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Exploiting Fermi Surface Anisotropy for Low-Dissipation Interconnects: A Study on Niobium Phosphide / Utnyttjande av Fermiytans anisotropi för låg-dissipativa förbindelser: En studie på niobiumfosfidMariani, Gianluca January 2024 (has links)
The increasing energy consumption of ICT technologies, driven by the rise in AI and data processing, requires the development of low-dissipation interconnects. This thesis addresses the challenge of increased resistivity in chip interconnects due to miniaturization, which stems from enhanced electron scattering at the boundaries. The study focuses on the anisotropy in the Fermi surface as a strategy to mitigate resistivity increase. Experimental methods, including the fabrication of devices made from niobium phosphide (NbP) using focused ion beam (FIB) techniques, are employed. Theoretical models predict that materials with an anisotropic Fermi surface can minimize resistivity by aligning electron velocities with the transport direction. Experimental results confirm significant anisotropy in the transport properties of NbP at reduced dimensions, validating the theoretical predictions. The findings suggest that exploiting Fermi surface anisotropy is a promising approach for developing low-dissipation interconnects, potentially contributing to the continued scaling of integrated circuits and reducing power consumption in ICT applications. / Den ökande energiförbrukningen hos IKT-teknologier, driven av ökningen inom AI och databehandling, kräver utvecklingen av lågförlustiga förbindelser. Denna avhandling tar upp utmaningen med ökad resistivitet i chipförbindelser på grund av miniatyrisering, vilket beror på ökad elektronsspridning vid gränsytorna. Studien fokuserar på anisotropin i Fermi-ytan som en strategi för att minska resistiviteten. Experimentella metoder, inklusive tillverkning av enheter gjorda av niobiumfosfid (NbP) med hjälp av fokuserad jonstråleteknik (FIB), används. Teoretiska modeller förutspår att material med en anisotrop Fermi-yta kan minimera resistiviteten genom att anpassa elektronernas hastigheter med transport riktningen. Experimentella resultat bekräftar betydande anisotropi i transportegenskaperna hos NbP vid reducerade dimensioner, vilket validerar de teoretiska förutsägelserna. Resultaten antyder att utnyttjandet av Fermi-yta anisotropi är ett lovande tillvägagångssätt för att utveckla lågförlustiga förbindelser, vilket potentiellt kan bidra till fortsatt skalförändring av integrerade kretsar och minska energiförbrukningen i IKT-applikationer.
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Simulation de la phase gazeuse des réactions tribochimiques des additifs phosphorés et soufrésMambingo Doumbe, Samuel 18 December 2012 (has links)
La maîtrise de l’additivation est l’un des enjeux majeurs de la formulation des lubrifiants, notamment pour l’industrie automobile. La formulation d’une huile est toutefois très complexe en raison du nombre important d’additifs et des nombreuses interactions possibles entre additifs, notamment entre les additifs de surface. Les phosphites organiques et les polysulfures organiques ont déjà montré leur efficacité en tant qu’additifs de surface. Toutefois malgré leur usage répandu dans les formulations des lubrifiants automobiles, peu d’études traitent des interactions pouvant avoir lieu entre ces deux types de composés. Ce travail de thèse a pour objectif la compréhension des mécanismes d’interaction (antagonisme/synergie) pouvant exister entre les phosphites organiques et les polysulfures organiques. Pour cela, une approche originale sur la lubrification par la phase gazeuse s’est avérée très pertinente. Le couplage du Tribomètre à Environnement Contrôlé (TEC) avec les systèmes d’analyses de surface XPS/Auger a permis d’analyser les tribofilms générés in situ et d’éviter ainsi toute contamination et/ou oxydation du tribofilm avant analyse. Les molécules choisies sont les additifs de lubrification industriels (polysulfures tertaires) à faibles poids moléculaires ou alors des molécules à faible poids moléculaires ayant les mêmes fonctions chimiques que les additifs usuels : trimethyl phosphite (TMPi), dimethyl phosphite (DMPi). L’étude des réactions des tribochimiques des molécules phosphorés a permis de mettre en évidence le rôle ambivalent du DMPi qui se comporte à la fois comme un phosphite pour former un phosphure de fer et comme un phosphate. Le mécanisme formation du phosphure de fer a peu être étayé par la réalisation de calculs ab initio sur l’adsorption dissociative du TMPi sur une surface de fer. Les TPS étudiés génèrent quant à eux des tribofilms à base disulfure de fer. Les mélanges binaires réalisés en phase gazeuse ont permis de mettre en évidence l’importance des rapports de concentrations des vapeurs introduites et du mode d’introduction des molécules dans le tribomètre. Les résultats obtenus en tribologie en phase gazeuse ont été corroborés par des essais complémentaires en phase