研究了用波长为632.8 nm的柱面波与平面波记录形成的体全息柱透镜用波长为800 nm的平面波重现下的波前转换情况。结合二维耦合波理论,推导了形成于LiNbO3双掺杂晶体中该全息柱透镜的耦合波方程,并求出了其积分形式的解析解,分析了改变读出波长下该透镜的布拉格失配因子的分布情况,讨论了它的几何尺寸和记录柱面光波对其衍射效率的影响,以及柱面衍射光振幅在出射口径上的分布情况。结果表明,记录所形成的全息柱透镜的焦距越长它的衍射效率越高; 该透镜厚度的增加会使它的衍射效率增加,但是透镜的衍射口径增加它的衍射效率会降低; 衍射光振幅在其出射口径上的分布出现了一定程度的失真,衍射光强度主要集中分布在布拉格失配值较小处对应的位置。最后,进一步讨论了全息透镜记录过程中满足布拉格匹配条件的参考点的选择对光栅衍射性质的影响,结果表明衍射效率不随参考点的改变而改变。

The wave-front conversion between cylindrical and plane waves by photorefractive local volume holograms recorded at 632.8 nm and reconstructed at 800 nm is investigated in this paper. Based on two-dimensional coupled-wave theory, the coupled wave differential equations of the cylindrical lenses on double-doped LiNbO3 crystal are derived, and the analytical integral solutions for the amplitudes of the space harmonics of the field inside the transmission geometry are presented. The values of off-Bragg parameter at the reconstructed process are analyzed. Furthermore, the dependences of diffraction efficiency on recording cylindrical wave and on the geometric size of the gratings are discussed, and the amplitude distribution of the diffracted beam at the output boundary is also analyzed. It is found that: 1) the diffraction efficiency increases as the focal length of the volume holographic cylindrical lenses increases; 2) the diffraction efficiency increases with increasing the grating thickness, but the diffraction efficiency decreases with increasing the width of the diffraction surface at vertical direction; 3) diffracted amplitude distribution derivates much from the desired uniform amplitude as the initial recording cylindrical, and the diffracted intensity mainly concentrates at the line B-B′ of the gratings. At last, the effect of selectivity of different on-Bragg reference points for recording hologram on the diffraction efficiency of the grating is discussed, the results show that reference points have no influence on diffraction efficiency.