The Buffered Block Forward Backward technique for solving electromagnetic wave scattering problems

This work focuses on efficient numerical techniques for solving electromagnetic wave scattering problems. The research is focused on three main areas: scattering from perfect electric conductors, 2D dielectric scatterers and 3D dielectric scattering objects. The problem of fields scattered from perfect electric conductors is formulated using the Electric Field Integral Equation. The Coupled Field Integral Equation is used when a 2D homogeneous dielectric object is considered. The Combined Field Integral Equation describes the problem of scattering from 3D homogeneous dielectric objects. Discretising the Integral Equation Formulation using the Method of Moments creates the matrix equation that is to be solved. Due to the large number of discretisations necessary the resulting matrices are of significant size and therefore the matrix equations cannot be solved by direct inversion and iterative methods are employed instead. Various iterative techniques for solving the matrix equation are presented including stationary methods such as the ”forwardbackward” technique, as well its matrix-block version. A novel iterative solver referred to as Buffered Block Forward Backward (BBFB) method is then described and investigated. It is shown that the incorporation of buffer regions dampens spurious diffraction effects and increases the computational efficiency of the algorithm. The BBFB is applied to both perfect electric conductors and homogeneous dielectric objects. The convergence of the BBFB method is compared to that of other techniques and it is shown that, depending on the grouping and buffering used, it can be more effective than classical methods based on Krylov subspaces for example. A possible application of the BBFB, namely the design of 2D dielectric photonic band-gap TeraHertz waveguides is investigated. i

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

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

Design and optimisation of integrated photonic waveguides and sensors

The study in this dissertation aimed to develop novel slot waveguide and resonator based compact integrated photonic sensors. Using guided photons as the probe for detection and measurement, and finally converting the signal magnitude from any domain to an electronic signal is one of the most effective approaches of sensing. Novel and efficient designs of hybrid and composite plasmonic horizontal slot waveguides and dielectric straight slot resonators are proposed and optimised to detect a small refractive index change. Practically, the concentrations of chemical liquid and gas or vapour are often expressed in terms of ‘grams per litre (g/l)’ and ‘parts per million (ppm)’, respectively. Thus, device sensitivities related to the detection of those substances may be expressed in amplitude or wavelength shift of the output optical signal per unit g/l or ppm. However, changes in the concentration and the chemical property of any liquid, gas, and chemical vapour result in refractive index variation of those substances. Therefore, we emphasised the detection of the refractive index change which, on the other hand, represents the concentration and/or chemical property change in the testing sample. Design, optimisations, and performance analyses of those waveguides are carried out by a direct divergence modified full-vectorial two-dimensional (2D) finite element method (FV-FEM). It provides an accurate spurious free better characterisation approach to handle all types of waveguides especially, the plasmonic and hybrid plasmonic waveguides where the guided mode is a complex mixture of the dielectric waveguide mode and surface plasmon polaritons (SPPs). Additionally, a full-vectorial three-dimensional (3D) FV-FEM dedicated to solve the 3D resonator problems is also developed and implemented. As an application of the 2D FV-FEM, first a metal nano-wire with identical and non-identical cladding conditions are considered and modal evolutions of its plasmonic fundamentals and complex supermodes are studied which also work as a benchmark of the direct divergence modified 2D FV-FEM code. Different mode effective area definitions are incorporated with this newly modified code and the low and high index contrast and hybrid plasmonic complex waveguides are simulated to determine the appropriateness of different effective area approaches for various waveguiding structures. Following this, the 2D FV-FEM is implemented in designing complex plasmonic slot based sensing waveguides. A horizontal slot composite plasmonic waveguide structure with a low index porous ZnO (P-ZnO) layer as slot material is reported and also incorporated in a compact symmetric Mach-Zehnder interferometer (MZI) to detect the presence of ethanol vapour in the environment. The waveguide is optimised to obtain a maximum slot confinement (41%) and overall a high phase sensitivity of the MZI device. A similar hybrid plasmonic horizontal slot waveguide is designed and optimised for detection of small refractive index change in the bio-layers (ssDNA and dsDNA) during DNA hybridisation. Next, a metal strip loaded horizontal slot hybrid plasmonic waveguide is designed for a high slot confinement and lower modal loss. The waveguide structure contains a suspended Si slab on top of an optimised thin metal layer (silver) to obtain a lower modal attenuation. It shows an enhanced 60% and 82% power confinement in the slot and sensing (slot+clad) sections, respectively with a small modal attenuation value of 0.036 dB/um. This waveguide is incorporated in an asymmetric Mach-Zehnder interferometer with an asymmetric power splitting scheme which results in an improved interferometric fringe visibility. This compact device exhibits a high temperature and chemical concentration sensitivity of 244 pm/±C and 437.5 nm/RIU, respectively. Beside these waveguides, a silicon-on-insulator (SOI) based vertically slotted straight resonator is also reported in this thesis. Due to its easy and straight structural design it is free from the bending losses and its fabrication steps are much easier compared to other complex devices such as ring, disk resonators, and grating based sensors. The slot cross-section is first optimised and then its length is calculated with those optimised parameters. The 3D straight resonator as a whole is then considered for bulk and surface sensing. Complete performance analyses and the resonating wavelength shift of the device due to small refractive index change during bulk and surface sensing applications are determined by using the newly developed 3D FV-FEM code. This straight resonator exhibits a 5.2 nm resonating wavelength shift for a 5 nm ultra-thin bio-layer and high bulk sensitivities of 820 nm/RIU and 683 nm/RIU for filled and empty slot conditions, respectively

