The transfer matrix method is used to investigate the reflectance properties in a symmetric defective annular photonic crystal (APC) containing semiconductor, high-$T_c$ superconductor and a radial defect layer. Numerical results offer many noteworthy features that can be very useful in designing optical devices. In this regard, the geometric effects of alternate layers on the optical reflectance of our defective APC structure by changing the thickness of different layers would be investigated. Then, the possibility of controlling the spectral position of existed photonic band gaps (PBGs) and defect modes would be discussed by our analysis. In addition, it is found that the characteristics of the reflectance spectrum and subsequently, the spectral position of PBG and defect mode are entirely independent on changes in the starting radius of the hollow core. This characteristic is desirable to manufacturers, since increasing the size of the core radius would offer flexibility and simplicity of fabrication in producing optical devices. This study reveals that the optical reflectance of defective APCs is strongly dependent on the azimuthal mode number. Lastly, our results show that by increasing the temperature of the superconductor layer, both of the existed band gaps and defect mode show a red-shift trend by moving towards higher wavelengths. The proposed structure and related results can lead to gain valuable information for designing and fabrication of new types of annular Bragg resonators surrounding a radial defect and integrated visible waveguide devices like optical switches and filters.

转移矩阵法用于研究对称缺陷半导体环形光子晶体（APC）的反射特性，${Ť}_C$超导体和径向缺陷层。数值结果提供了许多值得注意的功能，这些功能对于设计光学设备非常有用。在这方面，将研究通过改变不同层的厚度，交替层对我们有缺陷的APC结构的光反射率的几何影响。然后，通过我们的分析将讨论控制现有光子带隙（PBG）和缺陷模式的光谱位置的可能性。另外，发现反射光谱的特征以及随后的PBG的光谱位置和缺陷模式完全与中空芯的起始半径的变化无关。此特性是制造商所希望的，因为增加芯半径的尺寸将在生产光学器件时提供灵活性和简化的制造。这项研究表明，有缺陷的APC的光反射率很大程度上取决于方位角模数。最后，我们的结果表明，通过增加超导体层的温度，既存在的带隙和缺陷模式都通过向更高波长移动而显示出红移趋势。所提出的结构和相关结果可以为设计和制造围绕径向缺陷的新型环形布拉格谐振器以及集成的可见光波导器件（如光学开关和滤波器）提供有价值的信息。我们的结果表明，通过增加超导体层的温度，既存在的带隙和缺陷模式都通过向更高波长移动而呈现出红移趋势。所提出的结构和相关结果可以为设计和制造围绕径向缺陷的新型环形布拉格谐振器以及集成的可见光波导器件（如光学开关和滤波器）提供有价值的信息。我们的结果表明，通过增加超导体层的温度，既存在的带隙和缺陷模式都通过向更高波长移动而呈现出红移趋势。所提出的结构和相关结果可以为设计和制造围绕径向缺陷的新型环形布拉格谐振器以及集成的可见光波导器件（如光学开关和滤波器）提供有价值的信息。