矩形槽光栅的矢量模式理论

A vector modal theory for rectangular-groove grating

本文引进满足均匀矢量Helmholtz方程的矢量波函数作为基矢,对矩形槽光栅的槽内和槽外的光场分别进行矢量平面波展开和矢量模式展开,并由耦合条件导出了求解展开系数的方程组,可进行数值计算.该方法可研究入射场的方向和偏振任意时的衍射效率、偏振特性变化等问题.在p偏振和s偏振的特殊情况下所得到的公式与用标量模式理论得到的结果一致.

The vector wave functions satisfinga vector homogeneous Helmholtz equation are introduced as the basic vectors, and the field both outside and inside the grooves of the grating are expanded by vector plane wave functions and vector modes respectively. Equations of the amplitudes which can be solved numerically are dirived.The method can be used to study the diffraction of optical plane waves, the incident direction and the polarization of which can be arbitary. The results for P- and S-polarization are consistent with that published before.