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Design of Photonic Phased Array Switches Using Nano Electromechanical Systems on Silicon-on-insulator Integration PlatformHussein, Ali Abdulsattar 20 December 2013 (has links)
This thesis presents an introduction to the design and simulation of a novel class of integrated photonic phased array switch elements. The main objective is to use nano-electromechanical (NEMS) based phase shifters of cascaded under-etched slot nanowires that are compact in size and require a small amount of power to operate them. The structure of the switch elements is organized such that it brings the phase shifting elements to the exterior sides of the photonic circuits. The transition slot couplers, used to interconnect the phase shifters, are designed to enable biasing one of the silicon beams of each phase shifter from an electrode located at the side of the phase shifter. The other silicon beam of each phase shifter is biased through the rest of the silicon structure of the switch element, which is taken as a ground. Phased array switch elements ranging from 2×2 up to 8×8 multiple-inputs/multiple-outputs (MIMO) are conveniently designed within reasonable footprints native to the current fabrication technologies.
Chapter one presents the general layout of the various designs of the switch elements and demonstrates their novel features. This demonstration will show how waveguide disturbances in the interconnecting network from conventional switch elements can be avoided by adopting an innovative design. Some possible applications for the designed switch elements of different sizes and topologies are indicated throughout the chapter. Chapter two presents the design of the multimode interference (MMI) couplers used in the switch elements as splitters, combiners and waveguide crossovers. Simulation data and design methodologies for the multimode couplers of interest are detailed in this chapter. Chapter three presents the design and analysis of the NEMS-operated phase shifters. Both simulations and numerical analysis are utilized in the design of a 0º-180º capable NEMS-operated phase shifter. Additionally, the response of some of the designed photonic phased array switch elements is demonstrated in this chapter. An executive summary and conclusions sections are also included in the thesis.
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A polarization sensitive interferometer for Faraday rotation detectionLaForge, Joshua Michael 23 July 2007 (has links)
Time-resolved Faraday rotation (TRFR) is a pulsed laser pump/probe optical measurement used to characterize electron spin dynamics in semiconductor materials. A Mach-Zehnder type interferometer with orthogonally polarized arms is presented as a device for TRFR measurement that is superior to optical bridge detection, the traditional measuring technique, since Faraday rotation can be passively optically amplified via interference. Operation of the interferometer is analyzed under ideal conditions. Corrections to the ideal case stemming from imperfectly aligned optics, finite polarization extinction ratios, and an imperfect recombination optic are analyzed using a matrix transformation approach. The design of the interferometer is presented and chronicled. A description of the single-beam active control system utilized to stabilize the interferometer by continuous corrections to the optical path length of one arm with a piezoelectric actuator is given. Optical amplification by increasing the power in either arm of the interferometer is demonstrated and TRFR measurements taken with the interferometer at ambient temperatures are compared with measurements taken with the optical bridge. We find the interferometer to offer a detection limit on the order of 50 mrad at room temperature, which is five times more sensitive than the optical bridge. Isolation and stabilization of the interferometer were also successful in reducing signal noise to a level comparable with the optical bridge. Our results demonstrate that the interferometer is a better detection device for Faraday rotation under ambient conditions. In the immediate future, improvements to the control system should be made and experiments should be performed with high-quality samples at cryogenic temperatures to confirm that the interferometer performs as favorably under those conditions.
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A polarization sensitive interferometer for Faraday rotation detectionLaForge, Joshua Michael 23 July 2007 (has links)
Time-resolved Faraday rotation (TRFR) is a pulsed laser pump/probe optical measurement used to characterize electron spin dynamics in semiconductor materials. A Mach-Zehnder type interferometer with orthogonally polarized arms is presented as a device for TRFR measurement that is superior to optical bridge detection, the traditional measuring technique, since Faraday rotation can be passively optically amplified via interference. Operation of the interferometer is analyzed under ideal conditions. Corrections to the ideal case stemming from imperfectly aligned optics, finite polarization extinction ratios, and an imperfect recombination optic are analyzed using a matrix transformation approach. The design of the interferometer is presented and chronicled. A description of the single-beam active control system utilized to stabilize the interferometer by continuous corrections to the optical path length of one arm with a piezoelectric actuator is given. Optical amplification by increasing the power in either arm of the interferometer is demonstrated and TRFR measurements taken with the interferometer at ambient temperatures are compared with measurements taken with the optical bridge. We find the interferometer to offer a detection limit on the order of 50 mrad at room temperature, which is five times more sensitive than the optical bridge. Isolation and stabilization of the interferometer were also successful in reducing signal noise to a level comparable with the optical bridge. Our results demonstrate that the interferometer is a better detection device for Faraday rotation under ambient conditions. In the immediate future, improvements to the control system should be made and experiments should be performed with high-quality samples at cryogenic temperatures to confirm that the interferometer performs as favorably under those conditions.
