基于中心移动莫比乌斯变换的圆形变换腔
Circle-shaped Transformation Cavity via Center-Shift Möbius Transfomation
摘要：
中心偏移的圆形变换腔是最简单的变换腔，因为它们只有空间折射率变化而没有边界形状变形。对于这些腔，我们分析了共形回音壁模式的特点，根据中心移动坐标变换。在这项研究中，我们使用一种替代方案来设计一个转换腔，而不使用一个收缩参数，需要满足全内反射条件。结果表明，随着中心位移的增加，均匀折射率圆腔中回音壁模的各向同性发射转变为共形回音壁模的双向发射。此外，使用一个纯度因子，定量测量在RV空间中的转换腔中的谐振模式的内部波图案的完整程度相比，相应的回音壁模式在均匀盘腔中，我们表明，共形回音壁模式在圆形的转换腔不仅具有方向性，而且还具有很高的持续性的回音壁模式的特性。
英文摘要：
Circle-shaped transformation cavities of shifted center are the most simple transformation cavities in the sense that they have only spatial index variation without boundary shape deformation. For these cavities, we analyze the characteristics of conformal whispering gallery modes according to center-shift coordinate transformation. For this study, we use an alternative scheme for designing a transformation cavity without using a shrinking parameter that is needed to satisfy total internal reflection condition. It is observed that the isotropic emission of whispering gallery modes in the uniform index circular cavity changes to the bi-directional emission of conformal whispering gallery modes as the center-shift increases. Also, using a purity factor that quantitatively measures in RV space the degree of intactness for the internal wave pattern of resonant modes in transformation cavities compared with corresponding whispering gallery mode in uniform disk cavity, we show that the conformal whispering gallery modes in the circle-shaped transformation cavity has not only directionality but also high persistence for characteristics of whispering gallery modes.
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