arXiv subjects

Thomas Taimre

Publications and source records attributed to Thomas Taimre.

17 recordsLinked to original sources

arXiv2026

Quantum cascade laser roadmap

Quantum cascade lasers (QCLs) are unipolar semiconductor lasers first demonstrated in 1994. Since then, they have played a central role in advancing mid-infrared and terahertz photonics, becoming among the most reliable light sources in these regions of the electromagnetic spectrum. Their importance is further reinforced by their ability to generate self-starting optical frequency combs, whose investigation is motivated both by fundamental physics and by a wide range of applications, including molecular spectroscopy and free-space optical communications. This Roadmap provides a unified overview of current advances and emerging directions in QCL research. The chapters are organized into three main sections: device design and technology; frequency combs and pulse formation; and applications of QCLs. Each chapter reviews the relevant background, summarizes the current state of the art, and identifies key challenges and future directions within its specific research area.

physics.optics↗

arXiv2025

Optical feedback induced irregular and chaotic dynamics in terahertz quantum cascade laser combs

In this work, we systematically investigate the optical feedback dynamics of terahertz (THz) frequency combs generated from quantum cascade lasers (QCLs) using the effective semiconductor Maxwell-Bloch equations (ESMBEs). Starting from a free-running comb state at low bias (1.3Ith), we identify clear bifurcation routes as the external feedback is increased. In the weak feedback regime (C<1), the frequency comb operation remains stable; as feedback increases to the moderate feedback regime (1 13.86), complex feedback dynamics re-emerged but with significantly reduced complexity compared with the weak feedback regime. More interestingly, we show that optical feedback can induce chaotic THz emission at higher bias current conditions (>1.6Ith), when the free-running laser output (C=0) is originally a stable frequency comb. The resulting chaotic dynamics, characterized by broadband spectra and large positive Lyapunov exponents, are shown to depend strongly on the linewidth enhancement factor. Although THz QCLs widely considered as ultrastable under external perturbations, this work provides the first detailed report of chaotic dynamics and routes to chaos in THz QCLs under optical feedback. These findings not only deepen the understanding of nonlinear dynamics in THz QCLs but also open new possibilities for exploiting applications of chaotic light in THz sensing, imaging and secure communications.

physics.optics↗

arXiv2024

Detectorless 3D terahertz imaging: achieving subwavelength resolution with reflectance confocal interferometric microscopy

Terahertz imaging holds great potential for non-destructive material inspection, but practical implementation has been limited by resolution constraints. In this study, we present a single-pixel THz imaging system based on a confocal microscope architecture, utilising a quantum cascade laser as both transmitter and phase-sensitive receiver. Our approach integrates laser feedback interferometry detection to achieve a two-fold improvement in lateral resolution and a two-order-of-magnitude enhancement in axial resolution over conventional imaging through precise interferometric phase measurements. This translates to a lateral resolution near $\lambda/2$ and a depth of focus better than $\lambda/5$, significantly outperforming traditional confocal systems. The system can produce a 0.5 Mpixel image in under two minutes, surpassing both raster-scanning single-pixel and multipixel focal-plane array-based imagers. Coherent operation enables simultaneous amplitude and phase image acquisition, and a custom visualisation method links amplitude to image saturation and phase to hue, enhancing material characterisation. A 3D tomographic analysis of a silicon chip reveals subwavelength features, demonstrating the system's potential for high-resolution THz imaging and material analysis. This work sets a new benchmark for THz imaging, overcoming key challenges and opening up transformative possibilities for non-destructive material inspection and characterisation.

physics.optics↗

arXiv2024

Shaping terahertz harmonic frequency combs with frequency dependent external reflectors

We present a method for engineering harmonic frequency combs (HFCs) in the terahertz spectral region. This approach involves interfacing a quantum cascade laser (QCL) with an external reflector featuring frequency-dependent reflectivity. A notable advantage of this method over existing ones is its dual functionality in shaping HFCs, allowing for control over both the frequency offset and comb spacing based on the external reflectivity profile. Moreover, the resulting HFCs manifest as sequences of short pulses in the time domain. Consequently, our method enables the generation of ultrashort picosecond pulses passively, providing a distinct alternative to conventional pulse generation systems reliant on active bias current modulation, which struggle with modulation frequencies significantly higher than the first beatnote. This offers intriguing prospects for utilizing HFCs in pump and probe spectroscopy, a field already recognized in the literature as one of the most compelling applications of these states. Furthermore, we demonstrate that these HFCs can be triggered from an initial condition of free-running unlocked dynamics, eliminating the need for assuming free-running comb emission. Thus, the utilization of an external, frequency-dependent reflector is capable of enhancing the coherence of the QCL emission.

physics.optics↗

arXiv2024

Hawkes Models And Their Applications

The Hawkes process is a model for counting the number of arrivals to a system which exhibits the self-exciting property - that one arrival creates a heightened chance of further arrivals in the near future. The model, and its generalizations, have been applied in a plethora of disparate domains, though two particularly developed applications are in seismology and in finance. As the original model is elegantly simple, generalizations have been proposed which: track marks for each arrival, are multivariate, have a spatial component, are driven by renewal processes, treat time as discrete, and so on. This paper creates a cohesive review of the traditional Hawkes model and the modern generalizations, providing details on their construction, simulation algorithms, and giving key references to the appropriate literature for a detailed treatment.

