Diffractive Optics-Based Six-Wave-Mixing

As mentioned in Section 2.5.2 of this chapter, six-wave-mixing refers to fifth-order nonlinearities. The simplest six-wave-mixing spectroscopy is the pump-repump-probe, which adds a pump pulse to prepare a nonequilibrium state before measuring the transient absorption.1,

73-75 _{Because we primarily focused on the application of DOE, we do not discuss details about}

this technique in this dissertation. Another avenue for developing a six-wave-mixing technique involves adding beams to the diffractive optic-based four-wave-mixing transient grating

geometry shown in Figure 2.11.38, 59-60, 71, 76 These derivations from transient grating have shown higher sensitivity and an increased signal-to-noise ratio over the pump-repump-probe, and possess a unique ability to separate absorptive and dispersive signal components. In this

Figure 2.12. A diffractive optic-based four-beam interferometer used to measure the six-wave-

mixing signal in Chapter 3. Compared to the geometry used in the four-wave-mixing transient grating in Figure 2.11, an additional pump beam arrives before the formation of population grating. A nonequilibrium state of the sample molecules can be prepared before measuring the transient grating signal. The signal emits in the same direction as in the transient grating case, collinear to the reference field 4.

In Figure 2.12, one additional pump beam could be added to the four-wave-mixing transient grating geometry illustrated in Figure 2.11. This four-beam geometry was used to measure the photodissociation of triiodide in this dissertation. The pump induced photochemistry processes such as photodissociation and prepares a nonequilibrium state before measuring the transient grating signal. The delay τ between this pump and the time-coincident pair of pumps in transient grating could be controlled in order to examine the relaxation processes happening during this time interval. Two field-matter interactions were involved in the first pump, and the corresponding phase matching condition was

k

_sig

= − + − +k

₁

k

₂

k

₃

k

₄

k

₅, where

k

1

=k

2. Because

the first two wavevectors canceled out, the fifth-order signal would emit in the same direction as in the transient grating measurement and overlap with the third-order response. An optical

background was removed by subtracting the pump1-off measurement from the pump1-on. However, when the sample was not resonant to the wavelength used for the four transient grating beams and possesses no third-order signal, it was possible to measure the background-free fifth- order response without chopping directly. This situation could happen when applying 340 nm pump1 and 680 nm pump 2, pump 3, and probe to measure the photodissociation of the triiodide. Because the triiodide molecule was transparent at 680 nm, no third-order signal could originate from the ground state of triiodide, and only the diiodide molecules generated by pump 1 could react with the three 680 nm beams. In Chapter 3, we further discuss the details of this case.

Figure 2.13. A diffractive optic-based interferometer with five-beam geometry is used to

measure the six-wave-mixing signal in Chapter 3. The three incoming beams are split into -1, 0, and +1 diffraction orders with even intensity distribution. A mask on the spherical mirror blocks beams not marked with numbers. Beams 1 and 2 firstly excite the sample and produce a

population grating. After a delay τ, beams 3 and 4 arrive and re-excite the sample from a prepared nonequilibrium state. These four beams generate a two-dimensional crossing grating. The last, beam 5, is diffracted by this grating in the same direction as beam 6, the attenuated reference field, for heterodyne detection.

With one more beam added in, the five-beam six-wave-mixing geometry in Figure 2.13 can separate the fifth-order response from the third-order background and still maintain a

reference field automatically collinear with the signal. In this dissertation, we used this geometry to measure the degenerate two-dimensional resonance Raman spectroscopy of triiodide, as discussed in detail in Chapter 3.

In Figure 2.13, the three degenerate incoming beams are focused onto the diffractive optic and split into 0, 1 diffraction orders with identical intensities. A spherical concave mirror folds and focuses six of these nine beams onto the sample. A mask set against the mirror blocks the other three beams. The time-coincident pumps 1 and 2 arrive first and excite the sample to generate a population grating as in Figure 2.14(a). After a delay time



1, the second pair of time-

coincident pumps 3 and 4 forms a new grating pattern and re-excites the molecules in the

constructive interference regions. Figure 2.14(b) depicts the overall population grating generated by these four beams. Finally, the probe beam 5 arrives at the sample after the second delay



₂ and is diffracted by this grating into the phase matching direction,

k

_sig

= − + − +k

₁

k

₂

k

₃

k

₄

k

₅. Unlike the previous geometry, here

k

1

k

2. Considering the equal angles between the 0thorder

and the +1 or −1 order, the apparent calculation yields

k

_sig

=k

₆, which is the same direction of the attenuated reference field beam 6. The overlapped signal and reference field produce an interferrogram on the spectrometer for heterodyne detection, which needs to be processed by the method mentioned in Section 2.5.2 of this chapter. In this setup, the application of diffractive optic not only stabilizes the phase difference crucial to measuring a weak fifth-order signal, but also provides a local oscillator (beam 6) that helps find the direction of the emitted field without much effort.

Figure 2.14. Population grating generated by the six-wave-mixing geometry demonstrated in

Figure 2.13. A 266 nm deep UV laser beam generates the patterns, as described in Chapter 3. The angle between 1 orders of the diffracted light is 6.1 degrees. The figures represent the views observed from a direction perpendicular to the sample surface. (a) The population grating formed by the first two pumps, beams 1 and 2. (b) The population grating formed by all four pumps, beams 1 through 4. These gratings are not moving due to the degenerate condition for all beams.

In document Guo_unc_0153D_17898.pdf (Page 93-97)