2D IR Spectroscopy in the BoxCARS Geometry

Figure 1: Schematic representation of two-dimensional vibrational echo spectroscopy in the BoxCARS geometry. The sample is subjected to three, short infrared pulses with relative arrival times that have been precisely controlled. The resulting vibrational echo signal pulse is overlapped with an independently delayed local oscillator pulse for heterodyne detection on an MCT IR array detector.

Figure 1 is a schematic representation of the two-dimensional infrared (2D IR) spectroscopy pulse sequence and experimental layout in a BoxCARS geometry. There are three excitation pulses produced with a Ti:Sapphire regenerative amplifier pumped optical parametric amplifier (OPA). A description and diagram of the creation of these pulses can be found below in Figure 3. The OPA is tuned to the frequency of the vibrational mode under investigation. The IR pulses have sufficient bandwidth to span the spectral region of interest. The times between pulses 1 and 2 and between pulses 2 and 3 are called τ and Tw, respectively. The vibrational echo signal radiates from the sample and reaches its peak at a time ≤ τ after the third pulse in a unique direction. The vibrational echo signals are recorded by scanning τ at fixed Tw. The signal is spatially and temporally overlapped with a local oscillator for heterodyne detection, and the combined pulse is dispersed by a monochromator acting as a spectrograph onto an IR array detector. Heterodyne detection provides both amplitude and phase information. If the vibrational echo is detected directly as it emerges from the sample, there is no phase information. The experiment produces a 2D spectrum in the frequency domain. The measurements are made in the time domain. To go from the time domain to the frequency domain requires two Fourier transforms. To perform a Fourier transform requires both amplitude and phase information. The local oscillator is another IR fs pulse. When it overlaps with the vibrational echo wave packet, interference occurs. As shown below, when the time τ is scanned, the vibrational echo pulse advances in phase relative to the fixed local oscillator pulse. The result is a temporal interferogram that provides the necessary phase information

As shown in Figure 1, the combined vibrational echo/local oscillator pulse is passed through a monochromator acting as a spectrograph and recorded by an IR array detector. The array detector allows us to measure 32 wavelengths simultaneously, reducing the data acquisition time by a factor of 32. Taking the spectrum of the heterodyne-detected vibrational echo signal performs one of the two Fourier transforms and gives the ωm axis (m for monochromator) in the 2D IR spectra. When τ is scanned, a temporal interferogram is obtained at each ωm. The temporal interferograms are numerically Fourier transformed to give the other axis, the ωτ axis. 2D IR spectra are obtained for a range of Tw, the waiting time after interaction with pulse 2.

Figure 2: Sample experimental data acquired for a 2D IR experiment. The linear infrared spectrum for phenol-OD in CCl4 is shown in the upper left. An interferogram created by scanning τ at a fixed Tw is in the lower left. The lower right shows the doubly Fourier transformed data along with the energy level diagram and pulse sequence.

Figure 2 shows a very simple example of the nature of the data. The upper left portion of the figure shows the spectrum of the hydroxyl stretching mode of phenol-OD. The H in the OH hydroxyl group has been replaced by a D. The IR absorption spectrum shows a single peak. The structure of the molecule is shown as an inset. As outlined to the right of the spectrum, when τ is scanned, the phase of the vibrational echo electric field, which is the signal (S), changes relative to that of the fixed local oscillator electric field (L). L is much larger than S. The detector measures the absolute value squared of the sum of the electric fields. This gives the three terms. L² is constant in time. S² is very small, does not give rise to an interferogram, and is not detected relative to the much larger cross term, 2LS(τ). As τ is scanned, the temporal interferogram is created. A portion of an interferogram is shown in the bottom left side of the figure. The oscillations are aliased in the figure. There is one such interferogram for each monochromator frequency, ωm. ωm is the vertical axis of the 2D IR spectrum shown in the lower right portion of the figure. This axis is obtained from the frequency measurements performed by the monochromator. The horizontal axis, the ωτ axis, is obtained by numerical Fourier transformation of interferograms like that shown in the figure. There is one interferogram at each ωm where there is signal.