stat.ME↗

arXiv2023

Frequency combs induced by optical feedback and harmonic order tunability in quantum cascade lasers

This study investigates the interaction between frequency combs and optical feedback effects in Quantum Cascade Lasers (QCLs). The theoretical analysis reveals new phenomena arising from the interplay between comb generation and feedback. By considering the bias current corresponding to free-running single mode emission, the introduction of optical feedback can trigger the generation of frequency combs, including both fundamental and harmonic combs. This presents opportunities to extend the comb region and generate harmonic frequency combs with different orders through optimization of external cavity parameters such as losses and length. Furthermore, the study demonstrates that optical feedback can selectively tune the harmonic order of a pre-existing free-running comb by adjusting the external cavity length, particularly for feedback ratios around 1%, which are readily achievable in experimental setups. Under strong feedback conditions (Acket parameter C>4.6), mixed states emerge, displaying the features of both laser and external cavity dynamics. While the study is predominantly centered on Terahertz QCLs, we have also confirmed that the described phenomena occur when utilizing mid-infrared QCL parameters. This work establishes a connection between comb technology and the utilization of optical feedback, providing new avenues for exploration and advancement in the field. In fact, the novel reported phenomena open a pathway towards new methodologies across various domains, such as design of tunable comb sources, hyperspectral imaging, multimode coherent sensing, and multi-channel communication.

physics.optics↗

arXiv2022

Logic-Based benders Decomposition for Wildfire Suppression

We study the problem of locating fire suppression resources in a burning landscape in order to minimise the total area burned. The landscape is modelled as a directed graph, with nodes representing regions of the landscape, and arcs representing adjacency relationships. The fire spread is modelled using the minimum travel time principle. We propose a non-linear integer programming formulation and an exact solution approach utilising logic-based Benders decomposition. We benchmark the approach against a mixed integer program and an iterated local search metaheuristic from the literature. We are able to solve challenging instances to proven optimality in a reasonable amount of time.

math.OC↗

arXiv2022

Multi-mode Dynamics of Terahertz Quantum Cascade Lasers: spontaneous and actively induced generation of dense and harmonic coherent regimes

We present an extended study concerning the dynamics of dense and harmonic coherent regimes in quantum cascade lasers (QCLs) in a Fabry--Perot (FP) configuration emitting in the terahertz (THz) spectral region. Firstly, we study the device in free running operation, reproducing the main features of the self-generated of optical frequency combs (OFCs) and harmonic frequency combs (HFCs) in this spectral range, commenting on the points of difference from the mid-infrared region, and finding excellent agreement with the most recent experimental evidences. Then, we analyze the THz-QCL dynamics under radiofrequency (RF) injection, with a focus on the effect of the modulation of the current on the degree of locking of the system, and we perform a systematic investigation aimed to provide a procedure for the generation of train of pulses with short duration and high contrast. Furthermore, we extend our study to the generation of sequences of pulses with repetition frequency which is a multiple of the free-spectral range (FSR) of the laser cavity, reproducing harmonic mode-locking (HML) of the laser, a method which has been recently demontrated in experiments with THz-QCLs, and the results of which are particulary promising for a large stream of applications, ranging from optical communication to imaging.

physics.optics↗

arXiv2022

Combining Optimisation and Simulation Using Logic-Based Benders Decomposition

Operations research practitioners frequently want to model complicated functions that are are difficult to encode in their underlying optimisation framework. A common approach is to solve an approximate model, and to use a simulation to evaluate the true objective value of one or more solutions. We propose a new approach to integrating simulation into the optimisation model itself. The idea is to run the simulation at each incumbent solution to the master problem. The simulation data is then used to guide the trajectory of the optimisation model itself using logic-based Benders cuts. We test the approach on a class of stochastic resource allocation problems with monotonic performance measures. We derive strong, novel Benders cuts that are provably valid for all problems of the given form. We consider two concrete examples: a nursing home shift scheduling problem, and an airport check in counter allocation problem. While previous papers on these applications could only approximately solve realistic instances, we are able to solve them exactly within a reasonable amount of time. Moreover, while those papers account for the inherent variance of the problem by including estimates of the underlying random variables as model parameters, we are able to compute sample average approximations to optimality with up to 100 scenarios.

math.OC↗

arXiv2021

The Value of Information and Efficient Switching in Channel Selection

We consider a collection of statistically identical two-state continuous time Markov chains (channels). A controller continuously selects a channel with the view of maximizing infinite horizon average reward. A switching cost is paid upon channel changes. We consider two cases: full observation (all channels observed simultaneously) and partial observation (only the current channel observed). We analyze the difference in performance between these cases for various policies. For the partial observation case with two channels, or an infinite number of channels, we explicitly characterize an optimal threshold for two sensible policies which we name "call-gapping" and "cool-off". Our results present a qualitative view on the interaction of the number of channels, the available information, and the switching costs.

