体光栅二维耦合波方程解析解的再探讨

针对完全重叠型的体光栅,在布拉格衍射范畴内给出二维耦合波方程的完整推导,并给出方程组的闭形式解析解.该解析解能够解决完全重叠型的均匀光栅的普遍衍射问题.研究了二维有限尺寸体光栅的衍射性质特别是衍射效率与光栅二维尺寸及介质吸收系数之间的关系.对于无吸收的光栅,参考光束相对物光束越宽,衍射效率将越高.当介质的吸收不可忽略时,对于耦合较强的光栅,参考光尺寸的增大反而会引起衍射效率的下降.为了获得最优的衍射效率,应当根据介质的吸收率合理地设计光栅的几何尺寸.

Re-Investigation on the Solution to Two-Dimensional Coupled Wave Equations for Volume Holographic Gratings

The complete derivation of two-dimensional (2-D) coupled wave equations is given for total overlap gratings in the Bragg regime. The analytical solution in closed mathematical form is also given. General diffraction properties of total overlap gratings, can be solved with the solution. Diffraction properties, especially effects of the grating dimension and absorption coefficient on the diffraction efficiency are researched based on the solution in this paper. The results show that diffraction efficiency of a lossless grating increases with the higher ratio of reference beam width to object beam width. However, for strongly-coupled gratings if the absorption of medium cannot be ignored, the diffraction efficiency decreases with widening of reference beam. It is suggested that for efficiency optimization of a lossy grating the geometrical dimension of the grating should be carefully designed.