Kim Inbo, Cho Jinhang, Kim Yushin, Min Bumki, Ryu Jung-Wan, Rim Sunghwan, Choi Muhan
Opt Express. 2018 Mar 19;26(6):6851-6859. doi: 10.1364/OE.26.006851.
Dielectric cavity systems, which have been studied extensively so far, have uniform refractive indices of their cavities, and Husimi functions, the most widely used phase space representation of optical modes formed in the cavities, accordingly were derived only for these homogeneous index cavities. For the case of the recently proposed gradient index dielectric cavities (called as transformation cavities) designed by optical conformal mapping, we show that the phase space structure of resonant modes can be revealed through the conventional Husimi functions by constructing a reciprocal virtual space. As examples, the Husimi plots were obtained for an anisotropic whispering gallery mode (WGM) and a short-lived mode supported in a limaçon-shaped transformation cavity. The phase space description of the corresponding modes in the reciprocal virtual space is compatible with the far-field directionality of the resonant modes in the physical space.
迄今为止已被广泛研究的介质腔系统，其腔内具有均匀的折射率，而胡西米函数是腔内形成的光学模式最广泛使用的相空间表示，因此仅针对这些均匀折射率的腔推导得出。对于最近通过光学共形映射设计的梯度折射率介质腔（称为变换腔）的情况，我们表明通过构建一个互易虚拟空间，可以通过传统的胡西米函数揭示共振模式的相空间结构。作为示例，获得了各向异性回音壁模式（WGM）和在 limaçon 形变换腔中支持的短寿命模式的胡西米图。互易虚拟空间中相应模式的相空间描述与物理空间中共振模式的远场方向性兼容。
