The finite difference time domain (FDTD) method is commonly used for numerical simulations of the electromagnetic wave propagation in time domain. The FDTD method is easy to implement and the computational results are highly relevant to the analytical solution, so that the FDTD method is applied to variety application problems. However, the computational efficiency of the FDTD method is constrained by the upper limit of the temporal discretisation. The Courant Friedrich Lewy (CFL) stability condition limits the time step for the computation of the FDTD method, so that if the spatial discretisation of the computation is set to be small in order to obtain high accurate results, the size of the temporal discretisation need to be satisfy the CFL stability condition. The locally one dimensional FDTD (LOD-FDTD) method is unconditionally stable. The time step and the spatial step can be independently chosen for the computation of the LOD-FDTD method. The arithmetic operations of the LOD-FDTD method is fewer than that of the other implicit FDTD method, such as the Crank Nicolson FDTD (CN-FDTD) method and the alternating direction implicit FDTD (ADI-FDTD) method. Although the implementation of the LOD-FDTD method is simpler than that of the ADI-FDTD method,the numerical error in the computational results of the LOD-FDTD method is equivalent to that in the computational results of the ADI-FDTD method. In this thesis, a new three dimensional (3D) frequency dependent (FD) LOD-FDTD method is proposed. The one pole Debye model is incorporated into the 3D-FD-LOD-FDTD method in order to deal with practical applications. The proposed method is implemented in Fortran 90 and parallelised with OpenMP. A simulation model of the human phantom is developed in the 3D-FD-LOD-FDTD method with fine structures and frequency dependent dielectric properties of the human tissues, and numerical simulation of electromagnetic wave propagation inside the human head is shown.

Ground penetrating radar (GPR) is widely used to identify locations of sinkholes in covered karst terrain in Florida. Some sinkholes serve as hydraulic conduits between the surficial and underlying aquifers. Their role is critical in determining the surficial aquifer response to pumping in deeper aquifers. Improved methods for discriminating between hydraulically active sinkholes and plugged sinkholes could help regional water management. In the covered karst of west-central Florida a clay-rich weathering horizon forms over the limestone. The clay-rich layer is in turn overlain by surficial sands. Ground penetrating radar profiles typically show a strong reflector from the top of clay-rich horizon as well as internal layering within sands. Active sinkholes are expected to have sandy conduits that broach the clay layer, and perhaps layering in the overlying sand indicative of ongoing subsidence. Three dimensional simulations of GPR profiles over sinkhole with and without conduits were run with the finite-difference time-domain (FDTD) program GPRMAX. Results from the synthetic surveys were then processed with standard techniques, including migration. The modeling confirms that conduits appear in GPR records primarily as gaps in the return from the clay layer. The modeling also shows that non-traditional survey geometries (varying antenna spacing and orientation) are unlikely to recover more information than traditional proximal transmitter-receiver separation. Also examined are GPR profiles and 3D grids over a set of active and inactive sinkholes in Tampa, Florida. Results from these surveys showed decent structural recovery of a small sinkhole similar in structure to that of the modeled ones. Indications of active subsidence and possible conduit structure were apparent from this data. Finally, the dense surveys served as a benchmark to compare interpretations taken with the same surveys at lower spatial resolutions and profiles with 2D-only processing methods in order to understand errors in analysis and interpretation that are possible from 2D surveys. Two-dimensional surveys, 2D processed and migrated, showed some similarity to the 3D results previously mentioned but contained more complexities and artifacts, which led to poorer interpretation ability.

