In this paper, we analytically describe the parametric amplification in ring resonators using silicon and silicon nitride waveguides. Achievable gain and bandwidth of the ring-based amplifiers are studied taking into account the Kerr nonlinearity for silicon nitride and Kerr nonlinearity as well as two photon absorption and free carrier absorption for silicon waveguides. Both telecom and 2-μm wavelengths are investigated in case of silicon. An approach for obtaining the optimum amplifier design without initiating the comb generation has been introduced. It is shown that there is a trade-off between the input pump and amplifier bandwidth. It is estimated that using optimum designs an amplifier with a gain and bandwidth of 10 dB and 10 GHz could be feasible with silicon ring resonators in 2 μm.

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京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第18585号 / 工博第3946号 / 新制||工||1606(附属図書館) / 31485 / 京都大学大学院工学研究科機械理工学専攻 / (主査)教授 西脇 眞二, 教授 田畑 修, 教授 松原 厚 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

No description available.

[pt] Este trabalho propõe uma metodologia para a otimização de forma de estruturas geometricamente não-lineares. O objetivo desta metodologia é evitar os problemas de instabilidade apresentados por estruturas otimizadas de acordo com a formulação clássica. Ela foi implementada para problemas bidimensionais e os resultados obtidos na otimização de diferentes estruturas demonstraram o seu sucesso. Utilizando-se conceitos de modelagem geométrica, a forma da estrutura é defini-da através das curvas de seu contorno. Assim, a representação paramétrica de curvas e a definição destas em função de um conjunto de pontos de interpolação (pontos-chave) são discutidas detalhadamente. A ênfase é dada à interpolação através de B-splines,devido a sua grande flexibilidade. O problema de otimização é definido com base no modelo geométrico e as variáveis de projeto são as coordenadas dos pontos-chave. A simetria da estrutura é garantida através da ligação de variáveis. A estrutura é analisada através de elementos isoparametricos planos. Assim, antes de realizar a análise, é necessário discretizar a estrutura em um conjunto de elementos finitos. Para realizar esta tarefa foram implementados diferentes algoritmos de geração de malhas, tanto estruturadas quanto não-estruturadas. O método de Newton-Raphson é utilizado pa- ra determinar a configuração de equilíbrio e diferentes métodos podem ser aplicados para determinar os pontos críticos. Devido aos problemas de convergência apresentados pelos métodos diretos para a determinação dos pontos crticos, um método semi-direto foi desenvolvido neste trabalho. Os resultados obtidos na análise de diferentes exemplos mostraram a adequação dos elementos finitos e dos métodos numéricos implementados. Os algoritmos de programação matemática utilizados neste trabalho precisam dos gradientes da função objetivo e das restrições, que são calculadas com base nos gradientes das respostas da estrutura. Partindo-se de equações gerais válidas para quaisquer elementos,foram desenvolvidas expressões analíticas que permitem o cálculo exato das sensibilidades de elementos finitos isoparamétricos formulados através do procedimento Lagrangiano Total. O desenvolvimento e a implementação de expressões semelhantes para elementos mais complexos é uma tarefa bastante árdua. Por outro lado, o método das diferenças fi- nitas é simples e genérico, mas muito caro computacionalmente. O método semi-analítico mantémm as vantagens da utilização de diferenças finitas e possui um custo computacional baixo, porém pode apresentar sérios problemas de preciso. Devido a estes motivos, foi desenvolvido neste trabalho um procedimento para melhorar a qualidade das sensibilidades semi-analíticas de estruturas geometricamente não-lineares. O procedimento é baseado na diferenciação exata dos movimentos de corpo rígido do elemento utilizado. Os resultados numéricos obtidos demonstraram a sua eficácia. / [en] This work presents a methodology for shape optimization of geometrically nonlinear structures. The main purpose is to avoid the stability problems generated by optimization based on linear behavior. The methodology was implemented for two-dimensional problems, and several structures were successfully optimized. Using geometrical modeling concepts, the shape of the structure is defined by its boundary curves. Therefore, parametric representation and curve definition by a set of key points are discussed in detail. Due to its flexibility in shape definition, particular attention is given to interpolation using B- splines. The optimization problem is defined based on the geometrical model and the design variables are the positions of key points. Design variable linking can be applied to enforce symmetry.The structure it is analyzed using plane isoparametric elements. Thus, is necessary to perform the discretization of the structure in a set of finite elements. Different algorithms were implemented to generate structured or unstructured finite element meshes. The standard Newton-Raphson method is applied to find the equilibrium configuration, and different methods can be used to evaluate critical points. Due to the convergence problems presented by direct methods, a new semi-direct method was developed. The numerical results show the suitability of the finite elements and numerical methods implemented in the present work.The mathematical programming algorithms used in this work require the evaluation of design sensitivities in order to compute the search direction of the optimization process.Using basic sensitivity equations, which are independent from the particular element, analytical expressions were developed for the