Femtosecond Raman induced polarization spectroscopy studies of coherent rotational dynamics in molecular fluids Page: 57 of 130
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symmetric polarizability. Only under these circumstances are the two experiments related
by the Fourier transform.
3.23 Generalization to other time and frequency domain pump-probe experiments
The above tensor analysis is applicable to other scattering experiments as well. For
example, the three pulse impulsive stimulated Raman scattering (ISRS) technique of
Nelson et. al.21 typically utilizes two pump beams having x and z polarization,
respectively, an x-polarized probe, and z-polarized signal field. Use of Eqs. (3.22) shows
that this experiment, like RIPS, measures the autocorrelation of ao). However, ISRS has
also been done with all fields polarized identically, in which case both orientational and
isotropic properties are measured, since the signal has contributions from a(2) and a0( .
When resonances are involved, such as in transient absorption or fluorescence
experiments, the tensor analysis is analogous. In the case of transient absorption, for
example, the nonlinear polarization in Eq. (3.7) is replaced by22,23
3t t3 t2
Po(t) - - Tr{ N dt3 (t) f dt2 fdt,[ (t2)E,(t2)p0(tj)E,(t) +
in (3.24)
p(t,)E,(ti)pop(t2)E,(t2)]J(t3)Ed(t3) }+c.c.
As a result, the polarizability operators in Eq. (3.10) must be replaced by appropriate
products of dipole operators. The polarization dependence of the experiment, however,
can be analyzed in exactly the same manner as for the off-resonance case. For example,
from Eqs. (3.22) it can be shown that when the probe and signal fields are chosen to have
the same polarization, the measured response is given by
x c 3[G(t)]00)[G(0)]'O) + 3P2(cos0)([G(t)]Co [G(0)]o 1), (3.25)39
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Morgen, Michael M. Femtosecond Raman induced polarization spectroscopy studies of coherent rotational dynamics in molecular fluids, thesis or dissertation, May 1, 1997; California. (https://digital.library.unt.edu/ark:/67531/metadc695079/m1/57/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.