1D phononic crystal · mass-spring lattice · dispersion relation
Phononic metamaterials are periodic elastic structures with forbidden frequency bands (band gaps) where wave propagation is prohibited. The diatomic chain (alternating masses m₁, m₂ with spring k) has two phonon branches: an acoustic branch (ω→0 as k→0) and an optical branch, separated by a band gap of width Δω = ω₊ − ω₋. Waves in the gap decay exponentially (evanescent modes).