Engineering optical nonlinearities in metal nanoparticle arrays

Thesis (Ph.D.)--Boston UniversityMetal nanostructures supporting localized surface plasmon (LSP) resonances are an emerging technology for sensing, optical switching, radiative engineering, and solar energy harvesting, among other applications. The unique property of LSP resonances that enable these technologies is their ability to localize and enhance the optical field near the surface of metal nanoparticles. However, many questions still remain regarding the effects of nanoparticle coupling on the linear and nonlinear optical properties of these structures. In this thesis, I investigate the role of long-range photonic and near-field plasmonic coupling on the linear and nonlinear optical properties of metal nanoparticles in periodic and deterministic aperiodic arrays within a combined experimental and theoretical framework. In particular, I have developed optical characterization techniques to study various properties of planar metal nano-cylinder arrays fabricated by electron beam lithography (EBL). These include the effect of Fano-type coupling between structural grating modes and LSP resonances on linear diffraction and second harmonic generation (SHG), the influence of near-field coupling on the efficiency of plasmon enhanced metal photoluminescence (PL), the dependence of two-photon PL (TPPL) on nanoparticle size, and the multi-polar nature of SHG from planar plasmonic arrays. Experimental results are fully supported by linear scattering theory of the near and far-field properties of particle arrays based on a range of analytical, semi-analytical, and fully numerical techniques. The breadth of computational methods used allows the investigation of a wide range of structures including large aperiodic arrays with hundreds of discrete particles and periodic arrays with realistic particle shapes, substrates, and excitation conditions. The technological potential of engineered plasmonic structures is demonstrated by enhanced vibrational sum frequency generation (VSFG) spectroscopy, a novel nonlinear sensing technique. These studies have revealed design principles for engineering the interplay of photonic and plasmonic coupling for future linear and nonlinear plasmonic devices for sensing, switching, and modulation. The optical characterization techniques developed in this thesis may additionally be used across a wide range of devices in photonics and nano-optics

A cut in attention: reimagining attentional capacities for painting

This practice based PhD reimagines attentional capacities for painting. It asks how a contemporary painting practice can activate and critically engage with the limits and oscillations of attentional capacity. The cut in attention of the title instigates an interruption to restrictive models of attention, moving beyond expectations of attention that are idealised or characterised as though in deficit. Testing art historical and philosophical framings of attention against current cognitive and neuropsychological research, and in the context of wider social and economic levers for attentional manipulation, the attentional conditions of contemporary painting's production and reception are innovatively reevaluated. Drawing on the exchange between attention and the processes of memory and imagination, a pictorially generated methodology allows the practice to work within an expanded space for painting that can both picture and prompt attentional response. In considering painting as a set of conventions and discourses already attuned to attentional capture and modification, alongside painting's potential to resist attentional compliance through attentiveness to material, spatial and durational possibilities, a more complex and socially embedded position for painting opens up. The multi modalities, fluctuations and temporality of attention and distraction are positioned as attentional resources for painting. Navigating between the externally reactive and internally reflective, between tactile and visual stimuli or the shifts between focus and dispersal, enable attention to operate here as both subject and method in a radical process of reimagining

