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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 22, Iss. 1 — Jan. 1, 2005
  • pp: 174–176

Simplification of vector ray tracing by the groove function

Zhongwen Hu, Zuping Liu, and Qiuping Wang  »View Author Affiliations

JOSA A, Vol. 22, Issue 1, pp. 174-176 (2005)

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Tracing rays through arbitrary diffraction gratings (including holographic gratings of the second generation fabricated on a curved substrate) by the vector form is somewhat complicated. Vector ray tracing utilizes the local groove density, the calculation of which highly depends on how the grooves are generated. Characterizing a grating by its groove function, available for almost arbitrary gratings, is much simpler than doing so by its groove density, essentially being a vector. Applying the concept of Riemann geometry, we give an expression of the groove density by the groove function. The groove function description of a grating can thus be incorporated into vector ray tracing, which is beneficial especially at the design stage. A unified explicit grating ray-tracing formalism is given as well.

© 2005 Optical Society of America

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(220.2740) Optical design and fabrication : Geometric optical design

Original Manuscript: June 25, 2004
Revised Manuscript: August 9, 2004
Published: January 1, 2005

Zhongwen Hu, Zuping Liu, and Qiuping Wang, "Simplification of vector ray tracing by the groove function," J. Opt. Soc. Am. A 22, 174-176 (2005)

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