A polarizer which has and regularly arranged two-dimensional structure which has a pitch of 1 mm or so or less. The polarizer has structure in which two or more film-shaped materials which have a substantially regularly arranged one-dimensional undulation. The polarizer also has a substantially regularly arranged two-dimensional structure. For example, the polarizer consist of materials 1 and 2 which have different refractive indexes. A regularly arranged two-dimensional structure which has a pitch of 1 mm or less can be obtained by a simple method. Because of this structure, the polarizer transmits the incident light which has a specific polarized plane and reflects the incident light which has a polarized plane which is orthogonal to the plane.