Coherent Raman Scattering Microscopy - Emerging Raman Applications and Techniques in Biomedical and Pharmaceutical Fields - page 118

phase matching condition is satisfied in both the forward and backward (epi)
directions. Accordingly, the forward- and epi-detected CARS (F-CARS and E-
CARS) are equal in intensity. As illustrated in Fig. 6.3A, the phase matching
condition along z is always fulfilled for forward-detected CARS ( 0),

whereas in the case of epi-detected CARS a large wave vector mismatch of
|

| Δ k |≈

4 nπ/λ AS is introduced [60], where n is the refractive index of
the medium assumed to be independent of frequency. As a result, the F-CARS
signal starts to overwhelm the E-CARS signal with increasing L because of
the constructive interference in the forward direction and the destructive in-
terference in the backward direction. For large L , which resembles the case
of focusing into an isotropic bulk medium, the E-CARS intensity is signif-
icantly reduced as compared to the corresponding forward signal. Likewise,
a large wave vector mismatch is established in a geometry with collinearly
counter-propagating pump and Stokes beams, denoted counter-propagating
CARS (C-CARS) (not shown), with a signal dependence on the interaction
length similar to that of E-CARS [61, 16].

Δ k | =2 | k AS |≈

Nonlinear Susceptibility Contributions to the CARS Signal

For the understanding of CARS contrast mechanisms, it is essential to discuss
in more detail the proportionality of the CARS intensity to the modulus square
of the total nonlinear susceptibility in (6.9). Substituting (6.4) into (6.9) yields

χ (3)nr + χ (3)r = χ (3)nr 2 + χ (3)r +2 χ (3)nr Re χ (3)r . (6.10)

2 2

I CARS ∝

In their order of appearance the terms involved in this expression describe the
nonresonant background CARS signal, the purely resonant CARS contribu-
tions, and the CARS contribution due to mixing of the nonresonant and the
real part of the resonant Raman responses, respectively. Figure 6.4 displays
the spectral response of each CARS signal component for an isolated Raman
resonance in the presence of a nonresonant background contribution. Their
sum yields the well-known CARS dispersive line shape where the peak fre-
quency is red-shifted, an intensity minimum at the blue side of the resonance
line appears, and a constant offset is introduced [30]. All these features are
more pronounced the larger the relative intensity of the nonresonant contribu-
tion is in the sample. As a consequence, the often unknown relative intensity of
the nonresonant contribution not only introduces a background to CARS im-
age contrast and spectra, but also precludes their quantitative interpretation
in terms of known spontaneous Raman spectra from the literature.
A full description of polarization-sensitive CARS signal generation that
takes the polarization properties of the pump, Stokes, and CARS fields and
the tensor character of the nonlinear susceptibility components (cf. (6.5)-
(6.7)) into account can be found elsewhere [16].