Coherent Anti-Stokes Raman Scattering: Basics, Theoretical …
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which then develops in time and yields information about coherence lifetime and
vibrational relaxation processes. These superpositions can involve different overtones of vibrational modes and/or different vibrational modes of the sample resulting
in vibrational wave packets and beating phenomena. Some examples are given in the
following showing how possible applications of femtosecond time-resolved CARS
can look like.
In order to follow the ultrafast dynamics of vibrational excitations, the principle of
a typical pump-probe scheme used in time-resolved spectroscopy is also applied for
tr-CARS. In the first step, a combination of “pump” and “Stokes” pulses interact with
the sample in a precise spatial and temporal overlap. This interaction defines “timezero”. The wavenumber difference between pump and Stokes lasers define, which
vibrational states will be coherently excited. The bandwidths of the exciting pulses
will determine which vibrational (or rotational) states are accessed simultaneously.
The resulting superposition of wave functions results in beating, which develops over
time and is determined by both the lifetimes of the coherence (phase relations) and
the population of the exited states. Interactions with the molecular environment can
e.g. result in loss of coherence or vibrational relaxation, etc.
In a second step, the so-called “probe” pulse interacts with the sample with a welldefined time delay after time-zero. An anti-Stokes signal will be generated, which
depends on the temporal development of the initially prepared nonlinear polarization.
The transient signal is modulated by the beating of the coherently excited states and
at the same time shows a decay over time, which reflects the lifetime of the excitation.
Figure 4 demonstrates the principle of femtosecond time-resolved CARS in a
schematic way, showing a real CARS transient obtained from a polydiacetylene
(PDA) single crystal in our laboratories. Without going into details, the following
should be mentioned. The pump and Stokes lasers are spectrally broad as indicated
in the scheme, which shows the pulses along a wavenumber axis. The probe pulse is
assumed to be identical with the pump pulse except for the timing. Pump and Stokes
lasers are tuned such that several vibrational modes of the PDA are coherently excited
(e.g. C = C stretching vibration as most intense feature in the transient at time-zero,
here assigned to the arbitrary number “5”). The resulting anti-Stokes signal is also
spectrally broad and has (with relatively pure resolution) spectral features, which can
be assigned to vibrational modes. The transient CARS signal shown as 3-dimensional
plot yields this purely resolved spectrum probed by the time-delayed probe pulse for
different delay times (cuts parallel to the relative-wavenumber axis). Looking along
the time axis (cuts parallel to the delay-time axis), one recognizes beatings. These
are due to the coherent superposition of different modes. However, additionally, one
observes that obviously certain vibrational modes only start to contribute after a
certain delay time (e.g. the mode with the arbitrarily assigned number 4). While the
beating directly is related to the coherence, the delay of a mode excitation points
to an intramolecular vibrational energy transfer. As will be shown below, a Fourier
transform of the transient signal yields the mode frequencies involved in the coherent
superposition.
We would like to point out that there are many degrees of freedom, which allow
for a great variety of experimental schemes [25]. We have already mentioned the
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which then develops in time and yields information about coherence lifetime and
vibrational relaxation processes. These superpositions can involve different overtones of vibrational modes and/or different vibrational modes of the sample resulting
in vibrational wave packets and beating phenomena. Some examples are given in the
following showing how possible applications of femtosecond time-resolved CARS
can look like.
In order to follow the ultrafast dynamics of vibrational excitations, the principle of
a typical pump-probe scheme used in time-resolved spectroscopy is also applied for
tr-CARS. In the first step, a combination of “pump” and “Stokes” pulses interact with
the sample in a precise spatial and temporal overlap. This interaction defines “timezero”. The wavenumber difference between pump and Stokes lasers define, which
vibrational states will be coherently excited. The bandwidths of the exciting pulses
will determine which vibrational (or rotational) states are accessed simultaneously.
The resulting superposition of wave functions results in beating, which develops over
time and is determined by both the lifetimes of the coherence (phase relations) and
the population of the exited states. Interactions with the molecular environment can
e.g. result in loss of coherence or vibrational relaxation, etc.
In a second step, the so-called “probe” pulse interacts with the sample with a welldefined time delay after time-zero. An anti-Stokes signal will be generated, which
depends on the temporal development of the initially prepared nonlinear polarization.
The transient signal is modulated by the beating of the coherently excited states and
at the same time shows a decay over time, which reflects the lifetime of the excitation.
Figure 4 demonstrates the principle of femtosecond time-resolved CARS in a
schematic way, showing a real CARS transient obtained from a polydiacetylene
(PDA) single crystal in our laboratories. Without going into details, the following
should be mentioned. The pump and Stokes lasers are spectrally broad as indicated
in the scheme, which shows the pulses along a wavenumber axis. The probe pulse is
assumed to be identical with the pump pulse except for the timing. Pump and Stokes
lasers are tuned such that several vibrational modes of the PDA are coherently excited
(e.g. C = C stretching vibration as most intense feature in the transient at time-zero,
here assigned to the arbitrary number “5”). The resulting anti-Stokes signal is also
spectrally broad and has (with relatively pure resolution) spectral features, which can
be assigned to vibrational modes. The transient CARS signal shown as 3-dimensional
plot yields this purely resolved spectrum probed by the time-delayed probe pulse for
different delay times (cuts parallel to the relative-wavenumber axis). Looking along
the time axis (cuts parallel to the delay-time axis), one recognizes beatings. These
are due to the coherent superposition of different modes. However, additionally, one
observes that obviously certain vibrational modes only start to contribute after a
certain delay time (e.g. the mode with the arbitrarily assigned number 4). While the
beating directly is related to the coherence, the delay of a mode excitation points
to an intramolecular vibrational energy transfer. As will be shown below, a Fourier
transform of the transient signal yields the mode frequencies involved in the coherent
superposition.
We would like to point out that there are many degrees of freedom, which allow
for a great variety of experimental schemes [25]. We have already mentioned the