Lorenz-Mie theory for 2D scattering and resonance calculations

This PhD tutorial is concerned with a description of the two-dimensional generalized Lorenz-Mie theory (2D-GLMT), a well-established numerical method used to compute the interaction of light with arrays of cylindrical scatterers. This theory is based on the method of separation of variables and the application of an addition theorem for cylindrical functions. The purpose of this tutorial is to assemble the practical tools necessary to implement the 2D-GLMT method for the computation of scattering by passive scatterers or of resonances in optically active media. The first part contains a derivation of the vector and scalar Helmholtz equations for 2D geometries, starting from Maxwell's equations. Optically active media are included in 2D-GLMT using a recent stationary formulation of the Maxwell-Bloch equations called steady-state ab initio laser theory (SALT), which introduces new classes of solutions useful for resonance computations. Following these preliminaries, a detailed description of 2D-GLMT is presented. The emphasis is placed on the derivation of beam-shape coefficients for scattering computations, as well as the computation of resonant modes using a combination of 2D-GLMT and SALT. The final section contains several numerical examples illustrating the full potential of 2D-GLMT for scattering and resonance computations. These examples, drawn from the literature, include the design of integrated polarization filters and the computation of optical modes of photonic crystal cavities and random lasers.Comment: This is an author-created, un-copyedited version of an article published in Journal of Optics. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from i

Searching for supersymmetry using deep learning with the ATLAS detector

Le Modèle Standard de la physique des particules (MS) est une théorie fondamentale de la nature dont la validité a été largement établie par diverses expériences. Par contre, quelques problèmes théoriques et expérimentaux subsistent, ce qui motive la recherche de théories alternatives. La Supersymétrie (SUSY), famille de théories dans laquelle une nouvelle particule est associée à chaque particules du MS, est une des théories ayant les meilleures motivations pour étendre la portée du modèle. Par exemple, plusieurs théories supersymétriques prédisent de nouvelles particules stables et interagissant seulement par la force faible, ce qui pourrait expliquer les observations astronomiques de la matière sombre. La découverte de SUSY représenterait aussi une importante étape dans le chemin vers une théorie unifiée de l'univers. Les recherches de supersymétrie sont au coeur du programme expérimental de la collaboration ATLAS, qui exploite un détecteur de particules installé au Grand Collisioneur de Hadrons (LHC) au CERN à Genève, mais à ce jours aucune preuve en faveur de la supersymétrie n'a été enregistrée par les présentes analyses, largement basées sur des techniques simples et bien comprises. Cette thèse documente l'implémentation d'une nouvelle approche à la recherche de particules basée sur l'apprentissage profond, utilisant seulement les quadri-impulsions comme variables discriminatoires; cette analyse utilise l'ensemble complet de données d'ATLAS enregistré en 2015-2018. Les problèmes de la naturalité du MS et de la matière sombre orientent la recherche vers les partenaires supersymétriques du gluon (le gluino), des quarks de troisième génération (stop et sbottom), ainsi que des bosons de gauge (le neutralino). Plusieurs techniques récentes sont employées, telles que l'utilisation directe des quadri-impulsions reconstruites à partir des données enregistrées par le détecteur ATLAS ainsi que la paramétrisation d'un réseau de neurone avec les masses des particules recherchées, ce qui permet d'atteindre une performance optimale quelle que soit l'hypothèse de masses. Cette méthode améliore la signification statistique par un facteur 85 par rapport au dernier résultat d'ATLAS pour certaines hypothèses de masses, et ce avec la même luminosité. Aucun excès signifif au-delà du Modèle Standard n'est observé. Les masses du gluino en deçà de 2.45 TeV et du neutralino en deça de 1.7 TeV sont exclues à un niveau de confiance de 95%, ce qui étend largement les limites précédentes sur deux modèles de productions de paires de gluinos faisant intervenir des stops et des sbottoms, respectivement.The Standard Model of particle physics (SM) is a fundamental theory of nature whose validity has been extensively confirmed by experiments. However, some theoretical and experimental problems subsist, which motivates searches for alternative theories to supersede it. Supersymmetry (SUSY), which associate new fundamental particles to each SM particle, is one of the best-motivated such theory and could solve some of the biggest outstanding problems with the SM. For example, many SUSY scenarios predict stable neutral particles that could explain observations of dark matter in the universe. The discovery of SUSY would also represent a huge step towards a unified theory of the universe. Searches for SUSY are at the heart of the experimental program of the ATLAS collaboration, which exploits a state-of-the-art particle detector installed at the Large Hadron Collider (LHC) at CERN in Geneva. The probability to observe many supersymmetric particles went up when the LHC ramped up its collision energy to 13~TeV, the highest ever achieved in laboratory, but so far no evidence for SUSY has been recorded by current searches, which are mostly based on well-known simple techniques such as counting experiments. This thesis documents the implementation of a novel deep learning-based approach using only the four-momenta of selected physics objects, and its application to the search for supersymmetric particles using the full ATLAS 2015-2018 dataset. Motivated by naturalness considerations as well as by the problem of dark matter, the search focuses on finding evidence for supersymmetric partners of the gluon (the gluino), third generation quarks (the stop and the sbottom), and gauge bosons (the neutralino). Many recently introduced physics-specific machine learning developments are employed, such as directly using detector-recorded energies and momenta of produced particles instead of first deriving a restricted set of physically motivated variables and parametrizing the classification model with the masses of the particles searched for, which allows optimal sensitivity for all mass hypothesis. This method improves the statistical significance of the search by up to 85 times that of the previous ATLAS analysis for some mass hypotheses, after accounting for the luminosity difference. No significant excesses above the SM background are recorded. Gluino masses below 2.45 TeV and neutralino masses below 1.7 TeV are excluded at the 95% confidence level, greatly increasing the previous limit on two simplified models of gluino pair production with off-shell stops and sbottoms, respectively

