## Scattering of an electromagnetic plane wave by a Luneburg lens. I. Ray theory

JOSA A, Vol. 25, Issue 12, pp. 2971-2979 (2008)

http://dx.doi.org/10.1364/JOSAA.25.002971

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### Abstract

For a plane wave incident on either a Luneburg lens or a modified Luneburg lens, the magnitude and phase of the transmitted electric field are calculated as a function of the scattering angle in the context of ray theory. It is found that the ray trajectory and the scattered intensity are not uniformly convergent in the vicinity of edge ray incidence on a Luneburg lens, which corresponds to the semiclassical phenomenon of orbiting. In addition, it is found that rays transmitted through a large-focal-length modified Luneburg lens participate in a far-zone rainbow, the details of which are exactly analytically soluble in ray theory. Using these results, the Airy theory of the modified Luneburg lens is derived and compared with the Airy theory of the rainbows of a homogeneous sphere.

© 2008 Optical Society of America

**OCIS Codes**

(080.2710) Geometric optics : Inhomogeneous optical media

(080.5692) Geometric optics : Ray trajectories in inhomogeneous media

**ToC Category:**

Scattering

**History**

Original Manuscript: July 30, 2008

Manuscript Accepted: September 11, 2008

Published: November 12, 2008

**Citation**

James A. Lock, "Scattering of an electromagnetic plane wave by a Luneburg lens. I. Ray theory," J. Opt. Soc. Am. A **25**, 2971-2979 (2008)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-25-12-2971

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