Limiting absorption principle and perfectly matched layer method for Dirichlet Laplacians in quasi-cylindrical domains

We establish a limiting absorption principle for Dirichlet Laplacians in quasi-cylindrical domains. Outside a bounded set these domains can be transformed onto a semi-cylinder by suitable diffeomorphisms. Dirichlet Laplacians model quantum or acoustically-soft waveguides associated with quasi-cylindrical domains. We construct a uniquely solvable problem with perfectly matched layers of finite length. We prove that solutions of the latter problem approximate outgoing or incoming solutions with an error that exponentially tends to zero as the length of layers tends to infinity. Outgoing and incoming solutions are characterized by means of the limiting absorption principle.Comment: to appear in SIAM Journal on Mathematical Analysi

Sub-wavelength photonics from solution-processing

Light is pervasive: it transmits information at celeritas lucis, interfaces with everyday electronics and offers a source of renewable energy. The optics and photonics which manage light should satisfy its growing prevalence. One organic polymer and Titanium hybrid is synthesised simply in two steps and is processable as a liquid at room temperature at low capital intensity. It exhibits a tunable refractive index with a large range of 1.5 to 2.0. Light management applications are explored, focusing on two forms of light propagation: free radiation and guided waves. All devices are fabricated from solution-processable materials. The behaviour of light is manipulated by periodic modulations of refractive index. Two directions of periodicity are investigated: parallel and perpendicular to light propagation. Thin-film multilayers form dielectric mirrors with parallel periodicity. The radiation of selected wavelengths are suppressed whilst others are enhanced. These are used to modify emission properties of a photoluminescent dye; a method towards improving efficiencies in optoelectronic devices without chemical alterations. Perpendicular periodicity is provided by thin-film diffraction gratings, enabling coupling between guided and freely radiating light; a key function of solar concentrators and wearable augmented-reality displays. An experimental system is developed to measure coupled light transmissions. To facilitate the design and assessment of these devices, Transfer Matrix Method (TMM) and Finite-Element Method (FEM) models are used. Refractive indices of thin-films are extracted by fitting transmittance and reflectance spectra to TMM. For dielectric mirrors, a phase reconstruction algorithm is extended to account for incoherent substrates. In doing so, information on band-gap positioning is extracted. Meanwhile, diffraction spectra are modelled using the Fraunhofer expression and modified by TMM to include thin-film interferences. This is utilised to fit grating dimensions, which support FEM calculations to identify guided transmissions. A variety of devices are fabricated from solution and characterised using the models developed.Open Acces

Gratings: Theory and Numeric Applications

International audienceThe book containes 11 chapters written by an international team of specialist in electromagnetic theory, numerical methods for modelling of light diffraction by periodic structures having one-, two-, or three-dimensional periodicity, and aiming numerous applications in many classical domains like optical engineering, spectroscopy, and optical telecommunications, together with newly born fields such as photonics, plasmonics, photovoltaics, metamaterials studies, cloaking, negative refraction, and super-lensing. Each chapter presents in detail a specific theoretical method aiming to a direct numerical application by university and industrial researchers and engineers

Convergence of infinite element methods for scalar waveguide problems

We consider the numerical solution of scalar wave equations in domains which are the union of a bounded domain and a finite number of infinite cylindrical waveguides. The aim of this paper is to provide a new convergence analysis of both the Perfectly Matched Layer (PML) method and the Hardy space infinite element method in a unified framework. We treat both diffraction and resonance problems. The theoretical error bounds are compared with errors in numerical experiments

Holographic optical interconnects in dichromated gelatin

Abstract unavailable please refer to PD

Computational Electromagnetism and Acoustics

It is a moot point to stress the significance of accurate and fast numerical methods for the simulation of electromagnetic fields and sound propagation for modern technology. This has triggered a surge of research in mathematical modeling and numerical analysis aimed to devise and improve methods for computational electromagnetism and acoustics. Numerical techniques for solving the initial boundary value problems underlying both computational electromagnetics and acoustics comprise a wide array of different approaches ranging from integral equation methods to finite differences. Their development faces a few typical challenges: highly oscillatory solutions, control of numerical dispersion, infinite computational domains, ill-conditioned discrete operators, lack of strong ellipticity, hysteresis phenomena, to name only a few. Profound mathematical analysis is indispensable for tackling these issues. Many outstanding contributions at this Oberwolfach conference on Computational Electromagnetism and Acoustics strikingly confirmed the immense recent progress made in the field. To name only a few highlights: there have been breakthroughs in the application and understanding of phase modulation and extraction approaches for the discretization of boundary integral equations at high frequencies. Much has been achieved in the development and analysis of discontinuous Galerkin methods. New insight have been gained into the construction and relationships of absorbing boundary conditions also for periodic media. Considerable progress has been made in the design of stable and space-time adaptive discretization techniques for wave propagation. New ideas have emerged for the fast and robust iterative solution for discrete quasi-static electromagnetic boundary value problems

Gratings: Theory and Numeric Applications, Second Revisited Edition

International audienceThe second Edition of the Book contains 13 chapters, written by an international team of specialist in electromagnetic theory, numerical methods for modelling of light diffraction by periodic structures having one-, two-, or three-dimensional periodicity, and aiming numerous applications in many classical domains like optical engineering, spectroscopy, and optical telecommunications, together with newly born fields such as photonics, plasmonics, photovoltaics, metamaterials studies, cloaking, negative refraction, and super-lensing. Each chapter presents in detail a specific theoretical method aiming to a direct numerical application by university and industrial researchers and engineers.In comparison with the First Edition, we have added two more chapters (ch.12 and ch.13), and revised four other chapters (ch.6, ch.7, ch.10, and ch.11