Thursday, July 30, 2009

Last Day at LOB

I spent this morning (Thursday) meeting with Antoine and going over the presentation. Then I went back to ENSTA for the presentation at 2:00, only to find out when I got home around 4:30, that we were supposed to meet at LOA. We're supposed to present tomorrow, but the presentation is complete.

In essence, the project is complete, though there is still a good deal that I can do with my data and even more that I can do with a few more months on this particular setup.

Finishing the Presentation...

Believe it or not, I spent today (Wednesday) working on the presentation for tomorrow. Made a bunch of nice sketches, but no new data or analysis on past data. We are supposed to present tomorrow at 2:00.

Tuesday, July 28, 2009

More on Presentation...

Today (Tuesday) is just another day for preparing my presentation for later in the week -- nothing new to report on.

Blogging and Preparing for the End...

I spent all day today (Monday) first in updating the blog from all of last week and then in working on the presentation which will probably be on Thursday. No real new data or anything, though hopefully I can have something on Wednesday or Thursday to do with the waist of the beam and frequency dependence.

Monday, July 27, 2009

Aluminum Letters and Realignment of Microscope

Keeping the same exact setup as yesterday, Antoine wanted to look at what would happen if we placed an aluminum cutout of the letter "F" in the waist of the THz beam today (Friday). The basic idea is that we have a shape with easily-distinguishable features that we can put in the way of the beam to see if/how it effects the beam. Since the cutout was aluminum (with a paper back for support), we expect the THz to reflect off the letter and then we would not see this reflected light at the receiver.

This would be really interesting if it worked, as we would be able to build a profile of the resultant beam due to such an obstruction in the way. To look at this theory a bit, I made scans in the y-direction at two different x-positions -- x = max (16.5 mm) and x = 14.0 mm. For the scan at x = max, I used the scan from yesterday as a reference (which is maybe not the best reference), and for the x = 14 mm scan, I took a scan with the "F" in place and a scan with it removed to use as a reference. The only other problem with using such a scan for the reference is that the "F" is held in place with plastic wrap in a frame, and so there is going to be some reflection due to the plastic wrap. The plot for the x = max is shown below.

There seems to possibly be some sort of feature showing up around where the center of the beam is located, though it is not very easy to tell. One big problem ends up being that I do not know where I am scanning along the letter, so I do not know what features to be looking for. I think maybe the best thing to do with this is to be able to take some sort of a ratio of the two signals to see what the relative difference is of the two at each point.

The next plot shows the data I took at x = 14 mm (where the reference was taken right after the scan with the "F" in place).

It is very easy to see that these two scans are extremely similar in almost every way to each other. The only real difference comes in the relative amplitude of the signals, but that is probably due to the plastic wrap used to hold the letter in place and not anything else.

It is an overall very interesting thing to be looking at, though I think the best option is to be able to take a full roster scan of the cross-sectional area of the beam -- both a reference and one with the letter in place. I would like to look into this more, though I will have to see what time permits.

After taking these scans, Antoine wanted to adjust the parabolic mirrors to see if he could correct some of the skewness that I saw in the x-direction scan from earlier in the week. After he adjusted the mirrors, here is the scan that I acquired.

The shape is, in general, much more like what we would expect for a Gaussian beam, but is rather clearly skewed to the left. Also, for the "edges" of this scan, I have already mentioned that we can ignore them due to the lock-in and how it is working. Overall, the shape looks better, and if anything else, then this should suggest that this technique of profiling is indeed rather useful and with some more work might become a very accurate way of profiling such a beam.

In order to see how this scan differs from the scan taken earlier in the week, see the plot below.

The most important thing to notice from this is that changing the parabolic mirrors around and realigning the microscope will result in a change in beam shape to some extent. Adjusting the setup and then doing a scan by hand to test the profile is maybe not the easiest way to do this, but it is definitely a rather straight-forward way to see how the beam looks.

I hope to maybe look into some of these things a bit more in the final week, though there are a lot of things which I may focus on -- the waist size as a function of frequency, the N2 data, the "F" in the beam, etc.

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.

A Switch to Ellipsometry

Since I am running a bit short on time, we decided to move this setup today (Wednesday) from the spectroscopy setup to the ellipsometer setup to try and characterize the beam. Since the beam was probably too wide at the waist (in between the two parabolic mirrors), we placed the Si wafer in front of the receiver to look at the distribution at this position. A sketch of this is shown below (a very rough sketch... just to show placement of components).

The dotted black line again represents the excitation beam, the pink components represent the lens and lens arm, which are attached to the translational stage, shown as the grey square. The darker grey squares are the emitter and receiver for the THz signal, the blue ovals are the parabolic mirrors, and the black disc represents a mirror which the excitation beam reflects off. Finally, the grey disc again represents the Si wafer.

After taking an x- and y-lateral scan over the Si wafer, I found some very interesting looking profiles, especially in the x-direction. A plot showing both directional scans is shown below.

Clearly the x-direction is very strange, while the y-direction almost looks like an upside-down parabola. The features in the x-directional scan, I think, help to reinforce the idea that perhaps the incident angle does not have much effect on the profile of the beam and that possibly the alignment of the actual microscope is what should be adjusted in order to correct any sort of skewness. In terms of the y-direction, it would be nice to take a wider range of data; and by this, I simply mean having more data points on the edges of the scan. I hope to do this tomorrow after adjusting the lens and stage.

Overall, it is very interesting to see such an odd profile in the x-direction -- and I think the most interesting thing is that the scan is extremely smooth, as opposed to some more "rigid" scans.

