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Large-scale segmentation errors in optical gratings and their unique effect onto optical scattering spectra

: Heusinger, M.; Flügel-Paul, T.; Zeitner, U.-D.


Applied Physics. B 122 (2016), Nr.8, Art. 222, 12 S.
ISSN: 0340-3793
ISSN: 0721-7269
ISSN: 0946-2171
ISSN: 1432-0649
Fraunhofer IAP ()
Fraunhofer IOF ()

In this paper, we analyze the influence of large-scale segmentation errors in the morphology of high-performance optical gratings. It is thus assumed that the optical grating under consideration (typical lateral extends S are 10–1000 mm) can be spatially decomposed into a great many but unique sub-segments (≪S; typical extends are 10–100 μm). Any violation of the perfect periodicity will result in the generation of stray light, especially Rowland ghosts, which radiate into a small angular region around the grating’s diffraction orders. In this paper, we focus on three different kinds of segmentation errors. On the one hand, there are statistic as well as deterministic alignment errors between otherwise perfect sub-segments. On the other hand, we analyze the effect of chirping of geometrical parameters, i.e., the groove width, within every sub-segment. Most importantly, we find that the particular type of imperfection results in a unique characteristic of the according stray light spectrum which thus acts as a fingerprint. We come to this conclusion on three different ways. First, we rely on a simple theoretical model that is based on scalar diffraction theory. Second, we have performed rigorous numerical simulations for a high aspect ratio purely dielectric spectrometer grating (period=667nm). Third, the very same grating was then fabricated by e-beam lithography and its stray light spectrum was measured with a purposely designed optical setup. Eventually, all different routes to analyze the problem turn out to be in very good agreement, and we are confident that stray light measurements can be used as an important tool in the detection of fabrication imperfections.