sensitivity computation of isoparametric elements formulated according to the Total Lagrangian approach. Applying the analytical method for more complex elements is very cumbersome and error prone. On the other hand, the finite difference method is simple and generic, but its computational cost is prohibitive. The semi-analytical method preserves the advantages of the use of finite differences and has a low computational cost, but presents severe accuracy problems. Hence, a method based on the exact differentiation of the rigid body motions was developed in this work to improve the accuracy of the semi- analytical sensitivities of geometrically nonlinear structures. The numerical examples show that this method eliminates the abnormal errors presented by the semi- analytical sensitivities. / [es] Este trabajo propone una metodología para la optimización de forma de extructuras geométricamente no lineares. EL objetivo de esta metodología es evitar los problemas de inestabilidad que presentan las extructuras optimizadas de acuerdo con la formulación clásica. Ella fue implementada para problemas bidimensionales y los resultados obtenidos en la optimización de diferentes extructuras demuestran su éxito. Utilizando conceptos de modelaje geométrica, la forma de la extructura se define a través de las curvas de contorno. Así, la representación paramétrica de curvas y su definición en función de un conjunto de puntos de interpolación (puntos clave) son discutidas detalladamente. Se le da especial a la interpolación a través de B splines,debido a su gran flexibilidad. El problema de optimización se define con base en el modelo geométrico y las variables de proyecto son las coordenadas de los puntos clave. La simetría de la extructura se garante a través de la llamada de variables. La extructura se analiza a través de elementos isoparamétricos planos. Antes de realizar el análisis, es necesario discretizar la extructura en un conjunto de elementos finitos. Para realizar esta tarea fueron implementados diferentes algoritmos de generación de mallas, tanto extructuradas como no extructuradas. EL método de Newton Raphson es utilizado para determinar la configuración de equilibrio y pueden ser aplicados diferentes métodos para determinar los puntos críticos. Debido a los problemas de convergencia presentados por los métodos directos para la determinación de los puntos crticos, se desarrolló un método semidirecto. Los resultados obtenidos en el análisis de diferentes ejemplos muestran la adque los elementos finitos los métodos numéricos implementados son adequados Los algoritmos de programación matemática utilizados en este trabajo necesitan los gradientes de la función objetivo y de las restricciones, que son calculadas con base en los gradientes de las respuestas de la extructura. Partiendo de las ecuaciones generales válidas para cualesquiera elementos, fueron desarrolladas expresiones analíticas que permiten el cálculo exacto de las sensibilidades de elementos finitos isoparamétricos formulados a través del procedimiento Lagrangiano Total. EL desarrollo y la implementación de expresiones semejantes para elementos más complexos es una tarea bastante árdua. Por otro lado, el método de las diferencias finitas es simple y genérico, pero muy caro computacionalmente. EL método semianalítico mantiene las ventajas de la utilización de diferencias finitas y posee un costo computacional bajo, pero puede presentar serios problemas de precisión. Es por ello que se desarrolló en este trabajo un procedimiento para mejorar la calidad de las sensibilidades semianalíticas de extructuras geométricamente no lineares. EL procedimiento tiene como base la diferenciación exacta de los movimentos de cuerpo rígido del elemento utilizado. Los resultados numéricos obtenidos demuestran su eficacia.

Near-field acoustical holography (NAH) has been used extensively for acoustical imaging of infinitesimal-amplitude (or small-amplitude) sources. However, recent interests are in the application of NAH to image finite-amplitude (or high-amplitude) sources such as jets and rockets. Since NAH is based on linear equations and finite-amplitude sources imply nonlinear effects, which cause shock formation and consequently an altered spectral shape, a feasibility study is carried out to determine the effect of nonlinear propagation on NAH. Jet and rocket sources typically have a distinct spectral shape resembling a ‘haystack’ and center frequencies varying from 30 to 300 Hz. To test the effect of nonlinear propagation on jet or rocket noise, several waveforms with varying spectral shapes and center frequencies were created and numerically propagated in one dimension using a nonlinear propagation algorithm. Bispectral methods were used to determine the amount and effect of nonlinearity, showing that higher center frequencies lead to more nonlinearities for a given amplitude. Also, higher-order statistical analysis of the time derivative of the waveforms was used to determine information about the relative amount of waveform steepening and shock coalescence occurring. NAH was then used to reconstruct the original waveform magnitude and the errors were determined. It was found that the ‘haystack’ spectral shape can be preserved by the nonlinear effects leading to low amplitude-reconstruction errors, whereas a narrow-band spectral shape will become altered and reconstruct very poorly. However, if nonlinear effects become strong due to higher center frequencies, longer propagation distances or higher amplitudes, even the ‘haystack’ shape will become altered enough to cause poor reconstruction. Two-dimensional propagation studies were also performed from two point sources, showing differences between linear and nonlinear propagation.

