Publication details

Absolute optical instruments, classical superintegrability, and separability of the Hamilton-Jacobi equation

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TYC Tomáš DANNER Aaron James

Year of publication 2017
Type Article in Periodical
Magazine / Source Physical Review A
MU Faculty or unit

Faculty of Science

Keywords Absolute optical instrument; Hamilton-Jacobi equation; separation of variables; superintegrable systems
Description An absolute optical instrument is a region of space, typically defined by a spatially varying index of refraction, in which bound ray trajectories are closed. Traditional examples of such devices include Maxwell’s fisheye and the Eaton and Luneburg lenses. In this paper we employ the close analogy between classical mechanics and geometrical optics to develop a general theory of absolute instruments based on the Hamilton-Jacobi equation. Based on this theory, we derive many general properties of absolute instruments, and design a number of previously unknown examples. We also show how absolute optical instruments are related to superintegrable systems in mechanics and that the optical case is much less restrictive, which leads to an immense design space of absolute optical instruments.
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