Application of Transfer Matrix Method with Signal Flow-Chart to Analyze Optical Multi-Path Ring-Resonator

A multi-path ring-resonator (MPRR) was proposed to extend FSR of ring resonator. However, it is complicated to analyze the MPRR by using well-known analysis techniques such as scattering matrix or other numerical methods. This paper describes procedure for deriving transfer matrix by means of signal flow-chart to analyze the MPRR. We do not need complicated calculation for steady state analysis because transfer matrix elements are formulated clearly. As a result, The calcultaion time in this method can be reduced 1/3 to 1/20 times compared with using scattering matirx method. Furthermore, a transmittance characteristics of the MPRR at FSR extension-factor of 10 will also be shown. This suggests that analysis of other types of the MPRR by using this method can be performed simply and take a shorter time.