Theoretical and computational insights into the nonlinear optics of nanostructured bulk and 2D materials

In this thesis, a comprehensive analytical and computational study of linear and nonlinear optical response of nanostructured two-dimensional (2D) and bulk materials is presented. The new numerical methods developed in this thesis facilitate the efficient and accurate design of new artificial optical materials and novel nonlinear optical devices. Moreover, the presented results and conclusions can provide a deeper theoretical understanding of different resonant, nonlinear optical phenomena in photonic nanostructures. Two computational electromagnetic methods to calculate the interaction of light with linear and nonlinear diffraction gratings and more general periodic structures have been developed. An efficient formulation of the rigorous coupled-wave analysis (RCWA), a modal frequency domain method, for accurate near-field calculations and for complex oblique structures has been proposed. This method has been implemented into a powerful commercial software tool and applied to calculate diffraction in several nanophotonic devices highly relevant to practical applications. Beyond this commercial implementation, the RCWA has been extended to describe linear and nonlinear optical effects in nanostructured 2D materials, with second- and third-harmonic generation being the most important nonlinear processes. A key feature of this formulation is that it is independent of the height of the 2D material, and only requires knowledge of its linear and nonlinear optical properties. Using this method, plasmon resonances of nanostructured graphene have been investigated, and tuneable Fano resonances have been explored to increase the nonlinear efficiency of heterostructures containing transition metal dichalcogenide monolayers and nanopatterned slab waveguides. The second thrust of the thesis was devoted to extending the so-called generalised source method (GSM) to the area of nonlinear optics. In particular, its mathematical formulation has been extended to incorporate second- and third-order nonlinear optical effects, and the proposed nonlinear GSM has been used to design and optimise multi-resonant photonic devices made of nonlinear optical materials. In addition, this advanced computational method facilitated the understanding of strong nonlinear optical activity in plasmonic nanostructures, and explained the multipolar nonlinear optical response of certain nonlinear metasurfaces

Electromagnetic Waves

This book is dedicated to various aspects of electromagnetic wave theory and its applications in science and technology. The covered topics include the fundamental physics of electromagnetic waves, theory of electromagnetic wave propagation and scattering, methods of computational analysis, material characterization, electromagnetic properties of plasma, analysis and applications of periodic structures and waveguide components, and finally, the biological effects and medical applications of electromagnetic fields

Terahertz response of microfluidic-jetted fabricated 3D flexible metamaterials

Conventional materials exhibit some restrictions on their electromagnetic properties. Especially in terahertz region, for example, materials that exhibit magnetic response are far less common in nature than materials that exhibit electric response. However, materials can be designed, namely artificial man-made metamaterials that exhibit electromagnetic properties that are not found in natural materials by adjusting, for example, the dielectric, magnetic or structural parameters of the constituent elements. This dissertation demonstrates the use of new fabrication techniques to construct metamaterials in THz range via a material deposition system. The metamaterials are fabricated by stacking alternative layers with conventional designs such as single ring- split ring resonators (SRR) and microstrips to form a 3D metamaterial structure. Conductive nano-particle Ag, Cu and semiconductor polymer fluids are used as structural mediums. The metamaterials are fabricated on polyimide substrate. Their flexible nature will be advantageous in future device innovations. In order to obtain electromagnetic resonance in the terahertz range, the dimensions of the single ring-SRR and microstrips are first approximated by analytical methods and then confirmed by numerical simulation. The fabricated metamaterials are then characterized in transmission mode using Time-domain THz Spectroscopy (THz-TDS) in the 0.1 to 2 THz range