Equal point of two modes effective refractive indices in simplified modal method

The simplified mode method explains the physical processes inside the grating in terms of the Mach- Zehnder interferometer model. There are three modes include mode 0, 1, 2 in grating under second Bragg angle incidence. We report a special case of fused silica grating when its period is close to 1.3 times of wavelength, where the effective refractive index of mode 1 might be equal to mode 2. In this special case, we found that the joint effect of mode 1 and 2 on the diffraction efficiency for -2 order is not accurate entirely, and the diffraction of the 0th order is approaching to the maximum, both with a slight oscillation of efficiency when the depth of grating is increased. This phenomenon by using simplified mode method could help to understand the physics of grating theory.