The application of symmetrical equation of diffracted wavevectors in integral theory of gratings

The integral theory for electromagnetic theory of gratings, which has complex mathematical tool and long computation cost, is needed to improve computing speed of the algorithm. A very shot-cut equation, which is called symmetrical equation of diffracted wavevectors by us, is presented. It makes the number of Green's function expansion terms shorter and simplifies the integral kernel by taking into account its symmetry. Take the grating in Littrow mount for computing example, because of applying this equation, the computation cost of integral theory which has good convergence, is shorten to 1/2 to 2/5. This work modifies the integral theory and improves its computing speed.