When a molecule absorbs a photon, it imparts energy to the molecule, causing it to temporarily excite from the ground state to a higher electronic or vibrational energy level. Due to conservation of energy, absorption can only take place if the photon energy is precisely equal to the difference between the ground and excited states; only then can the light be absorbed. Additionally, since there is a direct correlation between the number of molecules and the number of photons absorbed, it is relatively straightforward to determine the molecular density. As a result, absorption is one of the most commonly used spectroscopic techniques, particularly for concentration measurements.
Most of the excited states induced by absorption are incredibly short-lived. The spontaneous lifetime of most transient excited states are typically on the order of femtoseconds or picoseconds, with the notable exception of meta-stable excited states. Based on this fact, George Porter and Ronald Norrish, while at the University of Cambridge, realized that they could use flash lamps to study these intermolecular energy transitions through a method they called flash photolysis in 1950 . Even though the foundation was set in the 1950s, it wasn’t until the development of the ultrafast mode-locked laser that scientists were able to fully take advantage of Porter and Norrish’s contributions. The two of them later went on to receive the Nobel Prize in Chemistry for this discovery in 1967, which they shared with Manfred Eigen, who also contributed to our current understanding of ultrafast chemistry. Today, ultrafast lasers have completely replaced flash lamps as the preferred excitation source for these types of experiments, and the technique is more commonly referred to as transient absorption spectroscopy (TAS).
Fundamentals of Absorption Spectroscopy
Traditionally, absorption spectroscopy has been discussed in terms of the Beer-Lambert Law, which relates the transmitted intensity to the absorption coefficient (α) and the pathlength (z), which can be expressed as follows:
While equation 1 is not the most commonly used expression of Beer’s law, it is the most useful for gaining an intuitive understanding of the underlying physics. In this form, we can clearly see that the absorption coefficient is wavelength dependent, therefore resulting in an absorption spectrum. By diving deeper into the absorption coefficient for a given transition, we can show the following relationship:
Here we see that the absorption coefficient depends on the transition cross-section () which represents the probability of an incoming photon exciting the sample to an excited electronic or vibrational state and the population difference (N) between the ground state (N1) and the excited state (N2) . Additionally, we can see that the transition cross-section is inversely proportional to the spontaneous lifetime (tsp) of the excited state.
Now we can see that unlike the more simplified version of Beer’s law taught in introductory chemistry, the absorption spectrum of a given analyte is not truly based on the molecular concentration, but rather on population difference. Furthermore, since the population difference is itself a time-dependent function based on the spontaneous lifetime, the absorption coefficient also has a temporal dependency associated with it. All of that being said, the population difference can be ignored most of the time because the spontaneous lifetime is so fast, and the light intensity is so weak, that it never significantly depletes the ground state population.
Measuring Transition Lifetimes
While there are many different ways to use ultrafast lasers to perform TAS, on the most fundamental level they are all variations on a single technique, known as pump-probe. The procedure requires two laser beams to excite the analyte and measure absorbance simultaneously.
First, the high-intensity pump laser excites a significant percentage of the molecules in the sample to a higher energy level, altering the population difference and reducing the absorption coefficient of the transition. Next, a low-intensity probe laser is passed through the sample to measure the absorption. Based on the difference between the probe laser absorption with and without the pump laser, you can then determine the change in absorption. This process is then systematically repeated for different delay times between the pump and probe pulses to measuring the change in transmitted probe pulse energy, as shown in Figure 1.
From this data, we can now build a picture of the kinetics of the energy level transitions and determine spontaneous lifetime and other transient effects.
As referred to in the previous section, we are not interested in only measuring one transition, but instead, we want to see the effects on the entire spectrum. To accomplish this goal with a monochromatic probe would be impractical, but utilizing a nonlinear optics process known as supercontinuum generation overcomes this issue. An explanation of how supercontinuum light is generated is far beyond the scope of this application note, but it should be understood that this process allows an ultra-short pulse laser to be converted into a white-light source while still maintaining most of the laser properties.
As a result, one can now measure the entire absorption spectra with a single probe pulse. Figure 2 shows a simplified schematic representation of a typical TAS set-up; a chopper and a lock-in amplifier are added into the system to improve the signal-to-noise ratio. Figure 3 shows a simulated transient absorption spectrum showing the subtle differences in absorption resulting from the population difference induced by the absorption of the pump pulse.
The spectrometer parameters of a typical TAS measurement are very similar to those required for traditional absorption spectroscopy with the exception of speed and dynamic range. First, it should be noted that the speed of data acquisition is in no way correlated to the laser’s pulse width or pulse repletion rate. Each spectral integration will contain a large number of individual laser pulses. Instead, the speed requirements are solely dependent on the number of data points that are required to capture the transient kinetics, and how well it can be triggered with the delay line. Additionally, the dynamic range of the spectrometer is so crucial because transient absorption is measured as difference spectra, and the differences can be extremely subtle. As a result, CMOS detectors are always preferable due to their faster readout speeds and larger dynamic ranges than CCD detectors.
