• Photonics Research
  • Vol. 7, Issue 11, 11001266 (2019)
Lin Xu1、4、†, Xiangyang Wang2、†, Tomáš Tyc3、5、†、*, Chong Sheng2, Shining Zhu2, Hui Liu2、6、*, and Huanyang Chen1、7、*
Author Affiliations
  • 1Institute of Electromagnetics and Acoustics and Key Laboratory of Electromagnetic Wave Science and Detection Technology, Xiamen University, Xiamen 361005, China
  • 2National Laboratory of Solid State Microstructures and School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
  • 3Department of Theoretical Physics and Astrophysics, Masaryk University, Kotlarska 2, 61137 Brno, Czech Republic
  • 4Institutes of Physical Science and Information Technology & Key Laboratory of Opto-Electronic Information Acquisition and Manipulation of Ministry of Education, Anhui University, Hefei 230601, China
  • 5e-mail: tomtyc@physics.muni.cz
  • 6e-mail: liuhui@nju.edu.cn
  • 7e-mail: kenyon@xmu.edu.cn
  • show less


    Starting from well-known absolute instruments that provide perfect imaging, we analyze a class of rotationally symmetric compact closed manifolds, namely, geodesic lenses. We demonstrate with a numerical method that light rays confined on geodesic lenses form closed trajectories, and that for optical waves, the spectrum of a geodesic lens is (at least approximately) degenerate and equidistant. Moreover, we fabricate two geodesic lenses in micrometer and millimeter scales and observe curved light rays along the geodesics. Our experimental setup may offer a new platform to investigate light propagation on curved surfaces.


    Absolute instruments (AIs) in optics mean devices that bring stigmatically an infinite number of light rays from a source to its image, which can perform perfect imaging in the perspective of geometrical optics [1,2]. Two well-known examples of AIs are a plane mirror and Maxwell’s fish-eye lens [with gradient refractive index profile; see Fig. 1(a)]. Actually, there are a lot of AIs, such as the Eaton lens, Luneburg lens, and invisible lens [3]. The invisible lens has a spherically symmetric index profile that forces light rays to make loops around its center and then propagate in their original directions, which makes it invisible. Recently, one author proposed a general method to design AIs with the help of the Hamilton–Jacobi equation [4], which has flourished in the family of AIs. No matter how perfectly stigmatic the geometrical-optics image might be, in the wave-optics regime, the resolution is always limited by diffraction. Owing to this limitation, “perfect imaging” in the perspective of geometrical optics and wave optics is quite different [3]. As far as we know, the only AI in both perspectives is Pendry’s slab [5]. However, the frequency spectrum of other AIs has been investigated by numerical method [6,7] and the Wentzel–Kramers–Brillouin (WKB) approximation [8,9]. It is found that their spectrum is (at least approximately) degenerate and equidistant, which contributes to periodical evolution of waves in AIs [6,8].