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Design of Photonic Phased Array Switches Using Nano Electromechanical Systems on Silicon-on-insulator Integration PlatformHussein, Ali Abdulsattar January 2014 (has links)
This thesis presents an introduction to the design and simulation of a novel class of integrated photonic phased array switch elements. The main objective is to use nano-electromechanical (NEMS) based phase shifters of cascaded under-etched slot nanowires that are compact in size and require a small amount of power to operate them. The structure of the switch elements is organized such that it brings the phase shifting elements to the exterior sides of the photonic circuits. The transition slot couplers, used to interconnect the phase shifters, are designed to enable biasing one of the silicon beams of each phase shifter from an electrode located at the side of the phase shifter. The other silicon beam of each phase shifter is biased through the rest of the silicon structure of the switch element, which is taken as a ground. Phased array switch elements ranging from 2×2 up to 8×8 multiple-inputs/multiple-outputs (MIMO) are conveniently designed within reasonable footprints native to the current fabrication technologies.
Chapter one presents the general layout of the various designs of the switch elements and demonstrates their novel features. This demonstration will show how waveguide disturbances in the interconnecting network from conventional switch elements can be avoided by adopting an innovative design. Some possible applications for the designed switch elements of different sizes and topologies are indicated throughout the chapter. Chapter two presents the design of the multimode interference (MMI) couplers used in the switch elements as splitters, combiners and waveguide crossovers. Simulation data and design methodologies for the multimode couplers of interest are detailed in this chapter. Chapter three presents the design and analysis of the NEMS-operated phase shifters. Both simulations and numerical analysis are utilized in the design of a 0º-180º capable NEMS-operated phase shifter. Additionally, the response of some of the designed photonic phased array switch elements is demonstrated in this chapter. An executive summary and conclusions sections are also included in the thesis.
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Lokalizace vibrace v okolí optického vlákna pomocí interferometrického senzoru / Location of vibration around the optical fiberDorazin, David January 2018 (has links)
This diploma thesis solves possibilities of utilization optical fiber as sensor. At the beginning, basic division of this sensors is desribed, their principles and usage. Then the thesis is focused on distributed sensors based on the interference of the light, interferometers. This optic fiber interferometers are described, mainly their modifications for detection and localization of vibrations along optical fiber. Significant part of the thesis deals with dual Mach--Zehnder interferometer. This interferometer is theoreticaly desribed and simulated in Matlab. Further the thesis deals with development of two aplication in Matlab software. One application is for simulation and theoretical computation of dual Mach--Zehnder interferometer. Second application serves for signal processing of acquired data that are measured on this interferometer. At the end of the thesis, dual Mach--Zehnder interferometer is designed and build in laboratory enviroment and executed measurement and localization of vibrations using this interferometer.
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Zpracování signálů z optovláknových senzorů / Processing of signals from fiber optic sensorsSikora, Vojtěch January 2018 (has links)
First two chapters of this paper deals with the division of optical fiber sensors, digital signal processing and includes price comparison of four experimental sensors. In chapter three analysis, description and evaluation of measurment has been demonstrated on Mach - Zehnder interferometer. Last chapter is about application for signal analysis from vibration sensors. Description contains snippets from source code and graphical user interface. This paper includes three fields - fiber optics, digital signal processing and creation of application - and thanks to them it provides solid basis for study of optic fiber sensors.
