The purpose of this paper is to fabricate optical waveguide reflectors to reflect the incident optical mode of multi-mode interference coupler by the etched vertical mirror surfaces. We used the design of etched vertical mirror surfaces to bend the incident optical mode, and changed the length of multi-mode interference coupler for the power splitting ratio. By the simulation and design, we could use the multi-mode interference coupler to fabricate optical waveguide reflectors. A 1.52µm symmetric quantum well InGaAlAs/InGaAs epitaxial wafer is used to fabricate the devices. In the device design, we designed a optical waveguide reflector of two inputs and outputs with 90¢X angle. We fabricated a Fabry-Perot laser by two optical waveguide reflectors with 90¢X angle, a 1x2 multi-mode interference coupler and a ring cavity. In addition, we designed optical waveguide reflectors of one input and two inputs, and utilized them to fabricate a Fabry-Perot laser. We also utilized an optical waveguide reflector of one input or two inputs directly to fabricate Fabry-Perot lasers. In fabrication process, firstly, we etched the waveguide to the depth of about 1.81µm by multi-step wet etching. In order to reduce bending loss, we made deep etching for the outside of curve waveguide. Then, we etched the mirror to the depth of about 6µm by multi-step wet etching to have a greater variation of refractive index to reflect the mode of optical waveguide reflectors. Finally, we used polyimide to flatten the sides of the ridge waveguides and evaporated metal pad over the polyimide.

The purpose of this thesis is to design and fabricate optical waveguide reflectors by the etched vertical mirror surfaces. In order to reflect the incident optical mode of multi-mode interference coupler, we fabricate the etched vertical reflective mirror surface with wet etch and dry etch processes. We used the design of etched vertical mirror surfaces to bend the incident optical mode, and changed the length of multi-mode interference coupler for the power splitting ratio and high power output. In order to reduce bending and transition losses and make the incident optical mode total internal reflection in the etched vertical mirror surfaces, we used ICP-RIE dry etch process to add the depth about 4 µm of the etched vertical mirror surfaces. A 1.52 µm symmetric multiple quantum well InGaAlAs/InGaAs epitaxial wafer is used to fabricate the devices. In the device design, we designed optical waveguide reflectors of one input and two inputs respectively, and utilized them to fabricate Fabry-Perot lasers. We also utilized a reflector of one input and two inputs directly to fabricate a Fabry-Perot laser. In addition, We fabricated a Fabry-Perot laser by two reflectors with 90¢X angle corner, a 1x2 3dB multi-mode interference coupler and a ring resonator. In fabrication process, firstly, we etched the epitaxial wafer the depth of about 1.79µm by multi-step wet etch to form waveguides. In order to reduce bending loss, we made deep etching for the outside of curve waveguides and optical waveguide reflectors. Then, we etched the reflective mirror to the depth of about 4µm by ICP-RIE dry etch process to have a greater variation of refractive index to reflect the optical mode of reflectors. Finally, we used polyimide to flatten the sides of the ridge waveguides and evaporated metal pad over the ridge waveguides to form the signal pad.

This thesis includes two topics. The first one is the architecture as well as the circuit implementation of an ultra low-power direct digital frequency synthesizer (DDFS) based on the straight line approximation. The second one is the circuit implementation of the low-power DDFS with an error compensation. The proposed approximation technique replaces the conventional ROM-based phase-to-amplitude conversion circuitry and the linear digital-to-analog converter with a nonlinear digital-to-analog converter (DAC) to realize a simple approximation of the sine function. Thus, the overall power dissipation as well as hardware complexity can be significantly reduced. Besides, by adding the error compensation, the spurious-free dynamic range (SFDR) of the synthesized output signal can be raised drastically.

We consider the pair of a smooth complex projective variety together with an anti-canonical simple normal crossing divisor (we call it "log Calabi- Yau"). Standard examples are toric varieties together with their toric boundaries (we call them "toric pairs"). We provide a numerical criterion for a general log Calabi-Yau to be toric by an inequality between its dimension, Picard number and the number of boundary components. The problem originates in birational geometry and our proof is constructive, motivated by mirror symmetry. / text

We explore supersymmetric quantum field theories in three and four dimensions via an analysis of their BPS spectrum. In four dimensions, we develop the theory of BPS quivers which provides a simple picture of BPS states in terms of a set of building block atomic particles, and basic quantum mechanical interactions. We develop efficient techniques, rooted in an understanding of quantum-mechanical dualities, for determining the spectrum of bound states, and apply these techniques to calculate the spectrum in a wide class of field theories including ADE gauge theories with matter, and Argyres-Douglas type theories. Next, we explore the geometric content of quivers in the case when the four-dimensional field theory can be constructed from the six-dimensional (2; 0) superconformal field theory compactified on a Riemann surface. We find that the quiver and its superpotential are determined by an ideal triangulation of the associated Riemann surface. The significance of this triangulation is that it encodes the data of geodesics on the surface which in turn are the geometric realization of supersymmetric particles. Finally we describe a class of three-dimensional theories which are realized as supersymmetric domain walls in the previously studied four-dimensional theories. This leads to an understanding of quantum field theories constructed from the six-dimensional (2; 0) superconformal field theory compactified on a three-manifold, and we develop the associated geometric dictionary. We find that the structure of the field theory is determined by a decomposition of the three-manifold into tetrahedra and a braid which species the relationship between ultraviolet and infrared geometries. The phenomenon of BPS wall-crossing in four dimensions is then seen in these domain walls to be responsible for three-dimensional mirror symmetries. / Physics

