本文采用麦克斯韦(Maxwell)方程微分积分方程对波长尺寸的梯形反射光栅在TE模式(横向电场)偏振状态入射下,进行严格理论的计算和分析.表面电场计算表明,光栅刻槽斜边边界对于金属材料金和铝光栅表面电场分布具有明显效应,对于入射波长为λ=1.0 μm附近的红外区域,金材料具有强烈的金属特性,此时表面电场的斜边边界效应更加明显.表面电场及其远场衍射效率伴随刻槽深度变化,而振荡特性进一步阐明了此效应对近,远场的作用.该方程适用于任意形状光栅或单一散射体对任意入射方向,任意偏振态的衍射和散射问题.

The differential integral equation derived from Maxwell's equations was used to rigorously deal with the wavelength- sized surface relief trapezium- shaped reflecting grating in TE (transverse electric) polarization. Numerical analyses of the surface electric field show that the effect of edge and wall of the grating has significant influence on the surface field of metallic materials, e. g. gold and aluminium. Particularly, for the incident wavelength λ=1.0 μm when gold is in strong metallic nature, the edge and wall effect becomes more apparent. The oscillating characteristics of the surface field at the bottom of the grooves and the far field diffraction efficiency against the groove depth are explained by its physical mechanism of the edge and wall effect. This technique can be used to tackle the diffraction problem for arbitrary shapes of grating or single scattering obstacle in arbitrary angles of incidence and polarization.