Mathematical Logic in High School: Hints and Proposals

In school, students learn how to reason and argue, and logic is the art of reasoning. Aristotle, who first developed it, held it to be so, i.e., the foundation of all science. But one certainly cannot impose on girls and boys an institutional course in logic as a prerequisite to all other knowledge. Not even in high school, when the matu- ration process of the students allows the teacher some more abstraction. In truth, in the Archive of Public Education - Cultural, Educational and Professional Pro- file of High Schools [129], it is stated that the logical-argumentative area assumes a central role, because it contributes to the formation of a citizen who “supports her/his own convictions, bringing adequate examples and counterexamples and us- ing concatenations of statements; accepts to change her/his opinion by recognising the logical consequences of a correct argumentation”. But education in logic must be done prudently, in the right formative ways. Some would argue that the practice of mathematics, often based on reasoning, in particular the model of Euclidean geometry, is in itself a cue to progressively in- sinuate logical mechanisms. Unfortunately, in recent times, however, Euclidean geometry seems to be a subject in disgrace, often neglected or forgotten. Instead, there are those who emphasise, in mathematics, the importance of intuition, dis- covery, experience and error, contrasting it with the excessive rigour of too many proofs. The purpose of this thesis is to propose various ideas that, within the fun- damental programmes of high school, specifically of Italian Liceo Classico and Liceo Scientifico, attempt to insinuate logic and accustom the students to logic in a way that we hope is light, clear and pleasant. We therefore do not propose a systematic treatment. We prefer to recall basic logic and then to give scattered ideas rather than a structured and definitive theory. But, as mentioned, we are confident that these hints can best prepare students of high school for logic. Indeed we address ourselves primarily to teachers and we believe that their knowl-edge of logic is useful and indeed necessary. But through them we also wish to address students. The thesis is organised as follows. The first chapter introduces and discusses the whole topic and explains why in our opinion logic is important in high schools. We also discuss how and when to propose it to students. The next two chapters introduce basic logic to teachers and students. The second illustrates the simplest logic, the Boolean one, recapitulating its essential points and emphasising in particular the use of connectives. The third deals with first-order logic, which we may consider the most classical of logics. Here we highlight in par- ticular the function of quantifiers. The following chapters propose several topics, belonging to logic or related to logic, that seem very intriguing and could be considered in high school. First, in chapter four, we treat Aristotelian syllogistics, which, even in recent times, frequently appears in various access tests. We will present some amusing introduc- tions to it, such as those of Lewis Carroll [25] or Pagnan-Rosolini [86]. Chapter five is dedicated to proofs without words. Relying on various examples from geometry, number theory and combinatorial calculus, it illustrates how reason- ing can sometimes be successfully expressed and developed through the images and intuitions they suggest. In this chapter, we also discuss the logic of images proposed by Leonardo in the Codex Atlanticus [73] to address and solve geometric questions often linked to the Pythagorean theorem. The sixth chapter is dedicated to what Henri Poincaré called the “mathematical reasoning” par excellence, namely the principle of induction. This law governs nat- ural numbers and is often used as a powerful demonstrative tool in various exercises. However, students seldom learn it and above all understand it properly. Drawing on the history of the principle of induction, from its primitive intuitions to its for- malisation by Peano and Dedekind, we attempt to approach it in what we hope will be a pleasant and appealing way, also o ering a wide range of examples. Logical paradoxes are another logical theme that is impossible to forget: mental games that not only disorientate but also intrigue and amuse, which are the heart of the seventh chapter. To the classical logics considered at the beginning of the thesis, based on two truth values, yes or no, we then contrast multi-valued and fuzzy logics, which are better suited to analysing situations of uncertainty. We link them, in chapter eight, to the Rényi-Ulam game, which searches for truth in contexts in which the information received may be lying and deceptive. The final chapter takes up a basic topic of high school mathematics: equations. Diophantine games show us how they can be an opportunity for challenge and fun, as well as suggesting intriguing insights into fundamental themes of modern math- ematics: not only number theory and algebra, but also game theory and the theory of computability and computational complexity. For a general and in-depth overview of mathematical logic, we refer to [10] and [114]. For the theory of computability and computational complexity we refer the reader to [37] and [83], for number theory to [60]

2011 program of study : shear turbulence : onset and structure

The theme for the Program in Geophysical Fluid Dynamics for the summer of 2011 was Shear Turbulence: onset and structure. Ten days of principal lectures by FabianWale e and Rich Kerswell began the summer, and a large number of seminars on this and a variety of other topics then continued through the eighth week. These lectures are presented in these Proceedings and form (we believe) the most complete, connected account of this subject) Eleven fellows from around the globe helped to record the principal lectures, and each carried out a project of his/her own, presented in seminar during the tenth and nal week. All these lectures and projects are also presented in this Proceedings volume. The further seminars presented throughout the summer by visitors and (in some cases) by GFD faculty are also listed here. The popular Sears Lecture was given by L. Mahadevan. The title was On growth and form: geometry, physics and biology. It was indeed popular, drawing a large and enthusiastic audience.Funding was provided by the National Science Foundation under Grant No. OCE-0824636 and the Office of Naval Research under Contract No. N00014-09-1084

Dedication to Professor Michael Tribelsky

Professor Tribelsky's accomplishments are highly appreciated by the international community. The best indications of this are the high citation rates of his publications, and the numerous awards and titles he has received. He has made numerous fundamental contributions to an extremely broad area of physics and mathematics, including (but not limited to) quantum solid-state physics, various problems in light–matter interaction, liquid crystals, physical hydrodynamics, nonlinear waves, pattern formation in nonequilibrium systems and transition to chaos, bifurcation and probability theory, and even predictions of the dynamics of actual market prices. This book presents several extensions of his results, based on his inspiring publications

