Vernier effect of multiple-ring resonator filters modeling by a graphical approach

We design and simulate a nonsymmetric vernier type of multiple ring resonator (MRR) filters to achieve wider free spectral range (FSR) with different ring radii. The expanded FSR is determined by the least common multiple of the FSRs of the individual ring resonators. The dependence of the transmission characteristics of the MRR on the coupling coefficients of directional couplers is studied. The improvement in suppression of interstitial resonances by using high-order vernier filters is also investigated. A graphical approach with a signal flow graph has been found very useful for quickly deriving the optical transfer functions of filters in the Z domain.