Efi Efrati, William T. M. Irvine
Chirality occupies a central role in fields ranging from biological self assembly to the design of optical meta-materials. The definition of chirality, as given by lord Kelvin in 1893, associates handedness with the lack of mirror symmetry, the inability to superpose an object on its mirror image. However, the quantification of chirality based on this definition has proven to be an elusive task. The difficulty in quantifying chirality is contrasted by the ease with which one determines the handedness of objects with a well defined axis such as screws and helices. We present table-top demonstrations that show that a single object can be simultaneously left handed and right handed when considered from different directions. The orientation dependence of handedness motivates a tensorial quantification of chirality relating directions to rotations, and suggests an extension of Lord Kelvin's definition. We give explicit examples of such tensorial measures of chirality and show how the tensorial nature of chirality can be probed in experiments and exploited as a design principle for chiral meta-materials.
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http://arxiv.org/abs/1301.4460
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