Implementation of the Finite Difference Time Domain algorithm for the analysis of terahertz waves

The aim of this report is to present results related to the application of the Finite Difference Time Domain (FDTD) method for the study of various devices at terahertz frequencies. The FDTD method has emerged as one of the most widely used numerical analysis methods used for electromagnetic simulations. The FDTD method can be used to solve numerous types of problems ranging from modelling the behaviour of microwave circuits, waveguides, and photonics to simulating terahertz devices and plasmas. In this study the FDTD approach is derived from first principles (finite differences) and explicit equations are shown based on Maxwell's equations. Furthermore, absorbing boundary conditions (ABCs) are discussed for the FDTD method. The algorithm is tested against a range of problems to ensure its validity and accuracy. The FDTD method is then applied for the numerical analysis of a range of devices at terahertz frequencies. The numerical results obtained from the application of the FDTD method to examine a microstrip circuit with filter loading and a Multi-mode Interference (MMI) coupler at terahertz frequencies are discussed in detail. Moreover, the results of the application of the FDTD method for the calculation of the dispersion characteristics of plasmonic waveguides are also presented. Finally, a summary of the work carried out is presented and an outline is given for future research which can be carried out by using the FDTD method for the study of terahertz frequency devices

Application of TLM for optical microresonators

Optical microresonators can form the basis of all-optical switching and control devices. The presented study is an exploration of the Transmission Line Modelling (TLM) method as a suitable candidate for designing optical microresonators. Chalcogenide glasses were identified as promising materials, with which to fabricate optical microresonators. The study presents the formulation of TLM in two dimensions to model nonmagnetic dielectric materials and a suitable computationally efficient yet flexible software design. Some methods for extracting spectral properties of resonators are compared and the modified difference Prony method was identified as a suitable tool to extract resonant frequencies and Q factors from a limited time signal. When applying TLM to microresonators of sub-wavelength dimensions it was understood that the method of discretisation plays an important role in accurately modelling microresonators. Two novel methods of discretisations -the same area method and the anti-aliasing method- were used to improve the accuracy significantly compared to existing mesh refinement techniques. Perfect matched layers (PMLs) were implemented to improve reflections from domain truncation using several methods. A Convolutional PML(CPML) was identified as the best, but it does not reach the efficiency of PMLs in the Finite Difference Time Domain (FDTD) method. Several frequency dependent refractive index models were proposed and implemented in TLM. A Tauc-Lorentz model was identified as the best fit to the experimental refractive index of three chalcogenide glasses, but a Sellmeier model with one term and a coefficient was efficient for TLM implementation. The main concern in the use of these models within TLM was shown to be the error arising due to mesh dispersion. Kerr nonlinear models were formulated and implemented in TLM and the models applied to the study of a waveguide junction. Compared to an equivalent implementation in a time domain beam propagation method, TLM models better represent the waveguide junction reflections

Application of TLM for optical microresonators

Optical microresonators can form the basis of all-optical switching and control devices. The presented study is an exploration of the Transmission Line Modelling (TLM) method as a suitable candidate for designing optical microresonators. Chalcogenide glasses were identified as promising materials, with which to fabricate optical microresonators. The study presents the formulation of TLM in two dimensions to model nonmagnetic dielectric materials and a suitable computationally efficient yet flexible software design. Some methods for extracting spectral properties of resonators are compared and the modified difference Prony method was identified as a suitable tool to extract resonant frequencies and Q factors from a limited time signal. When applying TLM to microresonators of sub-wavelength dimensions it was understood that the method of discretisation plays an important role in accurately modelling microresonators. Two novel methods of discretisations -the same area method and the anti-aliasing method- were used to improve the accuracy significantly compared to existing mesh refinement techniques. Perfect matched layers (PMLs) were implemented to improve reflections from domain truncation using several methods. A Convolutional PML(CPML) was identified as the best, but it does not reach the efficiency of PMLs in the Finite Difference Time Domain (FDTD) method. Several frequency dependent refractive index models were proposed and implemented in TLM. A Tauc-Lorentz model was identified as the best fit to the experimental refractive index of three chalcogenide glasses, but a Sellmeier model with one term and a coefficient was efficient for TLM implementation. The main concern in the use of these models within TLM was shown to be the error arising due to mesh dispersion. Kerr nonlinear models were formulated and implemented in TLM and the models applied to the study of a waveguide junction. Compared to an equivalent implementation in a time domain beam propagation method, TLM models better represent the waveguide junction reflections

Physical Knowledge Based Scalable Phased Array Antenna Modeling for Radar Systems

The development of a large-scale phased array radar system such as the future MPAR will need a cost-effective tool for predicting electromagnetic characteristics of antennas. Simulating and optimizing of large finite phased array antennas using commercially available solvers are time-consuming and memory-extensive even though they are highly capable of solving general electromagnetic problems with acceptable accuracy. In this work, a full-wave electromagnetic solver based on finite-difference time-domain (FDTD) method has been developed for simulating phased array antennas. The planar array or array element can be simulated, optimized, or analyzed using FDTD theory based on an orthogonal, regular Cartesian lattice. The FDTD updating equation for diagonally anisotropic material was obtained for periodic structure based on the cylindrical coordinate system. This FDTD algorithm can be used to simulate active element patterns of conformally cylindrical array antennas. The simulation of active element patterns in an infinite faceted-cylindrical array was accomplished with a nonorthogonal and unstructured grid. The derivation of FDTD theory and periodic boundary condition for a structure based on the nonorthogonal and unstructured grid is presented. In this work, two simulation schemes, which are based on computed near-field current density information and the physical knowledge of finite array antennas, were presented for predicting broadside array radiation characteristics with the consumption of relatively low computational resources. The validation of the simulation program and schemes was fulfilled by comparing simulation results with measurements taken by near-field and far-field techniques

