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Transient absorption spectroscopy, time-resolved absorption spectroscopy, pump-probe spectroscopy, or TA is a technique in which the absorption of a molecule (system) is analysed after its excitation with an ultrahsort laser pulse. This is a powerful technique employed for the characterisation of the electronical and structural properties of short-lived excited (transient) states of photochemically and photophysically interesting molecules. Transient absorption spectroscopy is used for answering questions such as which state was excited, does the sample form reaction products or intermediates, and what is the relaxation dynamics of the sample.

TA principle
In transient absorption spectroscopy, a fraction of the molecules is promoted to an electronically excited state by the excitation (or pump) pulse. A weak probe pulse is sent through the sample with a delay with respect to the pump pulse. A difference absorption spectrum is then calculated, i.e., the absorption spectrum of the excited sample minus the absorption spectrum of the sample in the ground state. By changing the time delay between the pump and the probe and recording a difference absorption spectrum at each time delay, a difference absorption profile as a function of time delay and wavelength is obtained.

In general, a transient absorption spectrum gives information about several processes: will appear as a positive signal in the TA spectrum.
 * Ground state bleaching: After the excitation of a fraction of the molecules to an excited state through the action of the pump pulse, the number of molecules in the ground state decreases. Thus, the ground-state absorption in the excited sample is less than that in the non-excited sample and a negative signal at the wavelength region of ground state absorption is obtained.
 * Stimulated emission: Upon the excitation of some of the molecules to an excited state, stimulated emission to the ground state can occur when the probe pulse passes through the excited volume of the sample.
 * Absorption of excited states: As the molecules have been promoted to an excited state, optically allowed transitions from this excited state to higher excited ones can be available at certain wavelength regions, which can occur through the absorption of the probe pulse. In this manner, a positive signal is observed in the transient absorption spectrum.
 * Absorption of the product: After the excitation of the photosynthetic system, a transient or long-lived molecular state can occur, such as triplet states or charge-separated states. The absorption of this transient product

Equipment
The transient absorption set-up uses a femtosecond laser based on chirped pulse amplification technique. This consists of an oscillator, which generates laser pulses of a few femtoseconds duration. These pulses, however, are too weak and they need to be amplified. This is usually performed in a regenerative amplifier (RA), which can use Pockels cells to change the polarization of the laser pulse when an electrical potential difference is applied to it. In this manner, the pulse is trapped in the amplifier's cavity and passes several times through an amplifying medium. When saturation is reached, the Pockels cell switches the polarization of the pulse and this is ejected from the RA. The amplified pulse is then compressed to a few femtoseconds by temporally synchronizing the ‘‘blue’’ and ‘‘red’’ wavelengths within the pulse bandwidth.

The first task is to get an estimate of the number of components that may be detected from the measurements. The next one is to postulate a photophysical model, which is based on a priori knowledge about the investigated system. The methodology of choice for the analysis of femtosecond TA data is global target analysis. This analysis is based on a scheme of discreet compartments connected by rate kinetics. The population is excited by the pump pulse in one or several compartments from where it decays into one or another compartment according to the chosen connectivity scheme. Each time-dependent population is assigned a spectrum and a decay life time is obtained

For the excitation of the sample in transient absorption spectroscopy, such a laser system as the one described above is limited to a single wavelength (eg. Ti:Sapphire lasers emit at 800 nm). In order to be able to excite different samples which absorb in the UV, VIS, or infrared region of the spectrum, optical parametric amplifiers (OPAs) are used. In an OPA, the laser beam is temporally and spatially overlapped in non-linear birefringent crystals, such as beta-barium-borate (BBO), with a white light continuum (WLC) pulse. Depending on the angle between the laser pulse and symmetry axis of the crystal, two beams called signal and idler are amplified from the WLC through energy conversion from the pump beam (phase matching condition). The sum of the frequencies of the signal and idler beams equal the frequency of the pump beam. Using such instruments and additional non-linear mixing processes such as frequency-doubling, sum-frequency generation, and difference-frequency generation in suitable non-linear crystals, all wavelengths from UV to mid-IR can be generated with rather high pulse energies.

Fig. (2) shows a typical TA setup. This consists of a femtosecond laser beam which acts as a pump for the sample. A weak probe pulse is sent through a delay line and focused on a non-linear crystal (sapphire, MgF2, water), where white light continuum is generated. The white light probe is sent through the sample and analysed by a spectrometer.

The two beams are focused and overlapped in the sample.

The first task is to get an estimate of the number of components that may be detected from the measurements. The next one is to postulate a photophysical model, which is based on a priori knowledge about the investigated system. The methodology of choice for the analysis of femtosecond TA data is global target analysis. This analysis is based on a scheme of discreet compartments connected by rate kinetics. The population is excited by the pump pulse in one or several compartments from where it decays into one or another compartment according to the chosen connectivity scheme. Each time-dependent population is assigned a spectrum and a decay life time is obtained

Collection of TA spectra
The idea of TA is to measure the differences between the sample absorbance in the presence and the absence of the pump pulse. This implies that two pulses are used, one to excite the sample, called the pump, and one to measure the sample transmittance, called the probe. The pump beam is sequentially blocked by a mechanical chopper in order to monitor the state of the pump beam. This sorts the measured points as "pump-on" or "pump-off". Additionally, a dark spectrum is measured when the probe light is blocked, which corresponds to both the open and the closed state of the chopper. This dark spectrum is subtracted from each of the measured probe signals. A spectrometer records the white light supercontinuum spectra for both blocked and unblocked pump light. The difference spectrum is then calculated according to: \newline

The difference absorption spectra are measured for several delays between the pump and the probe light, by delaying the probe light before the WL is produced in an optical delay line, which consists of a retroreflector on a motorized translation stage.

Measurement modes
From equation ($$) it can be seen that the difference absorption spectra can be a function of the detection wavelength $\lambda$ and the delay time between pump and probe, $t$. Implicitly this means that two different measurement modes are possible: measuring the dependence on the wavelength, called a transient absorption spectrum at a given delay, or measuring the dependence on the delay between pump and probe beams at a fixed wavelength, called a kinetic trace.

Data analysis
The data set obtained after a transient absorption experiment is a three-dimensional surface showing the wavelength, time delay, and difference absorption intensity of the measured signal. A good way to analyse the data is to employ global target analysis, which

The first task is to get an estimate of the number of components that may be detected from the measurements. The next one is to postulate a photophysical model, which is based on a priori knowledge about the investigated system. The methodology of choice for the analysis of femtosecond TA data is global target analysis. This analysis is based on a scheme of discreet compartments connected by rate kinetics. The population is excited by the pump pulse in one or several compartments from where it decays into one or another compartment according to the chosen connectivity scheme. Each time-dependent population is assigned a spectrum and a decay life time is obtained

The first task is to get an estimate of the number of components that may be detected from the measurements. The next one is to postulate a photophysical model, which is based on a priori knowledge about the investigated system. The methodology of choice for the analysis of femtosecond TA data is global target analysis. This analysis is based on a scheme of discreet compartments connected by rate kinetics. The population is excited by the pump pulse in one or several compartments from where it decays into one or another compartment according to the chosen connectivity scheme. Each time-dependent population is assigned a spectrum and a decay life time is obtained