I also should mention that the lock-in was much less noisy in this setup than in the spectroscopy setup. Perhaps this has to do with the THz setup in general, the excitation beam, or something else. Also note that the relative amplitude is much less than what we saw in the spectroscopy setup, where we would see amplitudes of 4 or 5 mV, here we see just over 2 mV.

Comparison of x- and y-scans With Symmetrical Setup

After aligning the excitation beam, I was able to take some scans in the x- and y-directions with the new angle of incidence of the excitation beam today (Tuesday). As I mentioned already, this "new angle" was completely opposite of the initial incident angle. To better see this, I have attached a sketch below in which the initial incidence is shown by the red setup and the switched incidence is shown by the green setup. The stand was moved a little between the two setups, but only to gain extra length on the arm which went to the lens for focusing the excitation beam.


The black dotted line represents the incident excitation beam and the grey disc this beam is incident on represents the Si wafer, while the grey square represents the translational stage. This is a view from above the setup. The angles of the two beams were not perfectly equivalent, but by "eyeballing" it, the two were very similar (and the exact angle does not matter much, just that the angle is on the other side of the initial angle).

Since the orientation of the stage was not changed, there is nothing to correct for in the beam profiles along the x- and y-directions. The scans for this switched incidence are shown below along with the scan from the initial setup, which I took yesterday.


It is rather clear that these two different scans are almost identical in shape over the x- and y-directions (with the x-direction scan looking almost more similar to the initial incidence scan than the initial vs. switched in the y-direction). The y-direction still gives us a Gaussian and symmetric shape, but with a little skewness maybe in one direction as compared to the initial scan. However, we are most interested in testing the obvious skewness that has been showing up in all of the x-scans as an attempt to see if the incident beam angle was what caused the skewness -- but by looking at the plot of the two x-directional scans, it should be pretty clear that the angle of the incident excitation beam probably does not effect the skewness very much and there is something else that causes this skewness.

One idea (which is pretty simple) is just that there is a misalignment of the parabolic mirrors in the actual microscope design... which is, in theory, why such a profiling technique is useful -- to test the shape of the beam in order to be able to adjust it for the desired shape (probably Gaussian).

Symmetrical Investigation

Today (Monday), I wanted to investigate the skewness of the x-direction lateral scan that I have been discussing for the past few weeks. The easiest way for me to do this was to switch the angle of incidence of the excitation beam, because, if the beam was skewed as a result of the angle of the incident light in the x-direction, then we would expect the exact opposite skewness with the exact opposite angle of incidence. In quiet simple terms, I did exactly this... I switched the angle of incidence so we would in fact see a change in skewness if this was in fact the case.

Before switching the angle and changing the setup too much, I took a scan along the x-direction and a scan along the y-direction for some kind of a reference after switching the setup (though I already had such scans, I wanted to check that nothing had changed much in the design). Plots of this are shown below.


The first plot is that of the x-direction, while the second plot is of the y-direction. We see very much the exact same features that we have been seeing in such x- and y-direction scans -- the x-direction is rather skewed while the y-direction is rather symmetrical and Gaussian looking. This is not much different from what I expected (if they were different, then that would be a problem with the overall technique).

In order to better compare these scans with the scans done in the earlier weeks on the same setup, I simply plotted the x-direction scans all on one plot and all the y-direction scans on another plot. There were three different scans -- one with the first lens I used which did not focus the beam too well, and then two scans with the new lens in place which gave a tighter beam. These plots are shown below.


The first plot is that of the x-direction, while the second is that of the y-direction. The green data correspond to the scans taken with the first lens and at a larger step size (0.25 mm vs. 0.20 mm). This is most likely the reason why the data from this scan looks so much cleaner in a certain sense -- it was less precise. For the x-direction scans, it is clear that there is the same skewness in each scan (though it is a bit harder to see in the "scan 1"). It is especially clear in the difference between "2nd lens (1)" and "2nd lens (2)", as the only real difference is that these scans were taken on different days, which probably explains the difference in amplitude. All of the same sort of features show up in all of theses scans (and especially those of the 2nd lens). Therefore, it might be safe to assume that this method is in fact accurate to a certain extent.

The y-direction scans need much less explaining -- we see a nice, Gaussian shape in almost all of the scans and the main difference becomes the relative amplitude of the scans, though, again, this can (probably) be attributed to the change in laser power over the course of the day.

In fact, I did not take any scans with the new incidence today, but I did get the stage and lens moved to the proper position. I hope to take these scans tomorrow.

Sunday, July 19, 2009

A Few Observations Under N2 Conditions

Today (Friday) and yesterday, I had a chance to look at some of the data that Antoine took last week under conditions in which he filled the microscope chamber with nitrogen gas in order to remove the polar molecules (i.e. water vapor). This was done because we know that THz is absorbed quite readily into polar molecules, of which water vapor is. In almost every spectral plot that I have looked at (many of which are in past posts), we see sharp spikes, or valleys, in which a certain frequency (or band of frequencies) is not very prominent. One suspicion as to what causes these sharp regions of no frequency is absorption of THz into water. Thus, removing the polar molecules may show us some interesting results.

I do not know the conditions too well under which Antoine took the data (as I will need to talk to him about this), but he simply took a few scans at some of the more interesting points of the THz beam. The plot below shows the spectra for the four points that Antoine took scans at. The plot is labelled, and so it should be clear which spectrum corresponds to which position.

There is clearly some very strange things happening here. I do not understand why there are oscillations for each spectra, and I do not understand how a spectrum could have this shape in general. Before I worry about this too much, I would like to talk with Antoine a bit more about his procedure in taking this data and if they usually see things such as this in spectroscopy measurements under N2 conditions.