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Coexistencia e integración de comunicaciones inalámbricas en sistemas de transmisión ópticosPérez Soler, Joaquín 25 November 2009 (has links)
Las redes y sistemas de telecomunicación actuales se enfrentan a la necesidad de proporcionar regímenes binarios en la red de acceso cada vez más elevados a un mayor número de usuarios. El principal objetivo de esta Tesis Doctoral es proporcionar y evaluar nuevas técnicas que permitan la distribución eficiente de señales de radiofrecuencia con elevado régimen binario, como las tecnologías inalámbricas UWB y WiMAX, en redes de acceso integradas basadas en sistemas radio-sobre-fibra. Por ello se ha contemplado el estudio de la coexistencia y distribución de comunicaciones UWB y WiMAX tanto en el acceso vía radio, como en la transmisión óptica. Sin olvidar el estudio de la linealización del modulador electro-óptico Mach-Zehnder como dispositivo clave en las redes de acceso integradas.
En primer lugar, esta Tesis Doctoral estudia los requisitos para la convergencia inalámbrica de servicios basados en MB-OFDM UWB y WiMAX 802.16e en entornos de redes inalámbricas personales, proporcionando márgenes de seguridad para asegurar la interoperabilidad entre ambas. Estos márgenes pueden aplicarse en el futuro desarrollo de tecnologías avanzadas de mitigación de la interferencia como detección y exclusión en cognitive radio. La coexistencia de MB-OFDM UWB y WiMAX en redes ópticas de acceso utilizando RoF. Los resultados obtenidos, tanto para sistemas RoF sobre fibra multimodo como monomodo, permiten delimitar el alcance en cada tipo de medio óptico para el despliegue de sistemas RoF sobre FTTH. A su vez, se propone y demuestra experimentalmente una nueva técnica de multiplexación por división de polarización en la transmisión óptica que facilita la coexistencia en RoF. Finalmente, se propone y demuestra experimentalmente una técnica de linealización óptica dual paralelo para moduladores Mach-Zehnder que permite aumentar el margen dinámico de este modulador y mejorar las prestaciones de los sistemas RoF con señales de banda ancha. / Pérez Soler, J. (2009). Coexistencia e integración de comunicaciones inalámbricas en sistemas de transmisión ópticos [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/6476
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Contribution à l'étude des transferts de matière gaz-liquide en présence de réactions chimiques / Contribution to the gas-liquid mass transfer study coupled with chemical reactionsWylock, Christophe 29 September 2009 (has links)
Le bicarbonate de soude raffiné, produit industriellement par la société Solvay, est fabriqué dans des colonnes à bulles de grande taille, appelées les colonnes BIR.<p>Dans ces colonnes, une phase gazeuse contenant un mélange d’air et dioxyde de carbone (CO2) est dispersée sous forme de bulles dans une solution aqueuse de carbonate et de bicarbonate de sodium (respectivement Na2CO3 et NaHCO3). Cette dispersion donne lieu à un transfert de CO2 des bulles vers la phase liquide. Au sein des colonnes, la phase gazeuse se répartit dans deux populations de bulles :des petites bulles (diamètre de quelques mm) et des grandes bulles (diamètre de quelques cm). Le transfert bulle-liquide de CO2 est couplé à des réactions chimiques prenant place en phase liquide, qui conduisent à la conversion du Na2CO3 en NaHCO3. Une fois la concentration de saturation dépassée le NaHCO3 précipite sous forme de cristaux et un mélange liquide-solide est recueilli à la sortie de ces colonnes.<p>Ce travail, réalisé en collaboration avec la société Solvay, porte sur l’étude et la modélisation mathématique des phénomènes de transfert de matière entre phases, couplés à des réactions chimiques, prenant place au sein d’une colonne BIR. L’association d’études sur des colonnes à bulles à l’échelle industrielle ou réduite (pilote) et d’études plus fondamentales sur des dispositifs de laboratoire permet de développer une meilleure compréhension du fonctionnement des colonnes BIR et d’en construire un modèle mathématique détaillé.<p>L’objectif appliqué de ce travail est la mise au point d’un modèle mathématique complet et opérationnel d’une colonne BIR. Cet objectif est supporté par trois blocs de travail, dans lesquels différents outils sont développés et exploités.<p><p>Le premier bloc est consacré à la modélisation mathématique du transfert bulle-liquide de CO2 dans une solution aqueuse de NaHCO3 et de Na2CO3. Ce transfert est couplé à des réactions chimiques en phase liquide qui influencent sa vitesse. Dans un premier temps, des modèles sont développés selon des approches unidimensionnelles classiquement rencontrées dans la littérature. Ces approches passent par une idéalisation de l’écoulement du liquide autour des bulles. Une expression simplifiée de la vitesse du transfert bulle-liquide de CO2, est également développée et validée pour le modèle de colonne BIR.