A fairly general method for studying electromagnetic induction in cases where any lateral variations in conductivity are confined to the near-surface region is developed using the thin-sheet technique. The significant feature is that extended anomalies, subject only to the restriction that well-defined two-dimensional problems are approached at infinity, can be handled. The approximate boundary condition is that gradients parallel to the coordinate axes vanish at infinity. / Graduate

In this report we describe simulation of the surface current density on a PEC cylinder and the diffracted field for a line source above a finite PEC ground plane as a means to verify the Nero2D program. The results are compared with the exact solution and give acceptable errors. A terrain model for a communication link is studied in the report and we simulate the wave propagation for terrain with irregular shapes and different materials. The Nero2D program is based on the fast multipole method (FMM) to reduce computation time and memory. Gaussian sources are also studied to make the terrain model more realistic

The problems of the scattering off the perfect conductor sphere and the dielectric sphere have the exact solutions. But there are no exact solutions for the scattering off a multi-layered dielectric sphere with a metallic cap like the Lunberg lens reflectors which is used as a strong omni-directional reflector found in many microwave applications. Haruo Sakurai applied the modal expansion technique and point-matching method (PMM) to study the scattering of the Lunberg lens reflectors. The problem is eventually formulated as 2MN by 2MN simultaneous matrix equation with M regions each having 2N unknowns due to two set of coupled polarization vectors. Strictly speaking, the formulae of the mode matching method for the problem of the scattering of the dielectric sphere are not exact. Furthermore, the size of the simultaneous matrix equation is also unnecessarily too larger. In this thesis, we employ an integral equation formulation in the Frequency-domain together with the modified impedance transformation technique for the spherically layers to study the scattering of the Lunberg lens reflectors. We show that the formulae of the integral equation are exact and using an equivalent matrix equation, that the entire problem can be reduced to a N by N matrix equation where N is the number of terms of the expansion of the unknown field in the opening. To verify our formulation we compute the total field of the plane wave incident upon the multi-layered micro lenses and compared the results with those from the geometric optics. We get good agreement for the regions that both theories apply. Small discrepancy is also observed and is consistent with the theoretical prediction.

Abstract Optical fiber communications have been become one of the most popular researches since 1970s. In this field, there are many studies on the coupling between semiconductor lasers and fibers and many conclusions are demonstrated. In this thesis we build a 2-D numerical model to simulate energy coupling between laser diodes (LDs) and tapered optical fibers. Our model is based on the spectral domain integral equation (SDIE) formulation which is derived from Maxwell equations and the principle of mode matching. Through this numerical model we will be able to show the field distribution in LD waveguide junctions. We may also use this tool to study the coupling parameters such as the separation distance and tapered fiber geometry.

Micro ring-cavity, like the Fabry-Perot cavity, is an optical device that resonates at certain frequencies. It is used as a phase compensator, and filter. Easily fabricated, the micro ring-cavity can be mass-produced, the ring-cavity is becoming evermore important as integrated opto-electronic technology advances. In this thesis, we begin with a novel one-dimensional theory that considers bi-directional traffic in the micro-ring cavity. By separating the device into easily manageable regions, and employing only fundamental modes in each of the sections, we obtain a closed-form formula for the transmission and reflection coefficient of this device. Under certain circumstances, when the directional coupler length is short but its coupling strength is strong, we observed a significant amount of reflection of optical energy at some frequencies. This phenomena is currently unknown to the opto-electronic industry. To further study this, we developed a more rigorous multi-mode propagation method for two-dimensional bi-directional ring cavities. The problem at hand is first being sliced into regions of multi-layered sections. Within each section, we can express the fields in terms of the underlying waveguide modes of the structure. At the interfaces of these sections, we construct coupled integral equations, which are derived from the continuity requirement of the tangential fields. We have complete formulations for both TE and TM cases, down to the coupled matrix equation for the unknown modal coefficients at each junction.

