Phononic Crystal Bandgap
Acoustic wave propagation through a periodic medium — bandgap formation
Parameters
Frequency ω/ω₀:
1.0
Impedance contrast Z₂/Z₁:
3.0
Fill fraction (d/a):
0.5
Number of unit cells:
8
Phononic crystal
: periodic elastic medium with lattice constant a. Bragg scattering opens
bandgaps
where no acoustic modes propagate.
cos(ka) = cos(k₁d)cos(k₂(a−d)) − ½(Z₁/Z₂+Z₂/Z₁)sin(k₁d)sin(k₂(a−d))
Bandgap when |RHS|>1. Transmission decays exponentially (evanescent wave).