Chemistry Reference
In-Depth Information
the electric field of the laser beam. The non-zero
χ
(2)
and
χ
(3)
affect the
refractive index of the media. The NLO effects associated with
χ
(2)
are the
Pockel effect, the second harmonic generation,
etc.
; and those related with
χ
(3)
are the Kerr effect, the third harmonic generation,
etc
..
In order to achieve high NLO coe
cients
χ
(2)
and
χ
(3)
, the medium
must follow two criteria: the constituent blocks must have high NLO polar-
izabilities, depending on the chemical structure; and the medium must have
the appropriate symmetry. For those possessing the center-symmetry,
χ
(2)
vanishes. Among them are amorphous and isotropic materials. However,
these media may have non-zero
χ
(3)
. In the presence of an electric field,
some of these materials may change from center-symmetrical to non-center
symmetrical.
The high molecular NLO polarizability is a basic requirement. For an
independent molecule under an electric field the molecular electric moment
(the
i
-th component) is as follows
µ
i
=
α
ij
E
j
+
β
ijk
E
j
E
k
+
γ
ijkl
E
j
E
k
E
l
+
···
,
(6.50)
where
α
,
β
and
γ
are the molecular polarizabilities of the individual
molecule.
The relation between the molecular polarizabilities to the bulk suscep-
tibilities depends on the molecular density,
N
, and the local internal field
factor
F
. Particularly, it relates to the molecular orientation. For example,
the second NLO coecient is expressed as
χ
(2)
IJK
=
NFβ
ijk
cos
θ
Ii
cos
θ
Jj
cos
θ
Kk
,
(6.51)
where
θ
Ii
is the angle between the
i
-th component of molecular polarization
and the
I
-th component of bulk polarization. The bracket designates the
statistical average over all the molecules. Similarly, the relationship for the
third NLO coe
cient is expressed as
χ
(3)
cos
4
θ
∝
γ
.
(6.52)
The three typical molecular configurations and the associated second and
third NLO polarization coecient summary are shown in Figure 6.30. Those
with the center symmetry have no second NLO property. However, they
may have a non-zero value if an electric field destroys the up and down
symmetry of molecular orientation.