Even though the minimum integration time of most CMOS cameras is on the order of 10 microseconds, the major bottleneck is often the spectrometers readout electronics that must transfer the data from the detector to the computer. Avantes’ new dynamic store to RAM capabilities represent a major leap forward in high-speed spectral readout. Utilizing the dynamic store to RAM feature allows the user to save scans to the RAM buffer onboard the instrument, and simultaneously offload the spectra to the computer. Using the dynamic store-to-RAM function, the AvaSpec-ULS2048CL-EVO is now capable of continually acquiring spectra at a rate of 2 kHz. Figure 4 shows an example of the new graphical user interface (GUI) when using dynamic store to RAM.
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N-H Bond Fission in Aqueous Adenine
The scientific community has widely used Avantes spectrometers for measuring TAS. An excellent example, which visually shows the functionality of TAS data, was published by a group at the University of Bristol while studying N-H bond fission in aqueous adenine . The results shown in Figure 5 below were obtained using an Avantes, AvaSpec-FAST spectrometer (now replaced with the AvaSpec-ULS2048CL-EVO), which used 750 pixels to measure a spectral range from 200 nm to 620nm. The sample was excited with a 266 nm pump laser and a supercontinuum probe laser, with a variable pulse delay from -500fs to 3ps. From this data, it is easy to see the time-dependent nature of the changing absorption coefficient after the pump pulse. Based on the curve fit shown in Figure 5b, the research team was able to determine that the spontaneous lifetime (or ‘time-constant’ as they referred to it) was 470 +/- 18 fs .
Behaviour of Cyanocobalamin in Excited States
A second exciting usage of TAS was published by a team at the University of Michigan while studying how cyanocobalamin-excited states behave in biological systems . In this study, they used an Avantes spectrometer to measure how different solvents affect electron transitions, as shown in Figure 6. The team then used this data to verify a complex quantum mechanical model that they developed to ‘lay the groundwork for detailed studies of a range of cobalamin cofactors proposed for use as anti-vitamins, photoactivated drug delivery agents, and in situ production of hydroxyl radicals .’
Photoreduction of Graphene Oxide
Lastly, a joint team from the Max Planck Institute, University of Hamburg, University of Ioannina, and University of Toronto used TAS to gain a better understanding of photoreduction of graphene oxide . In their study, they used TAS to show that the photoreduction process was actually a multistep process by observing that there where two overlapping decays, one which took place in under 2 picoseconds (ps) and a second taking place between 2ps and 250 ps. The fast decay correlated to the ionization of the graphene oxide and the water-producing solvate electrons, which then interacted with the graphene oxide to cause the reduction during the slow-decay period. The data shown in Figure 7 was collected using an Avantes fibre-coupled spectrometer and excited using 266 nm pump laser.
As researchers continue to probe more in-depth into the underlying physical chemistry of complex systems like the ones mentioned, it is becoming ever more critical to understand the internal transition kinetics within molecules and atoms.
While this application note is by no means a comprehensive review of the entire field of ultrafast transient absorption, it provides an introductory overview of the physics behind TAS as well as typical system configurations. Furthermore, TAS spectroscopy is currently undergoing a second renaissance with the recent invention of the attosecond pulsed laser, for which Gérard Mourou and Donna Strickland were awarded the Nobel Prize in 2018. Avantes is excited to keep providing the community with cutting-edge spectrometers for the next generation of ultra-fast spectroscopy.
For more information about the full range of laboratory and OEM spectrometer options available from Avantes, including our new dynamic store to RAM capabilities, please contact us. Our knowledgeable applications specialists are available to assist you.
 Porter, G.N., 1950. Flash photolysis and spectroscopy. A new method for the study of free radical reactions. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 200(1061), pp.284-300.
 Saleh, B.E. and Teich, M.C., 2019. Fundamentals of Photonics. john Wiley & Sons.
 Roberts, G.M., Marroux, H.J., Grubb, M.P., Ashfold, M.N. and Orr-Ewing, A.J., 2014. On the participation of photoinduced N–H bond fission in aqueous adenine at 266 and 220 nm: a combined ultrafast transient electronic and vibrational absorption spectroscopy study. The Journal of Physical Chemistry A, 118(47), pp. 11211-11225.
 Wiley, T.E., Arruda, B.C., Miller, N.A., Lenard, M. and Sension, R.J., 2015. Excited electronic states and internal conversion in cyanocobalamin. Chinese Chemical Letters, 26(4), pp.439-443.
 Gengler, R.Y., Badali, D.S., Zhang, D., Dimos, K., Spyrou, K., Gournis, D. and Miller, R.D., 2013. Revealing the ultrafast process behind the photoreduction of graphene oxide. Nature communications, 4(1), pp. 1-5.