Wavelength Resolved Measurement

The next step is the wavelength resolved time of flight measurement using band-pass filters. We used bandband-pass filters, as common spectral resolution techniques would fail since the transmitted intensity is very low and scattered in all direc-tions. Since the light is not collimated behind the sample a pinhole has to be used, drastically reducing the recorded intensity, thus making a different spectral time resolved experiment very hard to realise. Even with the bandpass filters we are restricted to a wavelength range between 560 nm and 620 nm due to the inev-itably decreasing intensity while moving away from the incident wavelength.

Chapter 6. Results

Figure 6.13: (left) The power dependent transmission over five decades of incid-ent intensity is shown. The solid line is a linear fit, showing very good agreement. Same figure as in [25], measured by Wolfgang Bührer.

(right) Evaluation of the integralΞ(eq. (6.3)) with respect to the OD3 data is shown. The solid line is a power fitΞ=m·(I/I_OD3)^a, showing sub-linear behaviour ofΞover three decades of incident power (see text).

The incident power is fixed in the experiment at 590 nm with I₀≈1GW/m². If needed the count-rate is decreased with an OD filter behind the sample, thus the incoming intensity is the same for every measurement. This way we can probe for possible inelastic components. We use the same two samples as before.

The time of flight data are shown in fig. 6.14for R104AA (left) and R700 (right).

The data show the relative wavelength dependent transmission according to the count rate of the photo multiplier, corrected for the different optical densities of the filters with respect to their central wavelength (see tab.4.2). Additionally the dark noise of the photomultiplier was subtracted. The data is normalised so that the curve with BP590 is one atτmax. For both samples the transmitted intensity is highest at the incident wavelength of 590 nm. There is a strong decrease of trans-mitted intensity visible for the spectrally shifted curves. The transtrans-mitted intens-ity for BP600 is near to BP590 because of an overlap of their transmission win-dows. We can conclude that most of the light transmitted is elastically scattered and diffusive for both samples. For the R104AA sample the shape of the curves does not depend strongly on the detected wavelength. This is different for R700 which shows much higher upturns for the wavelength shifted curves. Stimulated Raman scattering will lead to a power dependent spectral broadening in TiO₂, as shown by Evans et al. [192], which can be a possible effect for our powders. Addi-tionally thekl^∗scaling of the upturn is evident again (see [49] for other samples).

There are only small deviations ofτmax, being not comparable with those of the spectral measurements (fig.6.6) and are probably due to inaccuracy of measure-ment.

Furthermore we can observe that the inelastic scattered contributions do hardly

89

Inelastic Effects

Figure 6.14: (left) The wavelength resolved time of flight for R104AA relative to each other is shown. The incident wavelength is 590 nm with a power of I0≈1GW/m². There are red and blue shifted contributions ob-servable, showing a small deviation in the long time tail. The legend represents the bandpass filter. (right) The same measurement for R700 is shown. Again there are blue and red shifted contributions, showing stronger deviations at long times. Same figures as in [25].

exceed the elastic ones. As a consequence we still can measure a small upturn at the non shifted part of R700 not coming from wavelength shifts, see fig. 6.15 (left). In this case the long time tails seems to be mainly covered by the strong dif-fusive contribution and absorption. In contrast for the wavelength shifted meas-urements the non-diffusive part is mainly suppressed. In contrast R104AA is per-fectly diffusive for the non shifted case, showing again thekl^∗scaling. Addition-ally we can also measure the transmission profiles wavelength resolved, see fig.

6.15(right). These measurements are more difficult to perform, since we need more intensity in comparison to a time of flight measurement. The sample is a R700 powder with smaller size (L=0.86 mm) to be able to perform the measure-ment without too much noise. The mean square width without a filter shows a peak, which is also visible for BP580 and less pregnant for BP600. In agreement with the time of flight measurement the mean square width for BP590, the non-shifted photons are not purely diffusive as can be seen at the onset of a plateau.

We have seen that by decreasing the incoming wavelength and thuskl^∗ (sec.

6.2.2), the long time tail deviation is getting stronger. To check if we see the same behaviour wavelength resolved at another incoming wavelength we use the R700 sample and chose a different incident wavelength of 570 nm, see fig. 6.16. The data for 590 nm are the same as in fig.6.14(right) and additionally the measure-ment without a filter is shown. The measuremeasure-ment at an incident wavelength of 570 nm shows an upturn at long times too, being stronger than for 590 nm, which is also obvious in fig.6.6(right). By introducing a bandpass filter according to the incident wavelength the shape changes to be mainly diffusive with only a very small deviation present, similarly to the measurement at 590 nm. If we introduce

Chapter 6. Results

Figure 6.15: (left) The curve for BP590, giving the non shifted photons, is shown for R104AA (down shifted one decade). The diffusive fit (solid line) perfectly matches the data. The same data are also shown for R700.

In this case a small deviation from the fit is visible. Both are the same data as in fig. 6.14. Same figure as in [25], longer times are shown.

(right) Wavelength resolved transmission profiles for aL=0.86 mm R700 sample are shown. For comparison the measurement without filter is also shown. The wavelength shifted curves are showing sat-uration, as well as the non shifted curve. Same figure as in [25], with additional curves.

a BP570 at 590 nm we can see an upturn, which rules out that we see a wavelength specific effect. When we look at wavelength shifted contributions for 570 nm we can see an upturn again, being in agreement with the 590 nm measurement.

In the description of the time of flight setup (sec. 4.3.1) we have introduced the bandpass filters we use. The optical density for the different filters with respect to 590 nm are listed in tab.4.2, which are plotted in fig.6.17. Additionally we can measure the wavelength-resolved (total) transmission of the R700 sample using these filters. As can be seen in fig. 6.17the recorded signals are always stronger than the pure optical densities of the filters (except for BP590). However, we can hardly estimate the excess of photons since the bandpass filter broaden the sig-nal, see4.8(right). Thus a simple comparison with the count rate is not possible.

Therefore we will not give any numbers. There are no further features visible, but due to the broad FWHM of 10 nm possible features could be hidden.