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@article{1408345, author = {Tyc, Tomáš and Danner, Aaron James}, article_location = {MD USA}, article_number = {5}, doi = {http://dx.doi.org/10.1103/PhysRevA.96.053838}, keywords = {Absolute optical instrument; Hamilton-Jacobi equation; separation of variables; superintegrable systems}, language = {eng}, issn = {2469-9926}, journal = {Physical Review A}, title = {Absolute optical instruments, classical superintegrability, and separability of the Hamilton-Jacobi equation}, url = {https://journals.aps.org/pra/abstract/10.1103/PhysRevA.96.053838}, volume = {96}, year = {2017} }
TY - JOUR ID - 1408345 AU - Tyc, Tomáš - Danner, Aaron James PY - 2017 TI - Absolute optical instruments, classical superintegrability, and separability of the Hamilton-Jacobi equation JF - Physical Review A VL - 96 IS - 5 SP - 1-14 EP - 1-14 PB - AMERICAN PHYSICAL SOCIETY SN - 24699926 KW - Absolute optical instrument KW - Hamilton-Jacobi equation KW - separation of variables KW - superintegrable systems UR - https://journals.aps.org/pra/abstract/10.1103/PhysRevA.96.053838 N2 - 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. ER -
TYC, Tomáš and Aaron James DANNER. Absolute optical instruments, classical superintegrability, and separability of the Hamilton-Jacobi equation. \textit{Physical Review A}. MD USA: AMERICAN PHYSICAL SOCIETY, 2017, vol.~96, No~5, p.~1-14. ISSN~2469-9926. Available from: https://dx.doi.org/10.1103/PhysRevA.96.053838.
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