El territorio y la Red de Mujeres Creando y Construyendo

In this dissertation Femtosecond Stimulated Raman Spectroscopy (FSRS) by six-wave mixing (6WM) is developed and conducted in both four-beam and five-beam geometries. The

benefits over traditional three-beam FSRS68, the experimental conditions, and the technical details are given in Chapters 6 and 7. Figured 3.11 is based off of Figures 6.1 and 6.3 and is shown here to illustrate the beam geometries and pulse arrival scheme for the purpose of understanding the gratings formed in each experiment. Figure 3.11d shows the five-beam experiment but equally represents the four-beam technique if the number of actinic pump beams is reduced to one. In the five-beam geometry an electronic process is activated by a pair of identical actinic pump beams which form a static grating in the sample.42-44 They are beams 1 and 2 in Figure 3.11b. The pattern of this grating is similar to the initial grating formed in the 6WM experiments considered in the last section. An example is shown in Figure 3.12a. After a variable delay, time coincident Raman pump and Stokes beams arrive and stimulate a coherent Raman response. They are beams 4 and 5 in Figure 3.11b. They also produce a grating however it is more complex than those previously considered. Due to the relative orientation of the

Stokes beam and Raman pump the resulting grating is tilted diagonally as shown in Figure 3.12b. Also since these beams are not the same frequency the grating pattern is mobile and the fringes move quickly, diagonally down to the right. In fact, because of the broadband nature of the Stokes beam (i.e. its bandwidth contains many frequencies) the grating consists of different components moving at different rates. The final FSRS grating, shown in Figure 3.12c, is the convolution of the coherent Raman grating and the grating formed by the actinic pump beams. Its inference pattern moves diagonally down to the left. After a fixed delay the final Raman pump, beam 3 in Figure 3.11b, is scattered off this dynamic grating in the signal direction

1 2 3 4 5

s

k     k k k k k 61, experiencing a ‘Doppler’ shift to the red. The magnitude of the shift depends on the frequency differences between bandwidth components of the Stokes beam and the Raman pump that created the nonstatic grating. When a frequency difference matches a

vibrational frequency of the sample the signal is resonantly enhanced at the corresponding wavelength.

Figure 3.11. (a) The interferometer used for FSRS by 6WM experiments in this dissertation. This design is much like the interferometer shown in Figure 3.9. However each of the three incoming beams is a different color. Therefore each exits the DO at a different angle preventing collinearity with a reference field. (b) The five-beam FSRS geometry. (c) The four-beam FSRS geometry. (d) The pulse arrival scheme. Actinic pump(s) arrive(s) first activating some

electronic process. After a variable delay, ₁, the first Raman pump (beam 4) and the Stokes beam (beam 5) arrive. The window shown in (a) enforces another delay, ₂, and the final Raman pump (beam 3) is scattered off the FSRS grating.

In the four beam geometry a single actinic pump (beam 1,2 in Figure 3.11c) is used so there is no initial static grating. Additionally the fringe density in the dynamic coherent Raman grating is lesser due to the smaller angle between the time coincident Raman pump and Stokes

beams (beams 4 and 5 in Figure 3.11c). The diagonal tilt is less pronounced as well. In the four beam geometry there is a lower order signal collinear with the higher order signal that must be eliminated in a manner similar to the method used in the four beam experiment discussed in the previous section. In both the four and five beam geometries a broadband pump-repump-probe signal is separated from the fifth order Raman signal by numerical processing for which details are given in Chapter 6.

Figure 3.12. (a) The static grating formed by the time coincident noncollinear actinic pump beams in the 5-beam geometry experiment. In the 4-beam experiment a singular actinic pump is used and this grating is not formed (b) In both the 4 and 5-beam experiments the Raman pump and Stokes beams create a dynamic population grating in the sample because the beams have different frequencies. The fringes move down to the right. (c) In the 5-beam experiment the gratings in (a) and (b) interfere forming a more complicated dynamic grating whose fringes move down to the left. In both the 4 and 5-beam experiments the final Raman pump is scattered off the respective dynamic grating, experiencing a ‘Doppler’ shift based on the fringe velocities. When that velocity matches a resonance frequency in the sample the signal is resonantly

3.8. Summary

In Chapter 3 methods of femtosecond pulse generation relevant to this work were discussed, specifically spectral broadening in hollow-core fibers and third harmonic generation in filaments. The techniques in which these pulses are applied were also detailed, including transient absorption and transient grating spectroscopies, pump-repump-probe, a newly

developed 2D six-wave mixing form of transient grating, and the newly development FSRS by six-wave mixing. The methods of pulse generation and the experimental techniques, both one- dimensional and two-dimensional, that were discussed in this chapter will be critical for the investigations in the remaining chapters of this dissertation.

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CHAPTER 4: MULTIDIMENSIONAL RESONANCE RAMAN SPECTROSCOPY BY