Phononic Crystal

Elastic Wave Propagation with Periodic Band Gaps
Crystal Structure (1D periodic)
Wave Animation u(x,t)
Transmission Spectrum T(ω)
Dispersion Relation ω(k)

Phononic Crystal

Periodic material with alternating elastic moduli. Bragg scattering opens band gaps where no wave can propagate.

Transfer matrix method: T = ∏ Mi. Band gap condition: |tr(T)| > 2. Dispersion from cos(kΛ) = cos(k₁d₁)cos(k₂d₂) − ½(Z₁/Z₂+Z₂/Z₁)sin(k₁d₁)sin(k₂d₂)