利用严格耦合波理论(RCWA)计算了一维金属亚波长光栅刚好出现一级衍射透射波时的周期/波长比(临界周期点),并利用最小二乘法拟合出临界周期点随光栅基底折射率的变化关系,即y=1/x。为了验证该规律的正确性,选取不同的金属材料、占空比、金属厚度、光栅周期、入射光偏振态进行计算分析。结果表明,对于一维亚波长金属光栅,一级衍射的出现都满足临界周期点的变化规律,并且与入射光的偏振态及波长无关,从而为设计一维金属亚波长光栅提供了仅存在零级衍射的条件。

Rigorous coupled wave approach (RCWA) was used to calculate the value of one-dimensional (1D) subwavelenth metal grating′s maximum period that allows only propagation of the zeroth diffraction order (the maximum period is also called critical periodic point). Assuming the surrounding medium is air, some different refractive indexes of the substrate material are chosen to calculate the critical periodic point. It is shown that the critical periodic point is only decided by the refractive indexes of the substrate, no matter which kind of metal, refractive indexes of grating layer, grating period, duty cycle, grating thickness and the polarization and wavelength of incidence are chosen. The results are useful for designing and fabricating novel nano-optics based on 1D subwavelength metal grating by avoiding complicated calculation and the failure of fabricating.