|Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS|
This month's topics:
was the caption chosen by Nature's Emma Maris for this image, part of its 2008 Gallery of "the year's most eye-catching science" (December 17, 2008).
Imagine a device that could bend light rays around you and make you invisible. This is what Ulf Leondardt (Singapore) and Tomás Tyc (St. Andrews) are proposing in a January 2 2009 Science report, "Broadband Invisibility by Non-Euclidean Cloaking." The physical device that will actually carry out the transformation is not spelled out in detail, but the authors describe how the geometry of a region of space could be changed, keeping the topology intact, to create a pocket of invisibility. To keep things simple I will only describe the 2-dimensional analogue they give to motivate their construction; it proceeds in two steps. First a 2-dimensional spherical surface is spliced into the Euclidean plane: the sphere is sliced open along a proper segment of a meridian line, and the two edges of the cut are identified with the two edges of a same-length cut in the plane. In this illustration the plane is bent to be tangent to the sphere along the splice.
The round sphere and the flat plane are spliced together along a proper segment of a meridian line. The yellow curve represents the path of a light ray in the resulting space: a straight line in the plane crosses the first suture, loops once around a great circle, crosses the second suture and continues in the plane as a straight line. There is such a ray going through any point on the sphere except those on the meridian line and not on the splicing segment (and their antipodal images). Part of the forbidden region is shown in red. Image courtesy of Ulf Leonhardt.
Second step: another sphere is spliced to the first one along a sub-segment of the forbidden region. Light rays coming from the new sphere cannot reach the plane: points on the new sphere are invisible from the outside.
In this image the sliced-open spheres are flattened out into lens shapes bounded by two copies of their slicing segment (this shows that the constructed surface is topologically a plane). The inner one becomes the blank lens shape; it is bordered by two copies of a red (forbidden) segment. The outer one is bordered by two copies of the black segment where it joins the plane. The blue circle (in the plane) and the yellow light ray appear in both images. Note that the coordinate lines in this image match those above, and are not the standard latitudes-meridians on a round sphere. Image courtesy of Ulf Leonhardt.
Comments: Email Webmaster