Optimal dimensions of cone and pyramid moth-eye structures for $\mathrm{SiO}_{2}$ windows

We computationally investigate the transmission efficiency through moth-eye nanostructures that are fabricated on $\mathrm{SiO}_{2}$ windows in the wavelength range from 0.4 to 2 $\mathrm{\mu m}$. We investigated both truncated cones and truncated pyramids, and we varied the height, bottom width, and top width of these shapes in order to maximize the transmission efficiency. We found that there is no substantial difference in transmission between truncated cone and pyramid structures. Using the constraints from the current achievable experimental limits, a relatively uniform transmission coefficient of larger than 98.8% can be obtained from 0.4 $\mathrm{\mu m}$ to 2 $\mathrm{\mu m}$. These transmission results are only 0.4% in absolute value lower than the transmission of a structure that is not constrained by current experimental limits.