3. Género como categoría de análisis y empoderamiento
3.1 La construcción histórica del patriarcado y la vida de las mujeres
Under electronically resonant conditions, 90º phase-shifts are accumulated in each time interval shaded in blue in Figure 4.13. The additional electronic coherence involved in the
cascaded nonlinearity imposes a phase-difference of 90º between the two processes. Phase-shifts of 90º and 180º are also accumulated by the direct and cascaded nonlinearities when the numbers of emission events are taken into account, respectively. Thus, the total phase-difference between the absorptive components of the direct fifth-order and cascaded third-order signal fields is 180º under resonant conditions.94 This section presents control experiments based on this difference in sign.
Knowledge of the absolute signal phase requires a well-defined reference. To this end, we establish the phase-angle of the fifth-order signal field by comparing it to the phase-angle of the direct third-order signal field, which differs from the fifth-order signal by 180º (i.e. the sign of the polarization changes for every two levels in perturbation theory).85 It follows that the direct third-order signal and cascaded nonlinearity possess the same sign under resonant conditions. Here, we employ four-beam geometries to facilitate comparison of the third and fifth-order signal phases. The key advantage associated with four-beam geometries is that the direct third and fifth-order responses possess the same amount of phase-mismatch, thereby allowing a direct comparison between these two signal phases. Cascaded nonlinearities do not possess the same amount of phase mismatch as the direct processes, which can be problematic if the shift in the cascaded signal phase accumulated in the sample changes the signal sign.24 In order to rule out such undesired propagation effects, we have compared signals phases in three different four-beam geometries and a range of sample thicknesses.
Figure 4.17. (a)-(c) Three laser beam geometries are used to establish the relative phase-angles of third and fifth-order signals. Both signal fields are radiated in the direction, k3 k4 k5, because the first two field-matter interactions occur with the same beam (beam 1,2) in the fifth- order experiment. (d) The homodyne-detected signal intensity is measured with and without beam 1,2 using geometry (a). The reduction in signal intensity caused by beam 1,2 confirms that the nonlinearity interferes destructively with the third-order signal. Portions of interferograms are measured for the direct third-order (beam 1,2 blocked) and the direct fifth-order signals (obtained as the difference, beam 1,2 on – beam 1,2 off) at 1=0.3 ps and 2=0.3 ps. The
interference fringes show that the third and fifth-order signal phases differ by approximately 180º (this behavior has been confirmed for delay times up to 3 ps). The measurement in panel (e) corresponds to geometry (a); the measurement in panel (f) corresponds to geometry (b); the measurement in panel (g) corresponds to geometry (c).
Table 4.3. Parameters of Model Used to Compute Magnitudes of Direct Fifth-Order and Cascaded Third-Order Signals
(a) Parameter Value
L eg
/ 2c 2810 cm-1 d varied / vib c 10 cm-1 eg 2010 cm-1 eg 8.8 D N 1.21024 m-3 / 2 t c 37200 cm-1
t n 1.4 l 0.3 mm (a)Calculations employ a harmonic ground-state potential energy surface with a frequency of 112 cm-1 and the anharmonic excited state potential energy surface determined by Myers.48 Details are given in the Appendix A.
Figure 4.17 presents three four-beam geometries that facilitate analysis of the signal phase (i.e. these geometries are obtained by changing the mask in the six-wave mixing
interferometer). The indices in this figure carry the same meaning as those in Figure 4.4. The first two field-matter interactions, which are derived from a single laser beam (labeled beam 1,2 in Figure 4.17), initiate dynamics in 1, whereas 2 corresponds to the delay between the pulse- pair 3,4 and pulse 5. Both the third and fifth-order signals are radiated in the direction
3 4 5
k k k , because the wavevectors associated with the first two interactions cancel in the fifth-
fifth-order processes accumulate identical amounts of phase mismatch in each geometry. In contrast, the amount of phase mismatch associated with each of the four types of cascades may vary. Therefore, the relative signs of the third and fifth-order signals must be independent of the geometry and sample thickness if the direct fifth-order response is generally dominant.