For the sake of displaying this data, I have also shown a plot of the temporal trace at each of the points that was scanned. I first show the full time-domain traces, and then for the sake of cleanliness, I chop these pulses to try and "zoom in" on the primary pulse. Both plots are shown below.


The colors for each of the specific positions correspond exactly to those in the spectral plot from above. It is clear from these time-domain traces that we still get the reflections that are so obvious in the time-domain traces done without the N2 environment. It does, however, seem as though there may be a significant decrease in the amount of reflections, though these plots do not rightfully show this.

The following plot is that of the time-domain traces at (0,0) for the N2 environment and under the measurements which I made a few weeks ago in which I took four traces and averaged their signal.

This does not seem to tell too much other than there is a lag between the time of the two pulses (due to the speed of light in the given medium) and there is a clear difference in peak amplitude between the two different environmental conditions. There does, however, seem to be a similar amount of reflections/noise after the main pulses for both scans, which might suggest the N2 did not do much to decrease said reflections.

Finally, it is interesting to look at a comparison between the two spectra -- one at (0,0) in N2 and one at (0,0) in the typical environment. Such a plot is shown below, using the same data as the time-domain trace comparison above.

We still see this oscillatory effect in the N2-environment spectrum, while we see nothing of the sort when not using N2. Also, it is clear that there is a much greater percentage of the spectrum which is transmitted through the wafer, as the amplitude of the N2-environment spectrum is greater than that of the other spectrum. Again, I am not very certain why we see such effects using the N2 as opposed to not, but I would like to investigate this a good deal more.

In order to attain a better understanding of these absorptions and anomalies in the spectral plots, I think I first need to be able to truncate the data from the time-domain pulses to hopefully result in a better, smoother-looking spectra. From here I should be able to better determine waist-size dependence on frequency.

Catching Up and Making a Plan

Today (Thursday) was spent in a very similar manner to yesterday. I used my time in the lab to continue catching up with my notebook, blog comments, and notes. I was also able to look at some of the data for the N2 environment that Antoine took last week, however I will use tomorrow's post to write more about what I found. I still am trying to get a finalized plan for what I will be doing the next two weeks here and right now it looks like two main possibilities:

1.) Move everything from the spectroscopy setup to the ellipsometry setup and try to recreate these same results.

2.) Continue trying to understand the specific physical phenomena which occur using my current setup (spectroscopy). This includes mainly (but is not limited to) the skewness in the x-direction of the cross-section of the THz beam and the beam waist size as a function of frequency.

I might feel more comfortable working more on the second choice, though this is yet to be decided.

Thursday, July 16, 2009

Another Day of Catching Up

Having not been in the lab for the past five days, I took today (Wednesday) to catch up on my personal notebook and on the blogger. I did not have a chance to look too much at the blog comments or the data which Antoine took last Friday under N2 gas, and I hope to do so tomorrow. I also have some things that I want to work on changing in the lab which Antoine and I talked about at end of last week. I hope to get this done sometime this week or early next week at the latest.

Wednesday, July 15, 2009

Another Lateral Scan

Today (Thursday) I spent doing some more catching up and also taking another lateral scan of the Si wafer. This scan was done at a fixed position in the x-direction at approxtimately the "bump" that we see in both x-direction lateral scans (see the scans from Monday to see the bump... this was also done using the same, more-focused lens). This was to try and get an idea of the shape of the beam at this one point. Below is a plot of this.

We can see that the shape is indeed rather symmetrical, just with the other scan in the y-direction. There is a fair amount of skewness, as well. The general shape is Gaussian, but it seems to be too "rigid" to be a proper distribution. The whole idea from this scan is that the profile is rather different than what we would expect for a perfect Gaussian distribution.

The problem with doing a series of scans like this over multiple strips of the Si wafer is that we are able to find some rather interesting behavior, but do not have a very good idea what is happening in regions other than those which are scanned. This can be solved in a variety of ways, the easiest being switching out the current translational stage with an automatic one and writing a simple program to profile the entire beam. The problem with this is time and lack of equipment. I have about two weeks remaining, there is not a translational stage laying around that I could use, and there are perhaps more interesting things for me to be looking at.

This being said, I would like to comment on the noise in the signal that I am reading off the lock-in. In case I have not mentioned this before, I take these data manually, and to try and deal with the noise I take and average the highest value and the lowest value over the duration of a few moments. The signal on the lock-in happens to oscillate back and forth, and these maxima and minima are approximately what I average to get the value that I use to plot.

Antoine and I tried to cut-down on this noise later in the day by changing the chopping frequeny, but the best frequency we found was about 283 Hz (frequencies of about 250 Hz and 300 Hz gave a lot of noise due to the surronding environment). In an attempt to see if this averaging technique changes much the final data, I plotted all three sets of data over position (which includes the maximium, average, and minimum). All three series of data seem to correspond well with each other (which simply means that the difference between maximum and miniumum remains relatively consistent, regardless of the position on the wafer -- thus even further suggesting that it is in fact noise). A plot of this is shown below (Note, this is from the same scan that I am describing above, but I see this effect in every scan that I plot maximum, minimum, and average on).


We thought of some ways to reduce this noise, but could not figure anything out right away. I think the easiest thing would be to connect an oscilloscope directly to the lock-in that is able to look at the signal over time and average the signal even more than what the lock-in already is. From this we could hopefully attain a more accurate average value. This idea would not work, however, since we do not have such an oscilloscope around the lab. Also, because of the consistency with the change in signal due to noise, we might as well ignore this for now.

From here I would like to further look into the differences in signal over position and also to continue trying to learn about the waist of the beam as a function of wavelength.

Friday, July 10, 2009

Not Much Happening...

