Diffraction grating is a periodic structure which diffracts incident light into several beams in different directions . which depend on grating period and wavelength of the incident light . In the past few years , gratings have had different applications in optical frequencies , but today , with the development of technology , these structures have various and different applications from microwave to optical frequencies . Gratings are used in the fabrication of many devices in terahertz , such as polarizer , waveguide , absorber , sensor and etc . These structures are based on metal and dielectric , or their combination . Furthermore , in the last two decades with the discovery of graphene as a two-dimensional material with special electrical and mechanical properties , the gratings based on graphene are investigated and analyzed . Initial analysis of gratings goes back to early 20th century . Generally , analysis methods of gratings can be dir=rtl Key Words : Diffraction grating , Coordinate transformation method , Rigorous coupled-wave analysis , Terahertz , Graphene , Polarizer .