The Maxwell equations have a fairly simple form. However, finding solutions to Maxwell's equations is an extremely difficult task. Therefore, various simplifying approaches are often used in optics. One such simplifying approach is to use the approximation of geometric optics. The approximation of geometric optics is constructed with the assumption that the wavelengths are small (short-wavelength approximation). The basis of geometric optics is the eikonal equation. The eikonal equation can be obtained from the wave equation (Helmholtz equation). Thus, the eikonal equation relates the wave and geometric optics. In fact, the eikonal equation is a quasi-classical approximation (the Wentzel-Kramers-Brillouin method) of wave optics. This paper shows the application of geometric methods of electrodynamics to the calculation of optical devices, such as lenses Maxwell and Luneburg. The eikonal equation, which was transformed to the ODE system by the method of characteristics, is considered. The resulting system is written for the case of Maxwell and Luneburg lenses and solved by standard numerical methods. Describes the implementation details and images of the trajectories of rays and fronts of the waves. © 2018 CEUR-WS. All Rights Reserved.

Authors

Conference proceedings

Publisher

CEUR-WS

Language

English

Pages

25-32

Status

Published

Volume

2177

Year

2018

Organizations

^{1}Department of Applied Probability and Informatics, Peoples' Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya str., Moscow, 117198, Russian Federation^{2}Laboratory of Information Technologies, Joint Institute for Nuclear Research, 6 Joliot-Curie, Dubna, Moscow region, 141980, Russian Federation

Keywords

Characteristics method; Eikonal equation; Julia.; Luneburg lens; Maxwell lens

Date of creation

19.07.2019

Date of change

01.03.2021

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CEUR Workshop Proceedings.
CEUR-WS.
Vol. 2177.
2018.
P. 19-24

Article

CEUR Workshop Proceedings.
CEUR-WS.
Vol. 2177.
2018.
P. 11-18