This study examines the use of embedded shape memory alloy (SMA)actuators for adaptive control of the themomechanical response of composite structures. Control of static and dynamic responses are demonstrated including thermal buckling, thermal post-buckling, vibration, sonic fatigue, and acoustic transmission. A thermomechanical model is presented for analyzing such shape memory alloy hybrid composite (SMAHC) structures exposed to thermal and mechanical loads. Also presented are (1) fabrication procedures for SMAHC specimens, (2) characterization of the constituent materials for model quantification, (3) development of the test apparatus for conducting static and dynamic experiments on specimens with and without SMA, (4) discussion of the experimental results, and (5) validation of the analytical and numerical tools developed in the study. The constitutive model developed to describe the mechanics of a SMAHC lamina captures the material nonlinearity with temperature of the SMA and matrix material if necessary. It is in a form that is amenable to commercial finite element (FE) code implementation. The model is valid for constrained, restrained, or free recovery configurations with appropriate measurements of fundamental engineering properties. This constitutive model is used along with classical lamination theory and the FE method to formulate the equations of motion for panel-type structures subjected to steady-state thermal and dynamic mechanical loads. Mechanical loads that are considered include acoustic pressure, inertial (base acceleration), and concentrated forces. Four solution types are developed from the governing equations including thermal buckling, thermal post-buckling, dynamic response, and acoustic transmission/radiation. These solution procedures are compared with closed-form and/or other known solutions to benchmark the numerical tools developed in this study. Practical solutions for overcoming fabrication issues and obtaining repeatable specimens are demonstrated. Results from characterization of the SMA constituent are highlighted with regard to their impact on thermomechanical modeling. Results from static and dynamic tests on a SMAHC beam specimen are presented, which demonstrate the enormous control authority of the SMA actuators. Excellent agreement is achieved between the predicted and measured responses including thermal buckling, thermal post-buckling, and dynamic response due to inertial loading. The validated model and thermomechanical analysis tools are used to demonstrate a variety of static and dynamic response behaviors associated with SMAHC structures. Topics of discussion include the fundamental mechanics of SMAHC structures, control of static (thermal buckling and post-buckling) and dynamic responses (vibration, sonic fatigue, and acoustic transmission), and SMAHC design considerations for these applications. The dynamic response performance of a SMAHC panel specimen is compared to conventional response abatement approaches. SMAHCs are shown to have significant advantages for vibration, sonic fatigue, and noise control. / Ph. D.

Smart materials are intelligent materials that change their structural, chemical, mechanical, or thermal properties in response to an external stimulus such as heat, light, and magnetic and electric fields. With the increase in usage of smart materials in many sensitive applications, the need for a remote, wireless, efficient, and biologically safe stimulus has become crucial. This dissertation addresses this requirement by using high intensity focused ultrasound (HIFU) as the external trigger. HIFU has a unique capability of maintaining both spatial and temporal control and propagating over long distances with reduced losses, to achieve the desired response of the smart material. Two categories of smart materials are investigated in this research; shape memory polymers (SMPs) and piezoelectric materials. SMPs have the ability to store a temporary shape and returning to their permanent or original shape when subjected to an external trigger. On the other hand, piezoelectric materials have the ability to convert mechanical energy to electrical energy and vice versa. Due to these extraordinary properties, these materials are being used in several industries including biomedical, robotic, noise-control, and aerospace. This work introduces two novel concepts: First, HIFU actuation of SMP-based drug delivery capsules as an alternative way of achieving controlled drug delivery. This concept exploits the pre-determined shape changing capabilities of SMPs under localized HIFU exposure to achieve the desired drug delivery rate. Second, solving the existing challenge of low efficiency by focusing the acoustic energy on piezoelectric receivers to transfer power wirelessly. The fundamental physics underlying these two concepts is explored by developing comprehensive mathematical models that provide an in-depth analysis of individual parameters affecting the HIFU-smart material systems, for the first time in literature. Many physical factors such as acoustic, material and dynamical nonlinearities, acoustic standing waves, and mechanical behavior of materials are explored to increase the developed models' accuracy. These mathematical frameworks are designed with the aim of serving as a basic groundwork for building more complex smart material-based systems under HIFU exposure. / Doctor of Philosophy / Smart materials are a