Engineering aperiodic spiral order for photonic-plasmonic device applications

Thesis (Ph.D.)--Boston UniversityDeterministic arrays of metal (i.e., Au) nanoparticles and dielectric nanopillars (i.e., Si and SiN) arranged in aperiodic spiral geometries (Vogel's spirals) are proposed as a novel platform for engineering enhanced photonic-plasmonic coupling and increased light-matter interaction over broad frequency and angular spectra for planar optical devices. Vogel's spirals lack both translational and orientational symmetry in real space, while displaying continuous circular symmetry (i.e., rotational symmetry of infinite order) in reciprocal Fourier space. The novel regime of "circular multiple light scattering" in finite-size deterministic structures will be investigated. The distinctive geometrical structure of Vogel spirals will be studied by a multifractal analysis, Fourier-Bessel decomposition, and Delaunay tessellation methods, leading to spiral structure optimization for novel localized optical states with broadband fluctuations in their photonic mode density. Experimentally, a number of designed passive and active spiral structures will be fabricated and characterized using dark-field optical spectroscopy, ellipsometry, and Fourier space imaging. Polarization-insensitive planar omnidirectional diffraction will be demonstrated and engineered over a large and controllable range of frequencies. Device applications to enhanced LEDs, novel lasers, and thin-film solar cells with enhanced absorption will be specifically targeted. Additionally, using Vogel spirals we investigate the direct (i.e. free space) generation of optical vortices, with well-defined and controllable values of orbital angular momentum, paving the way to the engineering and control of novel types of phase discontinuities (i.e., phase dislocation loops) in compact, chip-scale optical devices. Finally, we report on the design, modeling, and experimental demonstration of array-enhanced nanoantennas for polarization-controlled multispectral nanofocusing, nanoantennas for resonant near-field optical concentration of radiation to individual nanowires, and aperiodic double resonance surface enhanced Raman scattering substrates

International Conference on Mathematical Analysis and Applications in Science and Engineering – Book of Extended Abstracts

The present volume on Mathematical Analysis and Applications in Science and Engineering - Book of Extended Abstracts of the ICMASC’2022 collects the extended abstracts of the talks presented at the International Conference on Mathematical Analysis and Applications in Science and Engineering – ICMA2SC'22 that took place at the beautiful city of Porto, Portugal, in June 27th-June 29th 2022 (3 days). Its aim was to bring together researchers in every discipline of applied mathematics, science, engineering, industry, and technology, to discuss the development of new mathematical models, theories, and applications that contribute to the advancement of scientific knowledge and practice. Authors proposed research in topics including partial and ordinary differential equations, integer and fractional order equations, linear algebra, numerical analysis, operations research, discrete mathematics, optimization, control, probability, computational mathematics, amongst others. The conference was designed to maximize the involvement of all participants and will present the state-of- the-art research and the latest achievements.info:eu-repo/semantics/publishedVersio

Statistical methods for sparse functional object data: elastic curves, shapes and densities

Many applications naturally yield data that can be viewed as elements in non-linear spaces. Consequently, there is a need for non-standard statistical methods capable of handling such data. The work presented here deals with the analysis of data in complex spaces derived from functional L2-spaces as quotient spaces (or subsets of such spaces). These data types include elastic curves represented as d-dimensional functions modulo re-parametrization, planar shapes represented as 2-dimensional functions modulo rotation, scaling and translation, and elastic planar shapes combining all of these invariances. Moreover, also probability densities can be thought of as non-negative functions modulo scaling. Since these functional object data spaces lack a natural Hilbert space structure, this work proposes specialized methods that integrate techniques from functional data analysis with those for metric and manifold data. In particular, but not exclusively, novel regression methods for specific metric quotient spaces are discussed. Special attention is given to handling discrete observations, since in practice curves and shapes are typically observed only as a discrete (often sparse or irregular) set of points. Similarly, density functions are usually not directly observed, but a (small) sample from the corresponding probability distribution is available. Overall, this work comprises six contributions that propose new methods for sparse functional object data and apply them to relevant real-world datasets, predominantly in a biomedical context