In this thesis, we have analyzed the coupling gap dependent micro-ring loss in a single ring all-pass filter configuration using the two dimension (2D) finite difference time domain (FDTD) and EIM (effective index method). We utilized a new analysis scheme by calculating the transmission signal as a function of input wavelength and fitting the transmission spectrum with a phenomenological ring loss parameter. This novel scheme circumvents the complex waveguide mode analysis process, when the coupling gap is narrow and the all-pass coupling region becomes multi-mode. We first find that the radiation loss increases rapidly with decreasing coupling gap width. Our results show that the intrinsic bending losses of silicon micro-rings (on oxide) with the radius of 1.5 £gm, 2.5£gm, and 5£gm are about 20 dB/cm, 3 dB/cm, 1 dB/cm for TE polarization modes, respectively. For TM modes, the intrinsic bending losses with the radius of 1.5£gm, 2.5 £gm, and 5£gm are about 2573 dB/cm, 64 dB/cm, and 0.8 dB/cm, respectively. Next, we find that power coupling coefficients of the single ring all-pass filter configuration using the ring to ring couplers are much higher than the bus to ring couplers. The radiation losses of the ring to ring couplers for TM modes are improved significantly in all coupling gap widths. In a high-density integrated optics circuit, specially designed ring coupling region device structure is needed to address this serious optical loss issue.