中文摘要：

本文通过分析比较给出了常用二维等效介质理论解析解的适用条件并且将有效介质理论的适用范围推广至零级衍射边界处,并通过FDTD模拟验证了该解析方法的准确性.这不仅解决了长期以来没有精确二维有效介质理论（2D-EMT）解析解的困境,而且使得直接用解析公式设计和定量解释减反微结构的减反效果变得可能,有着广泛的应用前景.

英文摘要：

By investigating the difference between the analytic solutions obtained from commonly used two-dimensional effective medium theory and the numerical solutions, we found that any analytical solution was quite accurate only at its right normalized cycle, determined by its own effective range. Thus, one should solve the problem that ＂there was no closed-form solution for the effective permittivity of a two-dimensional zero-order grating＂, and expand the applied scope of the effective medium theory to the boundary of zero-order diffraction. Secondly, by using the two-dimensional analytical solution, we have designed a nanowires anti-reflection layer in silicon, which fully meet the needs of the design that reach zero reflectance at 650 nm; and the spectrum averaged reflection from 310–1120 nm is 8%, lower than silicon nitride anti-reflection layer 9.9%. Stavenga formula can be used to design a large normalized period antireflective microstructure, while the Maxwell-Garnett formula can be used to design a small normalized cycle antireflective microstructure. Design of antireflection structure by two-dimensional closed form solution directly is viable, which have huge potential application value.