Multiphoton Imaging - Biomedical Optical Imaging Technologies: Design and Applications - page 238

variety of biological applications. Optical microscopy with SHG is widely used for
contrast generation in collagen [ 32 - 35 ] myocytes [ 34 , 36 ], plants and chloroplasts,
etc. [ 37 , 38 ]. SHG microscopy is based on noncentrosymmetric organization of
microstructures in a sample, and SHG signal can be generated due to a broken
symmetry at an interface or due to a noncentrosymmetric arrangement within bulk
structures. At an interface, biological membranes can produce detectable SHG
signal as in the case of a lipid bilayer [ 39 ]. Molecular structures having a symmetric
distribution of chirality in the membrane do not give rise to SHG signal; only an
ordered asymmetric distribution of chiral molecules in the membranes is responsible
for SHG. SHG can also be produced in biogenic crystal structures, for example,
in calcite or starch granules [ 37 ] and biophotonic crystalline and semicrystalline
structures in living cells [ 40 ].

7.3.3 Third Harmonic Generation (THG)

Third harmonic generation is a nonlinear optical process which has been intensely
studied since the early days of nonlinear optics [ 41 , 42 ]. This process has been
applied in imaging of lipids in cells and tissues [ 43 ], subcellular structure in neurons
[ 15 ], cell nuclei [ 44 ], and simultaneous SHG, THG, and TPEF imaging of live
biomaterial [ 45 ]. All materials have some third-order nonlinearity depending on
the material property, symmetry, and incident light. At the focus of microscope
objective lens, when a discontinuity or inhomogeneity is encountered, like an
interface between two media, the symmetry along the optical axis is broken, and
a third harmonic signal can be obtained. High optical sectioning can be achieved
because of the nonlinear process of third harmonic generation taking place only at
the focal plane. Being the property of all materials, third harmonic signal can be
used for noninvasive microscopy, particularly in biological materials without the
need of fluorescence labeling.
THG is a four-wave mixing process based on third-order nonlinear polarization
asshowninFig. 7.1 e. Unlike the second-order processes, the third-order process
is possible in all media, with or without inversion symmetry. The amplitudes of
nonlinear susceptibility for SHG and THG are very different: j .3/ jj .2/

j ,
resulting in the magnitude of THG being much smaller than SHG. Third harmonic
generation was first reported in1962 in a centrosymmetric calcite crystal [ 46 ]. Other
physical optical processes based on third-order susceptibility .3/ are Kerr effect,

DC-induced SHG, and AC Kerr effect.
The third-order induced polarization can be written as

.3!/ D " o X
jkl

P .3/
i

.3/

ijkl .!;!;!/E j .!/E k .!/E l .!/;

(7.3)

where E.!/ is the incident wave at frequency !, third-order susceptibility .3/

ijkl is a
fourth rank tensor, and indices ijkl are summed over linear polarization directions