We develop an analytical framework for self-stabilizing optical manipulation of freestanding metasurfaces in three dimensions. Our framework reveals that the challenging problem of stabilization against translational and rotational perturbations in three dimensions is reduced to a simpler scattering analysis of the metasurface unit cell in two dimensions. We derive universal analytical stiffness coefficients applicable to arbitrary three-dimensional radial metasurfaces and radial beam-intensity profiles. The analytical nature of our framework facilitates highly efficient discovery of optimal optomechanical metasurfaces. Such use of metasurfaces for mechanical stabilization enables macroscale and long-range control in collimated, but otherwise unfocused light beams, and could open up avenues for manipulation beyond traditional optical tweezing and transport.

中文翻译：

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独立光子超表面的光机械自稳定性

我们开发了一个分析框架，用于在三个维度上对独立超表面进行自稳定光学操作。我们的框架表明，针对三维平移和旋转扰动的稳定性具有挑战性的问题被简化为对二维超表面晶胞进行更简单的散射分析。我们推导出适用于任意三维径向超表面和径向光束强度分布的通用分析刚度系数。我们框架的分析性质有助于高效发现最佳光机械超表面。这种用于机械稳定的超表面的使用能够对准直但未聚焦的光束进行宏观和远程控制，