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T issue Imaging with CARS Micr oscopy 325

11.3.1 Nonlinear Electron Motions
In the CARS process, light beams are used with optical frequencies
13
17
(~10 -10 Hz), corresponding to wavelengths in the visible and near-
infrared range. Nuclei in molecules are unable to respond to an elec-
tric field that oscillates at such high frequencies. The electrons
surrounding the nuclei, however, will respond to the electric field by
oscillating at the frequency of the incoming electromagnetic field. For
relatively weak electric fields, the electrons respond linearly to the
driving field. Under these conditions, the spatial extent of the elec-
tronic oscillation is small and the motion in the potential well is har-
monic. For stronger fields, however, the electrons are pulled farther
from their equilibrium positions and the cloud picks up anharmonic
motions. As shown in Fig. 11.2, the response of the electrons to the
incoming field is no longer linear. CARS is based on these anharmonic
motions of the electron cloud.
If the electrons are driven at two strong optical frequencies simul-
taneously, the anharmonically oscillating cloud will contain oscilla-
tory motion at combination frequencies. Of relevance to the CARS
process is the electron cloud’s ability to shake at the difference fre-
quency between the pump and the Stokes fields, i.e., at the beat fre-
quency ω − ω . In practice, such oscillations occur in any molecular
p S
sample when the pump and Stokes beams are applied, irrespective of
the presence of nuclear resonances at ω − ω . Whenever the electrons
p S
shake at the beat frequency, the electronic properties of the material
will be slightly altered relative to the situation when the light beams
are absent. More specifically, the refractive index of the material is
modulated at the difference frequency. A changing refractive index
implies that a third light wave of frequency ω that travels through
pr

Anharmonic
P
Harmonic P(t)

–E d E d
Anharmonic

FIGURE 11.2 Polarization of the material as a function of the driving fi eld E .
d
For stronger fi elds, the polarization is no longer linearly proportional to the
driving fi eld as a consequence of the anharmonicity of the potential in which
the electrons reside. Under these conditions, the oscillation amplitude of the
polarization is distorted, which is the source of optical nonlinear signals,
including CARS.