<p>Dans un second temps, une modélisation complète des phénomènes de transport (convection et diffusion), couplés à des réactions chimiques, est réalisée en suivant une approche bidimensionnelle axisymétrique. L’influence de la vitesse de réactions sur la vitesse de transfert est étudiée et les résultats des deux approches sont également comparés.<p><p>Le deuxième bloc est consacré à l’étude expérimentale du transfert gaz-liquide de CO2 dans des solutions aqueuses de NaHCO3 et de Na2CO3. A cette fin, un dispositif expérimental est développé et présenté. Du CO2 est mis en contact avec des solutions aqueuses de NaHCO3 et de Na2CO3 dans une cellule transparente. Les phénomènes provoqués en phase liquide par le transfert de CO2 sont observés à l’aide d’un interféromètre de Mach-Zehnder.<p>Les résultats expérimentaux sont comparés à des résultats de simulation obtenus avec un des modèles unidimensionnels développés dans le premier bloc. De cette comparaison, il apparaît qu’une mauvaise estimation de la valeur de certains paramètres physico-chimiques apparaissant dans les équations de ce modèle conduit à des écarts significatifs entre les grandeurs observées expérimentalement et les grandeurs estimées par simulation des équations du modèle.<p>C’est pourquoi une méthode d’estimation paramétrique est également développée afin d’identifier les valeurs numériques de ces paramètres physico-chimiques sur base des résultats expérimentaux. Ces dernières sont également discutées.<p><p>Dans le troisième bloc, nous apportons une contribution à l’étude des cinétiques de précipitation du NaHCO3 dans un cristallisoir à cuve agitée. Cette partie du travail est réalisée en collaboration avec Vanessa Gutierrez (du service Matières et Matériaux de l’ULB).<p>Nous contribuons à cette étude par le développement de trois outils :une table de calcul Excel permettant de synthétiser les résultats expérimentaux, un ensemble de simulations de l’écoulement au sein du cristallisoir par mécanique des fluides numérique et une nouvelle méthode d’extraction des cinétiques de précipitation du NaHCO3 à partir des résultats expérimentaux. Ces trois outils sont également utilisés de façon combinée pour estimer les influences de la fraction massique de solide et de l’agitation sur la cinétique de germination secondaire du NaHCO3.<p><p>Enfin, la synthèse de l’ensemble des résultats de ces études est réalisée. Le résultat final est le développement d’un modèle mathématique complet et opérationnel des colonnes BIR. Ce modèle est développé en suivant l’approche de modélisation en compartiments, développée au cours du travail de Benoît Haut. Ce modèle synthétise les trois blocs d’études réalisées dans ce travail, ainsi que les travaux d’Aurélie Larcy (du service Transferts, Interfaces et Procédés de l’ULB) et de Vanessa Gutierrez. Les équations modélisant les différents phénomènes sont présentées, ainsi que la méthode utilisée pour résoudre ces équations. Des simulations des équations du modèle sont réalisées et discutées. Les résultats de simulation sont également comparés à des mesures effectuées sur une colonne BIR. Un accord raisonnable est observé.<p>A l’issue de ce travail, nous disposons donc d’un modèle opérationnel de colonne BIR. Bien que ce modèle doive encore être optimisé et validé, il peut déjà être utilisé pour étudier l’effet des caractéristiques géométriques des colonnes BIR et des conditions appliquées à ces colonnes sur le comportement des simulations des équations du modèle et pour identifier des tendances.<p>//<p>The refined sodium bicarbonate is produced by the Solvay company using large size bubble columns, called the BIR columns.<p>In these columns, a gaseous phase containing an air-carbon dioxyde mixture (CO2) is dispersed under the form of bubbles in an aqueous solution of sodium carbonate and sodium bicarbonate (Na2CO3 and NaHCO3, respectively). This dispersion leads to a CO2 transfer from the bubbles to the liquid phase. Inside these columns, the gaseous phase is distributed in two bubbles populations :small bubbles (a few mm of diameter) and large bubbles (a few cm of diameter).<p>The bubble-liquid CO2 transfer is coupled with chemical reactions taking places in the liquid phase that leads to the conversion of Na2CO3 to NaHCO3. When the solution is supersaturated in NaHCO3, the NaHCO3 precipitates under the form of crystals and a liquid-solid mixture is extracted at the outlet of the BIR columns.<p>This work, realized in collaboration with Solvay, aims to study and to model mathematically the mass transport phenomena between the phases, coupled with chemical reactions, taking places inside a BIR column. Study of bubble columns at the industrial and the pilot scale is combined to a more fundamental study at laboratory scale to improve the understanding of the BIR columns functioning and to develop a detailed mathematical modeling.