Lüneburg lens

from Wikipedia, the free encyclopedia
Principle of the reflection of the dielectric Lüneburg lens with reflector

The Lüneburg lens named after the mathematician Rudolf Karl Lüneburg , also known as the Luneburg lens or, more rarely, the Luneberg lens, is a spherical gradient index lens . It consists of a massive ball made of lossless dielectric material with a location-dependent dielectric constant . If its back is mirrored, it throws incoming parallel waves back exactly in the direction of their source and thus acts as a retroreflector .

construction

A Lüneburg lens in which the refractive index is indicated in blue. Rays incident in parallel are focused on the back of the sphere.

The refractive index inside the sphere is designed in such a way that rays incident in parallel are focused in a point opposite the point of contact of the wave front. It decreases with the distance from the center. Ideally, he follows the formula

,

where is the radius of the sphere. If the back of the sphere is now mirrored , the beam path is exactly reversed and the wave is reflected back exactly in the direction of its source. The arrangement thus functions as a retroreflector .

Lüneburg lenses can also be manufactured for all-round retroreflection, e.g. B. as a radar reflector , they then wear a narrow horizontal belt made of a conductive layer instead of the rear mirror. When used as a radar reflector on boats, they must always hang exactly vertically so that the radio waves entering the sphere horizontally on both sides of the belt are precisely bundled onto the reflective metal strips on the opposite side.

See also

literature

  • Rudolf Karl Luneburg: Mathematical Theory of Optics . Brown University, Providence 1944, pp. 189-213 .
  • Rudolf Karl Luneburg: Mathematical Theory of Optics . University of California Press, Berkley / Los Angeles 1964, p. 329 .
  • R. Grabau, K. Pfaff: radio direction finding technology . Franckh'sche Verlagshandlung, Stuttgart 1989, ISBN 3-440-05991-X , chapter 4.10.
  • AS Gutman: Modified Luneberg Lens . In: Journal of Applied Physics . tape 25 , no. 7 June 1954, p. 855-859 , doi : 10.1063 / 1.1721757 .
  • Samuel P. Morgan: General Solution of the Luneberg Lens Problem . In: Journal of Applied Physics . tape 29 , no. 9 , 1958, pp. 1358-1368 , doi : 10.1063 / 1.1723441 .
  • Richard C. Johnson, Henry Jasik: Antenna Engineering Handbook . McGraw-Hill, New York 1961, ISBN 0-07-032290-2 , pp. 15-3 to 15-8 .

Individual evidence

  1. ↑ According to his dissertation, the original name is Lüneburg. On the naming problem that came about when Lüneburg's last name changed after emigrating to the USA, cf. Discussion: Rudolf Karl Lüneburg (permanent link to the version of September 9, 2008 )