TERAHERTZ KERR EFFECT MEASUREMENTS OF SIMPLE LIQUIDS
6.3 Results and Discussion
The TKE signal of benzene is shown in Fig. 6.2(a). The electronic response at t=0 ps is clearly visible, as well as the long decay due to collective orientation in the liquid. All samples, including benzene, also show an early feature in the signal, due to the response from the fused quartz cuvette. Fortunately, the feature is shifted backward in time due to the index mismatch between the THz and optical light and reaches zero signal at t=0.
To determine the instrument response, we measured the THz field using electro-optic sampling and a 100 µm thick GaP crystal placed at the sample position. We then measured the TKE response of the spherical top CCl4, which shows no orientational
0 1 0 2 0 3 0 4 0 5 0 6 0 7 0
-4
-2 0 C
6H
5C H
3C
5H
5N C
6H
5N O
2C C l
4L n (T K E S ig n a l [A rb . U n it s ]) T im e ( p s )
C
6F
6C
6H
6C
6H
5B r
Figure6.3:MeasuredTKEsignalsforsixaromaticcompoundsandCCl4plottedonanaturallogscale.Allspeciesdecaylinearlyatlong times,indicatingsingleexponentialbehavior,butarecurvednear5-10ps.TheCCl4decayservesasaninstrumentresponsefunction, duetothesymmetryofthismolecule.0 1 0 2 0 3 0 4 0 - 6
- 4 - 2
0 0 1 0 2 0 3 0 4 0 5 0
( b ) ( a )
L n (T K E S ig n a l [A rb . U n it s ])
T i m e ( p s )
τ
2= 2 . 9 p s τ
1= 1 4 . 2 p s
Figure 6.4: (a) The collective orientational decay of hexafluorobenzene, with the fit shown as a dashed red line. (b) The fit residual reveals a second exponential component beyond the electronic response. The CCl4decay is plotted in blue.
0 1 0 2 0 3 0
- 8 - 6 - 4 - 2
0
0 1 0 2 0 3 0
( b )
τ
1= 5 . 3 p s ( a )
L n (T K E S ig n a l [A rb . U n it s ])
τ
2= 1 . 2 p s
T i m e ( p s )
Figure 6.5: (a) The collective orientational decay of toluene. (b) The fit residual is near, but distinct from the electronic response. The CCl4decay is plotted in blue.
Table 6.2: Goodness of fit parameters for the biexponential fit (b− χred2 ) and the exponential fit (e− χred2 ).
Species b− χred2 e− χred2
C6H6 1.2 4.3
C6D6 1.8 6.7
C6F6 1.0 6.6
C5H5N 1.0 2.0 C6H5CH3 1.2 7.2 C6H5NO3 1.0 3.4 C6H5Br 1.2 16.4
response and follows the THz field squared (Fig. 6.2(b)). The decay constant of the electronic response is∼250 fs, although it is not a purely single exponential decay.
Based on these traces we fit the experimental data >2 ps after the peak, to avoid the electronic responses of the samples.
The full data set is shown in Fig. 6.3, and the parameters used to fit the data are shown in Table 6.1. Benzene-d6 has been excluded from Fig. 6.3 as it is indistinguishable from benzene on this scale. With the increased sensitivity of the heterodyne detection and slower orientational timescales of the measured samples, we are able to measure TKE signals up to 70 ps of delay.
Initially, all samples were fit to a single exponential decay, as was done in previous work [37]. The goodness of fit for each decay was evaluated using the χr ed2 , and found to be relatively high (at 2-16, Table 6.2). Next, we fit the decays with a biexponential function of the form:
B[Aet/τ1+(1−A)et/τ2], (6.2) where B serves as an arbitrary scale factor and is not included in the analysis. The χred2 for the biexponential fits vary from 1-2 (Table 6.2), indicating a better fit to the data. The biexponential behavior is illustrated for hexafluorobenzene and toluene in Fig. 6.4 and 6.5, respectively. For both molecules, the long exponential collective orientational decay is linear on a natural log scale (Fig. 6.4a, Fig. 6.5a). Once this component has been subtracted, a second exponential is visible with a shorter time constant, distinct from the electronic response of CCl4(Fig. 6.4(b), Fig. 6.5(b)).
For the symmetric top, nonpolar species benzene, benzene-d6, and hexafluoroben- zene the collective orientational decay occurs as a single exponential decay that is
dependent on the polarizability, as these species lack a permanent dipole moment.
There are no other intramolecular THz active motions in these liquids, so any resid- ual signal is due to intermolecular motions, as has been shown in previous OKE experiments [152]. Given these constraints, we assign the 1 ps decay in benzene, benzene-d6 and the 2.9 ps decay in hexafluorobezene to overdamped intermolecular motions excited by the THz pulse. This is the first evidence of nonlinear excitation of intramolecular motions in a liquid by a THz pulse. Although the measured time constants agree well with OKE results from the literature [152], the relative am- plitudes are significantly changed. For all three species, the A constant is smaller, indicating a larger intermediate response relative to the orientational response. To further illustrate this point, we have overlayed the TKE and OKE response from hexafluorobenzene in Fig. 6.6. The OKE data was taken from the literature [155]
and scaled to match the peak TKE signal and zero signal level before the arrival of the pump pulse. We attribute the larger TKE intermediate response to the additional TKE dipole terms ∝ α0µ0µ0, α00µ0µ0, andα0µ00µ0that are not present in the OKE measurement.
Next, we consider the asymmetric top species pyridine, toluene, nitrobenzene, and bromobenzene. For these molecules the collective orientational signal includes terms ∝ αα and αµµ, since they all contain a permanent dipole moment. The intermediate OKE response has only been measured for nitrobenzene, pyridine, and bromobenzene and is believed to originate from intermolecular interactions, although the interpretation is more complex than in the symmetric top species [27, 153, 154]. With TKE we measure collective orientation and intermediate timescales similar to the values measured in OKE experiments, while our A constants are consistently smaller. One trend that emerges in the TKE A constants is a dependence on dipole moment. For benzene, benzene-d6, and hexafluorobenzene we see A constants that are 59%, 58%, and 66% of the OKE values. Pyridine and nitrobenzene are considerable larger, at 86% and 76%. We posit that this is due to the increased role of the permanent dipole moment in the orientational signal of these species, although further modeling is needed.
In addition to orientational and intermediate responses, many OKE signals have oscillatory components due to the excitation of intramolecular vibrational modes [27]. These features have never been observed in TKE experiments, although most small molecule liquids do not have intramolecular vibrations in the region covered by typical pulsed THz sources. To determine if such features exist in TKE, we