The 2D IR vibrational spectrum at the time Tw = 16 ps has two peaks. The peak on the diagonal (the dashed line) is positive going (red). The peak off-diagonal is negative going (blue). The ωτ axis is the frequency of the first interaction of the molecules with the radiation field (first pulse). This first interaction is represented by the dashed arrow on the left side of the energy level diagram that is to the right of the spectrum in Figure 2. The first pulse makes a coherent superposition state of the vibrational ground state (0) and the first vibrationally excited state, (1). The second pulse, represented by the solid arrow in the energy level diagram transfers the vibrational coherence to populations in the 0 and 1 levels. Phase information is stored in the populations. The third pulse between 0 and 1 (dashed arrow between 0 and 1) again produces a coherent superposition state (a coherence) which gives rise to the vibrational echo emission (wavy arrow) at the frequency the molecules interact with the third pulse. The emitted echo begins its oscillation at the final phase accumulated during τ (in the 0-1 coherence) and stored after pulse 2. The ωm axis is the axis of the vibrational echo emission. The 0-1 vibrational peak is on the diagonal because the first interaction of the molecules with the first radiation field (ωτ axis) is at the same frequency as the last interaction and vibrational echo emission (ωm axis).

The off-diagonal 1-2 peak in the spectrum is shifted along the ωm axis by the vibrational anharmonicity (unequal spacing of the vibrational energy levels as shown in the energy level diagram). The first two interactions are the same as discussed above. They produce population in the 1 level. Because the bandwidth of the laser is large, it is greater than the anharmonic shift of the levels. So the third interaction can produce a coherence between the 1 and 2 levels, which is represented by the dashed arrow connecting the 1 and 2 levels. The 1-2 coherence gives rise to vibrational echo emission at the 1-2 transition frequency. Because the first interaction (ωτ axis) is at the 0-1 transition frequency and the third interaction and vibrational echo emission (ωm axis) is at the shifted 1-2 transition frequency, the 1-2 peak appears off-diagonal.

The difference between diagonal and off-diagonal peaks is very important. If the first and last interactions are at the same frequency, a peak will be on the diagonal. If the first and last interactions are at different frequencies, a peak will be off-diagonal. The growth of 2D IR spectral features off the diagonal with increasing waiting time (Tw) can yield a large variety of information about molecular dynamics, such as spectral diffusion within an inhomogeneously broadened vibrational band, population transfer between distinct vibrations, and chemical exchange between different local environments or bonding configurations. While the on- and off-diagonal peak locations at short waiting times inform us of time-invariant spectral parameters, such as harmonic force constants (from the 0-1 absorption/emission frequency) and anharmonic shifts (from the 1-2 emission frequency), the changes in the spectrum as the waiting time is increased, particularly in off-diagonal regions, are rich in dynamical information.

Figure 3: Experimental setup for 2D IR echo experiments. BS = beam splitter, P1&P2 = parabolic mirrors, LO = local oscillator, tr = tracer.

Figure 3 is a simplified schematic of the optical system used to perform the 2D IR vibrational echo experiments. The upper portion of the figure shows the laser equipment. A continuous wave (CW) diode pumped neodymium-doped vanadate (Nd:YVO4) laser is used to pump a Ti:Sapphire oscillator, which seeds a Ti:Sapphire regenerative amplifier. The regen is typically pumped with 7 watts by a 1 kHz diode pumped neodymium-doped yttrium lithium fluoride (Nd:YLF) Q-switched laser. The output of the regen is about 2/3 mJ per pulse centered at 800 nm. The duration of these pulses is less than 100 fs. The 800 nm pulses drive a multi-stage OPA. Two laser setups operating under this scheme are designed to produce 3 µJ, 60 fs duration pulses with a large spectral bandwidth (Keck 124) or 6 µJ, 110 fs duration pulses with a narrower bandwidth (Keck 136) tunable throughout the mid-infrared. Depending on the system of interest, a large spectral bandwidth may be required to pump the whole vibrational line. In addition, the shorter pulse duration permits the examination of very fast dynamics. Alternatively, if the shortest possible pulses are not required, the OPA can be optimized for better conversion of the pump light, and hence higher energy mid IR pulses for investigation of more weakly absorbing samples.

