الفهرس 
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Abstract
Numerical simulations play an important role for the design and modeling of novel optical devices. Many investigations have been introduced for the developing of several numerical techniques that have been applied for the modal analysis of distinct waveguides. The analysis based on coupled mode theory (CMT) is very attractive because of its simple implementation. This thesis focuses primarily on the CMT for guided-wave optics. The CMT have been formulated for one- and two-dimensional structures. Moreover, coupling coefficients have been derived for different guiding media types such as lossless, lossy, uniform, non-uniform, isotropic, and anisotropic media. Further, the guided powers formulas are also obtained in each case. In addition, the full vectorial finite difference method (FVFDM) is also employed. This thesis can be divided to two parts. The first part concerns with coupled waveguide structures with one dimensional confinement. The wave guiding media are isotropic and lossless. The simplest model for the one dimensional coupled-waveguide system is a uniform directional coupler. The directional coupler is ideal for designing many important optical devices such as optical switches, modulators, power divider and filters. The directional coupler consists of two uniform, parallel waveguides in close proximity. If these waveguides have been subjected to periodic index perturbations along the direction of the wave propagation, a grating assisted coupler is constructed. A novel design of a compact optical wavelength filter is presented and analyzed by the CMT. An accurate characterizations of the novel design is introduced and the effect of the different structure geometrical parameters on the filter performance is studied. The crosstalk and bandwidth of the device are also calculated for various separations between the waveguides. The numerical results reveal that the proposed structure has a crosstalk of -34.909 dB and bandwidth of 14.8 nm for device length of 1646.26μm. A bandwidth of 10 nm can also be obtained with a device length of 3.1 mm. In addition, a novel design of cascaded structure of non-identical directional coupler is introduced and analyzed by the CMT. The objective of this design is to achieve the coupling between the waveguides modes which are originally not phase matched. The suggested design offers complete power exchange between two slab waveguides having modes with different propagation constants. The reported coupler exhibits low crosstalk of -38.38dB with a compact device length of 171.54μm. The second part of this dissertation work focuses on modeling and designing the PCF and its applications to directional coupler and multiplexer-demultiplexer (MUX-DEMUX). The guiding media is two- dimensional anisotropic and lossy media. The coupled mode equations, the coupling coefficients and the coupling power formulas have been derived. In addition, a novel design of polarization independent surface plasmon photonic crystal liquid crystal multiplexer-demultiplexer (MUX/DEMUX) based on dual core photonic crystal fiber with a central gold wire is proposed and analyzed. The cladding air holes are infiltrated with a nematic liquid crystal (NLC) of type E7 with rotation angle φ and the background material is a soft glass of type SF57 (lead silica). The simulation results are obtained using full vectorial finite difference method (FVFDM) and CMT. The numerical simulation reveals that, at φ = 90¬o, the suggested MUX/DEMUX has a short device length of 953.254 µm for x-polarized modes with broad bandwidths of 235 nm and 175 nm around wavelengths of 1.3 µm and 1.55 µm, respectively, with low crosstalk better than -20 dB. For y-polarized modes, the reported MUX/DEMUX has short device length of 1322.86 µm with broad bandwidths of 193 nm and 170 nm around 1.3 µm and 1.55 µm, respectively. Moreover, the polarization-independence is achieved with a short device length of 1138.06 µm and 1180 µm at φ = 90¬o and 0¬o, respectively. This thesis tracks in the following order, - Chapter One: Introduces the reader to the ground feature of the subject, and presents the objectives and importance of this research. - Chapter Two: Provides a brief historical review of the CMT and the basic assumptions and principles used in the formulation of the CMT. - Chapter Three: Provides a rigorous derivation of the conventional orthogonal, nonorthogonal, and self-consistent orthogonal coupled mode theory for uniform directional coupler is introduced. The derived formulas are employed to study in details the characteristics of the uniform directional couplers. - Chapter Four: Presents a detailed formulation of the coupled mode theory for the grating-assisted couplers. The accuracy and validity of the numerical results are discussed in details. - Chapter Five: A novel design of an optical wavelength filter of non-identical directional coupler have been presented and analysed by CMT. In addition, a novel design of cascaded structure of non-identical directional coupler is introduced and analysed by CMT. - Chapter six: Describes the formulation of CMT for photonic crystal fiber coupler consisting of anisotropic materials. In addition, a novel design of polarization independent surface plasmon liquid crystal photonic crystal multiplexer-demultiplexer is proposed and analyzed. The modal analysis is performed using the full vectorial finite difference method and CMT. The numerical simulations are discussed in details. - Chapter seven: Contains the conclusions of the research and recommendations for further work.