Modern nanoscale manufacturing techniques allow for a high degree of flexibility in designing surface microstructures and nanostructures. Injection molding of nanosized features allows for mass production of plastic components with a tailored nanostructure producing specific optical effects depending on the purpose. This work details the use of topology optimization for designing periodic polymer grating surfaces with complex optical properties. A method based on robust topology optimization is formulated for designing the nanostructure of plastic surfaces with extreme reflection or transmission properties. Topology optimization allows for free distribution of material but a mechanical constraint based on the fundamental free mechanical vibration frequency ensures connected structures. Several examples are given to illustrate the efficiency of the method.