Contact points open wide band gaps in all two-dimensional Bravais lattices

The propagation of waves in crystals is known to be strongly affected by the choice and the spatial distribution of inclusions in a matrix. We argue herewith that in-contact, impermeable inclusions lead to extremely wide band gaps for all 2D Bravais lattices. Contact points entail constrictions that efficiently slow wave propagation and lead to strongly flattened bands. A numerical demonstration is provided for a generic Helmholtz equation that is applicable to electromagnetic, acoustic, elastic, or water waves alike. Experiments conducted on square and hexagonal photonic crystals composed of touching copper tubes reveal that waves of certain radio frequencies quite remarkably traverse the minute gaps within the metallic framework, thereby confirming the theoretical predictions, including the presence of deeply subwavelength Bragg band gaps.