Biomedical Engineering Reference
In-Depth Information
SHG is well known to occur only in a material that is noncentrosymmetric. For a material that is
centrosymmetric (i.e., possesses inversion symmetry), each element of the second-order nonlinear sus-
ceptibility χ
(2)
must vanish and no SHG can be induced. This can be explained by changing the sign of
the electric field
E
( ) applied for the second-order nonlinear polarization, which is given by
P t
( )
(2)
=
ε χ
(2)
E t
( )
2
.
(14.4)
0
If the sign of the electric field is changed, the sign of the induced polarization also has to be changed
because the medium is assumed to possess inversion symmetry, and Equation 14.4 must be replaced by
(Boyd 1992)
−
P t
( )
( )
2
=
ε χ
( )
2
[
−
E t
( )]
2
=
ε χ
( )
2
E t
( ) ,
2
(14.5)
0
0
which shows that
P t
( )
( )
2
= −
ε χ
( )
2
E t
( ) .
2
(14.6)
0
Comparing Equations 14.4 and 14.6, the induced polarization described in these two equations must
be equivalent, which occurs only if χ
(2)
vanishes, that is
χ
(2)
= 0.
(14.7)
From this result, it is known that the contrast of the SHG is primarily provided by the noncentrosym-
metry created due to the nonlinear meta material effect (Chu et al. 2002). In bio-tissues, SHG can arise
from structural proteins, like collagen fibers (Campagnola et al. 2002; Cox et al. 2003; Mohler et al.
2003), nerve fibers (Dombeck et al. 2003; Chen et al. 2006), spindle fibers (Chu et al. 2003), and muscles
(Chu et al. 2004; Plotnikov et al. 2006; Nucciotti et al. 2010), but not from the tooth enamel, which has a
hexagonal symmetry and a vanishing χ
(2)
(Chen et al. 2008).
14.2.1.2 third Harmonic Generation
Similar to the SHG process, THG is a third-order nonlinear optical process described by terms χ
(3)
involving three electrical fields with the same frequency, that is, χ
(3)
(3ω: ω, ω, ω). The process of
THG is illustrated in Figure 14.3. It can be considered an up-conversion process, in which incident
radiation with a lower-frequency ω is up-converted to radiation with a higher frequency 3ω. During
ω
3
ω
ω
ω
FIgurE 14.3
Energy-level diagram of third-harmonic generation.