This study proposes a theory of texture for Elliott Carter's song cycle A Mirror on Which to Dwell. Texture is an important structural aspect of much recent music, as is exemplified in Carter's music. The first chapter is introductory and discusses other textural theories, and the concept of auditory streams. It also provides background to Elizabeth Bishop and to the poems that Carter selected for the cycle, and introduces the song cycle as a whole. The second chapter outlines a textural theory based on streaming. Texture is defined as comprising those contextually defined aspects of sound which lead one to perceive music as consisting of distinct streams. Individual streams are defined by properties, behaviours processes. The ways in which streams are combined, and the changes that occur in the streams during the combinations constitute textural behaviours and processes. The third chapter presents the ways in which textural behaviours and processes can function. They can have symbolic functions by representing personae and actions in the text. They can also have musical functions and thus can play a role in the delineation of form. In the fourth chapter each song in the Mirror cycle is analyzed. Songs that are texturally clear are analyzed first, followed by those that are more texturally complex. Because of the close relationship between text and music in these songs, each analysis starts with a discussion of the text before turning to the music. The main textural features of each song are presented, and then the analytical discussion focuses on form and text-setting. In the conclusion an overview of the songs is presented. The songs, although formally diverse, are similar in many respects. In all of them Carter establishes the important streams, some of which have significant symbolic roles, in the opening measures. The songs are characterized by similar textural processes, which help to delineate the form of the songs and to portray musically the meaning of the text. An analysis of these songs using the textural theory presented in this study provides insight into their form and meaning.

New four dimensional N = 2 field theories can be engineered from compactifying six dimensional (2, 0) superconformal field theory on a punctured Riemann surface. Hitchin’s equation is defined on this Riemann surface and the fields in Hitchin’s equation are singular at the punctures. Four dimensional theory is entirely determined by the data at the punctures. Theory without lagrangian description can also be constructed in this way. We first construct new four dimensional generalized superconformal quiver gauge theory by putting regular singularity at the puncture. The algorithm of calculating weakly coupled gauge group in any duality frame is developed. The asymptotical free theory and Argyres-Douglas field theory can also be constructed using six dimensional method. This requires introducing irregular singularity of Hithcin’s equation. Compactify four dimensional theory down to three dimensions, the corresponding N = 4 theory has the interesting mirror symmetry. The mirror theory for the generalized superconformal quiver gauge theory can be derived using the data at the puncture too. Motivated by this construction, we study other three dimensional theories deformed from the above theory and find their mirrors. The surprising relation of above four dimensional gauge theory and two dimensional conformal field theory may have some deep implications. The S-duality of four dimensional theory and the crossing symmetry and modular invariance of two dimensional theory are naturally related.

This thesis deals with the design and experimental validation of Deformable Mirror Electronics (DME) for Extremely Large Telescope (ELT) Adaptive Optics (AO) applications. Modern ground based telescopes achieve their best possible imaging resolution through the application of AO. However, due to the fundamental diffraction of optical elements, the next generation of ELTs will employ primary mirrors of an increasingly large diameter as the final means of improving imaging resolution further. The corresponding increase in diameter and actuator count of the Deformable Mirrors (DMs) in these systems has led to the rapid development of high order DM technology. A significant challenge to operating these multi-thousand channel DMs is related to the DM Electronics (DME), which are required to be highly efficient so-as to operate within practical budgetary constraints. This thesis develops a DME reference design based on the requirements for the Thirty Meter Telescope’s next generation AO system, the Narrow Field Infrared Adaptive Optics System (NFIRAOS), which operates two DMs with a total of 7673 piezoelectric actuators. The basis of the DME is the DM actuator driver, which has been developed to be suitable for very high order reproduction by optimization of its size, power, cost and reliability. A complication is that the piezoelectric actuators in NFIRAOS DMs require high voltage drive signals of ±400 V to obtain the rated stroke and must be current limited to avoid damage. Candidate amplifiers are evaluated in simulation and hardware based on a combination of performance, physical and functional criteria; with the most suitable circuit chosen for a multi-channel prototype implementation and testing with a DM breadboard prototype. The development and optimization of an amplifier capable of meeting NFIRAOS performance criteria and budgetary constraints is demonstrated. / Graduate / 0544 / 0606

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