Maxwell's Fishpond

Abstract

Most of us will have at some time thrown a pebble into water, and watched the ripples spread outwards and fade away. But now there is a way to reverse the process, and make those ripples turn around and reconverge again, ... and again, and again. To do this we have designed the Maxwell's Fishpond, a water wave or "Transformation Aquatics" version of the Maxwell's Fisheye lens [Tyc et al. 2011, Luneberg 1964] that is now well-known from transformation optics. These are transformation devices where wave propagation on the surface of a sphere is not modelled on an actual sphere, but in a flat device with carefully designed spatially varying properties. And just as for rays from a point source on a sphere, a wave disturbance in a Maxwell's Fisheye or Fishpond spreads out at first, but then reforms itself at its opposing point in the device. Here we show how such a device can be made for water waves, partly in friendly competition with comparable electromagnetic devices [Ma et al. 2011] and partly as an accessible and fun demonstration of the power of transformation mechanics. To the eye, our Maxwell's Fishpond was capable of reforming a disturbance up to five times, although such a feat required taking considerable care, close observation, and a little luck. What can you see in the video at http://www.qols.ph.ic.ac.uk/~kinsle/files/MFishpond/ ?

9 pages (v2 add links, improve fig.3, minor corrections, v3 add journal info)

References in corpus (7)

• Plasmonic Luneburg and Eaton Lenses
• Observation of negative-frequency waves in a water tank: A classical analogue to the Hawking effect?
• Perfect imaging without negative refraction
• A Shallow Water Analogue of the Standing Accretion Shock Instability: Experimental Demonstration and Two-Dimensional Model
• Comment on: Reply to comment on `Perfect imaging without negative refraction'
• Controlling surface plasmon polaritons in transformed coordinates
• Horizon effects for surface waves in wave channels and circular jumps

Cited by in corpus (4)

• Cloaks, editors, and bubbles: applications of spacetime transformation theory
• Transformation devices: carpets in space and space-time
• On Spacetime Transformation Optics: Temporal and Spatial Dispersion
• Generalized Transformation Design: metrics, speeds, and diffusion