Adding SALT to Coupled Microcavities: the making of active photonic molecule lasers

A large body of work has accumulated over the years in the study of the optical properties of single and coupled microcavities for a variety of applications, ranging from filters to sensors and lasers. The focus has been mostly on the geometry of individual resonators and/or on their combination in arrangements often referred to as photonic molecules (PMs). Our primary concern will be the lasing properties of PMs as ideal candidates for the fabrication of integrated microlasers, photonic molecule lasers. Whereas most calculations on PM lasers have been based on cold-cavity (passive) modes, i.e. quasi-bound states, a recently formulated steady-state ab initio laser theory (SALT) offers the possibility to take into account the spectral properties of the underlying gain transition, its position and linewidth, as well as incorporating an arbitrary pump profile. We will combine two theoretical approaches to characterize the lasing properties of PM lasers: for two-dimensional systems, the generalized Lorenz-Mie theory will obtain the resonant modes of the coupled molecules in an active medium described by SALT. Not only is then the theoretical description more complete, the use of an active medium provides additional parameters to control, engineer and harness the lasing properties of PM lasers for ultra-low threshold and directional single-mode emission.Comment: 16th International Conference on Transparent Optical Networks (2014

Optimization of integrated polarization filters

This study reports on the design of small footprint, integrated polarization filters based on engineered photonic lattices. Using a rods-in-air lattice as a basis for a TE filter and a holes-in-slab lattice for the analogous TM filter, we are able to maximize the degree of polarization of the output beams up to 98 % with a transmission efficiency greater than 75 %. The proposed designs allow not only for logical polarization filtering, but can also be tailored to output an arbitrary transverse beam profile. The lattice configurations are found using a recently proposed parallel tabu search algorithm for combinatorial optimization problems in integrated photonics

Ab initio investigation of lasing thresholds in photonic molecules

We investigate lasing thresholds in a representative photonic molecule composed of two coupled active cylinders of slightly different radii. Specifically, we use the recently formulated steady-state ab initio laser theory (SALT) to assess the effect of the underlying gain transition on lasing frequencies and thresholds. We find that the order in which modes lase can be modified by choosing suitable combinations of the gain center frequency and linewidth, a result that cannot be obtained using the conventional approach of quasi-bound modes. The impact of the gain transition center on the lasing frequencies, the frequency pulling effect, is also quantified

Phase Space Engineering in Optical Microcavities I: Preserving near-field uniformity while inducing far-field directionality

Optical microcavities have received much attention over the last decade from different research fields ranging from fundamental issues of cavity QED to specific applications such as microlasers and bio-sensors. A major issue in the latter applications is the difficulty to obtain directional emission of light in the far-field while keeping high energy densities inside the cavity (i.e. high quality factor). To improve our understanding of these systems, we have studied the annular cavity (a dielectric disk with a circular hole), where the distance cavity-hole centers, d, is used as a parameter to alter the properties of cavity resonances. We present results showing how one can affect the directionality of the far-field while preserving the uniformity (hence the quality factor) of the near-field simply by increasing the value of d. Interestingly, the transition between a uniform near- and far-field to a uniform near- and directional far-field is rather abrupt. We can explain this behavior quite nicely with a simple model, supported by full numerical calculations, and we predict that the effect will also be found in a large class of eigenmodes of the cavity.Comment: 12th International Conference on Transparent Optical Network

S and Q Matrices Reloaded: applications to open, inhomogeneous, and complex cavities

We present a versatile numerical algorithm for computing resonances of open dielectric cavities. The emphasis is on the generality of the system's configuration, i.e. the geometry of the (main) cavity (and possible inclusions) and the internal and external dielectric media (homogeneous and inhomogeneous). The method is based on a scattering formalism to obtain the position and width of the (quasi)-eigenmodes. The core of the method lies in the scattering S-matrix and its associated delay Q-matrix which contain all the relevant information of the corresponding scattering experiment. For instance, the electromagnetic near- and far-fields are readily extracted. The flexibility of the propagation method is displayed for a selected system.Comment: 15th International Conference on Transparent Optical Networks (2013

An Investigation of Response and Stimulus Modality Transfer Effects after Dual-Task Training in Younger and Older

It has been shown that dual-task training leads to significant improvement in dual-task performance in younger and older adults. However, the extent to which training benefits to untrained tasks requires further investigation. The present study assessed (a) whether dual-task training leads to cross-modality transfer in untrained tasks using new stimuli and/or motor responses modalities, (b) whether transfer effects are related to improved ability to prepare and maintain multiple task-set and/or enhanced response coordination, (c) whether there are age-related differences in transfer effects. Twenty-three younger and 23 older adults were randomly assigned to dual-task training or control conditions. All participants were assessed before and after training on three dual-task transfer conditions; (1) stimulus modality transfer (2) response modality transfer (3) stimulus and response modalities transfer task. Training group showed larger improvement than the control group in the three transfer dual-task conditions, which suggests that training leads to more than specific learning of stimuli/response associations. Attentional costs analyses showed that training led to improved dual-task cost, only in conditions that involved new stimuli or response modalities, but not both. Moreover, training did not lead to a reduced task-set cost in the transfer conditions, which suggests some limitations in transfer effects that can be expected. Overall, the present study supports the notion that cognitive plasticity for attentional control is preserved in late adulthood