liquide. / Mastering the addivation is one of the biggest issues for the lubricants formulation, especially in the automobile industry. However automotive lubricants are very complex systems due to the numerous additives mixed with base oils. Many interactions can occur between additives, especially between surface additives. Organic phosphites and organic polysulphides have already demonstrated their effectiveness as surface additives. However, despite their widespread use in the formulations of automotive lubricants, few studies deal with the interactions taking place between these two types of compounds. The aim of this study is to understand the interactions, antagonistic or synergetic effect between these kinds of additives using Gas Phase Lubrication (GPL) approach. A Environmental Controlled Tribometer (TEC) was used as a tool to simulate the interaction between organophosphate additives and polysulfurous additives. In situ surface analysis was performed in the tribofilm formed during friction using of X-ray Photoelectron Spectroscopy (XPS) and Auger Electron Spectroscopy(AES) in order to avoid any oxidation or air contamination. The molecules selected for the study can be same as the additive like the TPS molecules which are widely used as lubricant additives. Howeverto simulate the phosphite chemical function of phosphite additives, we need to select smaller molecule having the same chemical function. These molecules are dimethyl phosphite (DMPi), trimethylphosphate (TMPi) for simulating the phosphite chemical function and organic polysulphides (TPS44and TPS32). The study of the tribochemical reactions of organic phopshites allowed to clearly characterise the ambivalence of DMPi, which can react like a phosphite and induce iron phosphide formation or react like a phosphate. Ab initio numerical simulation on TMPi dissociative adsorption was carried out to identify the reactions pathways leading to iron phosphide formation. The tribochemical reaction of TPS44 on metallic iron surface leads to the formation of iron disulphidebased tribofilm. The binary vapours mixtures studied by GPL allowed to clearly identify the importance of the vapour concentration ratio between phosphite and polysulphide. Liquid phase experiments were also carried out to confirm the trend observed in GPL approach.
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Surface-enhanced optomechanical disk resonators and force sensing / Résonateurs à disques optomécaniques améliore par leurs surfaces et capteurs de forceGuha, Biswarup 11 July 2017 (has links)
L'optomécanique est la science des interactions entre la lumière et les mouvements mécaniques. Ce rapport de thèse décrit des expériences réalisées avec des microdisques fabriqué dans différents résonateurs semi-conducteurs III-V: l'Arséniure de Gallium (GaAs), l'Arséniure d'Aluminium Gallium (AlGaAs) et l'Arséniure d'Indium Phosphide (InGaP). Ces matériaux sont compatibles avec les fonctionnalités de l’optoélectronique et procurent un couplage optomécanique géant. Pour améliorer les performances des résonateurs en GaAs, nous avons développé des méthodes de traitement de surface permettant de réduire la dissipation optique par un facteur dix et ainsi d'atteindre un facteur de qualité de six millions. En plus de ces études sur le GaAs, nous avons réalisés une étude comparative des interactions optomecaniques dans des microdisques d'InGaP et d'AlGaAs, et nous avons mis en évidences leurs résonances optomécaniques. Finalement, nous avons réalisé des mesures de force avec des résonateurs en GaAs, démontrant un nouveau principe de détection basé sur notre étude de leur la trajectoire dans l'espace de phase et leur bruit de phase / Optomechanics studies the interaction between light and mechanical motion. This PhD thesis reports on optomechanical experiments carried with miniature disk resonators fabricated out of distinct III-V semiconductors: Gallium Arsenide (GaAs), Aluminium Gallium Arsenide (AlGaAs) and Indium Gallium Phosphide (InGaP). These materials are compliant with optoelectronics functionalities and provide giant optomechanical coupling. In order to boost performances of GaAs resonators, we implemented surface control techniques and obtained a ten-fold reduction of optical dissipation, attaining a Q of six million. On top of GaAs, we performed a comparative investigation of optomechanical interactions in InGaP and AlGaAs disk resonators, and demonstrated their operation as optomechanical oscillators. Finally, we carried out optomechanical force sensing experiments with GaAs resonators, analyzing a new sensing principle in light of the phase space trajectory and phase noise of the corresponding oscillators
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Two-Dimensional Photonic Crystals in InP-based MaterialsMulot, Mikaël January 2004 (has links)
