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The determination of propagation constant β for waveguiding structures is important both in intergrated- and fiber-optics because the designs of many optical waveguide devices such as directional couplers, polarizers, etc., depend on β. Except for those elementary three-layered step-index planar structures, the methods of finding β or dispersion relationship in optical waveguides are generally regarded as complicated ones and these materials are normally covered in graduate-level textbooks. Today, in-depth knowledges of guided-wave optics in conjunction with numerical techniques or the coupled-mode theory seem critical in analyzing or designing waveguiding structures and thereby potential researchers are discouraged from these interesting areas! With the familiar Fresnel's law of the lightwave reflection/transmission in the interface between two media learned in the Junior year, this thesis introduces a computationally and conceptually easy approach to find β for multi-planar waveguiding structures and thereby it is worth being included in textbooks for undergraduates. This proposed method, named evanescent-field excitation, should appear in undergraduate texts soon. We believe.
Other than planar waveguides, optical components based on fibers with a cylindrical geometry are also considered here. This thesis investigates doubly-clad cylindrical waveguides because of novel filtering properties in presence. A new kind of formulation incorporation the Goods-Hanchen shift was used to tell the power transmittance in such structures. To our best knowledge, the well-known Goos-Hanchen shift phenomenon is applied to estimate the transmittance of guided wave in fiber-optic components for the first time. Although some approximations are invoked, this method is applicabel for further complicated structures.
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