Finite-Difference Time-Domain Study of Guided Modes in Nano-plasmonic Waveguides

A conformal dispersive finite-difference time-domain (FDTD) method is developed for the study of one-dimensional (1-D) plasmonic waveguides formed by an array of periodic infinite-long silver cylinders at optical frequencies. The curved surfaces of circular and elliptical inclusions are modelled in orthogonal FDTD grid using effective permittivities (EPs) and the material frequency dispersion is taken into account using an auxiliary differential equation (ADE) method. The proposed FDTD method does not introduce numerical instability but it requires a fourth-order discretisation procedure. To the authors' knowledge, it is the first time that the modelling of curved structures using a conformal scheme is combined with the dispersive FDTD method. The dispersion diagrams obtained using EPs and staircase approximations are compared with those from the frequency domain embedding method. It is shown that the dispersion diagram can be modified by adding additional elements or changing geometry of inclusions. Numerical simulations of plasmonic waveguides formed by seven elements show that row(s) of silver nanoscale cylinders can guide the propagation of light due to the coupling of surface plasmons.Comment: 6 pages, 10 figures, accepted for publication, IEEE Trans. Antennas Propaga

Hybrid topological guiding mechanisms for photonic crystal fibers

We create hybrid topological-photonic localisation of light by introducing concepts from the field of topological matter to that of photonic crystal fiber arrays. S-polarized obliquely propagating electromagnetic waves are guided by hexagonal, and square, lattice topological systems along an array of infinitely conducting fibers. The theory utilises perfectly periodic arrays that, in frequency space, have gapped Dirac cones producing band gaps demarcated by pronounced valleys locally imbued with a nonzero local topological quantity. These broken symmetry-induced stop-bands allow for localised guidance of electromagnetic edge-waves along the crystal fiber axis. Finite element simulations, complemented by asymptotic techniques, demonstrate the effectiveness of the proposed designs for localising energy in finite arrays in a robust manner

Topological Photonics

Topological photonics is a rapidly emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light. Drawing inspiration from the discovery of the quantum Hall effects and topological insulators in condensed matter, recent advances have shown how to engineer analogous effects also for photons, leading to remarkable phenomena such as the robust unidirectional propagation of light, which hold great promise for applications. Thanks to the flexibility and diversity of photonics systems, this field is also opening up new opportunities to realize exotic topological models and to probe and exploit topological effects in new ways. This article reviews experimental and theoretical developments in topological photonics across a wide range of experimental platforms, including photonic crystals, waveguides, metamaterials, cavities, optomechanics, silicon photonics, and circuit QED. A discussion of how changing the dimensionality and symmetries of photonics systems has allowed for the realization of different topological phases is offered, and progress in understanding the interplay of topology with non-Hermitian effects, such as dissipation, is reviewed. As an exciting perspective, topological photonics can be combined with optical nonlinearities, leading toward new collective phenomena and novel strongly correlated states of light, such as an analog of the fractional quantum Hall effect.Comment: 87 pages, 30 figures, published versio

Numerical Modeling and Experiments on Sound Propagation Through the Sonic Crystal and Design of Radial Sonic Crystal

Ph.DDOCTOR OF PHILOSOPH

Análise dinâmica de cristais fonônicos e metamateriais elásticos utilizando abordagens semi-analíticas e numéricas