Photonic crystals (PhCs) are structures periodic in thedielectric constant. They exhibit a photonic bandgap, i.e., arange of wavelengths for which light propagation is forbidden.Engineering of defects in the PhC lattice offers new ways toconfine and guide light. PhCs have been manufactured usingsemiconductors and other material technologies. This thesisfocuses on two-dimensional PhCs etched in InP-based materials.Only recently, such structures were identified as promisingcandidates for the realization of novel and advanced functionsfor optical communication applications. The primary focus was on fabrication and characterization ofPhC structures in the InP/GaInAsP/InP material system. Thedemands on fabrication are very high: holes as small as100-300nm in diameter have to be etched at least as deep as 2µm. Thus, different etch processes had to be explored andspecifically developed for InP. We have implemented an etchingprocess based on Ar/Cl2chemically assisted ion beam etching (CAIBE), thatrepresents the state of the art PhC etching in InP. Different building blocks were manufactured using thisprocess. A transmission loss of 10dB/mm for a PhC waveguide, areflection of 96.5% for a 4-row mirror and a record qualityfactor of 310 for a 1D cavity were achieved for this materialsystem. With an etch depth of 4.5 µm, optical loss wasfound to be close to the intrinsic limit. PhC-based opticalfilters were demonstrated using (a) a Fabry-Pérot cavityinserted in a PhC waveguide and (b) a contra-directionalcoupler. Lag effect in CAIBE was utilized positively to realizehigh quality PhC taper sections. Using a PhC taper, a couplingefficiency of 70% was demonstrated from a standard ridgewaveguide to a single line defect PhC waveguide. During the course of this work, InP membrane technology wasdeveloped and a Fabry-Pérot cavity with a quality factorof 3200 was demonstrated. Keywords:photonic crystals, photonic bandgap materials,indium phosphide, dry etching, chemically assisted ion beametching, reactive ion etching, electron beam lithography,photonic integrated circuits, optical waveguides, resonantcavities, optical filtering, finite difference time domain,plane wave expansion.
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InP-based photonic crystals : Processing, Material properties and Dispersion effectsBerrier, Audrey January 2008 (has links)
Photonic crystals (PhCs) are periodic dielectric structures that exhibit a photonic bandgap, i.e., a range of wavelength for which light propagation is forbidden. The special band structure related dispersion properties offer a realm of novel functionalities and interesting physical phenomena. PhCs have been manufactured using semiconductors and other material technologies. However, InP-based materials are the main choice for active devices at optical communication wavelengths. This thesis focuses on two-dimensional PhCs in the InP/GaInAsP/InP material system and addresses their fabrication technology and their physical properties covering both material issues and light propagation aspects. Ar/Cl2 chemically assisted ion beam etching was used to etch the photonic crystals. The etching characteristics including feature size dependent etching phenomena were experimentally determined and the underlying etching mechanisms are explained. For the etched PhC holes, aspect ratios around 20 were achieved, with a maximum etch depth of 5 microns for a hole diameter of 300 nm. Optical losses in photonic crystal devices were addressed both in terms of vertical confinement and hole shape and depth. The work also demonstrated that dry etching has a major impact on the properties of the photonic crystal material. The surface Fermi level at the etched hole sidewalls was found to be pinned at 0.12 eV below the conduction band minimum. This is shown to have important consequences on carrier transport. It is also found that, for an InGaAsP quantum well, the surface recombination velocity increases (non-linearly) by more than one order of magnitude as the etch duration is increased, providing evidence for accumulation of sidewall damage. A model based on sputtering theory is developed to qualitatively explain the development of damage. The physics of dispersive phenomena in PhC structures is investigated experimentally and theoretically. Negative refraction was experimentally demonstrated at optical wavelengths, and applied for light focusing. Fourier optics was used to experimentally explore the issue of coupling to Bloch modes inside the PhC slab and to experimentally determine the curvature of the band structure. Finally, dispersive phenomena were used in coupled-cavity waveguides to achieve a slow light regime with a group index of more than 180 and a group velocity dispersion up to 10^7 times that of a conventional fiber. / QC 20100712
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Two-Dimensional Photonic Crystals in InP-based MaterialsMulot, Mikaël January 2004 (has links)