In order to establish the relative phase of the fifth-order signal, we begin with a simple and easily interpreted experimental test. In Figure 4.17d, homodyne-detected signals are displayed with and without beam 1,2 in the geometry shown in panel (a). The decrease in the measured signal intensity found with beam 1,2 blocked indicates that the nonlinearity induced by beam 1,2 interferes destructively with the third-order signal (the interferograms shown in Figure 4.17e follow from this result). These observations can be interpreted by considering the
components of the total signal intensity under perfect phase-matching conditions
2 2
3 5 3 3 5 3
2 cos 180 2 cos 0
cas cas
E E E E E E E E (4.25)
where it is assumed that the direct third order signal field, E 3 , is large compared to the direct fifth-orderand cascaded responses, E 5 and Ecas. The second and third terms on the right side of Equation 4.25 have negative and positive signs, respectively. Thus, a beam 1,2-induced decrease in signal intensity is predicted if E 5 Ecas , whereas an increase in signal intensity is predicted if Ecas E 5 . The sign of the second term is always negative in these four-beam
geometries, whereas the sign of the third term depends on both the geometry and sample thickness.
We have confirmed that indistinguishable results are obtained in all three geometries shown in Figure 4.17 with sample thickness of 200, 300, and 500 μm; beam 1,2 always induces a
decrease in the total signal intensity for delay times up to 3 ps (i.e. the delay range relevant to the present study). Reproducibility of the signal sign in various geometries, which are subject to different phase-matching conditions, suggests that the direct fifth-order signal is generally larger than the cascaded third-order signal under resonant conditions in I3-. These results may also be
understood in terms of the ground-state depletion induced by beam 1,2 (i.e. as in a pump- repump-probe experiment).100 For example, a 10% reduction in the homodyne-detected signal intensity suggests that approximately 5% of the molecules in the focal volume are photoexcited. Such an understanding of ground-state depletion is relevant only to the direct fifth-order process, because each molecule involved in a third-order cascade possesses independent ground and excited state populations.
The test described in Figure 4.17 establishes that the sign of the measured signal field is generally opposite to the four-wave mixing signal. Slightly more than 50% of signal
corresponds to the Raman response, whereas the remainder is incoherent (i.e. a pump-repump- probe signal). It is therefore desirable to take this test one step further and isolate the Raman component of the signal. In Figure 4.18, we present a more challenging measurement in which vibrational coherences in the third and fifth-order signals are compared to establish their phase- relationship. The absorptive component of the third-order signal is found using the all-optical phasing method demonstrated by Scholes and co-workers.101 The same phase setting is then applied to the fifth-order signal obtained by measuring differences with beam 1,2 blocked and unblocked.40,43
In Figure 4.18b, the vibrational coherence associated with the six-wave mixing response is obtained by setting the delay between pulses 1,2 and pulse-pair 3,4, 1, equal to 350 fs, which corresponds to the first maximum in the third-order vibrational coherence. The delay between
pulse-pair 3,4 and pulse 5 , 2, is then scanned to obtain the fifth-order vibrational coherence. The delay between pulse-pair 3,4 and pulse 5 is scanned a total of 70 times, where scans with beam 1,2 blocked and unblocked are interleaved (i.e. 35 of each). Attainment of a single 1D slice with signal-to-noise comparable to that shown in Figure 4.18b requires approximately 60 minutes of signal averaging (the intensity of beam 1,2 is not increased above 5GW/cm2 because of the potential for photoionization-induced artifacts).60,68
Figure 4.18. (a) Absorptive parts of the wavelength-integrated third and fifth-order signal fields are measured using the geometry shown in Figure 4.17a. The delay axis, 2, corresponds to the delay between the pulse-pair 3,4 and pulse 5 (1=350 fs and 2 is scanned). (b) Absorptive parts of vibrational coherences are fit with sinusoidal functions to quantify the phase difference. (c) The delay axis, 1, is translated in the phase-difference associated with the absorptive
components of third and (direct) fifth-order vibrational coherences. The response is measured at a delay time predicted to yield an approximate 120° phase difference (at the dashed line). This control experiment suggests that the direct fifth-order Raman response is much larger than the cascaded nonlinearity.