type of intelligent materials that have the ability to respond to external stimuli such as heat, light, and magnetic fields. When these materials respond, they can change their structural, thermodynamical, mechanical or chemical nature. Due to this extraordinary property, smart materials are being used in many applications including biomedical, robotic, space, microelectronics, and automobile industry. However, due to increased sensitivity and need for safety in many applications, a biologically safe, wireless, and efficient trigger is required to actuate these materials. In this dissertation, sound is used as an external trigger to actuate two types of smart materials: shape memory polymers (SMPs) and piezoelectric materials. SMPs have an ability to store a temporary (arbitrarily deformed) shape and return to their permanent shape when exposed to a trigger. In this dissertation, focused sound induced thermal energy acts as a trigger for these polymers. A novel concept of focused ultrasound actuation of SMP-based drug delivery capsules is proposed as a means to solve some of the challenges being faced in the field of controlled drug delivery. Piezoelectric materials have an ability to generate electric power when an external mechanical force is applied and vice versa. In this study, sound pressure waves supply the external force required to produce electric current in piezoelectric disks, as a method for achieving power transfer wirelessly. This study aims to solve the current problem of low efficiency in acoustic power transfer systems by focusing sound waves. This dissertation addresses the fundamental physics of high intensity focused ultrasound actuation of smart materials by developing comprehensive mathematical models and systematic experimental investigations, that have not been performed till now. The developed models enable an in-depth analysis of individual parameters including nonlinear material behavior, acoustic nonlinearity and resonance phenomena that affect the functioning of these smart systems. These mathematical frameworks also serve as groundwork for developing more complex systems.

<p>Fiber-optic communication systems have revolutionized the telecommunications industry and have played a major role in the advent of the Information Age. Thousands of kilometers of optical fiber are used by telecommunications companies to transmit telephone signals, Internet communication, and cable television signals throughout the world. So, working in this area has always been interesting. This thesis analyzes the nonlinearity of fiber-optic systems and proposes a system to mitigate fiber nonlinear e®ects. The topics of this thesis can be categorized into two parts. In the first part of thesis (Chapters 2, 3, and 4), analytical models are developed for fiber-optic nonlinear effects. It is important to have an accurate analytical model so that the impact of a specific system/signal parameter on the performance can be assessed quickly without doing time-consuming Monte-Carlo simulations. In the second part (Chapters 5, and 6), a multi-core/fiber architecture is proposed to reduce the nonlinear effects.</p> <p>In Chapter 2, intrachannel nonlinear impairments are studied and an analytical model for the calculation of power spectral density (PSD) and variance of the non- linear distortion is obtained based on quadrature phase-shift keying (QPSK) signal. For QPSK signals, intrachannel four-wave mixing (IFWM) is the only stochastic non- linear distortion. To develop the analytical model, a first order perturbation theory is used. For a Gaussian pulse shape, a closed form formula is obtained for the PSD of IFWM. For non-Gaussian pulses, it is not possible to find the PSD analytically. However, using stationary phase approximation approach, convolutions become multiplications and a simple analytical expression for the PSD of the nonlinear distortion can be found. The total PSD is obtained by adding the PSD of amplified spontaneous emission (ASE) PSD to that of the nonlinear distortion. Using the total PSD, bit error ratio (BER) can be obtained analytically for a QPSK system. The analytically estimated BER is found to be in good agreement with numerical simulations. Significant computational effort can be saved using the analytical model as compared to numerical simulations, without sacrificing much accuracy.</p> <p>In Chapter 3, the same approach as that in Chapter 2 is used to find an analytical expression for the PSD of the intrachannel nonlinear distortion of a fiber-optic system based on quadrature amplitude modulation (QAM) signal. Unlike the QPSK signal, intrachannel cross-phase modulation (IXPM) is a stochastic process for the QAM signal which leads to the increase of the nonlinear distortion variance. In this chapter, analytical expressions for the PSDs of self-phase modulation (SPM), IXPM, IFWM, and their correlations are obtained for the QAM signal. Simulation results show good agreement between the analytical model and numerical simulation.</p> <p>In Chapter 4, inter-channel nonlinear impairment is studied. This time, a first order perturbation technique is used to develop an analytical model for SPM and cross-phase modulation (XPM) distortions in a wavelength division multiplexing (WDM) system based on QAM. In this case, SPM distortion is deterministic and does not contribute to the nonlinear noise variance. On the other hand, XPM is stochastic and contributes to the noise variance. In this chapter, effects of input launch power, fiber dispersion, system reach, and channel spacing on the nonlinear noise variance are investigated as well.