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 HfO<sub>2</sub> grating and a fused-silica substrate, is optimized using rigorous coupled-wave analysis around the 800-nm wavelength, after which the modal guideline for cancellation of the 0th order in a phase mask is verified. The proposed MA method illustrates the inherent physical mechanism of multiple reflections of the grating modes in the diffraction process, which can help to analyze and design both low-contrast and high-contrast gratings.
© 2013 Chinese Optics LettersPDF Article