Topics in Current Chemistry (2018) 376:28
1 3
Fourier transformation of the detected signal in dependence of the delay between the
first two laser interactions.
2D Raman and other Raman-based multidimensional techniques (Fig. 3c, d) use
a slightly different approach. The reason for this variation is a fundamental difference between an absorptive UV–Vis, IR, or THz interaction and a scattering-based
(e.g., Raman) excitation process. Time-resolved impulsive vibrational spectroscopy methods for instance (like time-resolved impulsive vibrational spectroscopy
(TR-IVS) [53, 54] or pump degenerate four-wave-mixing (pump-DFWM) [55, 56],
Fig. 3c) plot the amplitude of active Raman modes in dependence of time. Here,
the Raman-frequency axis is obtained by a Fourier-transformation of an oscillatory
signal in dependence of the probe interaction delay. The second axis is a purely temporal axis, i.e., a delay between the first pair of excitations, which is most often not
Fourier-transformed [57]. 2D Raman goes one step beyond that and performs even
a second Fourier transformation on the initial temporal axis. This analysis leads
to a frequency–frequency correlation 2D plot with Raman frequencies on the two
axes. These two axes allow correlating the induced Raman frequencies in different time intervals, in a similar fashion as in other 2D spectroscopy methods such
as 2D IR. Importantly, TR-IVS and 2D Raman methods are of higher-order nonlinearity (in fact fifth-order) than predominately absorptive UV–Vis/IR/THz methods
(third-order). This implies that these methods allow and require scanning additional
temporal delays. As a consequence, the information content may be significantly
different in these two types of methods. To overcome this difference, third-order
methods are often combined with pre-excitation pulses or with other perturbations
not involved in the axis of the 2D plot. The additional delays that emerge from the
different perturbations allow generating an “evolution” of 2D plot [58–60]. In spite
of this additional time axis, each individual 2D plot is still generated in the same
way and is based on the same idea of correlating quantities as described above.
Finally, we note an additionally important aspect of 2D spectroscopy. This is the
inherence of the associated lower-dimensional time-resolved spectroscopy signals
from the respective multidimensional plot. In simple words, for example, the excitation axis can always be projected on the detection axis, thereby reducing the data
to one-dimensional difference spectra (the projection slice theorem) [41]. In some
methods, however, it is not very obvious to recognize this effect, but for other methods the interpretation can be straightforward, which is often even exploited as an
internal reference to validate the analysis and interpretability of the data.
4 Experimental Aspects of Multidimensional Time‑Resolved
Spectroscopy
Multidimensional time-resolved spectroscopy (TRS) signals, like all optical signals, can be detected in different ways. There are two major categories of detection schemes, which are shared by all spectroscopy methods in the next contributions, namely homodyne and heterodyne detection (Fig. 4). These two methods
of detecting the optical signal are so vital to multidimensional techniques that
the differences as well the advantages and drawbacks between homodyne and
8
Reprinted from the journal
1 3
Fourier transformation of the detected signal in dependence of the delay between the
first two laser interactions.
2D Raman and other Raman-based multidimensional techniques (Fig. 3c, d) use
a slightly different approach. The reason for this variation is a fundamental difference between an absorptive UV–Vis, IR, or THz interaction and a scattering-based
(e.g., Raman) excitation process. Time-resolved impulsive vibrational spectroscopy methods for instance (like time-resolved impulsive vibrational spectroscopy
(TR-IVS) [53, 54] or pump degenerate four-wave-mixing (pump-DFWM) [55, 56],
Fig. 3c) plot the amplitude of active Raman modes in dependence of time. Here,
the Raman-frequency axis is obtained by a Fourier-transformation of an oscillatory
signal in dependence of the probe interaction delay. The second axis is a purely temporal axis, i.e., a delay between the first pair of excitations, which is most often not
Fourier-transformed [57]. 2D Raman goes one step beyond that and performs even
a second Fourier transformation on the initial temporal axis. This analysis leads
to a frequency–frequency correlation 2D plot with Raman frequencies on the two
axes. These two axes allow correlating the induced Raman frequencies in different time intervals, in a similar fashion as in other 2D spectroscopy methods such
as 2D IR. Importantly, TR-IVS and 2D Raman methods are of higher-order nonlinearity (in fact fifth-order) than predominately absorptive UV–Vis/IR/THz methods
(third-order). This implies that these methods allow and require scanning additional
temporal delays. As a consequence, the information content may be significantly
different in these two types of methods. To overcome this difference, third-order
methods are often combined with pre-excitation pulses or with other perturbations
not involved in the axis of the 2D plot. The additional delays that emerge from the
different perturbations allow generating an “evolution” of 2D plot [58–60]. In spite
of this additional time axis, each individual 2D plot is still generated in the same
way and is based on the same idea of correlating quantities as described above.
Finally, we note an additionally important aspect of 2D spectroscopy. This is the
inherence of the associated lower-dimensional time-resolved spectroscopy signals
from the respective multidimensional plot. In simple words, for example, the excitation axis can always be projected on the detection axis, thereby reducing the data
to one-dimensional difference spectra (the projection slice theorem) [41]. In some
methods, however, it is not very obvious to recognize this effect, but for other methods the interpretation can be straightforward, which is often even exploited as an
internal reference to validate the analysis and interpretability of the data.
4 Experimental Aspects of Multidimensional Time‑Resolved
Spectroscopy
Multidimensional time-resolved spectroscopy (TRS) signals, like all optical signals, can be detected in different ways. There are two major categories of detection schemes, which are shared by all spectroscopy methods in the next contributions, namely homodyne and heterodyne detection (Fig. 4). These two methods
of detecting the optical signal are so vital to multidimensional techniques that
the differences as well the advantages and drawbacks between homodyne and
8
Reprinted from the journal