Utilizing the semiconductor processing technology, a large number of optical components can be integrated into a small area. It is of low cost and high reliability and can be massively produced. The PLC(planar light circuit) has become an important component with the opto-communication industry.In this thesis, we aim to study dielectric waveguide termination witha slightly tilted facet. A waveguide with normal termination in the air will have non-zero reflection coefficients due to the impedance difference at the core-air junction. To reduce the reflection of the fundamental mode, it is custom to terminate the waveguide with a small tilted angle. The angle is optimally chosen to avoid spurious scattering into high-order radiation modes.To analyze this problem, we employ the modal expansion method for both the reflected waves and the transmitted waves. We then analytically extend the waves and join the two fields on the bordering line by matching the fields and their normal derivatives. An incomplete transverse-mode integral equation (TMIE) is derived for the reflection and transmission coefficients. The incomplete TMIE is good for waveguide termination with small tilted angles. Our analysis show that for multi-mode 1-D slab waveguide (simulating the 1-D optical fiber), the fundamental mode reflection coefficient is about -28dB down. It gradually reduces to -60dB as we increase the tilt angle from around 8 degrees. The result agrees well with those calculate from frequency-domain finite-difference method.