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
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)