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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 a 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, roč.~96, č.~5, s.~1-14. ISSN~2469-9926. Dostupné z: https://dx.doi.org/10.1103/PhysRevA.96.053838.
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