Monday, July 27, 2009

A Better Scan in the y-direction

I spent most of today (Thursday) in catching up with my notebook and MATLAB graphics from this past week, though I was able to adjust the lens and stage in order to take a better range of data in the y-direction. The idea is pretty self-explanatory, so I do not feel as though I need to go into it too much -- I made it possible to scan over more distance in the y-direction by moving the lens.

The new y-scan is shown in the plot below. The second plot which directly follows is simply this new scan and the scan from yesterday.

It is pretty obvious that the two scans from today and from yesterday are very similar, with the scan today being a bit more symmetrical. What is interesting to look at is what is happening on the outer edges of this scan from today; after the signal goes to zero. We see that the signal increases a bit and it almost looks as though it could be similar to a diffraction pattern. However, I do not think this is the case.

What happens is that we get the signal by the lock-in being able to read a chopped signal and reference it with when the signal is on and off. When the excitation beam is not incident on the Si then the lock-in is not reading a chopped signal -- it is just reading a stream of signal which ends up just being noise, which is most likely what we are seeing here. It is possible to simply think of it as there being a threshold, after which point the signal does not mean anything. This is what we are seeing.


  1. I don't want to throw you off onto a tangent so that you're thinking about the mechanism for the way in which this detection is working in your experiment (rather than your results), but I sense you may have some confusion about the lock-in and what it's doing here. You may find this a little abstract, as it's not something you are likely to have encountered, and I would like to explain it when you could see me and some sketches on a white board. However, briefly, the key point is that the lock-in only senses electrical information input to it at a frequency that corresponds to a reference frequency. In your experiment, the information at this frequency (i.e., the chopper frequency) is the difference between the THz receiver output when the Si has the excitation beam incident on it and when it has the excitation beam blocked by the chopper wheel.

    If you blocked the excitation beam, in contrast to chopping it, then the lock-in would only see whatever noise was coming out of the THz receiver at the lock-in reference frequency (very small). If the excitation beam is choppped, however, then the lock-in will see whatever is happening at that frequency, as well as any noise that is present at the reference frequency. What is happening at the chopping frequency is that there is an extra THz field transmitted through the Si when the chopper interrupts the excitation beam.

    So, at the 2 excitation beam positions at the edges of the Gaussian, when the signal measured by the lock-in goes to zero, there could actually be two things happening:
    1) the transmission through the Si is the same regardless of whether the excitation beam is chopped or not; or
    2) the THz electric-field transmission when the excitation beam is blocked has reduced down to the noise level (thus also true when the excitation beam is not blocked).

    If #1 was true, then you would never expect to see a signal in this chopping configuration, so it would appear that you're seeing 2 locations of excitation on the Si where the THz field has dropped to a minimum.

    I don't know why it then increases as the excitation beam moves further from the center - could be diffraction as you point out. I can't think of anything else off the top of my head.

    Anyway, don't be too distracted by all this. If we can talk about it while you're still in France, then fine, but if not, then we can hopefully have a more direct conversation later.

  2. I follow most of what you are saying -- but I do agree that a white board and face-to-face conversation would be a lot better for something like this.

    I know that my description about the "edges" was rather quick and not precise, and so your description helps a lot. I understand how the lock-in works to read at a specific frequency, though I have yet to understand the exact specifics of its functionality.

  3. The key thing to understand is that at every frequency interval of an electromagnetic signal, there is a certain amount of noise lurking. If you need to make a measurement of a single transient, then (via the Fourier transform) you need to get information from a region of the spectrum that corresponds to the time-domain nature of the signal (a short-duration signal, a wide spectrum; a long, slow-duration signal; a narrow spectrum). The shorter the signal, the wider the measurement bandwidth needs to be to capture that signal with high fidelity. The wider the measurement bandwidth, the wider the range of frequencies you need to measure. Since each frequency interval has noise, the more frequency intervals you need to consider, the more the noise integrates to give you a larger total noise (which shows up as noisy time-domain waveforms).

    Now, we are lucky in that we have our THz signals repeating regularly at the period of the laser repetition rate. That allows us to do sequential sampling. When we measure the photocurrent from the THz receiver at one pump-probe delay time, the value measured corresponds to the part of the THz electric field arriving at the receiver coincident with the matching probe laser pulse. However, this current is too small compared to the noise present to measure by itself. Thus, we sit at one pump-probe delay time and measure many instances of the photocurrent (which is a transient coming from the photoconductive receiver, with its height being proportional to the THz amplitude at one small time interval of the THz waveform), with the lock-in essentially integrating these tiny current signals over the duration of the time constant. Because we have the luxury of doing this integration over many small photocurrent transients for each pump-probe delay time, we can take advantage of signal processing that will throw out a good deal of system noise. It is key to notice that if we measured each photocurrent transient out of the THz receiver, then we would still require a wide measurement bandwidth (to capture all the spectral information in the transient), but since all we really need to know is the average photocurrent at each pump-probe delay position, we can use a filter to read only a small portion of the current-transient spectra. This is why we chop one of the beams - to modulate the photocurrent spectra sent from the receiver to the lock-in. The lock-in looks at a very narrow spectral range of information around the chopping freq., where the modulation amplitude is determined by the amplitude of the individual photocurrent transients from the receiver. We thus throw out the noise at all other frequencies outside the passband of the lock-in filter.

    Clear as mud? Not all that important for your talk actually, but a very powerful noise-reduction technique that will ultimately be good for you to know. May as well start the exposure now.

  4. This does make it a lot more clear -- and helps me understand what it is that I am actually working with. It is, in fact, nice to get some exposure to this right now (especially because it is used so often).