We propose a simple compact interferometer using twisted light to detect picometer displacement on a solid or liquid surface. The heart of the interferometer lies in producing a daisy petal pattern formed by interference between two oppositely charged twisted beams. The sample being probed is an active component of the interferometer. By analyzing the rotation of the petal pattern, caused by the relative displacement between the cylindrical lens (CL) and solid/liquid surface, we exhibit picometer resolution in displacement measurements. Remarkably, we explore the significance of a radial quantum number in the measurement of surface displacement and surface tilt angle. We also investigate the arbitrary surface deformation profile with similar precision by modifying the set-up. We perform simulations in realistic experimental settings and show that they are in excellent agreement with the predictions of analytic expressions. The proposed set-up can be further miniaturized by a small focal length CL and will open routes for tremendous applications in picometer-scale displacement measurement of a solid or liquid interface by various excitations.

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使用扭曲光的紧凑型皮米级干涉仪

我们提出一种使用扭曲光的简单紧凑型干涉仪，以检测在固体或液体表面上的皮秒仪位移。干涉仪的核心在于产生由两个相反电荷的扭曲光束之间的干涉形成的雏菊花瓣图案。被探测的样品是干涉仪的有源组件。通过分析由柱面透镜（CL）和固/液表面之间的相对位移引起的花瓣图案的旋转，我们在位移测量中显示出皮克级分辨率。值得注意的是，我们探索了径向量子数在表面位移和表面倾斜角测量中的重要性。我们还通过修改设置来研究具有相似精度的任意表面变形轮廓。我们在现实的实验环境中进行仿真，结果表明它们与解析表达式的预测非常吻合。所提出的装置可以通过较小的焦距CL进一步小型化，并为通过各种激发进行固体或液体界面的皮克级位移测量提供了广阔的应用前景。