Graphical representation and analysis of the Z-shaped double-coupler optical resonator

A graphical technique for obtaining the transfer function between any input and output optical ports of photonic circuits is presented. The Z-shaped double-coupler optical resonator is chosen as an example for illustration of the graphical approach. A theoretical study of this photonic circuit is described using z-transformation of the optical transfer function. An expression for the pole-dependent resonator finesse analogous to the Fabry-Perot resonator finesse is derived. Possible applications of this resonating system as optical bandpass digital and/or notch filters and as an all-optical timing recovery circuit are discussed.>