsbibliothek, 2021. - 1 Online-Ressource (iii, 204 Seiten)
Technische Universität Ilmenau, Dissertation 2021

Diese Arbeit behandelt dreidimensionale optische Mikrokavitäten in Bezug auf ihre Resonanzmoden. Die optischen Mikrokavitäten reichen dabei von Möbiusband-Kavitäten über zylindrische und kegelförmige Ringkavitäten sowie kegelförmige Tube-Kavitäten bis hin zu Arrays von Lima¸con-Kavitäten. Im ersten Teil werden flüstergalerieartige Moden von dielektrischen Möbiusband-Kavitäten mit Hilfe von FDTD-Simulationen untersucht. Die Topologie des Möbiusbands erlaubt die Entstehung einer geometrischen Phase und zwar der Pancharatnam-Phase. Darauf aufbauend wird untersucht, wie die Pancharatnam-Phase durch Verkürzung der Länge des verdrehten Anteils oder durch Erhöhung der Dicke des Möbiusbands manipuliert werden kann. Dabei untersuchen wir, wie die Polarisation und die Fernfelder der flüstergalerieartigen Moden beeinflusst werden. Außerdem wird die Nonagon-Möbiusband-Kavität - eine Möbiusband-Kavität mit Querschnittsform dreifacher Rotationssymmetrie - eingeführt, die ebenfalls eine Manipulation der Pancharatnam-Phase ermöglicht. Im zweiten Teil werden propagierende flüstergalerieartige Moden in zylindrischen Ringkavitäten, konischen Ringkavitäten und konischen Tube-Kavitäten mittels FDTD-Simulationen und vektorieller Beugungstheorie untersucht. Der propagierende Charakter der Moden ermöglicht die sogenannte Spin-Richtungs-Wechselwirkung des Lichts. Darauf aufbauend wird untersucht, wie die Fernfeldpolarisation durch die axiale Morphologie der flüstergalerieartigen Moden und durch geometrische Eigenschaften der Kavitäten wie die Öffnungswinkel von konischen Ring- und Tube-Kavitäten beeinflusst wird. Mit Hilfe vektorieller Beugungstheorie wird ein qualitativer Zusammenhang zwischen den lokalen Eigenschaften der Moden im Inneren der Kavität und der Fernfeldpolarisation beschrieben. Dabei wird die Rolle von Beugung und Präzession des elektrischen Feldvektors um die Kavitätenachse diskutiert. Es wird gezeigt, dass elliptische und zirkulare Polarisationszustände im Fernfeld unmittelbar durch propagierende flüstergalerieartige Moden auftreten, auch ohne inhomogenes oder anisotropes Kavitätenmaterial. Im dritten Teil wird die Fernfeldabstrahlung von linearen Arrays bestehend aus Lima¸con-Kavitäten mithilfe von FDTD-Simulationen untersucht. Während das Fernfeld einer einzelnen Lima¸con-Kavität gerichtete Emission aufweist, wird untersucht, wie sich diese gerichtete Emission in Abhängigkeit der Arrayeigenschaften wie dem Abstand zwischen den Kavitäten und der Anzahl der Kavitäten ändert. Es wird gezeigt, dass die Abstrahlung des Arrays entweder weiter verstärkt (Superdirektionalität) oder sogar umgekehrt Kavitäten werden kann (Richtungsumkehr).



https://nbn-resolving.org/urn:nbn:de:gbv:ilm1-2021000314
Jaurigue, Lina; Robertson, Elizabeth; Wolters, Janik; Lüdge, Kathy
Reservoir computing with delayed input for fast and easy optimisation. - In: Entropy, ISSN 1099-4300, Bd. 23 (2021), 12, 1560, S. 1-13

Reservoir computing is a machine learning method that solves tasks using the response of a dynamical system to a certain input. As the training scheme only involves optimising the weights of the responses of the dynamical system, this method is particularly suited for hardware implementation. Furthermore, the inherent memory of dynamical systems which are suitable for use as reservoirs mean that this method has the potential to perform well on time series prediction tasks, as well as other tasks with time dependence. However, reservoir computing still requires extensive task-dependent parameter optimisation in order to achieve good performance. We demonstrate that by including a time-delayed version of the input for various time series prediction tasks, good performance can be achieved with an unoptimised reservoir. Furthermore, we show that by including the appropriate time-delayed input, one unaltered reservoir can perform well on six different time series prediction tasks at a very low computational expense. Our approach is of particular relevance to hardware implemented reservoirs, as one does not necessarily have access to pertinent optimisation parameters in physical systems but the inclusion of an additional input is generally possible.



https://doi.org/10.3390/e23121560
Bosch, Martí; Behrens, Arne; Sinzinger, Stefan; Hentschel, Martina
Husimi functions for coupled optical resonators. - In: Journal of the Optical Society of America, ISSN 1520-8532, Bd. 38 (2021), 4, S. 573-578

Phase-space analysis has been widely used in the past for the study of optical resonant systems. While it is usually employed to analyze the far-field behavior of resonant systems, we focus here on its applicability to coupling problems. By looking at the phase-space description of both the resonant mode and the exciting source, it is possible to understand the coupling mechanisms as well as to gain insights and approximate the coupling behavior with reduced computational effort. In this work, we develop the framework for this idea and apply it to a system of an asymmetric dielectric resonator coupled to a waveguide.



https://doi.org/10.1364/JOSAA.422740
Behrens, Arne; Bosch, Martí; Hentschel, Martina; Sinzinger, Stefan
Deformed microcavities with very high Q-factors and directional farfield emission. - In: EOS Annual Meeting (EOSAM 2020), (2020), 01006, S. 1-2

We report the design and optimized fabrication of deformed whispering gallery mode resonators in silica with solely ICP-RIE. This allows us to control the morphology of the resonators more freely and results in low surface roughness. The light was coupled into the resonator using a state of the art tapered fiber approach and we determined the Q-factor in the range of 10^5



https://doi.org/10.1051/epjconf/202023801006