General ring-resonator analysis and characterization by characteristic matrix

In this paper, a general analysis method for ring resonators is proposed. The method utilizes a characteristic matrix to express the recursive relationship between transfer functions of adjacent-order optical paths, and consequently, the total transfer function. The method provides a new way to express Mason´s rule in general. At the same time, it greatly simplifies the expression in the ring-resonator case. The method can be used to synthesize any ring-resonator devices. In addition, as individual optical paths´ transfer functions are derived in this process, the formulas can be applied to incoherent interferometric measurements and can characterize the device parameters of fabricated complex ring-resonator circuits.