Today (Wednesday) was a bit slower than the past few days. I spent the majority of my time at lab catching up with note-taking and playing around with MATLAB a little bit. Aside from this, I plan on taking at least one more lateral scan across the wafer to try and characterize the THz beam. I hope to get this done tomorrow.

Thursday, July 9, 2009

More Lateral Scans with a New Lens

I spent most of the day today (Tuesday) looking at the Fabry-Perot effect which is easy to see in the temporal pulses. Take the following plot:



This is a plot of the (0,0) position on the Si wafer. Like I said in a recent post, there are three distinct pulses -- the initial pulse which has the greatest amplitude which is then followed by a pulse of slightly less amplitude and then yet another peak of slightly less amplitude. If we look at the horizontal scale, which is measured in picoseconds, we can see that the difference between peaks is approximately 12 ps. We also notice that the three peaks are equally spaced with this same increment.

The math for this calculation is pretty straight-forward. Basically, we have the Si wafer of width l and refractive index n. Most of the signal transmits directly through the wafer, and is seen in the primary pulse in the above scan. Then some of the signal reflects off the boundary between the back of the Si disc (call it b), then reflects onto the first boundary which it has already passed through between the front of the Si and the air (call this a), and finally back through b. This gives us that second pulse. The third pulse is explained in precisely the same fashion -- signal transmits through a, reflects off b, reflects off a, reflects off b, reflects off a, and is then transmitted through b. Since the thickness of the wafer determines the path length of each piece of the pulse, they each show up at a different position on the time scale.

I understand the basic physics behind this effect, but I am interested in determining a method to effectively remove it from the data.

I also spent some time in changing the lens used to focus the excitation beam. We found a lens which had a longer focal length so as to get a tighter focus of the excitation beam on the Si wafer.

After doing this, I took more lateral scans across the Si wafer to determine if the beam shape is still about the same as before. The data that I found are shown in the plots below. First is that of the x- and y-direction on the same set of axis.


The scan traced with the blue line and markers is of the x-direction, while the red line and markers display the scan for the y-direction. We can see from the above plot that the beam profile for the x-direction seems to be even more distorted than what we saw when using the other lens. The reason for this, as Antoine explained, might be due to a low-pass filter effect in which the size of the excitation beam effectively changes the profile of the THz beam. Basically, since the excitation beam is so much tighter and we are creating more accurate measurements than with the wider beam from before, we may expect some of this sort of over-distortion to come about. We also see the same sort of skewness in this scan as the x-scan that was done with the other lens.

The y-scan shows the same sort of Gaussian distribution from before. It is still rather symmetric and looks relatively normal. It is also interesting to note that the peak amplitudes for the two scans do not match up perfectly. I am not really sure what this is due to, since I took both scans within about 30 - 60 minutes of each other.

The distortion in the x-direction and the normal, Gaussian shape in the y-direction suggest that perhaps the x-incidence excitation beam is distorted in some way and thus we see such strange profiles for the x-scans.

To further investigate the matter, I took another scan in the x-direction but at about -HM of the y-direction. This plot is shown below.


It is clear that we see the same sort of distortion in this scan... and skewness. Again, I feel as though the reason for this might be the incidence of the x-beam on the wafer. It would be interesting from here to take even more lateral scans and try to actually build a beam profile from this. I might look into taking what one might consider to be circular contours about the xy-plane to see if I can create a better 3D image, though there may be more interesting things to do.

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.

Monday, July 6, 2009

Changing the Time Constant and Taking More Scans

As I mentioned yesterday, I wanted to take some more precise scans today (Friday) and also learn how to plot the ratio of the two scans via MATLAB. I was able to take data at all five postions mentioned earlier:

(0,0)
(+HM,0)
(-HM,0)
(0,+HM)
(0,-HM)

I changed the time constant from 1 second per point (as we used earlier this week) to 100 ms. This changed the length of the scan to take about 9 min instead of the 90 min from earlier in the week. I took four scans at each of the above positions using the positions of FWHM that Antoine had determined. The only problem that I ran into was the position for the (0,+HM) gave scans a lot different from the others and the position was about 0.5 mm different from what I estimated on my initial data. Because of this, I took one more scan at the point I had expected the FWHM to be at. I labelled this point as:

(0,++HM)

For the first five positions listed above, I took data in a cyclic permutation, but for the point (0,++HM), I just took the four scans all right after each other.

During these scans, I was able to update my lab notebook and I made a note to look at how a Fabry-Perot effect might alter this data.

I tried to learn how to take the ratio with MATLAB but was unsuccessful. I talked to Guilhem about this and he gave me some commands to use. I plan on trying this out either this weekend or sometime next week. I should also have plots of the data early next week.

Spectral Plots and More MATLAB Functions

The plan for today (Thursday) was to learn more with MATLAB and to take some more scans at the FWHM of each x- and y- directions as well as the maximum. This is different from what we did earlier in the week, as I plan to take data at all five positions (max and FWHM for each) and take a series of shorter scans instead of one long scan. Then I can average the data for all of these scans, which should take better care of possible anomolies.

Unfortunately, I did not have time to take more data today. Instead I worked with MATLAB and importing data from the scans. To do this, I used specific functions that Guilhem wrote to handle such data. With said functions, it is possible to import and build the signal we initially took (temporal). Given a series of indexed data like what I mentioned above, this function will average those signals into one. The other important function was to take this temporal signal and create the spectrum.

I was able to make a few plots with this, one of which shows the spectra of each scan. This plot is shown below.


Notice that the red spectrum is that at the maximum position (0,0), and is greatest in amplitude, just as expected. We would expect the spectra colored in orange and green to be more symmetic, as they are on the positive and negative FWHM of the x-direction and so we would expect them to be very similar. Also, in this scan I took only one measurement in the y-direction. This is because the intensity plot showed the y-direction to be more symmetric than the x-direction (see plot from yesterday).

