In recent years, the scattering properties of optical gratings became of high interest. In particular, the effect of line edge roughness (LER) in lamellar diffraction gratings was identified to be a potential source of stray light. In this contribution the LER-induced scattering spectrum of such gratings is investigated. The straight-forward method to calculate the angle resolved scattering (ARS) is offered by two-dimensional simulation tools, e.g. the rigorous coupled wave analysis (RCWA). Unfortunately, this approach suffers from computation times that
typically lie in the range of several days. As a simplification, we apply a novel one-dimensional rigorous approach1 that permits the prediction of ARS along the dispersion direction of the grating within a feasible computation
time. As the 1D-model only accounts for the LER-parameter σ and neglects the correlation length ξ and the roughness exponent α, analytical considerations must be employed in order to adapt the 1D-simulation results to the 2D-reality.1 The model is verified by comparison to the 2D-model and ARS-measurements of E-beam exposed gratings with artificially induced (and strongly determined) LER. Based on the derived 1D-model, the effects of
different parameters on the straylight performance of a high performance spectrometer grating is investigated. As a result we find that not only the roughness parameters but also the grating geometry has a significant effect especially on the spatial distribution of the scattered light. In other words, the strength of the scattered light next to the (spectrometric) useful diffraction order can be controlled by the grating geometry, too. Hence, the presented algorithm might be a useful tool for designing gratings with strong straylight specifications.
Controlling the polarization of light is crucial in numerous applications such as spectroscopy, ellipsometry, photo
lithography or industrial vision. Polarization control can be realized by wire grid polarizers (WGPs), which are large
aspect ratio, zero order gratings. These elements provide an anisotropic transmittance depending on the polarization
direction of the incident light. WGPs’ high attractiveness originates from their large free aperture, while simultaneously
being extremely thin. Furthermore, these elements can be easily integrated into other nano-optical devices. Recently,
such elements were successfully developed for applications down to the deep ultra violet spectral range. However, at
shorter wavelengths the influence of roughness of the structures poses a severe limitation on the feasible optical
performance. To tackle this problem, we numerically simulated the impact of line edge roughness on the polarization
properties of WPGs. Therefore, we generated edge position data of rough grating lines by means of the Thorsos method
and calculated the resulting optical response by finite difference time domain method. With this procedure the influence
of standard deviation, correlation length, Hurst exponents and wavelength was investigated. We find that for standard
deviations of 2.5 nm and 5.0 nm the polarization contrast is reduced by a factor of 3 and 7, respectively. The polarization
contrast shows a minimum for intermediate correlation lengths, while virtually no impact of the Hurst exponent is
observed. This is explained by several mechanisms occurring for different ratios between the spatial frequency of the
roughness and the frequency of incident light. Our theoretical findings correlate well with experimental results we
retrieved with measured roughness parameters of fabricated elements.
Any violation of the periodicity of a perfect grating will result in diffuse scattering. In the particular case of a periodic violation the generated stray light shows deterministic, also periodic features that arise as distinct peaks in the stray light spectra, especially so-called Rowland ghosts. In this paper the characteristics of the spurious Rowland ghosts in binary spectrometer gratings are investigated and the potential of a randomization technique in order to suppress the Rowland ghosts is analyzed. Especially in sequential fabrication technologies, e.g. electron beam lithography, the Rowland ghosts originate in a segmentation process that is necessary in order to write large scale gratings. Hence several subareas are subsequentially exposed and stitched together leading to the final full size grating. Due to this stitching approach the subareas induce secondary periodic structures and thus generate the spurious Rowland ghosts in the order of magnitude of <10<sup>-4</sup> compared to the useful diffraction order. A randomization of this segmentation process is investigated both theoretically in rigorous simulations and experimentally by fabricating a purposely designed optical grating. As approach for the randomization in experiment we applied a special multi-pass-exposure. Here the sample is exposed multiple times with an accordingly shifted and dose-reduced subarea in each pass. The achieved simulation results show that a randomization of the subareas effectively reduces the Rowland ghosts. Furthermore the applied randomization technique during grating fabrication was able to suppress one kind of Rowland ghosts completely.