<p>Photonic crystals (PhCs) are structures periodic in thedielectric constant. They exhibit a photonic bandgap, i.e., arange of wavelengths for which light propagation is forbidden.Engineering of defects in the PhC lattice offers new ways toconfine and guide light. PhCs have been manufactured usingsemiconductors and other material technologies. This thesisfocuses on two-dimensional PhCs etched in InP-based materials.Only recently, such structures were identified as promisingcandidates for the realization of novel and advanced functionsfor optical communication applications.</p><p>The primary focus was on fabrication and characterization ofPhC structures in the InP/GaInAsP/InP material system. Thedemands on fabrication are very high: holes as small as100-300nm in diameter have to be etched at least as deep as 2µm. Thus, different etch processes had to be explored andspecifically developed for InP. We have implemented an etchingprocess based on Ar/Cl<sub>2</sub>chemically assisted ion beam etching (CAIBE), thatrepresents the state of the art PhC etching in InP.</p><p>Different building blocks were manufactured using thisprocess. A transmission loss of 10dB/mm for a PhC waveguide, areflection of 96.5% for a 4-row mirror and a record qualityfactor of 310 for a 1D cavity were achieved for this materialsystem. With an etch depth of 4.5 µm, optical loss wasfound to be close to the intrinsic limit. PhC-based opticalfilters were demonstrated using (a) a Fabry-Pérot cavityinserted in a PhC waveguide and (b) a contra-directionalcoupler. Lag effect in CAIBE was utilized positively to realizehigh quality PhC taper sections. Using a PhC taper, a couplingefficiency of 70% was demonstrated from a standard ridgewaveguide to a single line defect PhC waveguide.</p><p>During the course of this work, InP membrane technology wasdeveloped and a Fabry-Pérot cavity with a quality factorof 3200 was demonstrated.</p><p><b>Keywords:</b>photonic crystals, photonic bandgap materials,indium phosphide, dry etching, chemically assisted ion beametching, reactive ion etching, electron beam lithography,photonic integrated circuits, optical waveguides, resonantcavities, optical filtering, finite difference time domain,plane wave expansion.</p>
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Telecom wavelength quantum devicesFelle, Martin Connor Patrick January 2017 (has links)
Semiconductor quantum dots (QDs) are well established as sub-Poissonian sources of entangled photon pairs. To improve the utility of a QD light source, it would be advantageous to extend their emission further into the near infrared, into the low absorption wavelength windows utilised in long-haul optical telecommunication. Initial experiments succeeded in interfering O-band (1260—1360 nm) photons from an InAs/GaAs QD with dissimilar photons from a laser, an important mechanism for quantum teleportation. Interference visibilities as high as 60 ± 6 % were recorded, surpassing the 50 % threshold imposed by classical electrodynamics. Later, polarisation-entanglement of a similar QD was observed, with pairs of telecom-wavelength photons from the radiative cascade of the biexciton state exhibiting fidelities of 92.0 ± 0.2 % to the Bell state. Subsequently, an O-band telecom-wavelength quantum relay was realised. Again using an InAs/GaAs QD device, this represents the first implementation of a sub-Poissonian telecom-wavelength quantum relay, to the best knowledge of the author. The relay proved capable of implementing the famous four-state BB84 protocol, with a mean teleportation fidelity as high as 94.5 ± 2.2 %, which would contribute 0.385 secure bits per teleported qubit. After characterisation by way of quantum process tomography, the performance of the relay was also evaluated to be capable of implementing a six-state QKD protocol. In an effort to further extend the emitted light from a QD into the telecom C-band (1530—1565 nm), alternative material systems were investigated. InAs QDs on a substrate of InP were shown to emit much more readily in the fibre-telecom O- and C-bands than their InAs/GaAs counterparts, largely due to the reduced lattice mismatch between the QD and substrate for InAs/InP (~3 %) compared to InAs/GaAs (~7 %). Additionally, to minimize the fine structure splitting (FSS) of the exciton level, which deteriorates the observed polarisation-entanglement, a new mode of dot growth was investigated. Known as droplet epitaxy (D-E), QDs grown in this mode showed a fourfold reduction in the FSS compared to dots grown in the Stranski-Krastanow mode. This improvement would allow observation of polarisation-entanglement in the telecom C-band. In subsequent work performed by colleagues at the Toshiba Cambridge Research Labs, these D-E QDs were embedded in a p-i-n doped optical cavity, processed with electrical contacts, and found to emit entangled pairs of photons under electrical excitation. The work of this thesis provides considerable technological advances to the field of entangled-light sources, that in the near future may allow for deterministic quantum repeaters operating at megahertz rates, and in the further future could facilitate the distribution of coherent multipartite states across a distributed quantum network.
