滑翔机的射线光学
Ray Optics for Gliders
摘要：
自推进粒子的控制是许多微机器人技术发展的核心，从动态可重构材料到先进的芯片实验室系统。然而，很少有物理原理可以指定粒子轨迹，并可用于产生广泛的行为。在射线光学领域，控制光的轨迹的单一原理--斯涅耳定律--产生了一个直观的框架，用于设计从显微镜到照相机和望远镜的各种设备。在这里，我们表明，自推进粒子滑过阻力不连续的运动是由斯涅耳定律的变体，并开发相应的滑翔机射线光学。正如折射率的比值决定了光线的路径一样，阻力系数的比值决定了滑翔机的轨迹。折射的大小取决于滑翔机的形状，特别是它的长宽比，这相当于光的波长。这使得通过摩擦棱镜能够将多形态、多形状的滑翔机光束分离成不同的单形态、单一形状的光束。反过来，单形滑翔机的光束可以通过球面和梯度摩擦透镜聚焦。或者，全内反射的临界角可用于创建形状选择性滑翔机陷阱。总的来说，我们的工作表明，进一步将光和微观滑翔机之间的类比，将导致广泛的新设备的分类，集中和分析自推进粒子。
英文摘要：
Control of self-propelled particles is central to the development of many microrobotic technologies, from dynamically reconfigurable materials to advanced lab-on-a-chip systems. However, there are few physical principles by which particle trajectories can be specified and can be used to generate a wide range of behaviors. Within the field of ray optics, a single principle for controlling the trajectory of light -- Snell's law -- yields an intuitive framework for engineering a broad range of devices, from microscopes to cameras and telescopes. Here we show that the motion of self-propelled particles gliding across a resistance discontinuity is governed by a variant of Snell's law, and develop a corresponding ray optics for gliders. Just as the ratio of refractive indexes sets the path of a light ray, the ratio of resistance coefficients is shown to determine the trajectories of gliders. The magnitude of refraction depends on the glider's shape, in particular its aspect ratio, which serves as an analog to the wavelength of light. This enables the demixing of a polymorphic, many-shaped, beam of gliders into distinct monomorphic, single-shaped, beams through a friction prism. In turn, beams of monomorphic gliders can be focused by spherical and gradient friction lenses. Alternatively, the critical angle for total internal reflection can be used to create shape-selective glider traps. Overall our work suggests that furthering the analogy between light and microscopic gliders will result in a wide range of new devices for sorting, concentrating, and analyzing self-propelled particles.
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