Strange New Twist: Researchers Discover Möbius Symmetry in Metamaterials
ScienceDaily (Dec. 21, 2010) — Möbius symmetry, the topological phenomenon that yields a half-twisted strip with two surfaces but only one side, has been a source of fascination since its discovery in 1858 by German mathematician August Möbius. As artist M.C. Escher so vividly demonstrated in his "parade of ants," it is possible to traverse the "inside" and "outside" surfaces of a Möbius strip without crossing over an edge. For years, scientists have been searching for an example of Möbius symmetry in natural materials without any success.
Berkeley Lab researcher have discovered Möbius symmetry in metamolecular trimers made from metals and dielectrics. (Credit: Image by Chih-Wei Chang)
Now a team of scientists has discovered Möbius symmetry in metamaterials -- materials engineered from artificial "atoms" and "molecules" with electromagnetic properties that arise from their structure rather than their chemical composition.
Xiang Zhang, a scientist with the U.S. Department of Energy's Lawrence Berkeley National Laboratory (Berkeley Lab) and a professor at the University of California (UC) Berkeley, led a study in which electromagnetic Möbius symmetry was successfully introduced into composite metamolecular systems made from metals and dielectrics. This discovery opens the door to finding and exploiting novel phenomena in metamaterials.
"We have experimentally observed a new topological symmetry in electromagnetic metamaterial systems that is equivalent to the structural symmetry of a Möbius strip, with the number of twists controlled by sign changes in the electromagnetic coupling between the meta-atoms," Zhang says. "We have further demonstrated that metamaterials with different coupling signs exhibit resonance frequencies that depend on the number but not the locations of the twists. This confirms the topological nature of the symmetry."
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Phys. Rev. Lett. 105, 235501 (2010) [4 pages]
Optical Möbius Symmetry in Metamaterials
Chih-Wei Chang1, Ming Liu1, Sunghyun Nam1, Shuang Zhang1, Yongmin Liu1, Guy Bartal1, and Xiang Zhang1,2,*
1Nanoscale Science and Engineering Center, 3112 Etcheverry Hall, University of California, Berkeley, California 94720-1740, USA
2Materials Sciences Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA
See Also: Publisher's Note
Received 29 April 2010; revised 7 October 2010; published 2 December 2010; corrected 6 December 2010
We experimentally observed a new topological symmetry in optical composites, namely, metamaterials. While it is not found yet in nature materials, the electromagnetic Möbius symmetry discovered in metamaterials is equivalent to the structural symmetry of a Möbius strip, with the number of twists controlled by the sign change of the electromagnetic coupling between the meta-atoms. We further demonstrate that metamaterials with different coupling signs exhibit resonance frequencies that depend only on the number but not the locations of the “twists,” thus confirming its topological nature. The new topological symmetry found in metamaterials may enable unique functionalities in optical materials.
© 2010 The American Physical Society
URL:
DOI:
10.1103/PhysRevLett.105.235501
PACS:
81.05.Xj, 03.65.Vf, 73.20.Mf, 78.67.Pt
*Corresponding author: xiang@berkeley.edu
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