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Proceedings Paper

Numerical analysis of eikonal equation
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Paper Abstract

The Maxwell equations have a fairly simple form. However, finding solutions of 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 Maxwell and Luneburg lenses. 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.

Paper Details

Date Published: 3 June 2019
PDF: 8 pages
Proc. SPIE 11066, Saratov Fall Meeting 2018: Laser Physics, Photonic Technologies, and Molecular Modeling, 110660U (3 June 2019); doi: 10.1117/12.2525142
Show Author Affiliations
Dmitry S. Kulyabov, Peoples' Friendship Univ. of Russia (Russian Federation)
Joint Institute for Nuclear Research (Russian Federation)
Anna V. Korolkova, Peoples' Friendship Univ. of Russia (Russian Federation)
Tatiana R. Velieva, Peoples' Friendship Univ. of Russia (Russian Federation)
Migran N. Gevorkyan, Peoples' Friendship Univ. of Russia (Russian Federation)


Published in SPIE Proceedings Vol. 11066:
Saratov Fall Meeting 2018: Laser Physics, Photonic Technologies, and Molecular Modeling
Vladimir L. Derbov, Editor(s)

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