  An analytical method for diffraction of a plane electromagnetic wave at
periodically-modulated graphene sheet is presented. Both interface corrugation
and periodical change in the optical conductivity are considered. Explicit
expressions for reflection, transmission, absorption and transformation
coefficients in arbitrary diffraction orders are presented. The dispersion
relation and decay rates for graphene plasmons of the grating are found. Simple
analytical expressions for the value of the band gap in the vicinity of the
first Brillouin zone edge is derived. The optimal amplitude and wavelength,
guaranteeing the best matching of the incident light with graphene plasmons are
found for the conductivity grating. The analytical results are in a good
agreement with first-principle numeric simulations.
