Calculation of the Luneberg optical lens and applications

Arkady Khorunzhenko (), Mikhail Lavrentiev () and Andrey Marchuk ()

International Journal of Innovative Research and Scientific Studies, 2025, vol. 8, issue 12, 95-107

Abstract: This paper presents a numerical approach for designing radially symmetric Luneburg lenses with arbitrary source and image positions. The method reconstructs the refractive index distribution by inverting an Abel-type relation and uses adaptive Gauss–Kronrod quadrature to ensure high accuracy without manual tuning. The algorithm is validated against the classical Luneburg profile and applied to two focusing scenarios: transformation of a plane wave into a converging wave with a prescribed focal distance, and focusing of radiation from a finite-distance point source to a target point. Ray tracing with an explicit Euler scheme and Huygens-based wavefront simulations confirm that an initially planar front segment collapses precisely to the designed focus. Using the optical–hydrodynamic analogy, the obtained refractive index distribution is converted into a seamount depth profile, and nonlinear shallow-water simulations demonstrate significant wave amplitude amplification near the predicted focal area. The results provide a universal framework for the synthesis of gradient-index lenses and offer practical insights into tsunami wave focusing caused by natural seabed topography.

Keywords: Abel transform inversion; Bathymetry; Geometrical optics; Huygens principle; Luneburg lens; MacCormack scheme; Ray tracing; Refractive index profiling; Shallow-water equations; Tsunami focusing. (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://ijirss.com/index.php/ijirss/article/view/11018/2663 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:aac:ijirss:v:8:y:2025:i:12:p:95-107:id:11018

Access Statistics for this article

International Journal of Innovative Research and Scientific Studies is currently edited by Natalie Jean

More articles in International Journal of Innovative Research and Scientific Studies from Innovative Research Publishing
Bibliographic data for series maintained by Natalie Jean ().