Circular dichroism in biological photonic crystals and cubic chiral nets.

Nature provides impressive examples of chiral photonic crystals, with the notable example of the cubic so-called srs network (the label for the chiral degree-three network modeled on SrSi2) or gyroid structure realized in wing scales of several butterfly species. By a circular polarization analysis of the band structure of such networks, we demonstrate strong circular dichroism effects: The butterfly srs microstructure, of cubic I4(1)32 symmetry, shows significant circular dichroism for blue to ultraviolet light, that warrants a search for biological receptors sensitive to circular polarization. A derived synthetic structure based on four like-handed silicon srs nets exhibits a large circular polarization stop band of a width exceeding 30%. These findings offer design principles for chiral photonic devices.

Constant mean curvature surfaces with three ends.

We announce the classification of complete almost embedded surfaces of constant mean curvature, with three ends and genus zero. They are classified by triples of points on the sphere whose distances are the asymptotic necksizes of the three ends.

On Gyroid Interfaces

We use Brakke's Surface Evolver to construct a family of intersection-free triply periodic surfaces with constant mean curvature. The gyroid family models various physical interfaces. We calculate area and volume along the family, compare it with the Schwarz P and D families, and discuss the general problem of a comparison of triply periodic morphologies.