In this thesis by articles, I propose and demonstrate the full design, fabrication and characterization of optical biosensors based on (Bloch) Long Range Surface Plasmon Polaritons (LRSPPs). Gold waveguides embedded in CYTOP with an etched microfluidic channel supporting LRSPPs and gold waveguides on a one-dimensional photonic crystal (1DPC) supporting Bloch LRSPPs are exploited for biosensing applications. Straight gold waveguides embedded in CYTOP supporting LRSPPs as a biosensor, are initially used to measure the kinetics constants of protein-protein interactions. The kinetics constants are extracted from binding curves using the integrated rate equation. Linear and non-linear least squares analysis are employed to obtain the kinetics constants and the results are compared. The device is also used to demonstrate enhanced assay formats (sandwich and inhibition assays) and protein concentrations as low as 10 pg/ml in solution are detected with a signal-to-noise ratio of 20 using this new optical biosensor technology. CYTOP which has a refractive index close to water is the fluoropolymer of choice in current state of the art waveguide biosensors. CYTOP has a low glass transition temperature which introduces limitations in fabrication processes. A truncated 1D photonic crystal can replace a low-index polymer cladding such as CYTOP, to support Bloch LRSPPs within the bandgap of the 1DPC over a limited ranges of wavenumber and wavelength. Motivated by quality issues with end facets, we seek to use grating couplers in a broadside coupling scheme where a laser beam emerging from an optical fiber excites Bloch LRSPPs on a Au stripe on a truncated 1D photonic crystal. Adiabatic and non-adiabatic flared stripes accommodating wide gratings size-matched to an incident Gaussian beam are designed and compared to maximise the coupling efficiency to LRSPPs. The gratings are optimized, initially, through 2D modelling using the vectorial finite element method (FEM). Different 3D grating designs were then investigated via 3D modelling using the vectorial finite difference time domain (FDTD) method. Given their compatibility with planar technologies, gratings and waveguides can be integrated into arrays of biosensors enabling multi-channel biosensing. A multi-channel platform can provide, e.g., additional measurements to improve the reliability in a disease detection problem. Thus, a novel optical biosensor based on Bloch LRSPPs on waveguide arrays integrated with electrochemical biosensors is presented. The structures were fabricated on truncated 1D photonic crystals comprised of 15 period stack of alternating layers of SiO2/Ta2O5. The optical biosensors consist of Au stripes supporting Bloch LRSPPs and integrate grating couplers as input/output means. The Au stripes also operate as a working electrode in conjunction with a neighboring Pt counter electrode to form an electrochemical sensor. The structures were fabricated using bilayer lift-off photolithography and the gratings were fabricated using overlaid e-beam lithography. The planar waveguides are integrated into arrays capable of multichannel biosensing. The wafer is covered with CYTOP as the upper cladding with etched microfluidic channels, and wafer-bonded to a borofloat silica wafer to seal the fluidic channels and enable side fluidic interfaces. The proposed device is capable in principle of simultaneous optical and electrochemical sensing and could be used to address disease detection problems using a multimodal strategy.

This thesis has proposed a simplified model of corona discharge from an overhead wire struck by lightning for surge computations using the FDTD method. In the corona model, the progression of corona streamers from the wire is represented as the radial expansion of cylindrical conducting region around the wire. The validity of this corona model has been tested against experimental data. Then, its applications to lightning electromagnetic pulse computations have been reviewed. / 博士(工学) / Doctor of Philosophy in Engineering / 同志社大学 / Doshisha University

Quantitative Ultrasound (QUS) techniques with the advantages of an axial transmission measurement were applied to implement an ultrasonic system for cortical bone evaluation. This evaluation is focused on the measurement and characterization of shear waves propagating in the axial direction of the cortical layer of bone. Signals were analyzed in time and frequency domains. And, in order to understand the wave propagation phenomenon, and predict experimental results, simulations using the elastic Finite-difference-time-domain (FDTD) method were implemented considering isotropic and anisotropic bone models. Additionally, shear wave velocities using the axial method were verified by a simple thought transmission measurement. / 博士(工学) / Doctor of Philosophy in Engineering / 同志社大学 / Doshisha University

This thesis presents a theoretical and numerical investigation of silicon-on-insulator trench based passive optical components, bend and splitter, respectively. Compact 90 degree and 105 degree bend and splitter are designed with high index-contrast rib waveguide at wavelength 1550nm and serve as building blocks of splitting network in micro-cantilever biosensing application. The main characteristic of trench based bend and splitter structures is their miniature size and their low radiation loss due to the strong light confinement in high index-contrast systems. Thus large scale, high density optical integrated splitting network becomes possible with the associated advantages of compactness. With FDTD simulation, we show that single-mode trench based bends and splitters exhibit around 16000nm X 16000nm overall size with low loss for different bending angle. Total efficiency is about 92.9% (90 degree bend), 89.3% (105 degree bend), 92% (90 degree splitter) and 84% (90 degree splitter) respectively.

This thesis covers recent advances in the adjoint variable method for the sensitivity estimations through time-domain electromagnetic simulations. It considers both frequency-independent and frequency-dependent response functions, and at the same time, provides a novel adjoint treatment for addressing dispersive sensitivity parameters in the material constitutive relation. With this proposed adjoint technique, response sensitivities with respect to all N sensitivity parameters can be computed through at most one extra simulations regardless of the value of N. This thesis also extends the existing adjoint technique to estimate all N^2 second-order sensitivity entries in the response Hessian matrix through N additional simulations. All adjoint sensitivity techniques presented in this thesis are numerically validated through various practical examples. Comparison shows that our produced adjoint results agree with those produced through central finite-difference approximations or through exact analytical approaches. / Dissertation / Doctor of Engineering (DEng)

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