Applied validity of effortless method for design of sinusoidal surface microstructure

With the purpose of easily analyzing and designing the transmittance performance of a sinusoidal surface microstructure, the validity of effortless methods including scalar diffraction theory and effective medium theory has been evaluated quantitatively by the comparison of diffraction efficiencies predicted from scalar theory and effective indices theory, respectively, with exact results calculated with the rigorous vector method of Fourier modal method. Generally speaking, when the normalized period of surface microstructure is less than ten wavelengths of the incident light the scalar diffraction theory is believed to be inaccurate for designing and analyzing the diffraction efficiency of surface microstructure. But, in this paper, it is found that scalar diffraction theory can be used for predicting transmittance of the optical elements when the normalized period is more than three wavelengths of incident light within the error less than 5% at normal incidence. In addition, it is generally recognized that the effective medium theory is inaccurate for analyzing periodic surface microstructure when the normalized period is more than a tenth of the wavelength of incident light. However, the results in this study shows that effective medium theory is accurate as only zero-order waves are to propagate through the surface profiles, which the maximum difference between zero-order effective indices method and rigorous vector method reaches to 1%. Besides, the limitation of both simplified theories is dependent on not only the normalized period of a surface microstructure but also the normalized groove depth. Therefore, the range of applied validity of scalar theory and effective medium theory is expanded quantitatively compared to that of previous inaccuracy application for more easily designing and analyzing a sinusoidal surface microstructure.