</p> <p>In Chapter 5, a single-channel multi-core/fiber architecture is proposed to reduce intrachannel fiber nonlinear effects. Based on the analytical model obtained in the first part of thesis, the nonlinear distortion variance scales as P³, where P is the fiber input launch power, which suggests that decreasing the fiber input power can reduce the nonlinear distortion significantly. In this system, the input power is divided between multiple cores/fibers by a power splitter at the input of each span and a power combiner adds the output fields of multiple cores/fibers so that one amplifier can be used for each span. In this case, each core/fiber receives less power and hence adds less nonlinear distortion to the signal. In a practical system, individual fiber parameters are not identical; so the optical pulses propagating in the fibers undergo different amounts of phase shifts and timing delays due to the fluctuations of fibers' propagation constants and fibers' inverse group speeds. Optical and electrical equalizers are proposed to compensate for these inter-core/fiber dispersions. In the case of an optical equalizer, adaptive time shifters and phase shifters are adjusted such that the maximum power is obtained at the output of power combiner. Our numerical simulation results show that for unrepeatered systems, the performance (Q factor) is improved by 6.2 dB using 8-core/fiber configuration as compared to single- core fiber system. In addition, for multi-span system, the transmission reach at BER of 2.1*10^-3 is quadrupled in 8-core/fiber configuration.</p> <p>In Chapter 6, a multi-channel multi-core/fiber architecture is proposed to reduce the inter-channel nonlinear distortions. In this architecture, different channels of a WDM system are interleaved between multiple cores/fibers which increases the channel spacing in each core/fiber. Higher channel spacing decreases the inter-channel nonlinear impairments in each core/fiber which leads to system performance improvement. At the end of each span, a multiplexer adds the channels from different cores/fibers so that one amplifier can be used for all of the channels. Unlike the single-channel multi-core/fiber system, the WDM multi-core/fiber system does not require equalizers since different cores/fibers carry channels with different frequencies. Simulation results show that for a 39-span system, the 4-core/fiber system with negligible crosstalk outperforms the single-core system by 2.2 dBQ₂₀. The impact of crosstalk between cores of a multi-core fiber (MCF) on the system performance is studied. The simulation results show that the performance of the multi-core WDM system is less sensitive to the crosstalk effect compared to conventional multi-core systems since the propagating channels in the cores are not correlated in frequency domain.</p> / Doctor of Philosophy (PhD)

All wireless receivers have some degree of nonlinearity that can negatively impact performance. Two major effects from this nonlinearity are power compression, which leads to amplitude and phase distortions in the received signal, and desensitization caused by a high powered interfering signal at an adjacent channel. As the RF spectrum becomes more crowded, the interference caused by these adjacent signals will become a more significant problem for receiver design. Therefore, having bit and symbol error rate expressions that take the receiver nonlinearity into account will allow for determining the linearity requirements of a receiver. This thesis examines the modeling of the probability density functions of M-PAM and M-QAM signals through an AWGN channel taking into account the impact of receiver nonlinearity. A change of variables technique is used to provide a relationship between the pdf of these signals with a linear receiver and the pdf with a nonlinear receiver. Additionally, theoretical bit and symbol error rates are derived from the pdf expressions. Finally, this approach is extended by deriving pdf and error rate expressions for these signals when nearby blocking signals cause desensitization of the signal of interest. Matlab simulation shows that the derived expressions for a nonlinear receiver have the same accuracy as the accepted expressions for linear receivers. / Master of Science / All wireless receivers have some amount of nonlinearity that can distort a received signal and impact performance. For amplitude modulated signals, the power compression caused by the nonlinear receiver will cause distortions in the amplitude and phase of the received signal. Additionally, a high powered interfering signal at a close frequency can decrease the gain and distort the received signal. This thesis examines how the probability density of an amplitude modulated signal with a nonlinear receiver can be modeled for both of these situations. These theoretical probability density functions are used to derive theoretical error rate expressions for the signals both with and without the adjacent channel interference. Simulations in Matlab show that the accuracy of these derived expressions is similar to the accuracies of the linear receiver expressions. These derived expressions will be able to remove the need for time consuming simulation when designing receivers for wireless systems.