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

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.

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

• Original language: English
• Type of outcome: Article in a journal
• Field of Study: 10306 Optics
• Country of publisher: United States of America
• Confidentiality degree: is not subject to a state or trade secret
• WWW: 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
• Tags: NZ, rivok
• Tags: International impact, Reviewed

Abstract

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.

Abstract (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