局域体全息光栅衍射的平面波与柱面波的波前转换研究

Study of Wave-Front Conversion by Local Volume Holographic Grating Diffraction between Cylindrical and Plane Waves

利用一维耦合波理论研究了入射方向相互垂直的一束平面波与一束柱面波干涉形成光折变局域体全息光栅的波前转换情况。给出了透射波和衍射波振幅的解析表达式。讨论了该局域体全息光栅的几何尺寸以及全息透镜的焦距对光栅衍射效率的影响。结果表明,随着光栅横向尺寸的增加,光栅的衍射效率也逐渐增加。然而,光栅的衍射效率却随着光栅纵向尺寸的增加而减小。全息透镜的焦距越长,光栅的衍射效率也越大。此外,分析了光栅的布拉格选择特性,该光栅具有非常好的角度选择特性。在平面波与柱面波干涉形成全息透镜的设计中,为了获得最优的衍射效率,应当根据要求合理地选择记录所用柱面波和设计光栅的几何尺寸。

Based on the two-dimensional coupled-wave theory, the wave-front conversion by local volume holographic grating between cylindrical and plane waves in 90° recording geometry is investigated. The analytical integral solutions for the amplitude the transmissive and diffractive waves are presented. Furthermore, the dependences of grating diffraction efficiency on the geometric size of the grating and the focal length of the holographic lens are discussed. It is shown that, with the increase of the horizontal direction size of the grating, the diffraction efficiency of holographic grating increases. But with the increase of the size of the grating in the vertical direction, the diffraction efficiency of holographic grating decreases. The diffraction efficiency increases with the rise of the focal length of holographic lens. Furthermore the Bragg selectivity of the grating is studied, and excellent angle selectivity is proved. It is suggested that for the diffraction efficiency optimization of the holographic grating recorded by plane and cylindrical waves the recording cylindrical wave and the geometrical dimension of the grating should be carefully designed according to the request.