Biomedical Engineering Reference
In-Depth Information
where
0
is the dielectric constant of the vacuum and
χ
(1)
is the linear
susceptibility of the specimen. Moving to the non-linear domain, high power
intensity cause a large variety of unusual responses, with a non-linear depen-
dency on the applied electric field. Second harmonic generation is one of these
nonlinear optical effects in which the incident light is coherently scattered by
the specimen at twice the optical frequency and at certain angles [87]. We can
generally write the non-linear correspondent of (4.19) as
P
(
t
)=
0
χ
(1)
E
(
t
)+
χ
(2)
E
2
+
χ
(3)
E
3
...
,
(4.20)
where the first left term on the right is the linear scattering, the second is
related to SHG, the third to third harmonics, etc. In the above equation,
because the fields are vectors, the nonlinear susceptibilities are tensors. As
each atom acts as an oscillating dipole that radiates in a dipole radiation
pattern, the radiation phase among the enormous number of atoms must be
matched to induce constructive interference and thus non-linear generation is
allowed under phase-matching conditions (i.e. when the scattered light is in
phase).
For the same reason, only molecules that exhibit a specific symmetry.
In particular, only non-centrosimmetric materials can originate SHG. The
SHG signal depends strictly on the relative orientation between the polar-
ization of the incoming light and the direction of the symmetry constraints;
a polarization analysis of the second harmonic signal can provide useful in-
formation about the orientation of molecules, impurities in crystal structures
and characteristics of surfaces and optical interfaces. As for linear scattering,
second harmonic generation is not associated with absorption and involves
only virtual state transitions that are related to the imaginary part of the
nonlinear susceptibilities, and so no energy is deposited in the specimen and
no damage can be produced. This is one of the major advantages of applying
SHG to the microscopy field and in particular to the investigation of biological
samples [88, 89]. Furthermore, SHG imaging preserve the intrinsical capabil-
ity of 3D investigation of matter, since the high photon flux required for
generating this non-linear signal is achieved only within a femtoliter volume
around the focal point of the lens. Since both SHG and TPE can be observed
simultaneously from the same sample, the correlative analysis of these two
signals provide additional insight about the specimen, allowing not only to
identify the molecular source of the SHG, but also to probe radial and lateral
symmetry within structures of interest.
Recognition of the SHG relies on the property that the emitted light has
double wavelength of the incoming radiation. Therefore, by changing the color
of the illumination laser we expect to observe an analogue shift in the emis-
sion wavelength. The emission of SHG signal is not isotropic, as it will be
more e
cient in the forward direction. However, in dense samples, multiple
scattering allow for a detection in the backward direction too. Therefore, SHG
can be usually collected both along the transmitted light and along the
epi-
pathways of the microscope.
