Abstract

We introduce the concept of a generalized 2-D binary phase grating. A set of suitably distributed rectangular areas with appropriate phase delay is associated with the grating period, and the locations and sizes of the rectangles determine the inversion symmetric but otherwise arbitrary power spectrum of the element. We employed simulated annealing to find the structure of the grating period corresponding to the desired power spectrum $\widehat{P}(m,n)$ for diffraction orders |m| ≤ M, |n| ≤ N. The actual power spectrum P(m, n) of the optimized grating always coincided with $\widehat{P}(m,n)$ within 1%, and the diffraction efficiency was typically 60-65%, irrespective of $\widehat{P}(m,n)$. We fabricated several different generalized gratings using standard photolithography (pattern generator → wafer stepper → etching) to achieve sufficient accuracy of the rectangle locations and dimensions, typically 0.01 % of the grating period.

© 1988 Optical Society of America