A nonunitary transfer matrix method for practical analysis of racetrack microresonator waveguide

We report that a nonunitary transfer matrix (NU-TM) method that we have developed is highly accurate and effective in analyzing and designing racetrack microresonator devices. Relatively poor output efficiency of a fabricated racetrack microresonator, unexplained by the conventional unitary transfer matrix (U-TM) method, are analyzed successfully by the NU-TM method. The track-length dependence, which is not obvious in the U-TM analysis, is clearly shown in the NU-TM analysis and is found to stem from the nonorthogonal phase difference between two branching waves in the directional coupling process. The results show excellent agreement with the results obtained by the finite-difference time-domain simulation method, thus confirming the validity and superior capability of the NU-TM method.