We propose a design methodology for systematic design of surface relief transmission gratings with optimized
diffraction efficiency. The methodology is based on a gradient-based topology optimization formulation along with 2D
frequency domain finite element simulations for TE and TM polarized plane waves. The goal of the optimization is to
find a grating design that maximizes diffraction efficiency for the -1<sup>st</sup> transmission order when illuminated by
unpolarized plane waves. Results indicate that a surface relief transmission grating can be designed with a diffraction
efficiency of more than 40% in a broadband range going from the ultraviolet region, through the visible region and into
the near-infrared region.