Coherent Raman Scattering Microscopy - Emerging Raman Applications and Techniques in Biomedical and Pharmaceutical Fields - page 135

time domain by computing the normalized intensity autocorrelation function
(ACF), shown in Fig. 6.12B [162].
In analogy to FCS theory [164, 165], Xie and coworkers [163] have de-
veloped a theory of CARS-CS for Poisson-distributed particle concentration
fluctuations, which also takes the effect of wave vector mismatch for the dif-
ferent CARS detection geometries into account. For sub-wavelength particles
undergoing free Brownian diffusion, two regimes of average particle number
densities, << 1, the autocorre-

lation model functions for F- and E-CARS-CS are identical, reflecting the
symmetry in the forward and backward directions of the CARS radiation
field. Except for the introduction of a squared excitation Gaussian amplitude
profile [166], the ACF of CARS-CS resembles the mathematical form of that
for conventional FCS [167-169], reflecting the similar isotropic radiation pat-
terns of CARS and fluorescence. (ii) At

N , can be distinguished [163]: (i) At N

1, the coherent sum of CARS
fields from many scatterers causes additional contributions to the CARS-CS
ACF, and the expression becomes dependent on the CARS detection geome-
try. While in the forward detection scheme the ACF amplitude will vanish for

N ≥

>> 1 (like in FCS), the large wave vector mismatch in the epi-detected
CARS signal results in a high initial amplitude of the epi-detected ACF that
is independent of

N

and decays exponentially with correlation time. Unlike
FCS, which relies on very low particle concentrations, epi-detected CARS-
CS is thus sensitive to the detection of scatterers at high concentrations
and may therefore be advantageous in the study of cluster and aggregate
dynamics.
CARS-CS experiments have been reported in the low-concentration limit

N

( << 1) on freely diffusing submicron-sized polymer spheres of different

chemical compositions using both the E-CARS [162, 163] and the polarization-
resolved CARS [163] detection scheme for ecient nonresonant background
suppression. These experiments have unambiguously demonstrated the vibra-
tional selectivity of CARS-CS, the dependence of its ACF amplitude on the
particle concentration,

N

, the dependence of lateral diffusion time, τ D ,on
the sphere size, and the influence of the microviscosity on its Brownian motion.
The additional advantage of CARS-CS over DLS and FCS is the spectral
selectivity for individual chemical components in their native state, where flu-
orescent labeling is not desired. This may not only allow mapping of 3D diffu-
sion coecients, for example inside life cells, but also offer a method to monitor
the specific interaction of individual components within complex systems, e.g.,
aggregation processes of different chemical species. Another prospect is the
implementation of CARS cross-correlation spectroscopy that may allow the
investigation of correlated fluctuations between two different species. These
could be two distinct Raman spectral features of one and the same compound,
or a specific intrinsic Raman band and an emission of a more sensitive fluo-
rescence label [160].

N