
115Self-Focusing and Nonlinear Effects
Chapter 4
∂
()
∂
=
()
−
()
⎧
⎨
⎫
⎬
−
()
[]
⎧
⎨
⎫
⎬
−
nt
t
nt nt
n
nt
It
nt
S
CS
S
SMAX
SS
S
τ
σ
ω
1
(()
τ
SV
, (4.59)
∂
()
∂
=
()
−
()
⎧
⎨
⎫
⎬
−
()
[]
⎧
⎨
⎫
⎬
−
nt
t
nt nt
n
nt
It
n
D
CD
D
DMAX
DD
ND
τ
σ
ω
1
DD
DV
t
()
τ
,
(4.60)
where
n
S
and n
D
are the density of electrons captured by the shallow traps and by the deep
traps, respectively
σ
S
and σ
D
are the absorption cross sections of electrons in shallow and deep traps,
respectively
τ
CV
, τ
CD
, and τ
CS
are the relaxation time constants for the respective transitions:
conduction band to valence band (CV), conduction band to deep trap (CD),
andconduction band to shallow trap (CS)
τ
SV
and τ
DV
are the shallow-trap and deep-trap l ...