Validity of scalar diffraction theory and effective medium theory for analysis of a blazed grating microstructure at oblique incidence

The accuracy of scalar diffraction theory (SDT) and effective medium theory (EMT) for analyzing a blazed grating is quantitatively demonstrated by making a comparison of diffraction efficiencies calculated by the two simplified methods to exact results from the Fourier modal method (FMM). It is found that when the normalized period is more than fivefold wavelength of incident light at normal incidence and is more than about tenfold wavelength at larger incident angle, SDT can be used to easily analyze effectively the transmittance characteristics of a blazed grating with divergence less than 1%. Particularly, for zeroth-order diffraction when the groove depth is less than threefold wavelength, the transmittance calculated by SDT with refractive index of 1.5 and normalized period of 5.0 agrees well with that of FMM at normal incidence. But, for ±1 orders, the validity of SDT is degraded from that for zeroth order. Generally, the deviation of transmittances between the SDT and the FMM increases as the incident angle and refractive index augment. Furthermore, when higher diffraction orders other than zeroth order are not propagating, the EMT is valid to evaluate the transmittance of a blazed grating at normal incidence. Similarly, the error of transmittances between the EMT and the FMM increases with the increase of incident angle and refractive index. The effectiveness of the SDT and the EMT for analyzing a blazed grating in the range of the normalized period far more than and less than the wavelength of incident light, respectively, is dependent on the parameters including incident angle, refractive index, normalized period, and normalized groove depth.