<p>The applied objective of this work is to develop a complete and operational mathematical modeling of a BIR column. This objective is supported by three blocks of work. In each block, several tools are developed and used.<p><p>The first block is devoted to the mathematical modeling of the bubble-liquid CO2 transfer in an NaHCO3 and Na2CO3 aqueous solution. This transfer is coupled with chemical reactions in liquid phase, which affect the transfer rate.<p>In a first time, mathematical models are developed following the classical one-dimensional approaches of the literature. These approaches idealize the liquid flow around the bubbles. A simplified expression of the bubble-liquid CO2 transfer rate is equally developed and validated for the BIR column model.<p>In a second time, a complete modeling of the transport phenomena (convection and diffusion) coupled with chemical reactions is developed, following an axisymmetrical twodimensional approach. The chemical reaction rate influence on the bubble-liquid transfer rate is studied and the results of the two approaches are then compared.<p><p>The second block is devoted to the experimental study of the gas-liquid CO2 transfer to NaHCO3 and Na2CO3 aqueous solutions. An experimental set-up is developed and presented. CO2 is put in contact with NaHCO3 and Na2CO3 aqueous solutions in a transparent cell. The phenomena induced in liquid phase by the CO2 transfer are observed using a Mach-Zehnder interferometer.<p>The experimental results are compared to simulation results that are obtained using one of the one-dimensional model developed in the first block. From this comparison, it appears that a wrong estimation of some physico-chemical parameter values leads to significative differences between the experimentally observed quantities and those estimated by simulation of the model equations. Therefore, a parametric estimation method is developed in order to estimate those parameters numerical values from the experimental results. The found values are then discussed.<p><p>In the third block is presented a contribution to the NaHCO3 precipitation kinetic study in a stirred-tank crystallizer. This part of the work is realized in collaboration with Vanessa Gutierrez (Chemicals and Materials Department of ULB).<p>Three tools are developed :tables in Excel sheet to synthetize the experimental results, a set of simulations of the flow inside the crystallizer by Computational Fluid Dynamic (CFD) and a new method to extract the NaHCO3 precipitation kinetics from the experimental measurements. These three tools are combined to estimate the influences of the solid mass fraction and the flow on the NaHCO3 secondary nucleation rate.<p><p>Finally, the synthesis of all these results is realized. The final result is the development of a complete and operational mathematical model of BIR columns. This model is developed following the compartmental modeling approach, developed in the PhD thesis of Benoît Haut. This model synthetizes the three block of study realized in this work and the studies of Aurélie Larcy (Transfers, Interfaces and Processes Department of ULB) and those of Vanessa Gutierrez. The equations modeling the phenomena taking place in a BIR column are presented as the used method to solve these equations. The equations of the model are simulated and the results are discussed. The results are equally compared to experimental measurement realized on a BIR column. A reasonable agreement is observed.<p>At the end of this work, an operational model of a BIR column is thus developed. Although this model have to be optimized and validated, it can already be used to study the influences of the geometrical characteristics of the BIR columns and of the conditions applied to these columns on the behaviour of the model equation simulations and to identity tendencies. / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished
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Interferometrické měření fázových změn optického svazku v turbulenci / Interferometric measurement of phase changes of optical beam in turbulenceDěcká, Klára January 2018 (has links)
This master’s thesis deals with the impact of atmospheric turbulence on phase changes of a free space optical signal. This problematic is investigated by the interferometric method. A part of the thesis is focused on the phenomenon of atmospheric turbulence. Then the physical effect of interference is discussed and optical interferometers are described. The experimental part of the thesis is focused on measurement of phase shift of optical signal by interferometric method. The result of the thesis is to determine how phase shift of an optical beam depends on the strength of turbulence.
