arXiv subjects

Kathy Lüdge

Publications and source records attributed to Kathy Lüdge.

At least 37 records · Page 2Linked to original sources

arXiv2024

Efficient timing jitter simulation for passively mode-locked semiconductor lasers

Efficient simulation of the timing jitter in passively mode-locking lasers is key to their numerical investigation and optimization. We introduce a method based on the pulse-period fluctuation auto-correlation function and compare it against established methods with respect to their estimate error. Potential improvements of the computational cost by about two orders of magnitude are reported. This advantage may facilitate larger parameter studies of passively mode-locked laser on small scale clusters or even desktop computers and thereby guide the target-oriented design of future lasers with ultra low timing jitter.

physics.optics↗

arXiv2024

Optimizing the Cavity-Arm Ratio of V-Shaped Semiconductor Disk Lasers

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 are therefore of great relevance for the future development of passively mode-locking semiconductor disk lasers.

physics.optics↗

arXiv2024

Data-Driven Forecasting of Non-Equilibrium Solid-State Dynamics

We present a data-driven approach to efficiently approximate nonlinear transient dynamics in solid-state systems. Our proposed machine-learning model combines a dimensionality reduction stage with a nonlinear vector autoregression scheme. We report an outstanding time-series forecasting performance combined with an easy to deploy model and an inexpensive training routine. Our results are of great relevance as they have the potential to massively accelerate multi-physics simulation software and thereby guide to future development of solid-state based technologies.

physics.comp-ph↗

arXiv2024

Efficient Optimisation of Physical Reservoir Computers using only a Delayed Input

We present an experimental validation of a recently proposed optimization technique for reservoir computing, using an optoelectronic setup. Reservoir computing is a robust framework for signal processing applications, and the development of efficient optimization approaches remains a key challenge. The technique we address leverages solely a delayed version of the input signal to identify the optimal operational region of the reservoir, simplifying the traditionally time-consuming task of hyperparameter tuning. We verify the effectiveness of this approach on different benchmark tasks and reservoir operating conditions.

cs.ET↗

arXiv2023

Reducing hyperparameter dependence by external timescale tailoring

Task specific hyperparameter tuning in reservoir computing is an open issue, and is of particular relevance for hardware implemented reservoirs. We investigate the influence of directly including externally controllable task specific timescales on the performance and hyperparameter sensitivity of reservoir computing approaches. We show that the need for hyperparameter optimisation can be reduced if timescales of the reservoir are tailored to the specific task. Our results are mainly relevant for temporal tasks requiring memory of past inputs, for example chaotic timeseries prediciton. We consider various methods of including task specific timescales in the reservoir computing approach and demonstrate the universality of our message by looking at both time-multiplexed and spatially multiplexed reservoir computing.

physics.comp-ph↗

arXiv2023

Solving the time-complexity problem and tuning the performance of quantum reservoir computing by artificial memory restriction

Quantum reservoir computing is a computing approach which aims at utilising the complexity and high-dimensionality of small quantum systems, together with the fast trainability of reservoir computing, in order to solve complex tasks. The suitability of quantum reservoir computing for solving temporal tasks is hindered by the collapse of the quantum system when measurements are made. This leads to the erasure of the memory of the reservoir. Hence, for every output, the entire input signal is needed to reinitialise the reservoir, leading to quadratic time complexity. Overcoming this issue is critical to the hardware implementation of quantum reservoir computing. We propose artificially restricting the memory of the quantum reservoir by only using a small number inputs to reinitialise the reservoir after measurements are performed, leading to linear time complexity. This not only substantially reduces the number of quantum operations needed to perform timeseries prediction tasks, it also provides a means of tuning the nonlinearity of the response of the reservoir, which can lead to significant performance improvement. We numerically study the linear and quadratic algorithms for a fully connected transverse Ising model and a quantum processor model. We find that our proposed linear algorithm not only significantly reduces the computational cost but also provides an experimental accessible means to optimise the task specific reservoir computing performance.

quant-ph↗

arXiv2023

Self-induced ultrafast electron-hole plasma temperature oscillations in nanowire lasers

