Signal Flow Graph Theory And Its Applications In The Analysis Of Optical Ring Resonator

Optical filter in wavelength division multiplexing system is an important class ofdevices. Among them, the optical ring resonators due to their high frequencyselectivity and significant power storage at the resonance frequencies, have beenextensively researched and applied. In this dissertation, several optical filter based onring resonator are analyzed in detail using signal flow graph method. The maincontents of the dissertation are as follows:(1)The Mach-Zehnder interferometer(MZI) has the cosine output characteristics.To solve this problem, a device based on Mach-Zehnder interferometer with a fiberring resonator in one arm is proposed. Using the signal flow graph mehtod, influenceon the MZI interferometer by the stopband type fiber ring resonator is discussed. Andusing the transmission matrix method, the influence on the MZI by the passband typefiber ring resonator is also discussed. The result indicates that the width of 0.5dBpassband and 25dB stopband of proposed devices are simultaneously improvedremarkably, which are much wider than that of the conventional MZI interferometer.The filtering performance of these proposed devices, which achieve a nearly squarespectrum response, are much better than the conventional MZI. Therefore, therequirements of the incident optical signals by these devices are reduced.(2)A compound optical vernier filter with cascaded microring resonators isproposed. The proposed filter consists of two individual passband micoring resonators.Its output characteristics is analyzed. A comparison between this proposed vernierfilter and one individual micoring resonator is made. The simulation results show thatthe contrast and finesse of proposed vernier filter can be increased remarkablycompared to the individual one micoring resonator. And it is found that the freespectral range of proposed filter can be enhanced by the vernier operation.(3)A novel microring resonator based on Mach-Zehnder interferometer isproposed. Its transmission function is theoretically analyzed by using the signal flowgraph method. The expression fot the full width at half maximum of the transmissionspectrum is also derived. Numerical simulations show that transmission spectrum has the periodic narrow stopband filtering characteristic. The influence of phase differencebetween the two arms of MZI and coupling coefficient on the transmission spectrum isalso analyzed. The results, are of very important significance in its actual processingand improvement of filtering characteristic.(4)The transmission window of reflection spectrum for phase-shift gratingproducts is not tunable, To solve this problem, a device with Bragg grating-assistedring resonator is proposed. The mechanism of the device is analyzed in great detail.Meanwhile, analytical expressions of reflectivity and its finesse, full width at halfmaximum are derived. Matlab computation results show that reflection spectrum ofproposed device is similar to that of phase-shift grating. Location and depth oftransmission window are tunable in its reflection spectrum. Influences on its finesseand full width at half maximum by the parameters of ring resonator are also discussed,which provides the theoretical basis for improving its performance as frequencyselective element for a narrow line width of single-frequency fiber laser.