Orientador: José Maria Campos dos SantosTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia MecânicaResumo: Nesta tese, os métodos de expansão em ondas planas (PWE), expansão em ondas planas melhorado (IPWE) e expansão em ondas planas estendido (EPWE) são utilizados para obter a estrutura de banda de cristais fonônicos (PnCs) e de metamateriais elásticos (EMs) uni- (1D) e bi-dimensionais (2D), isto é, estruturas arti?ciais projetadas para criarem bandas proibidas de Bragg e/ou localmente ressonantes. Estas estruturas periódicas estão sendo aplicadas em vários ramos da ciência e possuem diversas aplicações ¿ controle passivo/ativo de vibração, ?ltros/barreiras acústicas, metamateriais para captação de energia, guias de onda, dentre outras. A principal aplicação considerada nesta tese é o controle passivo de vibração. Primeiro, as formulações do PWE, IPWE e EPWE são apresentadas para alguns casos e vantagens e limitações são discutidas. Os casos considerados são PnCs 1D de barra, cristais sônicos 2D e EMs 1D de viga de Euler-Bernoulli. Posteriormente, alguns exemplos de propagação de ondas mecânicas nestas estruturas periódicas são abordados através da análise da estrutura de banda. Em seguida, algumas aplicações dos PnCs e EMs para controle passivo de vibração são discutidas em artigos anexados. Inicialmente, a estrutura de banda e a resposta forçada harmônica de um PnC simples de viga de Euler-Bernoulli são calculadas. Vários métodos são aplicados e os resultados simulados podem localizar a posição e a largura das bandas proibidas de Bragg próximas dos resultados experimentais. Posteriormente, é considerada a formação de bandas proibidas de ondas de ?exão em um PnC de placa com diferentes inclusões em redes quadrada e triangular, considerando-se a teoria de Mindlin-Reissner. O melhor desempenho é encontrado para a inclusão com seção transversal circular em uma rede triangular. Em seguida, a estrutura de banda de ondas elásticas se propagando em PnCs com nanoestruturas de carbono e em nanocristais fonônicos piezoelétricos com diferentes tipos de rede e inclusão são calculadas. Bandas proibidas totais entre os modos XY e Z são observadas para todos os tipos de inclusão. A piezoeletricidade in?uencia signi?cativamente as bandas proibidas para inclusão circular vazada em frequências mais baixas. Posteriormente, um PnC magnético-elétrico-elástico 2D é considerado. Diferentes tipos de rede e de inclusão também são considerados. A piezoeletricidade e o piezomagnetismo in?uenciam signi?cativamente as bandas proibidas. Finalmente, são considerados EMs 1D de viga de Euler-Bernoulli e 2D de placa ?na. A in?uência de ressonadores de um grau de liberdade e de múltiplos graus de liberdade periodicamente conectados nas células unitárias do EM de viga de Euler-Bernoulli e EM 2D de placa ?na são investigadas. Diferentes con?gurações da distribuição dos ressonadores são consideradas para investigar os mecanismos de formação das bandas proibidas, isto é, ressonância local e espalhamento de BraggAbstract: In this thesis, plane wave expansion (PWE), improved plane wave expansion (IPWE) and extended plane wave expansion (EPWE) methods are used in order to obtain the band structure of one- (1D) and two-dimensional (2D) phononic crystals (PnCs) and elastic metamaterials (EMs), i.e., arti?cial structures designed to open up Bragg-type and/or locally resonant band gaps. Such periodic structures are being applied in many branches of science, and have many applications ¿ passive/active vibration control, acoustic barriers/?lters, metamaterials-based enhanced energy harvesting, waveguides, among others. The main application considered in this thesis is passive vibration control. First, PWE, IPWE and EPWE formulations are presented for some cases and advantages and drawbacks are discussed. The cases regarded are 1D PnC rods, 2D sonic crystals and 1D EM Euler-Bernoulli beams. Afterwards, some examples of mechanical wave propagation in these periodic structures are addressed by means of band structure analysis. Next, some applications of PnCs and EMs for passive vibration control are discussed in attached papers. Initially, the band structure and harmonic forced response of a simple 1D PnC Euler-Bernoulli beam are carried out. Several approaches are applied and the simulated results can localize the Bragg-type band gap position and width close to the experimental results. Next, it is considered the formation of ?exural wave band gaps in a PnC plate with different inclusions in square and triangular lattices, considering Mindlin-Reissner theory. The best performance is found for circular cross section inclusion in a triangular lattice. Afterwards, the band structure of elastic waves propagating in carbon nanostructure PnCs and nano-piezoelectric PnCs with different types of lattice and inclusion are calculated. Full band gaps between XY and Z modes are observed for all types of inclusions. Piezoelectricity in?uences signi?cantly the band gaps for hollow circular inclusion in lower frequencies. After that, a magnetoelectroelastic 2D PnC is considered. Different types of lattice and inclusion are also addressed. Piezoelectricity and piezomagnetism in?uence signi?cantly the band gaps. Finally, elastic wave propagating in 1D EM Euler-Bernoulli beams and in 2D EM thin plates is regarded. The in?uence of single degree of freedom and multiple degrees of freedom resonators periodically attached in unit cells of the EM Euler-Bernoulli beam and 2D EM thin plate are investigated. Different con?gurations of resonator distribution are carried out in order to investigate the band gap formation mechanisms, i.e., local resonance and Bragg scatteringDoutoradoMecanica dos Sólidos e Projeto MecanicoDoutor em Engenharia Mecânic