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This thesis proposes a new analytical self-adjoint sensitivity analysis to calculate the Jacobian of the S-parameters for metallic shape parameters. This method is independent of the full-wave numerical analysis and the respective system matrix. The theory works for both volumetric and infinitesimally thin metallic shapes. It exploits the computational efficiency of the self-adjoint sensitivity analysis (SASA) approach where only one EM simulation suffices to obtain both the responses and their gradients in the designable parameter space. There are three major advantages to this development: (1) the Jacobian computation for metallic structures is completely analytical and there is no approximation involved in the sensitivity analysis of shape parameters; (2) the implementation is straightforward and in the form of a post-processing algorithm operating on the exported field solutions on the surface or around the edge of the metallic structure; and (3) it provides the possibility for exact sensitivity analysis with all electromagnetic high-frequency simulators whose system matrices are not available to export or are not differentiable with respect to shape parameters, e.g., simulators based on the FDTD method and the MoM. The method was verified in a number of examples using a commercial finite-element solver. The agreement between the results calculated with the proposed method and the reference self-adjoint sensitivity curves provided with the simulator are very promising. Suggestions for future work are provided., Master of Applied Science (MASc)

Breast cancer is a serious health problem that severely affects the society. Science and engineering communities are looking to find more advanced and new cures to contain this deadly disease. There has been considerable success in increasing the efficacy of conventional imaging techniques for breast cancer detection such as mammography. However, the use of ionizing radiation, the incidence of patient discomfort and the low specificity are some of the negative aspects of mammography. Also, the chances to successfully cure breast cancer can increase manifold with early detection of the malignant tumors. Magnetic Resonance Imaging (MRI) is successful with its highly clear and detailed images, but it is considered too expensive for wide screening. Its low specificity is another disadvantage. Microwave imaging of the breast, which uses non-ionizing radiation, is a very active research area of recent times. It is hoped that once developed, it can override the negative aspects of the existing imaging modalities. The idea is to detect malignant lesions in the breast based on their electrical-property contrast with healthy breast tissues. The electrical properties of biological tissues in the microwave region are described by their complex permittivity. Previous studies claimed that malignant tumors have very high permittivity and high loss compared to the surrounding healthy tissue. It was assumed that the modality exploiting this contrast can easily detect sub-centimeter tumors. Hence, very simple models with high permittivity and loss tumor models embedded in low permittivity homogenous models were employed to show the detection capabilities of microwave imaging techniques. The examples were fairly amateurish and claimed unrealistic performance of the rather simplistic microwave imaging techniques. Recent studies have shown that the breast is not as simple an electromagnetic medium as was thought previously. It is a complex heterogeneous envi, Master of Applied Science (MASc)