A new modal analysis based on the simplified mode method and multi-beam interference theory is proposed. Multiple
reflection of propagating modes at grating interfaces is considered by introducing equivalent Fresnel coefficients into the
diffraction process analysis. Then the proposed modal analysis is applied to design a rectangular-groove fused-silica
grating as a three-port beam splitter. The diffraction efficiency expressions are derived in this paper, which are analogous
to the results of multi-beam interference of a plane-parallel plate. Dependence of diffraction efficiencies of the
transmission 0th and 1st diffractive orders on the groove depth is obtained with optimized grating period and duty cycle.
Compared with the simplified mode method, the results based on the proposed modal analysis can match much better
with those from rigorous coupled-wave analysis (RCWA), which proves the validity of the new modal analysis method.
Moreover, the analysis results give an intuitionistic proof that the ideal 100% diffraction efficiencies of the transmission
diffractive orders can’t be realized and the transmission 0th order can’t be cancelled in low-contrast grating. As the
effective refractive indices of diffractive orders are introduced into the diffraction process analysis, this modal analysis is
all valid under the usual incidence cases of normal incidence, Littrow mounting, and second Bragg angle incidence.
More importantly, the proposed modal analysis provides a more accurate physical image of grating diffraction process,
which should be a useful analysis tool for high-density grating.