Nanowire lasers can be monolithically and site-selectively integrated onto silicon photonic circuits. To assess their full potential for ultrafast opto-electronic devices, a detailed understanding of their lasing dynamics is crucial. However, the roles played by their resonator geometry and the microscopic processes that mediate energy exchange between the photonic, electronic, and phononic subsystems are largely unexplored. Here, we study the dynamics of GaAs-AlGaAs core-shell nanowire lasers at cryogenic temperatures using a combined experimental and theoretical approach. Our results indicate that these NW lasers exhibit sustained intensity oscillations with frequencies ranging from 160 GHz to 260 GHz. As the underlying physical mechanism, we identified self-induced electron-hole plasma temperature oscillations resulting from a dynamic competition between photoinduced carrier heating and cooling via phonon scattering. These dynamics are intimately linked to the strong interaction between the lasing mode and the gain material, which arises from the wavelength-scale dimensions of these lasers. We anticipate that our results could lead to new approaches for ultrafast intensity and phase modulation of chip-integrated nanoscale semiconductor lasers.

cond-mat.mes-hall↗

arXiv2023

Multiplexed random-access optical memory in warm cesium vapor

The ability to store large amounts of photonic quantum states is regarded as substantial for future optical quantum computation and communication technologies. However, research for multiplexed quantum memories has been focused on systems that show good performance only after an elaborate preparation of the storage media. This makes it generally more difficult to apply outside a laboratory environment. In this work, we demonstrate a multiplexed random-access memory to store up to four optical pulses using electromagnetically induced transparency in warm cesium vapor. Using a Λ-System on the hyperfine transitions of the Cs D1 line, we achieve a mean internal storage efficiency of 36% and a 1/e lifetime of 3.2 μs. In combination with future improvements, this work facilitates the implementation of multiplexed memories in future quantum communication and computation infrastructures.

quant-ph↗

arXiv2021

The role of delay-times in delay-based Photonic Reservoir Computing

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,there is still an misconception about the relationship between the delay-time and the input clock-cycle which has noticeable consequences for 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 there is no predefined relationship between these two times-scales. Further, we discuss ways to improve the computing performance of a reservoir formed by delay-coupled oscillators and show the crucial impact of delay-time tuning in those multi-delay systems.

physics.comp-ph↗

arXiv2021

Master memory function for delay-based reservoir computers with single-variable dynamics

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 reservoirs governed by known dynamical rules such as Mackey-Glass or Ikeda-like systems but also to reservoirs whose dynamical model is not available. We also present results comparing the performance of the reservoir computer and the memory capacity given by the MMF.

cs.ET↗

arXiv2021

Insight into Delay Based Reservoir Computing via Eigenvalue Analysis

In this paper we give a profound insight into the computation capability of delay-based reservoir computing via an eigenvalue analysis. We concentrate on the task-independent memory capacity to quantify the reservoir performance and compare these with the eigenvalue spectrum of the dynamical system. We show that these two quantities are deeply connected, and thus the reservoir computing performance is predictable by analyzing the small signal response of the reservoir. Our results suggest that any dynamical system used as a reservoir can be analyzed in this way. We apply our method exemplarily to a photonic laser system with feedback and compare the numerically computed recall capabilities with the eigenvalue spectrum. Optimal performance is found for a system with the eigenvalues having real parts close to zero and off-resonant imaginary parts.

cs.LG↗

arXiv2021

Feedback induced locking in semiconductor lasers with strong amplitude-phase coupling

The influence of optical feedback on semiconductor lasers has been a widely studied field of research due to fundamental interests as well as the optimization of optical data transmission and computing. Recent publications have shown that it is possible to induce a periodic pulsed like output in quantum-dot and quantum-well laser diodes utilizing the locking of the external cavity modes and the relaxation oscillation frequency. We present an in-depth analysis of this effect. We choose submonolayer quantum dots as a gain system, as these provide a relatively strong amplitude-phase coupling, which has proven to be very beneficial for these locking effects to occur. Introducing a new theoretical model we can correctly reproduce the essential features of the gain system and validate them by comparison to our experimental results. From this starting point we can further explore how the staircase behavior of the oscillation frequency with increasing pump current can be influenced by changing various laser parameters. The staircase behavior is induced by a reordering of the Hopf bifurcations giving birth to the regular pulsed-like oscillations.

physics.optics↗

arXiv2021

Phase incoherent photonic molecules in V-shaped mode-locked VECSELs

Passively mode-locked vertical external-cavity surface-emitting semiconductor lasers (VECSELs) composed of a gain chip and a semiconductor saturable absorber have been drawing much attention due to their excellent performance figures. In this work we investigate how localized structures and incoherent, non-locally bound, pulse molecules emerge in a long cavity VECSELs using a V-shaped cavity geometry. We show that these states are bistable with the laser off state and that they are individually addressable. Using a model based upon delay differential equations, we demonstrate that pulse clusters result from the cavity geometry and from the non-local coupling with the gain medium; this leads to locally independent, yet globally bound phase, incoherent photonic molecules. Using a multiple time-scale analysis, we derive an amplitude equation for the field that allows us to predict analytically the distance between the elements of a cluster.

physics.optics↗

arXiv2020

Anticipation-induced social tipping -- Can the environment be stabilised by social dynamics?

