Tapered waveguides are often used as spot-size converters and power dividers. In general, radiation in these devices is hard to analyze by either BPM or FD-TD methods. We apply the full eigenmode expansion technique (FEMET) to study the propagation of an adiabatic dielectric tapered waveguide. We often assume that wave propagation in an ideal ¡§adiabatic¡¨ dielectric waveguide suffer no reflection nor radiation loss. It is especially true for the fundamental mode propagation in an ¡§adiabatic¡¨ dielectric waveguide. Thus, the fundamental mode of the input waveguides will be converted to the corresponding fundamental mode of the output waveguide whenever the two are connected by an adiabatically tapered waveguide. However, the higher-order modes do not always propagate through the tapered waveguide when the output waveguide does not support that particular guiding mode. It is interesting to predict such radiation phenomena and to observe them in a numerical experiment. In this thesis we consider the titled straight waveguide (TSR) as our test example. Since TSR has an exact solution in its natural coordinate system, we can study computational characteristics of FEMET via TSR examples. Using FEMET and FD-FD method, we carefully examine mode evolution, conversion radiation and reflection of many quasi-adiabatic tapered waveguides. Finally the apparent visual radiation angles are defined and computed as function of taper angle core/cladding indices and incident mode order for both TE and TM mode cases.

Propagation properties of linearly tapered parabolic-index optical waveguides are investigated. Tapers with planar (two-dimensional) and fiber (three-dimensional) geometries are considered. A ray optics approach is used in the analysis, assuming that the characteristic dimensions of tapered waveguides are small compared to the wavelength of light. Closed form analytical solutions are obtained for ray trajectories in tapers with small slope and small index difference between the core and cladding. To assess the accuracy of analytical solutions, exact ray trajectories in planar waveguides are determined using numerical techniques and compared to those obtained from the analytical method. The agreement between the analytical and numerical solutions is excellent. It is observed that ray trajectories exhibit the behavior of modulated sinusoidal functions with decreasing amplitude and period as light travels toward the smaller end of the taper. This illustrates the power concentrating capability of the taper. Applications of these graded-index tapers when used to couple power from light sources to planar and fiber waveguides and when they are used to connect two waveguides of different core sizes are addressed. Coupling efficiencies for light source coupling and radiation loss of tapers when used to connect two dissimilar waveguides are calculated. Numerical results for example cases are provided. A novel application of the taper as collimated beam concentrator is also proposed. / Master of Science

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Polarization dependences of optical devices in highly-integrated optical systems become a major problem. To overcome this issue, one can implement polarization diversity scheme to achieve a single polarization on-chip network. One of the essential components in a polarization diversity scheme is the polarization beam splitter (PBS). In this thesis, we will a PBS based on a silicon-on-insulator (SOI) platform with reduced device size and broad operation bandwidth. We use the three-dimensional Finite-Difference Time-Domain (3D-FDTD) method to perform the simulation. First, we use two asymmetric waveguides to design an asymmetric directional coupler with only TE-like mode phase matching condition. We then tape the lower waveguide to keep the TE-polarized light, and split the TE- and TM- polarized light. By utilizing an asymmetrical directional coupler with a tapered waveguide, we have achieved a 7.3