Biomedical Engineering Reference
In-Depth Information
where
n
0
is the linear refractive index. It should be noted that Equation 2.22 is
often written in other forms. In addition, either electrostatic units (esu) or SI
units (mks) are frequently used. For this reason, we now list various conver-
sion factors that can be used between the nonlinear coefficients [98].
en
=
⎛
⎞
⎟
0
2
γ
[
esu
]
n
[
m /W
]
(2.23)
⎜
2
40
π
3
2
γ
[
cm /erg
]
=
n
(
238 7
. )
n
[
cm /W
]
0
2
2
2
−
6
2
γ
[
m /V
]
=
n
( .
3 333 10
×
)
n
[
cm /W
]
0
2
3
7
2
2
γ
[
cm /erg
]
=
( .
7 162 10
×
)
γ
[
m /V
]
The change in path length is usually written as a phase difference relative
to a wave propagating in the other leg of the interferometer. In terms of the
nonlinear index, this change can be written in the form [99]
Δ∅ =
ω
pr
c
n
2
(2.24)
where
l
is the interaction length of the pump and probe beams. It is the rela-
tionship of the nonlinear index
n
2
, or the index change Δ
n
, to the third-order
susceptibility that is finally developed, usually written as
=
Δ
(
n
E
n
)
(2.25)
2
2
The last three factors to consider are the crystallographic orientation along
which the pump and probe beams travel, the polarization of these beams,
and the optical frequency that is used. Because it is quite lengthy to dis-
cuss the relationships for general crystallographic directions and polar-
izations, we give only the results for the <011> orientation and crossed
beam polarizations used in the Double-Y device. As for the frequencies of
the beams, two cases may be developed that are termed the resonant and
nonresonant cases.
The nonresonant case is the simpler of the two and is based on the Born-
Oppenheimer (BO) approximation. The assumption is made that the elec-
trons follow the optical fields and nuclear motions adiabatically; that is, the
optical frequency is much too low to interact with the electronic vibrations.
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