Phononic Crystal — 1D Band Gap
Transfer matrix method · periodic elastic layers · forbidden frequency bands
Parameters
Layer A density ρ₁:
1.0
Layer B density ρ₂:
4.0
Speed ratio c₂/c₁:
0.50
Layer A thickness d₁:
0.50
Unit cells N:
8
Incident freq ω:
1.00
Bloch k (real)
—
In band gap?
—
Transmission |T|²
—
Transfer matrix:
M = M_A · M_B for each bilayer.
M_layer = [[cos(kd), sin(kd)/Z], [-Z·sin(kd), cos(kd)]]
Band gap when |tr(M)/2| > 1 → Bloch k imaginary → evanescent waves → exponential attenuation.