Multiphoton Imaging - Biomedical Optical Imaging Technologies: Design and Applications - page 233

process of light-induced polarization in a molecule that results in the emission of
a secondary electromagnetic wave. The induced polarization in a medium depends
on the strength of the applied field E.t/ and can be written as

P.t/ D " o .1/ E.t/ C " o .2/ E 2 .t / C " o .3/ E 3 .t/:::;

(7.1)

where " o is the permittivity of free space; .1/ ; .2/ ,and .3/ are the linear, second-
order, and third-order susceptibilities of the medium; E.t/ is the incident field;
and P is the induced polarization. The electric susceptibility indicates the
ability of the electric dipoles in a medium to align themselves with the incident
electric field. First term in Eq. 7.1 represents the linear polarization that gives rise
to linear absorption and refraction in terms of linear susceptibility .1/ D n 2 C 1,

where n is the refractive index. Second term in Eq. 7.1 gives the second-order
nonlinear polarization P .2/ .t / D " o .2/ E 2 .t / and P .3/ .t / D " o .3/ E 3 .t / as third-
order nonlinear polarization, and so on. Each of these polarization terms gives rise to
a different physical phenomenon. For example, second-order polarization is used to
produce second harmonic generation and sum/difference frequency generation, and
third-order polarization is responsible for two-photon excited fluorescence, third
harmonic generation, Raman scattering, Brillouin scattering, self-focusing, and
optical phase conjugation. The second-order nonlinear optical interactions based on
.2/ can only occur in noncentrosymmetric materials having no inversion symmetry,
while third-order nonlinear phenomena can take place in any medium regardless of
whether it possesses inversion symmetry or not.
The higher harmonic generation is a parametric process that is governed by a
real susceptibility. On the other hand, nonparametric processes, such as multiphoton
absorption, have a complex susceptibility associated with them [ 16 ]. In parametric
processes, the initial and final quantum mechanical states are identical, as shown
in Figs. 7.1 d, e, and f. A virtual state represents the population inversion, as shown
by dashed lines in Fig. 7.1 , which is a superposition of one or more photon fields
and an eigenstate of the molecule. The unique property of a parametric process is
that photon energy is conserved, that is, no energy is deposited into the system.
This property is the hallmark of multiphoton imaging using SHG/THG modes of
nonlinear excitation for noninvasive and live tissue imaging in biological material
without causing heating or other photodamage. In nonparametric processes, the
initial and final states are different, as shown in Figs. 7.1 a, b, and c, where the
molecule after excitation relaxes back to a different ground state. Nonparametric
interactions may cause photon absorption in the sample resulting in effects such as
bleaching and thermal damage. In resonant parametric processes that are resonantly
enhanced at some wavelengths, the absorption of the laser radiation also increases.
Hence, there has to be a balance between the laser intensity and the wavelength
used in order to obtain the strong nonlinear signal while minimizing effects like
photobleaching and photodamage.