Characteristics of complementary ring-resonator add/drop filters modeling by using graphical approach

In this paper, the filtering characteristics of the two kinds of complementary ring-resonator add/drop filters are modeled and investigated. A graphical approach with signal flow graph is employed here for the analytical derivation of the optical transfer functions in Z-domain of filters. The characteristics of the complementary circuits including the transmittance and group delay of the drop port with respect to the input port are simulated. The present analysis is restricted to directional couplers characterized by two parameters, the power coupling coefficient κ and power coupling loss γ. Explicit expressions for the phase delay, the full-width at half maximum, the Q-factor and the finesse are also given. Using appropriate coupling coefficients, the filtering characteristics can be optimized.