We can see from this plot that there are distinct frequencies at which there is no signal. This may be caused by absorption via water in the air. We might try to reduce this by putting the microscope in an air-tight container and filling it with nitrogen to remove the water.

From this point, I want to look at the relative ratio of signal at each point on the wafer. To do this, I need some sort of a reference spectrum to compare the other spectra to. The way to do this will be to use the (0,0) maximum point as the reference. I want to divide the spectra from each other position into this reference spectrum, and I should look at this in the next few days.

Also, I have added the compilation of the temporal scans, which is shown below. It is not very easy to see each pulse, but this plot is just to show the relative intensity of each position.















So I will hopefully be able to find the ratio of these two signals tomorrow and also take some more data which I can average out to attain more precise spectra.

Wednesday, July 1, 2009

MATLAB and Gaussian Curves

I spent the better part of the day (Wednesday) learning how to use MATLAB. The main source that I used to do this was “MATLAB Guide”, by Desmond J. Higham and Nicholas J. Higham. I made it through the first chapter or so and did some interesting examples including Mandelbrot set, Fibonacci numbers, and simple 2D plots.

I was then able to use MATLAB to input my data from yesterday and plot the two curves on the same set of axes (though it would have been nice to tell MATLAB to put them on orthogonal axes).

Note: I corrected for the x- and y- positions by setting the point of maximum intensity at (0,0).

That data is shown in the image below:









The red shows the data from the x-scan, while the blue corresponds to the y-scan. Notice the final data point at the origin for the y-scan. This is simply because I put the data from the two scans into the same matrix and there were more points for the x-scan than the y, and so the these points were all plotted at (0,0).

Also, below is a plot that Antoine constructed with the same data by using an iterative procedure in MATLAB:








[I apologize for the poor picture quality, but I had to use Paint since I saved these as PDF at lab and Blogger couldn't insert a PDF].

Regardless of the quality, it should be clear that the beam is Gaussian in shape (at least via this method).

I would like to make some more scans to better build up images such as those above, which would probably include scans along y = x and y = -x.

Aside from learning to use MATLAB today, we took a series of scans at specific positions of the excitation beam. We took a scan at maximum (0,0), at maximum x and the lower portion of the HM of y, and then at maximum y with both the upper and lower portions of the HM of x. These were full spectral scans, and each took about 1.5 hours to complete.

Note: There was a major shift in maximum signal change from yesterday to today. The maximum went from about 4.5 mV yesterday to about 7.5 mV today. This may be due to a few things: more power out of the laser OR the excitation beam is locally destroying the Si OR some other thing yet to be determined.

Antoine was going to take one final scan today with the Si wafer slightly shifted so that if the effective change in amplitude was due to a local defect then we should be able to see it right away. For tomorrow, I intend to work some more on learning MATLAB and possibly changing the incident excitation beam on the Si to try and understand the skewness of the x-position (though I think it may have to do with a slight tilt in the wafer (i.e. not perfectly orthogonal to the incident THz beam)). Also, if I have time then I may try to take some more data, as I had mentioned, with the scans being along y = x and y = -x.

Horizontal and Vertical Profiles of THz Beam

I began the day (Tuesday) with trying to center the excitation beam on the Si wafer. I did this by first roughly guessing where the maximum x- and y- displacements were and then performing two manual scans: one along the horizontal with the vertical displacement constant at maximum and then the same thing for the vertical scan (horizontal position constant at about maximum value).

These initial scans I did in increments of 0.5 mm and scanned about 7 mm in the x-direction and about 5 mm in the y-direction. Also, note that I have set x to be horizontal and y to be vertical. The idea of these scans was pretty simple: move the excitation beam across the wafer and record the change in THz signal from the lock-in. The greater the change, the more effective this local mirror was.

Plotting the points from these scans showed some pretty nice looking curves for such quick/crude measurements. Both curves were Gaussian in shape, with some minor anomalies.

Note: These initial measurements were done with an aperture which did two things: limited the amount of THz signal and made it possible to see a Fabry-Perot effect between the aperture and the Si wafer. This is why it was removed in later measurements.

Note: The signal tended to be rather noisy (the signal would oscillate in upwards of 0.1 mV at each position, with the relative maximum being about 4 – 5 mV). To reduce the effective noise, I looked for the signal to ‘oscillate’ and took the maximum and minimum values, later to be averaged together.

I then decided to take more precise measurements of this signal and so I changed the step size to 0.25 mm. I first did this with the x – position and plotted it. I found it to be slightly skewed, but still Gaussian. After this measurement, I removed the aperture and took scans in both the x- and y- directions. I found some very nice looking Gaussian curves for both of these scans, with the x- still being slightly skewed.

These scans ended up being pretty convincing that the THz beam is indeed Gaussian in distribution. I approximated the FWHM of the x- and y- directions to be 2.5 mm and 1.5 mm, respectively. I found the maximum signal difference to be 4.548 mV. The integration constant was 1 s, with 24 dB and 10 mV sensitivity, which were all set on the lock-in.

I also need to check if the excitation beam is stretched too much in the horizontal direction because of its angle of incidence on the wafer. I also need to see if the translation on the stage corresponds to the same translation on the wafer (i.e. if moving the stage 2 mm moves the beam 2 mm).

Tuesday, June 30, 2009

Reduced Path Length, Translational Stage, and Measuring the Displacement of a Speaker Membrane

This afternoon (Monday), we removed the delay line from the excitation beam, therefore effectively decreasing the path length of the excitation beam. This should not matter too much since the lifetime of the charge carriers seems to be long enough for the pulses to not need to be timed. This arrangement was simple, as we just took out the delay and moved some of the mirrors.

