Micro ring-cavity, like the Fabry-Perot cavity, is an optical device that resonates at certain frequencies. It is used as a phase compensator, and filter. Easily fabricated, the micro ring-cavity can be mass-produced, the ring-cavity is becoming evermore important as integrated opto-electronic technology advances. In this thesis, we begin with a novel one-dimensional theory that considers bi-directional traffic in the micro-ring cavity. By separating the device into easily manageable regions, and employing only fundamental modes in each of the sections, we obtain a closed-form formula for the transmission and reflection coefficient of this device. Under certain circumstances, when the directional coupler length is short but its coupling strength is strong, we observed a significant amount of reflection of optical energy at some frequencies. This phenomena is currently unknown to the opto-electronic industry. To further study this, we developed a more rigorous multi-mode propagation method for two-dimensional bi-directional ring cavities. The problem at hand is first being sliced into regions of multi-layered sections. Within each section, we can express the fields in terms of the underlying waveguide modes of the structure. At the interfaces of these sections, we construct coupled integral equations, which are derived from the continuity requirement of the tangential fields. We have complete formulations for both TE and TM cases, down to the coupled matrix equation for the unknown modal coefficients at each junction.