| The circular grating resonators (CGRs) consist of concentric cylindrical layers of alternating dielectric materials. They can be used as all-optical switches, resonant cavity of lasers, optical filters and optical storage and so on, owing to the advantages of high symmetry, low loss, high quality-factor, optimal light confinement, small size, compact structure. They are the important devices of optical communication systems.In the paper, we have built a two-dimensional cylindrical model of CGRs based on a transfer-matrix method (TMM), found the resonant state and photonic band gap(PBG) and got the analytical expression of quality factor(Q). Firstly, we have studied and expanded the electromagnetic field based on the Hankel functions, due to the cylindrical symmetry of the problem. We have obtained the transfer matrix by means of the boundary condition and trace the resonant modes and PBG in the cavity. Secondly, the analytical expression of the quality factor from the basic definition of the quality factor in a microcavity is obtained. Then, we have numerically simulated the model and analyzed the influence of structural parameters on the characteristics resonances, transmission and quality factor of CGRs. Finally, we have summarized the method which improve the CGRs performances by optimizing structural parameters. |
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