Kavli Affiliate: Paul W. K. Rothemund
| First 5 Authors: Tyler D. Ross, Dino Osmanović, John F. Brady, Paul W. K. Rothemund,
| Summary:
Snell’s law, which encompasses both refraction and total internal reflection,
provides the foundation for ray optics and all lens-based instruments, from
microscopes to telescopes. Refraction results when light crosses the interface
between media of different refractive index, the dimensionless number that
captures how much a medium retards the propagation of light. In this work, we
show that the motion of self-propelled particles moving across a resistance
discontinuity is governed by an analogous Snell’s law, allowing for glider ray
optics. We derive a variant of Snell’s law for gliders moving across regions of
different frictions. 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. We find that the magnitude of refraction depends on
the glider’s shape, specifically the aspect ratio, as analogous 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. Completing the analogy, we show that
the shape-dependence of the total internal reflection critical angle can be
used to create glider traps. Such analogies to ray optics suggest a universe of
new devices for sorting, concentrating, and analyzing microscopic gliders is
possible.
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