Abstract
Achromatic beam-splitting grating doublets are designed for both continuous phase and binary phase gratings. By analyzing the sensitivity to lateral shifts between the two grating layers, it is shown that continuous-profile grating doublets are extremely difficult to fabricate. Achromatic grating doublets that have profiles with a constant first spatial derivative are significantly more resistant to lateral shifts between grating layers, where one design case showed a 17 times improvement in performance. Therefore, binary phase, multi-level phase, and blazed grating doublets perform significantly better than continuous phase grating doublets in the presence of a lateral shift between two grating layers. By studying the sensitivity to fabrication errors in the height of both grating layers, one grating layer height can be adjusted to maintain excellent performance over a large wavelength range if the other grating layer is fabricated incorrectly. It is shown in one design case that the performance of an achromatic Dammann grating doublet can be improved by a factor of 215 if the heights of the grating layers are chosen to minimize the performance change in the presence of fabrication errors.
Highlights
A common design problem is to split one laser beam into multiple beams with equal energy
By studying the sensitivity of these achromatic grating doublets, it is shown that grating profiles with constant spatial derivatives perform significantly better than continuous grating profiles with respect to fabrication errors
Simulations for an achromatic continuous phase grating doublet and an achromatic Dammann grating doublet are shown in this paper
Summary
A common design problem is to split one laser beam into multiple beams with equal energy. Romero and Dickey found analytical expressions for the optimal continuous phase functions of one- and two-dimensional gratings that maximize energy into N desired output beams [6,7]. While these gratings theoretically provide optimal efficiency into N outgoing beams, the presence of fabrication errors can significantly degrade their performance. By optimizing the levels of a single relatively thin multilevel phase grating, a grating can be achromatized at multiple wavelengths [14] These designs typically have several closely spaced large discontinuities in the height profiles, which may make fabrication difficult.
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