Numerical analysis of eikonal equation

Dmitry S. Kulyabov; Anna V. Korolkova; Tatiana R. Velieva; Migran N. Gevorkyan

doi:10.1117/12.2525142

3 June 2019 Numerical analysis of eikonal equation

Dmitry S. Kulyabov, Anna V. Korolkova, Tatiana R. Velieva, Migran N. Gevorkyan

Proceedings Volume 11066, Saratov Fall Meeting 2018: Laser Physics, Photonic Technologies, and Molecular Modeling; 110660U (2019) https://doi.org/10.1117/12.2525142
Event: International Symposium on Optics and Biophotonics VI: Saratov Fall Meeting 2018, 2018, Saratov, Russian Federation

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.

Citation Download Citation

Dmitry S. Kulyabov, Anna V. Korolkova, Tatiana R. Velieva, and Migran N. Gevorkyan "Numerical analysis of eikonal equation", Proc. SPIE 11066, Saratov Fall Meeting 2018: Laser Physics, Photonic Technologies, and Molecular Modeling, 110660U (3 June 2019); https://doi.org/10.1117/12.2525142

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available

Members: $17.00

Non-members: $21.00 ADD TO CART

PROCEEDINGS
8 PAGES

DOWNLOAD PAPER SAVE TO MY LIBRARY

GET CITATION

RIGHTS & PERMISSIONS

Get copyright permission Get copyright permission on Copyright Marketplace

KEYWORDS

Numerical analysis

Lenses

Refractive index

Wavefronts

Geometrical optics

Visualization

Numerical modeling

Show All Keywords

Keywords/Phrases

Search In:

Publication Years