• Photonics Research
  • Vol. 9, Issue 7, 07001197 (2021)
Wen Xiao, Sicen Tao, and Huanyang Chen*
Author Affiliations
  • Institute of Electromagnetics and Acoustics and Department of Physics, Xiamen University, Xiamen 361005, China
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    General relativity establishes the equality between matter-energy density and the Riemann curvature of spacetime. Therefore, light or matter will be bent or trapped when passing near the massive celestial objects, and Newton’s second law fails to explain it. The gravitational effect is not only extensively studied in astronomy but also attracts a great deal of interest in the field of optics. People have mimicked black holes, Einstein’s ring, and other fascinating effects in diverse optical systems. Here, with a gradient index lens, in the geometrical optics regime, we mimic the Schwarzschild precession in the orbit of the star S2 near the Galactic Center massive black hole, which was recently first detected by European Southern Observatory. We also find other series of gradient index lenses that can be used to mimic the possible Reissner–Nordstr?m metric of Einstein’s field equation and dark matter particle motion. Light rays in such gradient lenses will be closed in some cases, while in other cases it would be trapped by the center or keep dancing around the center. Our work presents an efficient toy model to help investigate some complex celestial behaviors, which may require long period detection by using high-precision astronomical tools. The induced gradient lenses enlightened by the gravitational effect also enrich the family of absolute optical instruments for their selective closed trajectories.


    Einstein’s general theory of relativity is one of the cornerstones in modern physics. It holds the best understanding of gravity so far, explaining that the nature of universal gravitation originates from matter-energy, resulting in curved spacetime. To date, general relativity (GR) has passed all the experimental tests with flying colors, such as the precession of Mercury [1], gravitational redshift [2], the observations of solar-mass pulsars in binary systems [3], and the gravitational waves from several stellar mass, black hole candidate in-spirals [4]. Recently, the report of first detection of the Schwarzschild precession in S2’s orbit around the nearest massive black hole (candidate) in the Galaxy Center has received attention, being more prominent evidence of GR [5]. In optics, in analogy to the equality between matter-energy and curved spacetime, macroscopic Maxwell’s equations in complex inhomogeneous media can be mapped into free-space Maxwell’s equations of an arbitrary spacetime metric [610], leading to lots of transformation optical applications like invisibility cloaks [1117], field rotators [18,19], and illusion devices [20]. Moreover, despite the functionality of controlling the flow of light, this analogy has also been utilized to mimic some exciting gravitational effects related to GR in return, for instance, black holes [2127], Einstein’s ring [28], de Sitter space [29,30], and cosmic strings [31,32].

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    Wen Xiao, Sicen Tao, Huanyang Chen. Mimicking the gravitational effect with gradient index lenses in geometrical optics[J]. Photonics Research, 2021, 9(7): 07001197
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    Category: Optical and Photonic Materials
    Received: Jan. 5, 2021
    Accepted: Apr. 19, 2021
    Published Online: Jun. 9, 2021
    The Author Email: Huanyang Chen (kenyon@xmu.edu.cn)