Modelling of photonic components based on ÷(3)nonlinear photonic crystals

En esta tesis se llevó a cabo un estudio de diversas propiedades de los cristales fotónicos 1D y 2D no lineales de tercer orden y de cómo se pueden aplicar dichas propiedades al desarrollo de dispositivos totalmente ópticos (por ejemplo, limitadores y conmutadores, compuertas lógicas, transistores ópticos, etc.). Se propuso una aproximación numérica para calcular las características básicas de los cristales fotónicos no lineales como, por ejemplo, el diagrama de bandas o la transmisión. La aproximación numérica presentada en la tesis tiene ciertas ventajas útiles para cualquiera que diseñe dispositivos ópticos basados en cristales fotónicos no lineales. El sofware desarrollado a base de esta aproximación numérica ha permitido diseñar y simular numéricamente un conmutador totalmente óptico cuyas prestaciones son superiores a las de dispositivos optoelectrónicos convencionales.This dissertation represents a summary of a study of different properties of 1D and 2D third-order nonlinear photonic crystals. It is shown how these properties can be utilized to develop various all-optical devices (e.g. optical limiters and switches, logical gates, optical transistors, etc.) In the dissertation, a novel numerical approximation has been proposed for analyzing the basic characteristics of the nonlinear photonic crystals like dispersion characteristics or transmittance curves. This numerical approximation possesses some important advantages useful in designing all-optical devices based on nonlinear photonic crystals. The software based on its algorithm has allowed to design and simulate a high-production all-optical switching device

Probing ultra-subwavelength inhomogeneities embedded within dielectric targets using photonic nanojets

The use of optics to detect ultra-subwavelength features embedded within structures is a hot topic for a broad diversity of applications like spectroscopy, nanotechnology, microscopy, and optical data storage discs. Conventional objective lens based optical systems have a fundamental limit on the best possible resolution of about 200 \u03b7m due to the diffraction of light as it propagates into the far-field. There already exist several near-field techniques with the capability to overcome this limitation, but each of these systems has certain drawbacks related to the complexity of the system or to limitations imposed by the system. A photonic nanojet is a very particular beam of light that can provide a practical way to overcome the diffraction limit inherent to far-field techniques. A nanojet is an electromagnetic field envelope formed on the shadow-side surface of a plane-wave-illuminated dielectric microsphere of diameter larger than the wavelength and with refractive index contrast relative to the background medium of less than 2:1. It can maintain a subwavelength transversal beamwidth for distances greater than 2 wavelengths away from the surface of the generating microsphere. This Dissertation provides a computational test of the hypothesis that the backscattered spectrum resulting from photonic nanojet illumination of a three-dimensional (3-D) dielectric structure can reveal the presence and location of ultra-subwavelength, nanoscale-thin weakly contrasting dielectric inhomogeneities within dielectric targets. The effect of surface roughness on the illuminated side of the target is analyzed, and targets ranging from simple dielectric slabs to complex biological cells are studied. The present work is performed through computational electrodynamics modeling based upon the rigorous, large-scale solution of Maxwells equations. Specifically, the 3-D finite-difference time-domain (FDTD) method is employed to test the above hypothesis.\u2

Simulation de la propagation d'ondes électromagnétiques en nano-optique par une méthode Galerkine discontinue d'ordre élevé

The goal of this thesis is to develop a discontinuous Galerkin time-domain method to be able to handle realistic nanophotonics computations. During the last decades, the evolution of lithography techniques allowed the creation of geometrical structures at the nanometer scale, thus unveiling a variety of new phenomena arising from light-matter interactions at such levels. These effects usually occur when the device is of comparable size or (much) smaller than the wavelength of the incident field. This work relies on the development and implementation of appropriate models for dispersive materials (mostly metals), as well as on a large panel of classical computational techniques. Two major methodological developments are presented and studied in details: (i) curvilinear elements, and (ii) local order of approximation. This work is complemented with several physical studies of real-life nanophotonics applications.L’objectif de cette thèse est de développer une méthode Galerkine discontinue d’ordre élevé capable de prendre en considération des simulations réalistes liées à la nanophotonique. Au cours des dernières décennies, l’évolution des techniques de lithographie a permis la création de structure géométriques de tailles nanométriques, révélant ainsi une large gamme de phénomènes nouveaux nés de l’interaction lumière-matière à ces échelles. Ces effets apparaissent généralement pour des objets de taille égale ou (très) inférieure à la longueur d’onde du champ incident. Ce travail repose sur le développement et l’implémentation de modèles de dispersion appropriés (principalement pour les métaux), ainsi que sur un large éventail de méthodes computationnelles classiques. Deux développements méthodologiques majeurs sont présentés et étudiés en détails: (i) les éléments courbes, et (ii) l’ordre d’approximation local. Ces études sont accompagnées de plusieurs cas-tests réalistes tirés de la nanophotonique