The theory about the further factorization of the dispersion equation of the grating mode under the incidence of Bragg angle and transverse electric and transverse magnetic polarizations is proposed, and the equivalent relationship between the factorized equation and the symmetry of the grating mode is confirmed. The symmetry of grating modes is beneficial to illustrate the physical picture of the diffraction process within gratings. By the analysis of the distribution property of the root of the grating mode equation, a method to improve the computation efficiency of the effective refractive index is proposed.