Biomedical Engineering Reference
In-Depth Information
SHG nonlinear process. All third-order nonlinear processes can be viewed as four-wave mixing pro-
cesses, and the material wave in the case of TPA is induced by two optical waves of the same frequency.
TPA in semiconductors is among the most thoroughly studied in nonlinear optics [22]. The resonant
condition (a stable upper state) is characterized by an imaginary χ
(3)
, while a real χ
(3)
is attributed to the
third-order nonlinear refraction, much in the same way that the real and imaginary components of the
linear susceptibility χ
(1)
are associated for linear refraction and absorption.
4.2.3 tHG Photophysics
THG is another third-order nonlinear process, which involves a real χ
(3)
susceptibility. Here, three
fundamental photons at the frequency of ω interact with the material to generate one photon at the
third-harmonic frequency, 3ω (Figure 4.3) [7,9]. For systems with inversion symmetry, χ
(2)
is zero and
third-order processes are the dominant nonlinearities. It should be pointed out that third harmonic
(3ω) can also be generated involving a χ
(2)
SHG process and a sequential SFG (also a χ
(2)
process) of the
SHG photon (2ω) and another fundamental photon (ω), for noncentrosymmetric systems where χ
(2)
processes are allowed. However, for biological materials, the
direct
χ
(3)
process prevails [7] and we use
THG in this chapter to denote the direct χ
(3)
nonlinear process shown in Figure 4.3, which can be easily
understood in analogy to the χ
(2)
SHG process.
THG is related to the nonlinear refractive coefficient
n
2
according to the following equation
3
{
}
n
=
e
χ
( )
3
(4.6)
R
2
4
ε
n c
2
0
χ
( )
), and ℜ
e
denotes the real component of a complex value. As a result, THG is sensitive to inhomogeneities such as
aqueous medium interfaces and microstructures, where
n
2
is mismatched [23]. Again, this reveals the
similarity between
n
2
and
n
0
(or χ
(3)
and χ
(1)
) for linear optics governed by the first-order susceptibility,
where signals (reflections or scattering) are generated only at interfaces and inhomogeneities where
there is a mismatch of the refractive index
n
0
. For laser scanning microscopy where a Gaussian beam is
focused using an objective tightly onto an inhomogeneous sample, the third-harmonic power is given by
where ε
0
is the vacuum dielectric constant,
n
0
is the linear refraction coefficient (
n
2
∝
R
{
e
1
}
0
−
1
4
z
b
2
2
∝
(
)
2
(4.7)
I
1
+
ω
δχ
( )
3
3
ω
ω
ω
ω
ω
1
ω
AS
ω
2
ω
1
ω
2
3
ω
ω
1
ω
S
ω
ω
1
ω
ω
ω
ω
vib
ω
vib
TPA
CARS
SRS
THG
FIgurE 4.3
χ
(3)
Nonlinear processes commonly used in NLO microscopy. Solid lines are real molecular states;
dashed lines are virtual states. Solid arrows (ω, ω
1
, ω
2
) refer to interaction between the applied optical waves and
the material; dotted arrows (3ω, ω
AS
, ω
SRS
,) refer to emitted optical waves. ω
vib
is the vibrational frequency of a
molecular ground state.
