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Normal Modes in a Periodic Square Lattice

​
ratio of spring constants
1.
atoms
30
wave vectors
x
0.2
y
0.2
polarization
x
0.1
y
0.1
t
0.
Normal modes in a monatomic periodic square chain are simulated. You can adjust the number of atoms, the ratio between the two "spring constants", the two components of the wave vector
k=(
k
x
,
k
y
)
(red arrow) in the first Brillouin zone (red square), and the two components of the polarization
ϵ=(
ϵ
x
,
ϵ
y
)
. Sound waves (small
|k|
) and stationary waves (within the boundary of the Brillouin zone) can be easily identified. Longitudinal (
ϵ
parallel to
k
) and transverse (
ϵ
perpendicular to
k
) waves are also clearly reproduced.
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