3.3 THz Time-Domain Waveform Preparation
3.3.1 Acquisition of THz-TDS Waveforms
3.3.1.3 The Acquired Time-Domain Waveforms
The time-domain waveforms acquired by the digitizer card are recorded as two 1-dimensional matrices; one data point per element of each matrix. One matrix is for the 16-bit (2-byte) signal level in electrical potential, in units of volts, the other for the timestamps generated by the digitizer hardware, in units of seconds. An
0 1 2 3 4 5 6 7 8
Time(milliseconds)
Signal (arb. units)
1.355 1.36 1.365
Figure 3.5: A THz-TDS time-domain waveform of water vapor, from the balanced detector scheme. The inset provides a much zoomed-in view of the first THz pulse at left. Even in the inset, though, the limited dynamic range of the printed image prevents a clear view of the small signal-dependent oscillations after the initial pulse. The secondary peak at right is a reflection, and is described further in the main text.
example of such a time-domain waveform is presented in Figure 3.5. Here we see a scan through the nitrogen- purged enclosure, with the sample cell present in the THz beampath and filled with approximately 2 Torr of water vapor, as described above in§3.3.1.1. The signal levels are shown in arbitrary units, linear to measured voltage, as explicit voltage values has little mention without relation to a reference scan. There has been no processing of this waveform, other than the conversion of the timestamps to milliseconds from seconds and setting the initial time in the scan record to zero; this is essentially the ’raw’ time-domain waveform upon which all analysis is based, as discussed in the sections that follow. With a 100-Hz repetition rate offset between the pump and probe lasers, as used here, each scan will last for 10 ms. In the present case, the displayed scan runs to a total duration of approximately 8 ms; this was a result of a perhaps overly-cautious attempt to make sure one scan was finished well before a new trigger arrived in the next (scan durations and triggers are discussed further in the chapter 2).
Upon simple inspection of Figure 3.5, three attributes stand out. First, the signal appears zero-valued, or nearly so, for most of the time duration. Secondly, there are two widely-spaced peaks in time. And lastly, the time axis, of course, spans milliseconds not picoseconds. Dealing with this in turn, we first note that much of the zero-valued appearance is a limitation of the dynamic range available in a printed/electronic page, and not in the underlying time-domain data. Indeed, in the main plot, we can see a slight ’fuzzy tail’ on the later side of the main waveform peak at left. And in the inset, zoomed-in view of this main peak, there are additional oscillations following the peak—even here, the displayed dynamic range is limiting to the data. An
important aspect to keep in mind is that this is a relatively large dataset, approximately 1 million datapoints, to be displayed on the page, so that there is a high degree of undersampling in Figure 3.5. For example, the main peak at left is actually a succession of a few peaks that is squeezed in the figure so as to look almost like one; and the ’fuzzy tail’ following the peak is the result of many smaller oscillations similarly squeezed, and not just the few small, later peaks shown in the inset plot. In short, this is a dataset best viewed in an interactive plot viewer program.
As noted above, there is clearly a second major peak or set of peaks later in the scan, at a time value of approximately 5.2 milliseconds. This second peak is the result of a relatively strong reflection of the main THz pulse along the beam path. Based on the timing, as discussed more in chapter 2, this is a reflection of the main THz pulse off of the detection crystal, all the way back through the THz beam path and reflected off of the emitter back down the THz beam path towards the detector again. For the purposes of the present analysis, this additional peak can be ignored and will approximately ’divide out’ between the sample waveform (as shown in Figure 3.5) and the reference waveform (not shown, but similar in appearance); this issue of pulse reflections and referencing was briefly discussed earlier in§3.1.3.
The reference waveform is not shown herein, as it would appear largely the same as the sample wave- form, given the limited dynamic range and undersampling of the image as already discussed; other than an attenuation of the main THz peaks, there would appear to be little, if any, difference. As an instrumental note, it should be pointed out that the near-real time capability of the ASOPS THz-TDS instrument, means that this waveform can be viewed essentially ’live’ on a monitor screen. This enables the experimental to optimize the alignment of the optics, the positioning of the sample cell, etc. so as to maximize the peak in the THz time-domain waveform. Further, as the sample is loaded and its pressure increases in the sample cell, the main THz peak can be seen to attenuate. Another important aspect of the THz time-domain waveform shown in Figure 3.5 as noted above, is that the time axis spans milliseconds, not picoseconds. The delay-time scan spans a pump-probe delay time range of up to 12.5 nanoseconds—certainly not milliseconds! Due to the ASOPS time-scaling effect, as discussed in chapter 2, we observe this short delay-time scan over a period of a much longer amount of ’lab time’. An approximate rule-of-thumb, given a rep rate of approximately 80 MHz and an offset of about 100 Hz, is that every millisecond as shown in Figure 3.5 is roughly 1 nanosecond of delay time. For the upcoming Fourier analysis, the quantitative assignment of a proper delay-time axis is required, and that is the subject of the next section. As a closing note to this section, it should be noted that the MATLAB script utilized to generate Figure 3.5 is included in for the interested reader.