Finite-Difference (FD) based complex modes solver and Complex Mode Matching Method (CMMM) is one of the most popular combinations in modeling and simulation of opti- cal waveguides. This thesis covers the basic theories behind the approaches and impor- tant implementation details. Weighted Optical Path Distance is proposed to speed up convergence and improve numerical accuracy to deal with asymmetric structures. An improved formula is derived for Complex Mode Matching Method expansion process based on matrix optimization. The latter part applies the above approach in the mod- eling of bending structures and grating structures. Typical structures, including bend- ing structures, straight-bend-straight structures, long-period gratings, gratings with de- posited layer, gratings with deep corrugations, are investigated and analyzed. / Thesis / Master of Science in Electrical and Computer Engineering (MSECE)

The electromagnetic coupling of a microstrip transmission line (MS-TL) to a metamaterial backward wave Negative-Refractive-Index transmission line (NRI-TL) is the primary investigation of this dissertation. The coupling of forward waves in the MS-TL to the backward waves in the NRI-TL results in the formation of complex modes, characterized by simultaneous phase progression and attenuation along the lossless lines. Through network-theoretic considerations, we investigate the properties of these modes in the complex-frequency plane of the Laplace domain to help unravel the confusion that has existed in the literature regarding the independent excitation of a pair of conjugate complex modes. We show that it is possible to arbitrarily suppress one of the modes over a finite bandwidth and completely eliminate it at a discrete set of frequencies using proper source and load impedances. Hence we use conjugate modes with independent amplitudes in our eigenmode expansion when we analyse various coupling configurations between the two types of lines (MS/NRI-TL coupler). We derive approximate closed-form expression for the scattering parameters of the MS/NRI-TL coupler and these are complemented by design charts that allow the synthesis of a wide range of specifications. Moreover, these expressions reveal that such couplers allow for arbitrary backward coupling levels along with very high-isolation when they are made half a guided wavelength long. The MS/NRI-TL coupler offers some interesting applications which we highlight through the design and testing of a 3-dB power splitter, a high-directivity signal monitor and a compact corporate power divider. We have included design, simulation and experimental data for the fabricated prototypes exhibiting good agreement and thereby justifying the theory that has been developed in this work to explain the coupling between a right-handed MS-TL and a left-handed NRI-TL.

The electromagnetic coupling of a microstrip transmission line (MS-TL) to a metamaterial backward wave Negative-Refractive-Index transmission line (NRI-TL) is the primary investigation of this dissertation. The coupling of forward waves in the MS-TL to the backward waves in the NRI-TL results in the formation of complex modes, characterized by simultaneous phase progression and attenuation along the lossless lines. Through network-theoretic considerations, we investigate the properties of these modes in the complex-frequency plane of the Laplace domain to help unravel the confusion that has existed in the literature regarding the independent excitation of a pair of conjugate complex modes. We show that it is possible to arbitrarily suppress one of the modes over a finite bandwidth and completely eliminate it at a discrete set of frequencies using proper source and load impedances. Hence we use conjugate modes with independent amplitudes in our eigenmode expansion when we analyse various coupling configurations between the two types of lines (MS/NRI-TL coupler). We derive approximate closed-form expression for the scattering parameters of the MS/NRI-TL coupler and these are complemented by design charts that allow the synthesis of a wide range of specifications. Moreover, these expressions reveal that such couplers allow for arbitrary backward coupling levels along with very high-isolation when they are made half a guided wavelength long. The MS/NRI-TL coupler offers some interesting applications which we highlight through the design and testing of a 3-dB power splitter, a high-directivity signal monitor and a compact corporate power divider. We have included design, simulation and experimental data for the fabricated prototypes exhibiting good agreement and thereby justifying the theory that has been developed in this work to explain the coupling between a right-handed MS-TL and a left-handed NRI-TL.

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