Desing of integrated and fiber optical micro-ring resonators for telecommunication

This project is a theoretical study of multiple coupled ring resonators, which can be used as demultiplexing filters in optical transmission systems, especially DWDM. We have chosen two approaches: analytical and numerical. Our aim is to design a boxlike filter, which is the best spectral profile for most of the modulation formats existing. Therefore, we compare different multiple coupled ring structures and we use different techniques to design them. We use the compound ring resonator theory formulated by Elshoff and Rautenberg [1] and that formulated by P. Urquhart to calculate analytically the transfer functions of one-, two-, three-, and four-ring resonators. We perform a numerical method to calculate transfer functions of N-ring resonators. The two methods (analytical and numerical) are compared to ensure that the numerical approach is valid for the rest of our calculations. With the analytical method we make a study of the Vernier effect, with three- and four-ring resonators. The rings have different circumferences but they are in the ratio of two integers, as in Vernier rulers, and we study different kinds of symmetry between these circumferences. With the numerical method we calculate the transfer function of N-ring resonators with different symmetry categories between the coupling ratios. We investigate the influence of waveguide losses and the fabrication errors in the effective reflectances. Finally, we present an application of the ring resonators to a DWDM signal modulated with a bipolar non-return-to-zero code, to indicate how it can be used in a system