Advertisement

Comparative Study on Efficiency of Mirror Retroreflectors

  • João Pedro CruzEmail author
  • Alexander Plakhov
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 499)

Abstract

Here we study retroreflectors based on specular reflections. Two kinds of asymptotically perfect specular retroreflectors in two dimensions, Notched angle and Tube, are known at present. We conduct comparative study of their efficiency, assuming that the reflection coefficient is slightly less than 1. We also compare their efficiency with the one of the retroreflector Square corner (the 2D analogue of the well-known and widely used Cube corner). The study is partly analytic and partly uses numerical simulations. We conclude that the retro-reflectivity ratio ofNotched angle is normally much greater than those of Tube and the Square corner. Additionally, simple Notched angle shapes are constructed, whose efficiency is significantly higher than that of the Square corner.

Keywords

Retroreflectors Geometric optics Shape optimization Billiards 

Mathematics subject classifications

49Q10 49M25 78A05 

Notes

Acknowledgements

This work was supported by Portuguese funds through CIDMA– Center for Research and Development in Mathematics and Applications and FCT – Portuguese Foundation for Science and Technology, within the project PEst-OE/ MAT/ UI4106/ 2014, as well as by the FCT research project PTDC/ MAT/ 113470/ 2009.

References

  1. 1.
    Bachurin, P., Khanin, K., Marklof, J., Plakhov, A.: Perfect retroreflectors and billiard dynamics. J. Mod. Dynam. 5, 33–48 (2011)zbMATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Eaton, J.E.: On spherically symmetric lenses. Trans. IRE Antennas Propag. 4, 66–71 (1952)CrossRefGoogle Scholar
  3. 3.
    Luneburg, R.K.: Mathematical Theory of Optics. Brown University, Providence (1944)Google Scholar
  4. 4.
    Ma, Y.G., Ong, C.K., Tyc, T., Leonhardt, U.: An omnidirectional retroreflector based on the transmutation of dielectric singularities. Nat. Mater. 8, 639–642 (2009)CrossRefGoogle Scholar
  5. 5.
    Plakhov, A.: Mathematical retroreflectors. Discr. Contin. Dynam. Syst.-A 30, 1211–1235 (2011)zbMATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Plakhov, A.: Exterior Billiards: Systems With Impacts Outside Bounded Domains, XIII, 284 pp., 108 illus. Springer, New York (2012)Google Scholar
  7. 7.
    Plakhov, A., Gouveia, P.: Problems of maximal mean resistance on the plane. Nonlinearity 20, 2271–2287 (2007)zbMATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    Tyc, T., Leonhardt, U.: Transmutation of singularities in optical instruments. New J. Phys. 10(115038), 8pp (2008)Google Scholar
  9. 9.
    Walker, J.: Wonders with the retroreflector. The Amateur Scientist. Scientific American, April 1986Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Universidade de AveiroAveiroPortugal

Personalised recommendations