Maxwell's Fishpond (1206.0003v3)

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/ ?