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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。
In the case of completely overlapping volume gratings, the complete derivation of the two-dimensional coupled wave equation is given in the Bragg diffraction range and the closed form analytical solution of the system is given. The analytical solution can solve the general diffraction problem of a completely overlapping homogeneous grating. The relationship between the diffraction properties, especially the diffraction efficiency, the grating two-dimensional size and the dielectric absorption coefficient of a two-dimensional finite size grating is studied. For non-absorbing gratings, the wider the reference beam relative to the object beam, the higher the diffraction efficiency will be. When the absorption of the medium can not be neglected, the increase of the reference light will lead to the decrease of the diffraction efficiency for the strongly coupled grating. In order to obtain the optimal diffraction efficiency, the geometry of the grating should be properly designed according to the absorption rate of the medium.