Improvement of accuracy of simple methods for design and analysis of a blazed phase grating microstructure

In order to precisely analyze and design the transmittance characteristics of a blazed grating, the validity of both the scalar diffraction theory and the effective medium theory is quantitatively demonstrated. By making a comparison of diffraction efficiencies calculated by the two simplified methods and Fourier modal method, the accuracy can be obtained. It is found that when the normalized period is more than three wavelengths of the incident light, the scalar diffraction theory is useful to calculate the transmittance of the blazed grating within the error of less than 3%. The validity of the scalar diffraction theory increases when the normalized period increases. Importantly, by considering the Fresnel reflection effect, the validity of scalar diffraction theory can be significantly enhanced. Furthermore, when no higher-order diffraction waves appear and only zeroth order diffraction wave propagates, the effective medium theory is accurate to compute the diffraction efficiency within the difference of less than 1% between the zeroth order effective medium theory and Fourier modal method. The polarization characteristics of the validity of effective medium theory are also quantitatively demonstrated. The validity of the two simplified theories is dependent on not only the normalized period of surface microstructure but also the normalized groove depth.