I then took the focusing lens and attached it to a manual translational stage. This will allow me to change the incident position of the excitation beam on the Si wafer.

Once this lens was attached to the stage, I tried to optimize the signal by tweaking the final mirror that the excitation beam was reflected from. I then took a few scans:

- reference scan without the excitation beam or Si wafer and THz chopped
- reference scan without the excitation beam but with the Si wafer and THz chopped
- reference scan with excitation beam and Si wafer with THz chopped

- initial scan with potential difference maximized and excitation beam chopped

These are saved and are mainly for reference later on.

We then wanted to determine the dispalcement of a mirror attached to a speaker (i.e. the distance between all the way up and all the way down on the speaker). This is because we plan on placing this vibrating mirror in the experiment somewhere in order to modulate the wave.

We tried to determine this distance by reflecting a visible laser beam off the vibrating mirror and onto a wall. The beam on the wall was stretched due to the different incident positions that the beam was on the mirror. The problem with this approach is that the "stretching" increases with the increase in distance from the mirror to the wall. Common sense (well, at least simple ray optics) suggests that the stretching should be the same, as there would just be a "fan" of parallel light rays that all travel without diverging from each other.

We did not have enough time look into this more, but the suggestion was made to use interferometry. Also, perhaps this widening is due to some frequency shift of the incident light...

Monday, June 29, 2009

Success!

Although today (Friday) was one of the more eventful days with a cocktail party in the afternoon and a going-away party later in the day, we managed to finally see a change in THz signal when blocking/unblocking the excitation beam.

We switched again to the spectroscopy microscope and arranged a series of mirrors to end with our excitation beam incident on the Si wafer that we were testing. The better part of the time spent to set this up was on getting the optical path of the excitation beam and the THz beam to match (with the excitation pulse incident just before the THz pulse). This included setting up a delay for the excitation pulse (and the reason for trying to time the two pulses was in case the carrier lifetime was not long enough).

We next took a scan with the excitation beam blocked and the THz beam being chopped. We saved this scan and then autoscaled the lock-in to set it at zero. Then we turned off the THz chopper and chopped the excitation beam, and allowed it to be incident on the Si. On the lock-in we saw a change from zero to about 1-1.5 mV when we blocked and then unblocked the excitation beam. We then found a focusing lens and used it to focus the excitation beam on the Si.

We then then tried to optimize the signal and were able to read just under 2 mV on the lock-in. Also, after moving the delay line of the excitation beam, we concluded that the optical path probably does not matter since the lifetime of the charge carriers is long enough.

The last thing that we did is take two scans -- one with the THz beam chopped and the excitation beam blocked and the other with the THz beam NOT chopped and the excitation beam incident and chopped. We found that the amplitude of the second beam (the beam with the excitation beam incident) was slightly lower than that of the full THz signal through the Si. We also looked at the spectra of the two scans and again, the second signal showed a slight decrease in amplitude, though still not very prominent.

From this point, we need to optimize this effect, rearrange the path length of the excitation beam (since path length does not matter), put the excitation beam on a translational stand so that we may scan across the surface of the semiconductor, and try to take scans which better contrast the difference between the two signals (which optimizing the system should do).

Reading, Lab Work, and Skype

I spent this morning (Thursday) reading more in the optoelectronics text and then spent the afternoon in the lab. One thing that I was going to maybe look into is "dielectric relaxation time", which Antoine suggested as being a possible problem with our current setup.

In the lab this afternoon, we set up an optical delay on the ellipsometry setup and tried to synchronize the THz and excitation beams. We tested again to look for a signal with the Si sample and all of the GaAs samples, yet still found nothing. We also turned off the lights, but could still not detect any changes. Finally, we altered the position of the optical delay line to see if the path length made a difference for the two pulses, but could not really say whether or not it did because we were not able to detect any changes in the transmitted THz signal.

Finally, I talked tonight on Skype with John and learned a great deal of information and got some ideas for this project. A few notable things that we talked about are: carrier lifetime, Fresnel reflections, beam choppers, how a lock-in amplifier reads a signal, where to place the delay line, whether or not to focus the excitation beam, etc.

An Introduction to Optoelectronics

Today (Wednesday), I spent reading more papers and also through a section of textbook on semiconductor physics. The two articles that I spent the most time reading were that same one from the Japanese group and also one entitled "Near-field THz imaging with dynamic aperture", which is from a group at RPI. In the Japanese article, I looked mainly at characteristics of the two beams and specific experimental design. The other article was mainly about introducing near-field to the THz regime and how this method vastly increases the microscope's spatial resolution, etc.

I also began reading through a textbook entitled "Optoelectronics: An Introduction". I read mainly over the section devoted to elements of solid state physics. Some of this was review (de Broglie wavelength, finite well, uncertainty principle, n-type and p-type semiconductors, etc), and that was very helpful in refreshing my memory of certain concepts. Also, it was interesting to learn new things such as: excitons, intrinsic materials, recombination, and others. I hope to maybe read some more of this section and then maybe also start on another more specific semiconductor text.

Wednesday, June 24, 2009

Not a Whole Lot

Today (Tuesday) was the LOB BBQ, so I just caught up on notes and organized everything in the morning and then had the BBQ in the afternoon.

I did manage to read over the Japanese article again and note a few things, though I will write about that for Wednesday's post.

Tuesday, June 23, 2009

Still Nothing... Even With GaAs

I spent Monday working in the lab more with Antoine to try and see a change in photocurrent between having the fs beam (non-THz) incident on the wafer as opposed to blocking it.

