Diffuse scattering of lamellar optical gratings due to line edge roughness

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.