
132
Laser-Induced Damage in Optical Materials
where E is the (linearly polarized) electric eld amplitude; e and m are the electron
charge and eective mass, respectively; and ω
0
/2π is the eld’s carrier frequency.
e direct photo excitation rate, K(I), from the VB to CB is oen described by the
theory of Keldysh (1965) developed for a monochromatic laser eld. Figure 5.3 illus-
trates the ionization rate according to Keldysh and several limiting cases.
In the low- and high-intensity limits, the Keldysh formula reduces to MPA of order m
and tunneling, respectively. In the MPA limit, the ionization rate is proportional toI
m
.
e value of the Kel