To provide a plasma display panel and a field emission display having an anti-reflection function which can further reduce reflection of incident light from an external source. By providing an anti-reflection layer which geometrically includes a plurality of adjacent hexagonal pyramid-shaped projections, reflection of light is prevented. The reflective index changes from a surface side of display screen to an out side (an atmosphere side) due to a physical shape of a hexagonal pyramid. The plurality of hexagonal pyramid-shaped projections can be provided densely without any space remaining, and six surfaces of side of the hexagonal pyramid-shaped projection are each provided at different angles to a base surface. Therefore, light ray can be effectively scattered in many directions.