Improvement of the validity of the simplified modal method for designing a subwavelength dielectric transmission grating

Abstract

To accurately and easily design the diffraction characteristics of a rectangular transmission grating under the illumination of Littrow mounting, the validity and limitation of the simplified modal method is evaluated by a comparison of diffraction efficiencies predicted by the modal approach to exact results calculated with rigorous coupled-wave analysis. The influence of the grating normalized period, the normalized groove depth, and the fill factor on the accuracy of the modal method is quantitatively determined. More importantly, the reflection effect of two propagating grating modes with the optical thin-film model and the nonsymmetrical Fabry-Perot model is proposed and applied in the modal method to improve the accuracy of the calculated diffraction efficiencies. Generally, it is found that the thin-film model of reflection loss is valid at the smaller normalized period, but the Fabry-Perot model can exactly calculate the reflection loss of grating modes at the larger normalized period. Based on the fact that the validity of the modal approach is determined independently of the incident wavelength, the exact design and analysis of grating diffraction elements can be implemented at different wavelengths by simply scaling the grating parameters. Moreover, the polarization effect of diffraction properties on the limitation of the modal method without and with the reflection loss of grating modes is clearly demonstrated.