In the past decades human activities caused global Earth system changes, e.g., climate change or biodiversity loss. Simultaneously, these associated impacts have increased environmental awareness within societies across the globe, thereby leading to dynamical feedbacks between the social and natural Earth system. Contemporary modelling attempts of Earth system dynamics rarely incorporate such co-evolutions and interactions are mostly studied unidirectionally through direct or remembered past impacts. Acknowledging that societies have the additional capability for foresight, this work proposes a conceptual feedback model of socio-ecological co-evolution with the specific construct of anticipation acting as a mediator between the social and natural system. Our model reproduces results from previous sociological threshold models with bi-stability if one assumes a static environment. Once the environment changes in response to societal behaviour the system instead converges towards a globally stable, but not necessarily desired, attractor. Ultimately, we show that anticipation of future ecological states then leads to metastability of the system where desired states can persist for a long time. We thereby demonstrate that foresight and anticipation form an important mechanism which, once its time horizon becomes large enough, fosters social tipping towards behaviour that can stabilise the environment and prevents potential socio-ecological collapse.

physics.soc-ph↗

arXiv2020

Limitations of the recall capabilities in delay based reservoir computing systems

We analyze the memory capacity of a delay based reservoir computer with a Hopf normal form as nonlinearity and numerically compute the linear as well as the higher order recall capabilities. A possible physical realisation could be a laser with external cavity, for which the information is fed via electrical injection. A task independent quantification of the computational capability of the reservoir system is done via a complete orthonormal set of basis functions. Our results suggest that even for constant readout dimension the total memory capacity is dependent on the ratio between the information input period, also called the clock cycle, and the time delay in the system. Optimal performance is found for a time delay about 1.6 times the clock cycle

cs.ET↗

arXiv2020

Deep Time-Delay Reservoir Computing: Dynamics and Memory Capacity

The Deep Time-Delay Reservoir Computing concept utilizes unidirectionally connected systems with time-delays for supervised learning. We present how the dynamical properties of a deep Ikeda-based reservoir are related to its memory capacity (MC) and how that can be used for optimization. In particular, we analyze bifurcations of the corresponding autonomous system and compute conditional Lyapunov exponents, which measure the generalized synchronization between the input and the layer dynamics. We show how the MC is related to the systems distance to bifurcations or magnitude of the conditional Lyapunov exponent. The interplay of different dynamical regimes leads to a adjustable distribution between linear and nonlinear MC. Furthermore, numerical simulations show resonances between clock cycle and delays of the layers in all degrees of the MC. Contrary to MC losses in a single-layer reservoirs, these resonances can boost separate degrees of the MC and can be used, e.g., to design a system with maximum linear MC. Accordingly, we present two configurations that empower either high nonlinear MC or long time linear MC.

nlin.AO↗

arXiv2020

How carrier memory enters the Haus master equation of mode-locking

We present a generalization of the Haus master equation in which a dynamical boundary condition allows to describe complex pulse trains such as the Q-switched and harmonic transitions of passive mode-locking as well as the weak interactions between localized states. As an example, we investigate the influence of group velocity dispersion on the stability boundaries of the Q-switched regime. We compare our results with that of a time-delayed system.

physics.optics↗

arXiv2020

Performance boost of time-delay reservoir computing by non-resonant clock cycle

The time-delay-based reservoir computing setup has seen tremendous success in both experiment and simulation. It allows for the construction of large neuromorphic computing systems with only few components. However, until now the interplay of the different timescales has not been investigated thoroughly. In this manuscript, we investigate the effects of a mismatch between the time-delay and the clock cycle for a general model. Typically, these two time scales are considered to be equal. Here we show that the case of equal or resonant time-delay and clock cycle could be actively detrimental and leads to an increase of the approximation error of the reservoir. In particular, we can show that non-resonant ratios of these time scales have maximal memory capacities. We achieve this by translating the periodically driven delay-dynamical system into an equivalent network. Networks that originate from a system with resonant delay-times and clock cycles fail to utilize all of their degrees of freedom, which causes the degradation of their performance.

nlin.AO↗