Design of photonic crystals having large band gaps above a prescribed band is a well-known physical problem with many applications. A connection to an interesting mathematical construction was pointed out some time ago: It had been conjectured that optimal structures for gaps between bands $n$ and $n$ $+$ 1 correspond, in the case of transverse magnetic polarization, to rods located at the generators of centroidal Voronoi tessellation (CVT) and, in the case of transverse electric polarization, to the walls of this tessellation. We discover another mathematical recipe which produces even better solutions: optimal packing of disks in square and triangular tori. It provides solutions qualitatively different from CVT, sometimes increasing the resulting band gap size several times. We therefore introduce two classes of periodic structures with remarkable properties which may find applications in many other areas of modern solid state physics: arrays of particles located at the centers of optimally packed disks on tori and nets corresponding to the walls of their Voronoi tessellations.

Close

PrevNext

View figure in article

• Emergence of patterns
• Photonics
• Photonic crystals
• Classical electromagnetism
• Plane-wave expansion