INSTITUTE OF APPLIED PHYSICS - Straylight modelling for diffraction gratings
URL: http://www.iap.uni-jena.de/Micro_+structure+Technology/Research/Micro_+_Nanooptics/Straylight+modelling+for+diffraction+gratings.print
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Straylight modelling for diffraction gratings

Nowadays, many optical applications employ diffraction gratings, which have turned into one of the most critical components. Especially in high-performance spectrometry the gratings, which are used as dispersive elements, are required to fulfill strong demands, e.g. on the diffraction efficiency, the bandwidth, and the spectral dispersion. It has been shown that these requirements can be addressed even by simple binary phase gratings [1-3].
Nevertheless, the stray light performance of spectrometer gratings becomes increasingly critical as the radiometric accuracy of spectroscopic measurements is constrained by diffuse scattering. In case of binary diffraction gratings, there are different stray light sources due to shape deviations of the microscopic grating structure and fabrication inaccuracies.
Basically, the stray light can be classified into deterministic and stochastic stray light. Deterministic stray light artefacts occur as discrete peaks (Rowland ghosts) in the scattering spectra and have their origin in periodic large-scale perturbations of the grating geometry [4]. Such perturbations occur, e.g., when large-area gratings are fabricated by means of so-called sequential technologies, meaning that a large-scale optical grating is divided into several subareas that are sub-sequentially exposed and stitched together leading to the final full size grating (fig. 1). It is thus characteristic, e.g., for e-beam lithography (EBL), direct laser writing or projection lithography.

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Figure 1: Illustration of the sequential exposure principle in e-beam-lithography
(EBL) and origin of the structures that may cause the spurious stray light peaks.
(rights: IAP)


On the other hand, stochastic stray light generates a homogeneous scattering background and originates in stochastic shape deviations. A prominent source of stochastic stray light is Line Edge Roughness (LER), which describes the stochastic deviation of the grating line edge from its ideal position (fig. 2) [5].

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Figure 2: Illustration of a LER-disturbed grating structure and the cross-section
profile of the structure. In the frame of optical simulation tools (e.g. RCWA)
methods must be developed that allow to calculate 1D- and 2D-scattering within
a feasible numerical effort. (rights: IAP)

In order to predict the scattering of gratings that suffer from such deterministic and stochastic shape deviations we develop both analytical models and optical simulation methods that allow for calculating the stray light spectrum [4,5]. With the developed tools we are able to study the influence of perturbation parameters and illumination parameter but also of grating design parameters onto the stray light performance of the developed gratings.
As a consequence, the models allow to understand the measured angle resolved scattering (ARS) of fabricated gratings, to identify the occurring fabrication errors and to develop strategies that improve the fabrication process (fig. 3) [6-8].

Heusinger_3a Heusinger_3b
Figure 3: (a) Illustration of a simulated scattering distribution of a LER-disturbed grating. The stray light
shows certain maxima and minima within the angular half space. (b) Comparison of angle resolved stray
light measurements on EBL-fabricated binary diffraction gratings with simulated stray light spectra.
The black and gray curves can be related to both axes, the red and blue curve must be related to the axes
in the corresponding color. Within an unoptimized writing process the diffuse scattering is dominated by
stochastic line position errors (LPR) and line width errors (LWR). The optimized writing process shows a
reduced LER-dominated scattering background. (rights: IAP)


References:
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     E.-B. Kley, High performance diffraction gratings made by e-beam lithography,
     Applied Physics A, 109(4), 789-796, (2012).
[2] H.T. Nguyen, B.W. Shore, S.J. Bryan, J.A. Britten, R.D. Boyd, M.D. Perry,
     High-efficiency fused-silica transmission gratings, Optics letters, 22(3),
     142-144, (1997).
[3] T. Clausnitzer, T. Kämpfe, E.-B. Kley, A. Tünnermann, A. Tishchenko,
     O. Parriaux, Investigation of the polarization-dependent diffraction of deep
     dielectric rectangular transmission gratings illuminated in Littrow mounting,
     Applied optics, 46(6), 819-826, (2007).
[4] M. Heusinger, T. Flügel-Paul, U.D. Zeitner, Large-scale segmentation errors
     in optical gratings and their unique effect onto optical scattering spectra,
     Applied Physics B, 122(8), 222, (2016).
[5] M. Heusinger, M. Banasch, D. Michaelis, T. Flügel-Paul, U.D. Zeitner,
     Diffuse scattering of lamellar optical gratings due to line edge roughness,
     Proc. of SPIE 10692, pp. 106920I-1, (2018).
[6] M. Heusinger, M. Banasch, U.D. Zeitner, Rowland ghost suppression in high
     efficiency spectrometer gratings fabricated by e-beam lithography, Optics
     express, 25(6), 6182-6191, (2017).
[7] M. Heusinger, M. Banasch, U.D. Zeitner, E.-B. Kley, High precision electron-
     beam-lithography for optical high performance applications, In Engineering
     for a Changing World: Proceedings; 59th IWK, Ilmenau Scientific Colloquium,
    Technische Universität Ilmenau, September 11-15, 59 (1.3.09), (2017).
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     optimization of Rowland ghosts in high efficiency spectrometer gratings
     fabricated by e-beam lithograph, In Advanced Fabrication Technologies for
     Micro/Nano Optics and Photonics IX, OSA, 9759, p. 97590A, (2016).