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Efeito de interface nas propriedades ópticas de pontos quânticos de InP/GaAs / Interface effect on the optical properties of InP/GaAs quantum dotsGirardi, Tiago Illipronti, 1986- 21 August 2018 (has links)
Orientador: Fernando Iikawa / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-21T01:34:49Z (GMT). No. of bitstreams: 1
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Previous issue date: 2012 / Resumo: Neste trabalho, estudamos o efeito de diferentes condições de interface de InP/GaAs nas propriedades ópticas de pontos quânticos auto-organizados, crescidos por epitaxia de feixe químico, no modo Stranskii-Krastanov. Espera-se que os pontos quânticos de InP/GaAs apresentem alinhamento de bandas do tipo II, e somente os elétrons ficam confinados, enquanto os buracos ficam localizados nas camadas de GaAs em volta do ponto quântico, atraídos pelo elétron. No entanto, devido ao efeito de mistura de átomos nas interfaces o perfil de potencial nas interfaces pode ser alterado significativamente, afetando, com isso, as propriedades ópticas dos pontos quânticos. Foram estudadas amostras com as seguintes condições de interface entre a camada de InP e as camadas de GaAs: inclusão ou não de uma camada de InGaP em uma ou nas duas interfaces. O InGaP gera uma barreira para ambos os tipos de portadores de carga em uma junção tanto com o GaAs como InP e evita a difusa de As das camadas de GaAs para a de InP. Através de medidas de fotoluminescência resolvida no tempo, observamos a variação do tempo de decaimento da emissão óptica associada aos pontos quânticos de acordo com as diferentes condições de interface. Foi observado um tempo curto de decaimento em amostras sem a inclusão de InGaP e com a inclusão apenas na interface superior, enquanto foi observado um tempo longo quando incluímos camadas de InGaP em ambas as interfaces. O tempo de decaimento curto é incompatível com o alinhamento de bandas do tipo II, que deveria separar espacialmente o elétron do buraco. A partir desses resultados e estudos anteriores a esse trabalho, pudemos concluir que o tempo curto se deve à mistura de átomos nas regiões de ambas as interfaces, gerando ligas que localizam os portadores próximos um ao outro. O tempo longo na amostra contendo InGaP nas duas interfaces é atribuído à separação espacial do elétron e do buraco. O efeito de mistura de átomos nas interfaces, neste caso, não forma uma liga na interface que localize os dois tipos de portadores próximos um ao outro. Isso pode ser uma alternativa de preparação de pontos quânticos de InP/GaAs onde se mantém separados espacialmente o elétron e o buraco / Abstract: We studied the effect of different interface conditions on the optical properties of InP/GaAs self-assembled quantum dots grown by chemical beam epitaxy in the Stranskii-Krastanov mode. InP/GaAs quantum dots is expected to present type II band alignment, and only electrons are confined, whereas the holes are localized in the GaAs layers around the quantum dot, attracted by the electron. However, due to the atomic intermixing effect in the interface the potential profile can be strongly changed, affecting the optical properties of the quantum dots. We studied samples with the following conditions at the interfaces between the InP layer and GaAs layers: the inclusion, or the lack of, a InGaP layer at one of or both interfaces. InGaP generates a barrier for both types of carriers in a junction with GaAs and InP, and avoid the diffusion of As from the GaAs layers to the InP one. Using time-resolved photo-luminescence, we observed a change of the optical emission decay times associated to the quantum dots as the interface condition is changed. We observed a short decay lifetime in samples without InGaP layers and with the inclusion in the top interface only, whereas we observed a long decay time when we included InGaP layers in both interfaces. The short decay lifetime is incompatible with the type II band alignment, where the electron and the hole should be spatially separated. Using these and other previous results, we concluded that the short decay lifetime is due to the atomic intermixing in both interfaces regions, forming alloys that localize the carriers near each other. The long lifetime observed for sample containing InGaP in both interfaces is attributed to the large electron-hole spatial separation. In this case intermixing effects at the interfaces do not form a potential well to localize the carries near each other / Mestrado / Física / Mestre em Física