[Before this we talked more about chopping the beam and the lifetime of the charge carriers, but the conclusion was to not worry about this too much and instead just read about lock-in amplifiers a little].

As far as what we tried to do in the lab, nothing really worked. We first tried a GaAs wafer in the same THz setup as before (the ellipsometry-esk one). This was done using the same setup as on Friday with the only exception being a variable aperture placed in front of the GaAs wafer which was used to limit the size of the THz beam that was incident on the wafer. This was used today and not on Friday because the Si wafer was much larger in diameter than this GaAs wafer, and so we did not have to worry about part of the beam going around the object and the other part going through. I think we measured a pulse throught this GaAs wafer, but I know that we did not detect any change in photocurrent with the beam blocked vs. unblocked.

We then tried this same thing with another THz microscopy setup, this one being for spectroscopy. We thought that maybe the more tightly-focused THz beam would make a difference -- but we found the same null results as with the other microscopy setup for both the Si and the GaAs.

The final thing that we tried was making the optical path of the two beams (the fs beam used to excite the electrons and the THz beam) almost equal, but still so that the fs beam would be incident on the Si wafer first. This we did on the initial ellipsometry setup. The length of the fs beam was about 330 cm and the length of the THz beam was about 350 cm. The hope was that this would ensure the creation of charge carriers right before the THz beam was on the wafer. However, this again showed us no difference in the signal.

I think that at this point the best thing to do is get some more reading done and try to think more about what the possible problems might be. I also plan on emailing the group who published a paper on this method to ask a few questions: one about depth of modulation and the other about the type of doping used in their design.

Some other things I want to look at are:

* How important is it that the excitation laser be cw (which is what it was in the paper)?
* Is the excitation beam stretched too much (in the x- and y- directions) due to reflections off the mirrors?
* Do we have the right type of semiconductor/laser light combination?
* Is the THz beam focused enough on the wafer?
* Is there simply too much noise to detect such a small effect? And if so, how to remove the noise?

I hope to have some time this week to read through some articles and answer these questions.

Femtosecond Laser Beam on an Si Wafer

I spent this morning (Friday) trying to update the blog and follow up some more of John's comments. I also found a plethora of interesting articles that were cited on the original Japanese paper on spatial profiles. One of the articles was by the RPI group that John mentioned in a comment from a few days ago. The other articles that I found look rather interesting (most of which are different techniques of spatially profiling a beam, etc.).

I then worked with Antoine a bit in the lab. We knew that the Si wafer did in fact transmit THz and so the next logical thing to do was try to create a local semi-metallic area on the wafer to see if we can change the amount of THz beam that transmits through. To do this, we took part of the fs laser beam from one of the other microscopy setups and reflected it off two mirrors and onto the Si wafer. This Si wafer had been placed directly in the THz beam and the reflected fs beam was centered on the wafer.

We then put a chopper in front of the fs beam (non-THz beam) and tried looking at the signal. The signal that we found was just a lot of noise. All we wanted to accomplish in this demonstration was finding if, when the fs beam was blocked, the THz signal changed. The problem is that the THz signal (photocurrent) was varying slightly both with and without the fs beam incident on the wafer, meaning that if there was indeed a small change in photocurrent, we could not detect it.

Maybe there was too much noise in the surrounding environment, and so maybe having everything inside of a box could decrease this – though I seem to think we should be able to at least see a slight change in signal. Also, perhaps the beam is too wide or too focused… but we tried focusing the beam and still found nothing. We would like to try switching this Si wafer with a GaAs wafer to see if this semiconductor might work better.

Monday, June 22, 2009

Optical Properties of an Si Disc

The morning, like every Thursday morning, began with a seminar by Delphine Debarre on "Image-based aberration correction in microscopy". The work was conducted at Oxford. The general idea was how to get rid of aberrations in different images. Sources of aberrations: optical system elements and specimen. From what I was able to gather, the way to correct for aberrations is to choose a proper "metric" for a given type of microscopy and use this to maximize the image. Basically:

image FFT = OTF * sample FFT

Where OTF is the optical transfer function and it depends on the aberration. Two forms of microscopy that this can be used for are structured-illumination microscopy and two-photon microscopy. I do not understand enough of this talk to write much more than this.

Before the seminar, Antoine and I talked more about the physics behind attaining this spatial profile. A few notable things that I have not talked about yet are the lifetime of the charge carriers and more about the Fabry-Perot effect. In terms of charge carriers, it is interesting to have an idea of their lifetime, as we are measuring both the THz beam with the carriers present and without the carriers present for each location that the laser diode spot is on the Si wafer. We want there to be a small relative excitation and de-excitation time relative to life time of the carriers, as we will be chopping the beam to have moments of essentially semi-metal and then semi-conductor. The lock-in will be used to analyze this signal. (More about this later).

The second notable effect is the Fabry-Perot effect, as I have mentioned in previous posts. One thing that I wanted to note about this effect is that the waveform which we see may not simply look like the initial pulse with a shifted phase and altered amplitude (i.e. it might not look simply as though it transmitted through the material) – the FP effect will cause this waveform to look like the sum of multiple waves. The majority of this is the part of the wave that is fully transmitted and then a number of internal reflections and then transmissions which all add together in our detected signal. It should be obvious that herein lays a problem, as we need to be able to tell how much of the wave is transmitted in the initial transmission, etc.

I also spent time trying to align the IR beam in the afternoon. I first aligned the height of the beam along a length of the optical bench and then put the laser in place to align it through the mirrors. I was able to align the beam decently well through all of the components, but I think maybe tweaking some of the mirrors would allow me to center it perfectly. I did not, however, change any of the mirrors – just the IR laser.

