界面对矢量光束超分辨聚焦和焦区光斑整形影响研究

Vector beams are those beams that have space-variant polarization distributions. It is found that vector beams can be focused by a high NA lens to a spot size beyond the diffraction limit, meanwhile they can also be used in the area of focus shaping, realizing some special intensity distributions such as “optical needle”, “flat-topped profile”, and “three dimensional optical cage” in the focal region. These unusual focusing properties have great applicable value in areas such as optical lithography, optical storage, laser micro-nano fabrication, and the optical tweezer. At present, most of the research work focuses on how to realize super-resolution focusing and focus shaping using various vector beams and modulation methods in homogeneous medium. But in real applications, it is often met that vector beams are tightly focused through an interface between media of different refractive indices. Influenced by the discrepancy of the two refractive indices, and the different interface positions relative to the geometrical focus, the tight focusing properties of vector beams will become very different from those in homogeneous medium. In this project, the effects of the discrepancy between the two refractive indices, the interface position, the NA of the lens, and the obstruction factor of incident pupil on the super-resolution focusing properties of vector beams will be thoroughly studied, and special attention will be paid to the effect of evanescent wave on the reduction of focus spot size when the vector beam is focused through an optically denser medium to an optically thinner medium. In addition, the effect of the dielectric interface on the focus shaping of vector beams will also be thoroughly studied. It is expected that the conclusions drawn in this project will be more practical and will provide a better theoretical guidance to real applications.

矢量光束是指在横截面上具有空间变化的偏振分布的光束。研究发现，矢量光束可实现超衍射极限聚焦，同时还可进行焦区光斑整形，实现光针、平顶、三维光学围栏等特殊光强分布。矢量光束这些奇特聚焦特性在很多领域具有巨大应用价值，如光刻，光存储，激光微纳加工，光镊等。目前理论研究主要集中于探索在均匀介质中如何用矢量光束实现超分辨聚焦和焦区光斑整形。但在矢量光束实际应用中，经过两种不同折射率介质形成的界面聚焦是常见情形。受两种介质折射率差异特性影响，以及界面相对几何焦点位置的影响，矢量光束紧聚焦特性将和均匀介质情况显著不同。本项目拟研究界面两侧介质折射率差异特性，界面位置，数值孔径，振幅光阑遮光比等因素对矢量光束超分辨聚焦特性的影响，特别当光束从光密介质向光疏介质超分辨聚焦时，倏逝波对光斑尺寸影响规律。同时，还开展界面对矢量光束焦斑整形影响研究。项目研究结论可为矢量光束紧聚焦实际应用提供更确切理论指导。

矢量光束是与标量光束相对的概念，偏振特性是矢量光束的重要特点。矢量光束在超分辨显微、光存储、光刻、激光微纳加工、光镊等领域有重要应用，因为这些领域都涉及到大数值孔径透镜聚焦，此时光束偏振性会有重要影响，从而带来一些奇特聚焦特性。我们在傍轴条件下求解了矢量亥姆霍兹方程，得到了贝塞尔-高斯矢量光束解，以及拉盖尔-高斯矢量光束解。为了更好理解矢量光束，我们研究了在谐振腔外产生各种矢量光束的实验方法，并给出了谐振腔外产生的矢量光束的一般数学描述公式。我们开展了两种复杂偏振分布矢量光束紧聚焦特性研究工作，分别为角向变化局域椭圆偏振矢量光束和径向变化杂化偏振矢量光束。对角向变化局域椭圆偏振矢量光束，我们主要研究了偏振阶数q和椭圆率对其紧聚焦特性的影响。我们发现当q=1时，这种光束在焦平面总具有圆对称光强分布，随椭圆率增大，焦平面光强分布逐渐由一个实心光斑演化成圆环状光斑。当q≠1时，只有椭圆率取值为1的涡旋圆偏振光束在焦平面形成圆环状光强分布，而椭圆率取其它值的矢量光束将在焦平面形成2abs(q-1)个聚焦光斑。随椭圆率取值增加，焦平面的光强分布逐渐由2abs(q-1)个聚焦光斑演化成圆环状光强分布，然后又重新演化成2abs(q-1)个聚焦光斑。椭圆率取值互为倒数的两种角向变化局域椭圆偏振矢量光束在焦平面的光强分布形状相同，但相对旋转了90/abs(q-1)角度。我们从光束偏振态分布特点角度对以上聚焦特性进行了解释。对径向变化杂化偏振矢量光束的研究发现，当光束的偏振态在庞加莱球面的小圆上变化时，其紧聚焦后将得到一个聚焦光斑，且该光斑能够产生靠近或远离透镜的焦移。当光束的偏振态在庞加莱球面大圆上变化时，紧聚焦后将得到两个相对几何焦点对称分布的焦斑。对后一种光束，用环形振幅光阑对焦区光斑进行整形，可以在焦区得到光针状的光强分布，特别是这种光针的横截面光强分布一般具有椭圆形状，而且随传输距离增加，该椭圆的取向会不断旋转。