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Théorie et Pratique de l'Amplificateur Distribué : Application aux Télécommunications Optiques à 100 Gbit/s / Theory and Practice of the Distributed Amplifier : Application to 100-Gb/s Optical TelecommunicationsDupuy, Jean-Yves 17 December 2015 (has links)
La théorie, la conception, l'optimisation et la caractérisation d'amplificateurs distribués en technologie TBDH InP 0,7 µm, pour les systèmes de communications optiques à 100 Gbit/s, sont présentés. Nous montrons comment l'exploitation adaptée du concept d'amplificateur distribué avec une technologie de transistors bipolaires à produit vitesse-amplitude élevé a permis la réalisation d'un driver de modulateur électro-optique fournissant une amplitude différentielle d'attaque de 6,2 et 5,9 Vpp, à 100 et 112 Gbit/s, respectivement, avec une qualité de signal élevée. Ce circuit établit ainsi le record de produit vitesse-amplitude à 660 Gbit/s.V sur tranche et 575 Gbit/s.V en module hyperfréquence. Dans le cadre du projet Européen POLYSYS, il a été associé à un laser accordable et un modulateur pour la réalisation d'un module transmetteur optoélectronique compact, démontrant des performances avançant l'état de l'art des communications optiques courtes distances à 100 Gbit/s. / The theory, design, optimisation and characterisation of distributed amplifiers in 0.7-µm InP DHBT technology, for 100-Gbit/s optical communication systems, are presented. We show how the appropriate implementation of the distributed amplifier concept in a bipolar transistors technology with high swing-speed product has enabled the realisation of an electro-optic modulator driver with 6.2- and 5.9-Vpp differential driving amplitude at 100 and 112 Gb/s, respectively, with a high signal quality. This circuit thus establishes the swing-speed product record at 660 Gb/s.V on wafer and at 575 Gb/s.V in a microwave module. In the frame of the European project POLYSYS, it has been co-packaged with a tunable laser and a modulator to realise a compact optoelectronic transmitter module, which has demonstrated performances advancing the state of the art of short reach 100-Gb/s optical communications.
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Photonic Integration with III-V Semiconductor TechnologiesPaul, Tuhin 13 April 2022 (has links)
This dissertation documents works on two projects, which are broadly related to
photonic integration using III-V semiconductor platform for fiber-based optical
communication. Our principal project aims to demonstrate continuous variable
quantum key distribution (CV-QKD) with InP-based photonic integrated cir cuit at the 1550 nanometer of optical wavelength. CV QKD protocols, in which
the key is encoded in the quadrature variables of light, has generated immense
interest over the years because of its compatibility with the existing telecom
infrastructure. In this thesis, we have proposed a design of a photonic inte grated circuit potentially capable of realizing this protocol with coherent states
of light. From the practical perspective, we have basically designed an optical
transmitter and an optical receiver capable of carrying out coherent communi cation via the optical fiber. Initially, we established a mathematical model of
the transceiver system based on the optical transfer matrix of the foundry spe cific (Fraunhofer Heinrich Hertz Institute-Germany) building blocks. We have
shown that our chip design is versatile in the sense that it can support multiple
modulation schemes. Based on the mathematical model, we estimated the link
budget to assess the feasibility of on-chip implementation of our protocol. Then
we ran a circuit level simulation using the process design kit provided by our
foundry to put our analysis on a better footing. The encouraging result from
this step prompted us to generate the mask layout for our transceiver chips,
which we eventually submitted to the foundry. The other project in the thesis
grew out of a collaboration with one of our industry partners. The goal of the
project is to enhance the performance of a distributed feedback laser emitting
at the 1310 nanometer of optical wavelength by optimizing its design. To that
end, we first derived the expression for transmission and reflection spectrum
for the laser cavity. Those expressions contained parameters which needed to
be obtained from the transverse and the longitudinal mode analysis of the laser.
We performed the transverse mode analysis and the longitudinal mode analysis
with commercially available numerical solvers. Those mode profiles critically
depend on the grating physical parameters. Therefore by tweaking grating dimensions one can control the transmission characteristics of the laser.
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