论文标题
双工Mikaelian镜头和双工麦克斯韦的鱼眼镜
Duplex Mikaelian lenses and duplex Maxwell's fish eye lenses
论文作者
论文摘要
在本文中，我们报告了两种新型的绝对光学仪器，它们可以在二维空间中为几何光学器件制作污名化图像。一个被称为双面Mikaelian镜头，该镜头是通过在不同时期的两个半镜镜头剪接的半镜镜头来制作的。另一个是双工Mikaelian镜头的指数形式的共形变压器，其两个半Mikaelian镜头的不同时期的比例是合理的，我们称之为Duplex Maxwell的Fish Eye Lens。双链镜镜具有连续的翻译对称性，并具有任意的实际数字，而双工麦克斯韦的鱼眼镜则具有从0到2*pi的连续旋转对称性。因此，每个双工麦克斯韦的鱼眼镜镜头对应于双面的mikaelian镜头。我们进一步证明了几何光学元件在双链镜镜片和双工麦克斯韦的鱼眼镜片中的腐蚀性效应。此外，我们根据数字计算研究了双链镜镜中波光学的塔尔伯特效应。我们的发现基于剪接和指数保形映射扩大了绝对光学仪器的家族。
In this paper, we report two new kinds of absolute optical instruments that can make stigmatically images for geometric optics in two dimensional space. One is called the duplex Mikaelian lens, which is made by splicing two half Mikaelian lenses with different periods. The other is exponential conformal transformer of duplex Mikaelian lens with the ratio of different periods of its two half Mikaelian lenses a rational number, which we call duplex Maxwell's fish eye lens. Duplex Mikaelian lenses have continuous translation symmetry with arbitrary real number, while duplex Maxwell's fish eye lenses have continuous rotational symmetry from 0 to 2*Pi. Hence each duplex Maxwell's fish eye lens corresponds to a duplex Mikaelian lens. We further demonstrate the caustic effect of geometric optics in duplex Mikaelian lenses and duplex Maxwell's fish eye lenses. In addition, we investigate the Talbot effect of wave optics in the duplex Mikaelian lens based on numeric calculations. Our findings based on splicing and exponential conformal mapping enlarge the family of absolute optical instruments.
