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

J 2017

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

TYC, Tomáš and Aaron James DANNER

Basic information

Original name

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

Authors

TYC, Tomáš (203 Czech Republic, guarantor, belonging to the institution) and Aaron James DANNER (840 United States of America)

Edition

Physical Review A, MD USA, AMERICAN PHYSICAL SOCIETY, 2017, 2469-9926

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10306 Optics

Country of publisher

United States of America

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

Impact factor

Impact factor: 2.909

RIV identification code

RIV/00216224:14310/17:00095500

Organization unit

Faculty of Science

DOI

http://dx.doi.org/10.1103/PhysRevA.96.053838

UT WoS

000415671700017

Keywords (in Czech)

Absolutní optický instrument; Hamiltonova-Jacobiho rovnice; separace proměnných; superintegrabilní systémy

Keywords in English

Absolute optical instrument; Hamilton-Jacobi equation; separation of variables; superintegrable systems

Abstract

ORIG CZ

V originále

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.

In Czech

Článek podává ucelenou teorii absolutních optických instrumentů. Ja založen na těsné analogii optických a mechanických systémů a využívá metod klasické mechaniky (především Hamiltonovy-Jacobiho rovnice) pro nalezení obecných vlastností absolutních instrumentů. Pomocí uvedené metody je rovněž navrženo několik nových, dosud neznámých instrumentů.

Links

GBP201/12/G028, research and development project

Name: Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku

Investor: Czech Science Foundation

Citovat

TYC, Tomáš and Aaron James DANNER. Absolute optical instruments, classical superintegrability, and separability of the Hamilton-Jacobi equation. 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.

@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.

Detailed Information on Publication Record