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Six-wave mixing (6WM) techniques are fifth order in perturbation. The simplest 6WM spectroscopy executed in this dissertation is ‘pump-repump-probe’ (PRP). The experimental conditions and technical details for this experiment are given in Chapter 5. Figure 3.7 is based off Figure 5.5 and depicts the experimental setup for the purpose of local illustration. PRP can be thought of as TA spectroscopy with an additional pump step before the probe step. Like in TA the equilibrium system interacts twice with a pump beam and is promoted to a

system at a specific point along the decay defined by the time between pump beams. After a second delay the probe arrives inducing signal emission. In this way it is possible to measure chemical processes beginning from nonequilibrium nuclear geometries. Lower order

spectroscopies can only measure chemistry beginning from equilibrium. This principle of inducing chemistry from nonequilibrium reactant states and then probing components of the system extends to all six-wave mixing spectroscopies, allowing measurement of nuclear coherences between the photochemical reactant and product.

Figure 3.7. Experimental design of the pump-repump-probe experiments completed in this dissertation. A 400nm pump beam excites the sample from equilibrium. After a delay, ₁, another identical pump beam reexcites the system from a nonequilibrium state. There is another delay, ₂, and the probe arrives passing through the excited volume. Transmitted probe light is then dispersed by frequency on a suitable detector. Choppers in the paths of both pump beams spinning at 250Hz, a quarter of the laser’s rep rate, alternate between the four conditions needed to measure the signal according to Equation 3.16. Appropriate delay ranges are chosen based on the sample and dynamics of interest.

The PRP spectrum is generated by varying the delay between pump beams as well as the delay between the second pump and probe. For each combination of delays, measurements are taken under four conditions: pumps-on, pump1-on pump2-off, pump1-off pump2-on, and pumps-off. As such the PRP spectrum is determined according to Equation 3.16.65-67

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1 2 1 2 1 1 2 1 1 2 2 2 1 2 1 2 1 2 1 1 2 1 1 2 2 2 , , , , , , , , , , , , , , , , , , ,

pumps on pump on pump off

pump off pump on

pumps on pumps on pumps off

pump on pump on pumps off

pump off pump off

A A A A A A A A A A                                                       

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1 2 1 1 2 1 1 2 1 2 2 2 , , , , , , ,

pump off pump off pumps off

pump on pump on A A A                   (3.16)

This is necessary because all three signals (i.e. A terms in Equation 3.#) are collinear with the probe (k₅) according to the phase matching condition ks      k1 k2 k3 k4 k5 where k1k2

and k₃ k₄.

To increase sensitivity, reduce data acquisition time, and achieve resolution of the dispersive and absorptive signal components, a greater number of beams can be used to obtain information at the same order in perturbation. In this dissertation four-beam and five-beam geometries are utilized. The experimental conditions and technical details can be found in Chapters 4 and 5. Figures 3.8 and 3.9 show the DO interferometers used for the four and five- beam experiments. These figures are based off Figures 5.4 and 4.4 and are shown here for local illustration. Four-beam geometry six-wave mixing experiments can be thought of as an initial TA style pump step followed by the steps of a TG measurement. First, two interactions with a pump beam prepare a nonequilibrium system. After a delay a pair of noncollinear time coincident pump beams reexcites the system and creates a population grating in the sample similar to that illustrated in Figure 3.5.42-44 There is a final delay and the probe arrives scattering off the grating

according to the phase matching condition k_s     k₁ k₂ k₃ k₄ k₅61 where k₁k₂. If the reactant is resonant with the ‘TG beams’, as is the case for experimental tests in Chapter 6, then the fifth-order signal is collinear with a third-order signal and the initial pump beam must be chopped to isolate the higher order signal. Spectra are obtained under pump1-on and pump1-off conditions. If the reactant is not resonant with the ‘TG beams’, as is the case in Chapter 5, then the higher order signal is background free and can be measured directly without chopping any beams. Interferometric detection is readily achieved because of a reference field that is automatically collinear with the signal as in TG.

Figure 3.8. The diffractive optic (DO) based interferometer used for 4-beam six wave mixing experiments in Chapter 5. This setup operates much like the TG interferometer shown in Figure 3.6 but with a preliminary pump step (340nm pulse 1) such that there are two delay periods and four beams induce the polarization response of the sample. Again the signal is emitted

Figure 3.9. The diffractive optic (DO) based interferometer used for 5-beam six wave mixing experiments in Chapter 4. Each of the three incoming beams is split into -1, 0, and +1 diffraction orders with equal intensities producing the portrayed view on the spherical mirror. Beams represented by open circles are blocked by a mask. Beams 1 and 2 arrive first exciting the sample and producing a population grating. After a delay beams 3 and 4 arrive reexciting the sample from a nonequilibrium state. Beam 5 induces signal emission collinearly with an attenuated reference field, beam 6, for interferometric detection.

For five-beam geometries the phase matching condition is the same as for the four-beam geometry (i.e. k_s     k₁ k₂ k₃ k₄ k₅61) but k₁ k₂ such that the higher order signal is always background free.61 In this geometry all beams are generated in a DO by splitting three incoming beams into their +1, 0, and -1 orders. Initially a pair of time coincident noncollinear pump beams creates a population grating in the sample. After a delay another pair of pump beams interferes with the initial grating creating a more complicated pattern from which the probe is scattered after a second delay. Here the angle between the pump beams in each pair is half of what it is in the four-beam geometry and TG experiments (i.e. for 266nm beams the angle is

6.1°/2=3.05°). This reduction in the separation angle increases the spacing between fringes and reduces the fringe density42-44 such that there are 9 fringes within the 120 micron FWHM laser spot rather than 17. Regardless, when the probe arrives the desired signal is scattered sharply in the phase matched direction, collinear with a weak reference field for interferometric detection. Examples of the initial grating and the total grating produced in the five-beam 6WM experiments detailed in Chapter 4 are illustrated in Figure 3.10.

Figure 3.10. (a) An example population grating produced by the first pair of time coincident noncollinear pump beams in the 5-beam 6WM experiment. The number of fringes within the 120 micron FWHM spot size is reduced from 17 to 9 in comparison to TG experiments conducted under similar conditions. This reduction in fringe density originates in the lesser angular separation between pump beams. (b) The final 6WM grating from which the probe is scattered. The pattern is more complicated because two pairs of time coincident noncollinear pump beams interfere to generate this grating. The parameters used to calculate both gratings correspond to experimental conditions in Chapter 4. Both gratings are viewed along the propagation direction. X and Y are dimensions in the laboratory frame.

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