Theoretical analysis of triple-coupler ring-based optical guided-wave resonator

A comprehensive theoretical analysis of the triple-coupler ring-based optical guided-wave resonator (TCRR) is presented. Channel-passing and channel-dropping transmittance characteristics of the TCRR are derived by using a combination of transfer matrix and chain matrix formulations. The dependence of the transmittance characteristics on the amplitude coupling ratios of the three directional couplers are investigated, and optimum design relationships are determined. It is shown that the TCRR is ideally a nonterminating filter at antiresonance. An extensive comparison between the TCRR and a double-coupler ring resonator (DCRR) with same radius of curvature, waveguide propagation loss, coupling loss and finesse, is carried out. It is shown that the TCRR, by suitably sizing its waveguide lengths, has a free spectral range double that of the DCRR and features also higher transmission at resonance and better extinction ratio. These characteristics make the TCRR particularly advantageous for frequency selective filtering applications in optical frequency division multiplexing transmission systems