In integrated optics, there are many adiabatic dielectric waveguides. Examples include bending waveguides, multi-mode interferometers (MMI), taper waveguides, grating assisted directional couplers (GADC), etc. Among these waveguide devices, adiabatic bending waveguides are the most important basic devices. They are used to connect various vertical or horizontally displaced waveguides. There are many approximate methods such as the beam propagation method (BPM), finite-difference time-domain, (FD-TD) and finite-difference frequency-domain (FD-FD) methods that have been used to analyze and optimize the waveguide designs. BPM can not calculate wide angle optical traffic due to its intrinsic paraxial limitation. Both FD-TD, FD-FD handle wide-angle bi-directional traffic but both demand tremendous computational resources. In this thesis, we develop a new formulation called full eigen-mode expansion technique (FEMET) that considers only forward propagating but all wide-angle traffic. It is a simplified version of our existing bidirectional, coupled transverse-mode integral-equation (CTMIE) formulation. FEMET includes all forward propagating, high-order mode field but neglects reflection at the dielectric discontinuities. Since FEMET uses no matrix equations, it is much faster than CTMIE. To verify the accuracy of FEMET we consider the titled straight waveguide (TSR) as our test example. TSR has an exact solution in its natural coordinate system which allows us to study computational characteristics of FEMET. The two FEMET computational control parameters are the total number of waveguide sections and the number of modes used in each section. Together they control the speed and accuracy of FEMET. We use FEMET to analyze radiation and mode interference of both S-bend waveguides and two-corner bends. These results compare well with result computed by other methods.