The lower portion of Figure 3 shows the optical setup that performs the vibrational echo experiment. The input IR pulse from the OPA is split into 5 beams using beam splitters (BS). Three of them are the three excitation pulses, 1, 2, and 3 in the pulse sequence shown at the bottom of Figure 1. A fourth pulse is the local oscillator (see Figure 1). The fifth pulse is called the tracer. It is aligned along the path that the vibrational echo will emerge from the sample (see Figure 1) and is used for alignment purposes. It is blocked during the experiments. Pulses 1, 2, and the LO are passed down ultra-precision translation stages labeled 1, 2, and LO. These stages can take 10 nm steps and are exceedingly reproducible in their position. The ultra-precision is necessary because the vibrational echo is a type of IR holography. The interferogram produced by scanning τ shown in Figure 2 must be accurate and reproducible. The translation stages labeled 3 and tr (tracer) are manual translation stages. Once these timings are set, they do not change. In addition to the three ultra-precision translation stages shown, the Keck 136 system also includes a 30 cm delay stage which is less precise (0.5 µm steps) which shifts both pulse 3 and the LO relative to pulses 1 and 2. By introducing a long delay in Tw, we can collect dynamical information beyond 1 ns.

The three excitation beams (1, 2, and 3) are focused into the sample using an off-axis parabolic reflector (P1) or individual mirrors and lenses. After passing through the sample the vibrational echo beam is collimated by a second off-axis parabolic reflector (P2) or a lens with matched focal length. The beams other than the vibrational echo are blocked. The LO takes a separate path around the sample and is overlapped with the vibrational echo using a beam splitter (this is a Mach-Zehnder interferometer). The combined pulses pass through the monochromator and are detected by the 32 element array detector. The signals on the array detector are read out after each laser shot by a computer for processing into the 2D IR vibrational echo spectrum.

Performing 2D IR experiments in the BoxCARS geometry has a few distinct advantages over pulse shaping methods, discussed elsewhere. First, we have exquisite control over the polarization of all beams involved. By manipulating the input beams and detection polarization, we are able to extract more information on the structural evolution of our sample. Besides polarization control, we are also able to attenuate the local oscillator independent of the signal before it and the echo are combined. If the signal is very small, the detected 2LS(τ) cross term will only be a very slight modulation of L by S, sitting on top of a large L². By decreasing the intensity of the local oscillator, the percentage modulation by the signal is increased. Thus, we are better able to look at very weak vibrational echo signals. Such signals can be small either due to origination from intrinsically weak transitions or collection of the signals at Tw long compared to the vibrational lifetime. We are beginning to employ some new experimental procedures to gain some of the advantages of the pulse shaping methods. By leveraging the capabilities of the precision delay stages, we can collect with phase cycling and in a partially rotating frame to improve data acquisition time and scatter suppression.

Relevant Publications

332. “Ultrafast Dynamics of Solute-Solvent Complexation Observed at Thermal Equilibrium in Real Time,” Junrong Zheng, Kyungwon Kwak, John Asbury, Xin Chen, I. Piletic, and M. D. Fayer, Science 309, 1338-1343 (2005).

361. “Ultrafast 2D-IR Vibrational Echo Spectroscopy: A Probe of Molecular Dynamics,” Sungnam Park, Kyungwon Kwak, and M. D. Fayer Laser Phys. Lett. 4, 704-718 (2007).

363. “Frequency-Frequency Correlation Functions and Apodization in 2D-IR Vibrational Echo Spectroscopy, a New Approach,” Kyungwon Kwak, Sungnam Park, Ilya J. Finkelstein, and M. D. Fayer, J. Chem. Phys. 127, 124503 (17 pages) (2007).

374. “Taking Apart 2D-IR Vibrational Echo Spectra: More Information and Elimination of Distortions,” Kyungwon Kwak, Daniel E. Rosenfeld, and M. D. Fayer J. Chem. Phys. 128, 204505 (2008).

443. “Separation of Experimental 2D IR Frequency-Frequency Correlation Functions into Structural and Reorientation-induced Contributions,” Patrick L. Kramer, Jun Nishida, and Michael D. Fayer J. Chem. Phys. 143, 124505 (2015).