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Enhancing the Performance of Si Photonics: Structure-Property Relations and Engineered Dispersion RelationsNikkhah, Hamdam January 2018 (has links)
The widespread adoption of photonic circuits requires the economics of volume manufacturing offered by integration technology. A Complementary Metal-Oxide Semiconductor compatible silicon material platform is particularly attractive because it leverages the huge investment that has been made in silicon electronics and its high index contrast enables tight confinement of light which decreases component footprint and energy consumption. Nevertheless, there remain challenges to the development of photonic integrated circuits. Although the density of integration is advancing steady and the integration of the principal components – waveguides, optical sources and amplifiers, modulators, and photodetectors – have all been demonstrated, the integration density is low and the device library far from complete. The integration density is low primarily because of the difficulty of confining light in structures small compared to the wavelength which measured in micrometers. The device library is incomplete because of the immaturity of hybridisation on silicon of other materials required by active devices such as III-V semiconductor alloys and ferroelectric oxides and the difficulty of controlling the coupling of light between disparate material platforms. Metamaterials are nanocomposite materials which have optical properties not readily found in Nature that are defined as much by their geometry as their constituent materials. This offers the prospect of the engineering of materials to achieve integrated components with enhanced functionality. Metamaterials are a class of photonic crystals includes subwavelength grating waveguides, which have already provided breakthroughs in component performance yet require a simpler fabrication process compatible with current minimum feature size limitations.
The research reported in this PhD thesis advances our understanding of the structure-property relations of key planar light circuit components and the metamaterial engineering of these properties. The analysis and simulation of components featuring structures that are only just subwavelength is complicated and consumes large computer resources especially when a three dimensional analysis of components structured over a scale larger than the wavelength is desired. This obstructs the iterative design-simulate cycle. An abstraction is required that summarises the properties of the metamaterial pertinent to the larger scale while neglecting the microscopic detail. That abstraction is known as homogenisation. It is possible to extend homogenisation from the long-wavelength limit up to the Bragg resonance (band edge). It is found that a metamaterial waveguide is accurately modeled as a continuous medium waveguide provided proper account is taken of the emergent properties of the homogenised metamaterial. A homogenised subwavelength grating waveguide structure behaves as a strongly anisotropic and spatially dispersive material with a c-axis normal to the layers of a one dimensional multi-layer structure (Kronig-Penney) or along the axis of uniformity for a two dimensional photonic crystal in three dimensional structure. Issues with boundary effects in the near Bragg resonance subwavelength are avoided either by ensuring the averaging is over an extensive path parallel to boundary or the sharp boundary is removed by graded structures. A procedure is described that enables the local homogenised index of a graded structure to be determined. These finding are confirmed by simulations and experiments on test circuits composed of Mach-Zehnder interferometers and individual components composed of regular nanostructured waveguide segments with different lengths and widths; and graded adiabatic waveguide tapers. The test chip included Lüneburg micro-lenses, which have application to Fourier optics on a chip. The measured loss of each lens is 0.72 dB.
Photonic integrated circuits featuring a network of waveguides, modulators and couplers are important to applications in RF photonics, optical communications and quantum optics. Modal phase error is one of the significant limitations to the scaling of multimode interference coupler port dimension. Multimode interference couplers rely on the Talbot effect and offer the best in-class performance. Anisotropy helps reduce the Talbot length but temporal and spatial dispersion is necessary to control the modal phase error and wavelength dependence of the Talbot length. The Talbot effect in a Kronig-Penny metamaterial is analysed. It is shown that the metamaterial may be engineered to provide a close approximation to the parabolic dispersion relation required by the Talbot effect for perfect imaging. These findings are then applied to the multimode region and access waveguide tapers of a multi-slotted waveguide multimode interference coupler with slots either in the transverse direction or longitudinal direction. A novel polarisation beam splitter exploiting the anisotropy provided by a longitudinally slotted structure is demonstrated by simulation.
The thesis describes the design, verification by simulation and layout of a photonic integrated circuit containing metamaterial waveguide test structures. The test and measurement of the fabricated chip and the analysis of the data is described in detail. The experimental results show good agreement with the theory, with the expected errors due to fabrication process limitations. From the Scanning Electron Microscope images and the measurements, it is clear that at the boundary of the minimum feature size limit, the error increases but still the devices can function.
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