NEWS & VIEWS

z mirror, reduced-loss backward waves in y related metal–dielectric–metal waveguide x Input y structures1–3, as well as in conceptually t Negative x 1 refraction z distinct photonic metamaterials4,5. As Lezec (φ < 0) t 2 and colleagues demonstrate, such tailored 2 Output Input metallic nanostructures provide us with φ2 slit slit φ1 many new opportunities for optics and Ouput Positive photonics applications that natural optical W2 W1 refraction substances just do not have. More surprises W2 W1 W2 (φ2 > 0) can be expected in future. Al Ag Si3N4 Au Air © 2007 AAAS © 2007 References 1. Lezec, H. J., Dionne, J. A. & Atwater, H. A. Science 316, 430–432 (2007). Figure 2 Plasmonic waveguide structure. Illustration of the plasmonic nanostructure used by Henri Lezec and 2. Tournois, P. & Laude, V. Opt. Commun. 137, 41–45 (1997). co-workers for the demonstration of all-angle negative refraction in the visible region1. The W1 regions support 3. Shin, H. & Fan, S. Phys. Rev. Lett. 96, 073907 (2006). 4. Soukoulis, C. M., Linden, S. & Wegener, M. Science backward waves for green light (forward waves for red light), the W2 regions support forward waves. a, Side view 315, 47–49 (2007). and b, Top view. Reprinted in part with permission from ref. 1. 5. Shalaev, V. Nature Photon. 1, 41–48 (2006). 6. Shelby, R. A., Smith, D. R. & Schultz, S. Science 292, 77–79 (2001). 7. Pendry, J. B. Phys. Rev. Lett. 85, 3966–3969 (2000). 8. Fang, N., Lee, H., Sun, C. & Zhang, X. Science 308, 534–537 (2005). 9. Liu, Z., Lee, H., Xiong, Y., Sun, C. & Zhang, X. Science optics the sign of the beam displacement slower by factor n inside the material than 315, 1686 (2007). 10. Smolyaninov, I. I., Hung, Y.-J. & Davis, C. C. Science in Fig. 1 is strictly identical to that of the the vacuum speed of light c0. 315, 1699–1701 (2007). refractive index n. Th e logical conclusion Backward waves may seem strange 11. Lai, H. M., Kwok, C. W., Loo, Y. W. & Xu, B. Y. Phys. Rev. E is that we should stop calling the refractive but they are certainly much less rare 62, 7330–7339 (2000). index n ‘refractive index’. We should rather a species than it is tempting to believe 12. Russell, P. St. J. Phys. Rev. A 33, 3232–3242 (1986). 13. Zengerle, R. J. Mod. Opt. 34, 1589–1617 (1987). call it the ‘slowness factor’ according to its at fi rst sight. In the visible, damped 14. Zhang, Y., Fluegel, B. & Mascarenhas, A. Phys. Rev. Lett. defi nition: Th e phase velocity of light c is backward waves occur in your bathroom 91, 157404 (2003).

MATERIAL WITNESS Tendentious tilings

Quasicrystal enthusiasts may Although nearly all of the designs Most provocatively, Bonner have been baffl ed by a rather evident on Islamic buildings of this time are discusses the late-fi ft eenth-century cryptic spate of comments periodic, Lu and Steinhardt found that those Topkapi architectural scroll that and clarifi cations following on a fi ft eenth-century shrine in modern- furnishes the key evidence for Lu and in the wake of a recent article day Iran can be mapped almost perfectly Steinhardt’s girih scheme. Bonner points claiming that medieval Islamic onto another tiling scheme, devised by out how this scroll reveals explicitly the artists had the tools needed mathematician Roger Penrose, which does “underlying polygonal sub-grid” used to construct quasicrystalline generate true quasicrystals. to construct the pattern it depicts. He patterns. Th at suggestion But in 1992 Makovicky made a very proposes that the artists commonly used was made by Peter Lu at similar claim for a diff erent Islamic tomb such a polygonal matrix, composed of Harvard University and Paul Steinhardt at dating from 1197. Some accused Lu and tile-like elements, and demonstrates Princeton (Science 315, 1106–1110; 2007). Steinhardt of citing Makovicky’s work in how these can create aperiodic But in a news article in the same issue, staff a way that did not make this clear. Th e space-fi lling designs. writer John Bohannon explained that these authors, meanwhile, admitted that they were Bonner does not mention claims had already caused controversy, unconvinced by Makovicky’s analysis and quasicrystals, and his use of terms such as being allegedly anticipated in the work didn’t want to get into an argument about it. self-similarity and even symmetry do not of crystallographer Emil Makovicky at Th e dispute has ruffl ed feathers. Science always fi t easily with that of physicists and the University of Copenhagen (Science subsequently published a ‘clarifi cation’ that mathematicians. But there’s no doubting 315, 1066; 2007). irons out barely perceptible wrinkles in that his work deepens the “can of worms” Th e central thesis of Lu and Steinhardt Bohannon’s article, while Lu and Steinhardt that Bohannon says Lu and Steinhardt is that Islamic artists used a series of attempted to calm the waters with a letter have opened. tile shapes, which they call girih tiles, in which they ‘gladly acknowledge’ earlier All this suggests that the satellite to construct their complex patterns. work (Science 316, 982; 2007). It remains conference of the forthcoming Th ey can be used to make patterns of to be seen whether that will do the trick, European Crystallographic Meeting in interlocking pentagons and decagons with for Makovicky wasn’t the only one upset by Marrakech this August, entitled “Th e the ‘forbidden’ symmetries characteristic their paper. Design consultant Jay Bonner enchanting crystallography of Moroccan of quasicrystalline metal alloys, in which in Santa Fe has also made previous links ornaments”, might be more stormy than these apparent symmetries, evident in between Islamic patterns and quasicrystals enchanting — for it includes back-to-back diff raction patterns, are permitted by a (see http://www.bonner-design.com/ talks by Makovicky and Bonner. lack of true periodicity. publications/self-similar.htm). Philip Ball

476 nature materials | VOL 6 | JULY 2007 | www.nature.com/naturematerials