Modal analysis of the 0th order nulled phase masks

A simple modal analysis (MA) method to explain the diffraction process of 0th order nulled phase mask is presented. In MA, multiple reflections of the grating modes at grating interfaces are considered by introducing equivalent Fresnel coefficients. Analytical expressions of the diffraction efficiencies and modal guidelines for the 0th order nulled phase grating design are also presented. The phase mask structure, which comprises a high-index contrast HfO2 grating and a fused-silica substrate, i