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Geometric approach to design of photonic crystals and metamaterials via optimal toric packings
Publikationstyp
Journal Article
Date Issued
2025-03-10
Sprache
English
Volume
111
Issue
12
Article Number
L121404
Citation
Physical Review B 111 (12): L121404
Publisher DOI
Scopus ID
Publisher
APS
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.
DDC Class
600: Technology