Tuesday, July 7, 2009

Spectral Ratios and More

I spent the day (Monday) looking at the scans I took last Friday. I imported the data and made a variety of different plots. The main things that I looked at were:

Temporal signal with spectrum side-by-side
Spectra of all the data on the same set of axes
Spectra of positive and negative HM of both the x- and y-directions
Ratio of two spectra

I found some interesting things, but did not spend too much time on quantifying the data. Following are a series of images from each of the four characteristic plots that I mention above.

First is a plot which shows the temporal pulse and the spectrum of this pulse in side-by-side plot windows.

This happens to be the average over four sets of data at the maximum, or most intense, part of the THz beam. In the temporal pulse to the left, it is noticeable that there is the initial peak of the pulse and then shortly thereafter and spaced equally apart there are two other peaks. We think this is due to a Fabry-Perot effect in which the THz signal reflects within the Si before transmitting. I would like to write a script which removes this effect, as it has an influence on the spectrum.

The plot to the right shows the spectrum of this same temporal pulse. The green is the actual spectrum while the blue is the same spectrum after being smoothed out.

Following is a plot which shows the spectra of at each point. This includes the maximum position and the positions for the HM of both directions.

The legend shows the coordinate for each of these spectral scans. It is interesting that the +/- scans at the FWHM in the x-direction do not match up better. This is a little bit more clear in the following plot, which compares the +HM to the -HM of the x-direction.

There is clearly some great variation in these two spectra. Recall that the beam did appear to be skewed in the x-direction, and perhaps this is part of the explanation. We see some different things in the y-direction, which, contrary to the x-direction, seemed to be more symmetric. This plot is shown below.

These spectra seem to be much more symmetric, though there is that sharp valley for the spectra of the +HM direction (recall that I have labelled it ++HM since the other value of +HM seemed to be off). I have not yet taken the time to try and explain this sharp drop.

In order to look at the spectra relative to the reference spectra, I divided the spectra at each position into the spectra for (0,0). A sample plot of this is shown below.

This happens to be the ratio of the (+HM,0) position. This is plotted on a double y-axis plot to show the ratio in green (corresponding to the right vertical axis) as well as the spectrum of the given position (in red) and the spectrum of the maximum position (in blue). Both of the spectra correspond to the left vertical axis.

The idea of taking this ratio is to determine the beam waist size as a function of frequency, though I need to read into this more.

A few more things to look at are possibly taking an even better spatial profile of the beam since there is such a difference in the x-position. This will also allow me to find a better estimate of the FWHM in both x- and y-directions. I also need to look at how our excitation beam may be destroying the Si and thus determine if this effect is negligible for our purposes or not. Also, there is the idea of removing most of the moisture content of the air via replacing it with gaseous nitrogen.


  1. The spectral comparison between ++HM and -HM, I think, is outstanding. They are extremely close by any standard for THz signals, with essentially every major trend of one spectrum being exhibited by the other. The few large spikes in the green trace are likely anomalies due to the FFT of the long, reflection-filled temporal waveforms. To me, they look like spectra that would come from identically-spaced locations on either side of the peak of a Gaussian beam profile.

    For the previous spectral plots with more traces, there appear to be some locations that have more high frequencies than others, some that have less high frequencies, etc. These trends are good, assuming they canbe explained eventually. I would try to get the cleaner, truncated waveforms and look at the comparisons again before drawing conclusions. However, I do imagine that the trends you have seen could easily still be there in the re-processed data.

    Looks like you've been doing a great job. Hope you're having fun with it.

  2. I hope that maybe I can clean up the data and then take another look at these comparisons of FWHM for both the x- and y-directions. I would like to see why there is such a sharp spike in the data for the ++HM vs -HM spectra.

    Also, it will be interesting to investigate the similarities between the x-direction spectra at FWHM a bit more, since this is the direction of skewness, as talked about before. Hopefully I will be able to change around the incidence of the excitation beam and then this will allow me to see some skewness in the y-direction and a more Gaussian shape in the x-direction.

    Hopefully truncating the waveform and changing the incidence of the excitation beam will allow for a better explanation to these spectral phenomena.