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Published October 25, 2022 | public
Journal Article

Ray Optics for Gliders


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 analogue 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 may be used for sorting, concentrating, and analyzing self-propelled particles.

Additional Information

This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences Biomolecular Materials program under Award Number DE-SC-0020993. P.W.K.R. was partially supported by the Office of Naval Research award N00014-18-1-2649. T.D.R. was partially supported by Sloan Foundation award G-2021-16831. D.O. was partially supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Award Number DE-SC-0010595 and partially through the Moore foundation. J.F.B. was funded by the National Science Foundation Grant 1803662.

Additional details

August 22, 2023
October 24, 2023