cs.IT↗

arXiv2021

Exact simulation of extrinsic stress-release processes

We present a new and straightforward algorithm that simulates exact sample paths for a generalized stress-release process. The computation of the exact law of the joint interarrival times is detailed and used to derive this algorithm. Furthermore, the martingale generator of the process is derived and induces theoretical moments which generalize some results of Borovkov & Vere-Jones (2000) and are used to demonstrate the validity of our simulation algorithm.

stat.CO↗

arXiv2020

Rare Events in Random Geometric Graphs

This work introduces and compares approaches for estimating rare-event probabilities related to the number of edges in the random geometric graph on a Poisson point process. In the one-dimensional setting, we derive closed-form expressions for a variety of conditional probabilities related to the number of edges in the random geometric graph and develop conditional Monte Carlo algorithms for estimating rare-event probabilities on this basis. We prove rigorously a reduction in variance when compared to the crude Monte Carlo estimators and illustrate the magnitude of the improvements in a simulation study. In higher dimensions, we leverage conditional Monte Carlo to remove the fluctuations in the estimator coming from the randomness in the Poisson number of nodes. Finally, building on conceptual insights from large-deviations theory, we illustrate that importance sampling using a Gibbsian point process can further substantially reduce the estimation variance.

math.PR↗

arXiv2018

Rare tail approximation using asymptotics and $L^1$ polar coordinates

In this work, we propose a class of importance sampling (IS) estimators for estimating the right tail probability of a sum of continuous random variables based on a change of variables to $L^1$ polar coordinates in which the radial and angular components of the IS distribution are considered separately. When the asymptotic behaviour of the sum is known we exploit it for the radial change of measure, and the resulting estimator has the appealing form of the (known) asymptotic multiplied by a random multiplicative correction factor. Given we assume knowledge of the asymptotic behaviour of the sum in this framework, traditional notions of efficiency that appear in the rare-event literature hold little practical meaning here. Instead, we focus on the practical behaviour of the proposed estimator in the pre-asymptotic regime for right tail probabilities between roughly $10^{-3}$ and $10^{-7}$. The proposed estimator and procedure are applicable in both the heavy- and light-tailed settings, as well as for independent and dependent summands. In the case of independent summands, we find that our estimator compares favourably with exponential tilting (iid light-tailed summands) and the Asmussen--Kroese method (independent subexponential summands). However, for dependent subexponential summands using the same simple angular distribution as for the independent case, the performance of our estimator rapidly degenerates with increasing dimension, suggesting an open avenue for further research.

stat.ME↗

arXiv2017

Tail asymptotics of light-tailed Weibull-like sums

We consider sums of $n$ i.i.d. random variables with tails close to $\exp\{-x^β\}$ for some $β>1$. Asymptotics developed by Rootzén (1987) and Balkema, Klüppelberg & Resnick (1993) are discussed from the point of view of tails rather of densities, using a somewhat different angle, and supplemented with bounds, results on a random number $N$ of terms, and simulation algorithms.

math.PR↗

arXiv2017

Transient Provisioning and Performance Evaluation for Cloud Computing Platforms: A Capacity Value Approach

User demand on the computational resources of cloud computing platforms varies over time. These variations in demand can be predictable or unpredictable, resulting in `bursty' fluctuations in demand. Furthermore, demand can arrive in batches, and users whose demands are not met can be impatient. We demonstrate how to compute the expected revenue loss over a finite time horizon in the presence of all these model characteristics through the use of matrix analytic methods. We then illustrate how to use this knowledge to make frequent short term provisioning decisions --- transient provisioning. It is seen that taking each of the characteristics of fluctuating user demand (predictable, unpredictable, batchy) into account can result in a substantial reduction of losses. Moreover, our transient provisioning framework allows for a wide variety of system behaviors to be modeled and gives simple expressions for expected revenue loss which are straightforward to evaluate numerically.

cs.DC↗

arXiv2015

Hawkes Processes

Hawkes processes are a particularly interesting class of stochastic process that have been applied in diverse areas, from earthquake modelling to financial analysis. They are point processes whose defining characteristic is that they 'self-excite', meaning that each arrival increases the rate of future arrivals for some period of time. Hawkes processes are well established, particularly within the financial literature, yet many of the treatments are inaccessible to one not acquainted with the topic. This survey provides background, introduces the field and historical developments, and touches upon all major aspects of Hawkes processes.

math.PR↗

arXiv2014

A Correction Term for the Covariance of Renewal-Reward Processes with Multivariate Rewards

We consider a renewal-reward process with multivariate rewards. Such a process is constructed from an i.i.d.\ sequence of time periods, to each of which there is associated a multivariate reward vector. The rewards in each time period may depend on each other and on the period length, but not on the other time periods. Rewards are accumulated to form a vector valued process that exhibits jumps in all coordinates simultaneously, only at renewal epochs. We derive an asymptotically exact expression for the covariance function (over time) of the rewards, which is used to refine a central limit theorem for the vector of rewards. As illustrated by a numerical example, this refinement can yield improved accuracy, especially for moderate time-horizons.

math.PR↗