Figure 4.18c explains how to convert the delay, 1, into the predicted phase-difference between third and fifth-order signal fields. A phase-difference of exactly 120º is predicted based on the delay, 1=350 fs, and the 300-fs period of the vibrational mode (i.e. 50 fs is 17% of the
300-fs period of the vibration). The measured phase difference of 145° differs from the value predicted for the direct fifth-order signal by 25°. It should also be noted that the phase of the vibrational coherence in the six-wave mixing signal shifts towards negative time (to the left in Figure 4.18a), because the value of 1 is not an integer-multiple of the 300-fs vibrational period. It may be instructive to consider that the nodes in the wave, cos vib
1 2
, shift toward lesser values of 2 as the amount of phase accumulated in 1,
vib
1 , increases.While useful for establishing generality of the signal phase, the interpretation of signals acquired in the four-beam geometries is somewhat complicated by variability in the phase- matching efficiencies for cascaded nonlinearities (e.g. see tables of phase-matching efficiencies in Appendix A). For this reason, we also compare signs of third and fifth-order signal phases using a three-beam geometry in which both direct and cascaded nonlinearities are well phase- matched. The three laser pulses are derived from the zeroeth-order beams in our experimental setup (see Figure 4.4). In this geometry, the efficiencies of the direct fifth-order and parallel cascaded responses are equal, whereas the sequential cascades are roughly 90% less efficient. The signals are detected using a CMOS array mounted on a miniature spectrometer. The resolution of the spectrometer is comparable to the width of the laser spectrum, so we simply integrate over the few pixels on which the probe light is incident. The two pump beams are chopped at 250 Hz using synchronized chopper wheels. Thus, pump-probe and pump-repump- signals are acquired for every four shots of the laser system. The delay lines are scanned 20 times over a total of 50 points, and 500 spectra are acquired at each point per scan.
Pump-probe and pump-repump-probe signals measured in the three-beam gometry are displayed in Figure 4.19. As in Figure 4.18, the two signals have opposite signs, and the signal
magnitudes differ by roughly a factor of 10. As in the four-beam geometries, the observation of signals with opposite signs indicates that the magnitude of the direct fifth-order nonlinearity is larger than that of the cascaded response. The relative magnitudes of the pump-probe and pump- repump-probe signals are also consistent with dominance of the direct response; cascades would interfere destructively with the direct fifth-order response, thereby reducing the overall signal magnitude. The signal-to-noise ratio of the pump-repump-probe signal is not sufficient for detecting vibrational coherences (noise level is 0.1 mOD). Nonetheless, as mentioned above, the Raman response is greater than 50% of the total signal magnitude in I3-. It should also be noted
that the six-wave mixing geometry employed in this work is superior to the three-beam geometry in terms of cascade suppression (see Table 4.4) .
In summary, we have confirmed that the signs of the third and fifth-order signals are opposite and that this behavior is independent of the laser beam geometry and sample thickness. Tests were conducted in both four-beam geometries and a conventional three-beam (pump- repump-probe) geometry. We have also shown that the third and fifth-order vibrational phases shown in Figure 4.18 deviate by approximately 25º and 155º from (the simplest) theoretical prediction, respectively. It is not clear if the 25º deviation reflects an experimental issue (e.g. uncertainty in phase calibration, uncertainties in time-zeroes) or some aspect of the system that has not been accounted for. For example, higher-energy electronic resonances in I3- may
influence the dispersive part of the signal even though the laser pulse is resonant with a single excited state (i.e. dispersive line shape have long tails). The blue-shift of the laser from the peak of the absorbance spectrum may also be a factor. In any case, the main conclusion to be drawn from the measurements described in this section is that the magnitude of the direct fifth-order response of I3- is generally larger than that associated with third-order cascades. Extraordinary
engineering solutions, such as those employed in off-resonance studies,24 are therefore not required to suppress cascades in I3-.
Figure 4.19. (a) Pump-probe (ΔA) and (b) pump-repump-probe (ΔΔA) signals are measured simultaneously in a jet with a 300-μm path length using the three zeroeth-order laser beams in interferometer (signals are represented in mOD). The observation of signals with opposite signs in (a) and (b) indicates that the direct fifth-order response is greater than that associated with third-order cascades. The three-beam geometry is useful for establishing the intrinsic relative magnitudes of the direct and cascaded responses, because both nonlinearities are well-phase matched.