Page 352 - Vibrational Spectroscopic Imaging for Biomedical Applications

326 Cha pte r Ele v e n

the sample will be scattered. The scattered light will naturally be
modulated at the difference frequency, which corresponds to scat-
tered light components at the frequencies ω ± ( ω − ω ). In the case
pr p S
that the third light wave is of similar frequency as the pump light, we
will thus find anti-Stokes radiation at 2ω − ω .
p S
This type of anti-Stokes scattering is very different from sponta-
neous Raman scattering in that the scattered light components are all
modulated with the same phase, i.e., the anti-Stokes radiation is coher-
ent. This coherence also implies that the waves add up constructively
in a specific direction, and destructively interfere in all other direc-
tions, producing radiation with a well-defined propagation direction.
In the CARS microscope, the direction in which the waves add up,
i.e., the phase-matching direction, is the forward propagation direc-
tion that is collinear with the incident beams. For comparison, because
of the lack of coherence, the signal resulting from the spontaneous
Raman process is scattered isotropically.

11.3.2 Resonant and Nonresonant Contributions
The process we have discussed so far is responsible for the generation
of the nonresonant background in CARS. Clearly, the occurrence of
this contribution is purely electronic and bears no dependence on the
presence of vibrational modes. Why, then, is the CARS process sensi-
tive to vibrational resonances that are nuclear in nature? This sensi-
tivity stems from the notion that the electrons are bound by a potential
that is defined by the location of the nuclei. At some frequencies,
namely, the nuclear resonance frequencies, this potential becomes more
malleable. Consequently, the electron cloud becomes more polarizable
at these frequencies. In other words, the presence of nuclear modes
perturbs the polarizibility of the molecule’s electron density at well-
defined frequencies, which can now be shaken into resonance when-
ever the difference frequency ω − ω matches the nuclear resonance
p S
frequency. The oscillation amplitude of the electron cloud will be larger
at such frequencies and produce more scattered light at 2ω − ω .
p S
From this discussion we also see that the CARS process brings
about two types of coherent anti-Stokes fields: one field contribu-
tion generated from purely electronic motions and the other field
contribution resulting from electron motions that depend on the
presence of nuclear modes. The total CARS signal is the square
modulus of the coherent sum of this nonresonant and resonant field
component. The coherent mixing of the nonresonant and resonant
signals makes it particularly difficult to detect each contribution
separately. Many research efforts are devoted to suppressing the
nonresonant portion of the CARS signal. Polarization sensitive
detection, 51,52 interferometric mixing 41,53 and frequency modula-
54
tion are examples of techniques that reduce the nonresonant back-
ground in practical and rapid CARS imaging.