Numerical calculation of the accuracy of approximate analysis methods for binary rectangular groove diffraction phase grating

Abstract

The range of the accuracy of scalar diffraction theory and effective medium theory for binary rectangular groove phase grating is evaluated by the comparison of diffraction efficiencies predicted from scalar theory and effective medium theory, respectively, to exact vector results calculated by Fourier modal method. The effect of element parameters (depth, period, index of refraction, angle of incidence, and fill factor) on the accuracy of scalar treatment and effective medium theory is quantitatively determined. Generally, it is found that the scalar method is valid when the normalized period is more than fourfold wavelength of incident light at normal incidence. The error of transmittances between vector method and scalar method increases as the incident angle and refractive index increase. Furthermore, when the higher diffraction orders other than zero-th order are not to propagate, the effective medium theory is accurate to evaluate the transmittance of grating at normal incidence. The error of transmittances between effective medium method and rigorous vector theory increases as the incident angle and refractive index increase. Also, the error of diffraction efficiencies between the simple methods and the vector method on the polarization state of incident light is clearly demonstrated.