A periodically structured substrate includes a slab and a periodic structure formed on the slab and including a plurality of spaced apart first surrounding elements and a plurality of spaced apart central elements. The first surrounding elements are periodically arranged in such a manner to form repeating polygonal patterns. Each of the central elements is disposed at a center of a respective one of the polygonal patterns. The periodic structure further includes a spacer medium that fills a space among the central element and the first surrounding elements of each of the polygonal patterns and that has a refractive index different from those of the central element and the first surrounding elements.