
110
Laser-Induced Damage in Optical Materials
collisions with longitudinal optical phonons. A simplified equation for the ava-
lanche rate (Sparks 1975),
w
Ae Ft
m
A
AV Sp
K
CK
ph
L
_
()
,=
+
()
−
22 2
22
1
τ
ωτ
ω
τ
Δ
Δ
(4.46)
suggests linear scaling of the rate with laser irradiance I and includes a constant coe-
cient A, average phonon energy ℏ ω
ph
, total scattering rate 1/τ
L
that includes all types of
electron-particle scattering, and time of electron-momentum relaxation τ
K
for large-
angle scattering on phonons. Evaluation of the relaxation rate and time of Equation
4.46 is quite challenging and is usually done either by tting experimental data on LID
or by numeric ...