This thesis focuses on some mathematical aspects and a few recent applications of the polarization tensor (PT). Here, the main concern of the study is to characterize objects presented in electrical or electromagnetic fields by only using the PT. This is possible since the PT contains significant information about the object such as shape, orientation and material properties. Two main applications are considered in the study and they are electrosensing fish and metal detection. In each application, we present a mathematical formulation of the PT and briefly discuss its properties. The PT in the electrosensing fish is actually based on the first order generalized polarization tensor (GPT) while the GPT itself generalizes the classical PT called as the P\'lya-Szeg\H PT. In order to investigate the role of the PT in electrosensing fish, we propose two numerical methods to compute the first order PT. The first method is directly based on the quadrature method of numerical integration while the second method is an adaptation of some terminologies of the boundary element method (BEM). A code to use the first method is developed in \textit while a script in \textit is written as an interface for using the new developed code for BEM called as \textit. When comparing the two methods, our numerical results show that the first order PT is more accurate with faster convergence when computed by \textit. During this study, we also give a strategy to determine an ellipsoid from a given first order PT. This is because we would like to propose an experiment to test whether electrosensing fish can discriminate a pair of different objects but with the same first order PT such that the pair could be an ellipsoid and some other object. In addition, the first order PT (or the P\'{o}lya-Szeg\H{o} PT) with complex conductivity (or complex permittivity) which is similar to the PT for Maxwell's equations is also investigated. On the other hand, following recent mathematical foundation of the PT from the eddy current model, we use the new proposed explicit formula to compute the rank 2 PT for a few metallic targets relevance in metal detection. We show that the PT for the targets computed from the explicit formula agree to some degree of accuracy with the PT obtained from metal detectors during experimental works and simulations conducted by the engineers. This suggests to alternatively use the explicit formula which depends only on the geometry and material properties of the target as well as offering lower computational efforts than performing measurements with metal detectors to obtain the PT. By using the explicit formula of the rank 2 PT, we also numerically investigate some properties of the rank 2 PT where, the information obtained could be useful to improve metal detection and also in other potential applications of the eddy current. In this case, if the target is magnetic but non-conducting, the rank 2 PT of the target can also be computed by using the explicit formula of the first order PT.

Time-domain NMR, in one and higher dimensionalities, makes routine use of inversion algorithms to generate results called \T2-distributions' or joint distributions in two (or higher) dimensions of other NMR parameters, T1, diffusivity D, pore size a, etc. These are frequently referred to as \Inverse Laplace Transforms' although the standard inversion of the Laplace Transform long-established in many textbooks of mathematical physics does not perform (and cannot perform) the calculation of such distributions. The operations performed in the estimation of a \T2-distribution' are the estimation of solutions to a Fredholm Integral Equation (of the First Kind), a different and more general object whose discretization results in a standard problem in linear algebra, albeit suffering from well-known problems of ill-conditioning and computational limits for large problem sizes. The Fredholm Integral Equation is not restricted to exponential kernels; the same solution algorithms can be used with kernels of completely different form. On the other hand, (true) Inverse Laplace Transforms, treated analytically, can be of real utility in solving the diffusion problems highly relevant in the subject of NMR in porous media.

Electromagnetic scattering from a rough two dimensional homogeneous scatterer has been computationally modeled. The scatterer is intended to simulate reflection from a two interface multilayer. The rough scatterer was created from Gaussian random points centered about an ideal interface. The points were connected with a third order spline interpolant which accounts for correlation between neighboring surface atoms. The scalar electric field integral equation (EFIE) and magnetic field integral equation (MFIE) were solved using the Nystrom method to obtain the reflected intensity as a function of observation angle. Verification of the accuracy of the code was obtained by means of comparison with well-known analytic solutions and approximations. The predicted Nevot-Croce factor drop in reflectance was found to be in general agreement with the computed decrease in reflectance due to surface roughness. However, an angle dependent difference was also noticed, indicating the Nevot-Croce factor might need revision. The code is being modified to run on a supercomputing cluster where longer, more realistic surfaces can be analyzed to determine whether an improved roughness correction factor is needed.

Industrial processes are subject to changes that can adversely affect product quality. A change in the process that increases the variability of the output of the process causes the output to be less uniform and increases the probability that individual items will not meet specifications. Statistical control charts for monitoring process variance can be used to detect an increase in the variability of the output of a process so that the situation can be repaired and product uniformity restored. Control charts that increase the sampling rate when there is evidence the variance has changed gather information more quickly and detect changes in the variance more quickly (on average) than fixed sampling rate procedures. Several variable sampling rate procedures for detecting increases in the process variance will be developed and compared with fixed sampling rate methods. A control chart for the variance is usually used with a separate control chart for the mean so that changes in the average level of the process and the variability of the process can both be detected. A simple method for applying variable sampling rate techniques to dual monitoring of mean and variance will be developed. This control chart procedure increases the sampling rate when there is evidence the mean or variance has changed so that changes in either parameter that will negatively impact product quality will be detected quickly. / Ph. D.

京都大学 / 新制・課程博士 / 博士(工学) / 甲第23918号 / 工博第5005号 / 新制||工||1781(附属図書館) / 京都大学大学院工学研究科分子工学専攻 / (主査)教授 佐藤 啓文, 教授 作花 哲夫, 教授 佐藤 徹 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DGAM