Independent electromagnetic optimization of the two coating thicknesses of a dielectric layer on the facets of an echelle grating in Littrow mount

Electromagnetic investigations using the integral equation system method with parametrization (IESMP) show that the two-coating thicknesses of a dielectric layer on the facets of an echelle grating in a Littrow mount have to be independently optimized. While the optimal coating thickness on the blaze facet is the same for maximal efficiency and minimal absorption in both polarizations, this is not the case for the anti-blaze facet. Therefore, it is only possible to optimize the two-coating thicknesses for one of the purposes. On the blaze facet, a simple formula based on thin-film optical considerations describes the optimal thickness very well. Additionally, we found that resonance anomalies can significantly reduce efficiency if the wrong coating thickness is used on the anti-blaze facet. The coating thickness creating the resonance anomaly can be deduced by investigating the poles of the reflection coefficient of a dielectric coated metallic mirror in grazing incidence. This value can be used to optimize the layer for maximal efficiency. Consequently, we are generally able to describe the optimal coating thicknesses for minimal absorption as well as for maximum efficiency in both, TE- and TM-polarization, using only thin-film optical considerations without any further rigorous calculation.