After aligning the beam, I was able to get into the lab with Dr. Gallot to look at the Si wafer that I will be using. We wanted to be sure that the THz beam did in fact transmit through the disc. For today, all we did was place the disc in the path of the THz beam and measure the waveform. We then took another reference signal. The two waveforms differed in amplitude and time. By measuring the thickness of the disc with calipers (0.524 mm), the distance between the two signals (0.63 mm), and the relative amplitudes of the two pulses, we were able to determine the index of refraction (3.405) and the absorption constant (0.021 cm^-1). We also measured the percent transmission, which was about 70%. Of course, these were all approximate measurements, but note that they are about what we expect for impure Si – ~ 3.4 index of refraction and about 70% transmission. Also note, this is not a pure wafer... either an n-type or p-type.

I was then going to measure the same properties using a GaAs disc, but did not have enough time. Should be able to later this week or next week.

Thursday, June 18, 2009

For the Record

Today (Wednesday) is combined with the post from yesterday...

Beam Alignment and More Reading

Today (Tuesday, June 16), I spent time doing both reading and some laser alignment in the lab. The reading consisted primarily of the article which I have been referring to about spatially profiling the THz beam with an n-type Si wafer. Reading through the majority of this article cleared up many things.

The first thing of interest was that this list gave a variety of other groups and sources for which I may refer and which discuss alternative methods of attaining a spatial beam profile. Perhaps the most notable being a technique which combines an electro-optic (EO) technique with a charge-coupled device (CCD) camera. As I may have mentioned in an earlier post or comment, the problem with most of these techniques is that the detector is positioned at the observation point, which means having to rearrange the apparatus to do spectroscopy, imaging, etc. There is also mention of an older method which uses a bolometer and knife-edge method to measure the focusing profile from a surface emitter (surface emitter I think meaning THz generator). This is presumably not the best method because there is no frequency dependence (i.e. it measures the profile composed of all the beams).

As far as this aspect of the paper goes, I am mainly interested in looking up some of these papers and trying to see what other types of methods there are.

What this group wanted to do was develop a new technique for attaining a beam profile at various frequencies (well, the whole range of frequencies (the whole signal) is taken and then a single frequency of interest is taken from that). Their method involved scanning an optical beam of nm wavelength over the Si and detecting the change in THz signal caused by optical excitation in the semiconductor. The altered signal is measured by a photoconductive antenna placed a focal distance away from the Si wafer.

What happens physically is that the transmittance of the THz beam through the Si decreases as the free charge carrier density increases due to excitation of electrons and the change into a semi-metal. This means that the amount of change of the THz amplitude is proportional to the amplitude of the THz wave at the point where the nm beam is incident on the Si. Thus we find the amplitude distribution of the THz wave by chopping the CW nm optical beam and lock-in detecting the change in amplitude by scanning over the surface of the Si.

What I have just written about is many of the actual notes which I took during the re-read. However, I would also like to better address the questions that John asked in a recent comment.

The first question deals with how the group distinguished between the three frequencies that it mentions creating a spatial profile of.

The other question (which went hand-in-hand with the previous one) was about how this group measured total power, since this would make it indecipherable to tell which part of the spectrum is which and in turn make it impossible to tell spatial profile by frequency.

Because I have yet to answer these completely, I will do so in another post later this week.

During the afternoon, I was able to go into the lab and begin working a little with one of the microscope setups. I had to move the alignment laser to another location, change the stand it was in, and align the beam. Just to note, the laser is a class 1 infrared laser so that the beam can go through the optical components. I got as far as securing the laser into the holder and getting it to the approximate correct height, but in trying to get the horizontal angle set, I was having some trouble. I want to set the horizontal angle correctly before setting the laser in place on the table. I was going about doing this by trying to pass the beam through two slits drilled in vertical rods. (For lack of a more concise description, this is the idea of setting two holes far apart and by passing the beam through those two holes, it will be aligned properly… the farther the two holes, the better).

The plan is to finish aligning the laser on Wednesday or Thursday.

Tuesday, June 16, 2009

Plan for the Week

I spent the day today (Monday) looking over everything from the past few days and getting a plan for the week. I also spent some time taking notes on what Antoine showed me in the lab last Friday.

With one of their setups in the lab, there is a Si disc which is placed horizontally in a sample holder so that there is air on both the top and the bottom of the disc (i.e. the disc is not placed simply on another solid or liquid). A THz beam is incident on the surface and does two things -- reflects off the first interface (air/Si) AND transmits through the disc and then reflects back off the second interface (Si/air) and travels back through the initial interface (this is just reflection upon transmission). These two waves will differ in both phase and time.

The data we get out is of the initial pulse (off the air/Si interface) and then of the secondary pulse (off the Si/air interface) measured on a time scale. We can easily tell the thickness of the disc by knowing when the two pulses occur in time and what the speed of the wave is (or this is at least a rough estimate of thickness). Also note that the secondary pulse is inverted upon reflection.

After this initial collection, we are able to change the second interface to something like water. This will cause the reflected wave to change in amplitude relative to that same wave off the initial Si/air boundary. By saving the initial collection (showing the two pulses) and then collecting data again but with the second boundary being Si/water, we will see the two signals to agree with each other (aside from a little noise) for everything but the amplitude of the reflected wave off of this second boundary.

Once we have this data, we may use the Fresnel reflection and transmission expressions to determine index of refraction and dielectric properties of the (in this case) water (I think there are other properties which may be measured, though I am not aware of them currently). Also note that I think this operates around the Brewster angle for Si.

Now that I have spent some time looking over material from the previous week (and actually had a little time in the lab) I have a plan for this week.

- re-read article by the Japanese group to answer questions posed by John in last few posts
- read through the books on optics and diffraction to try and better understand why the current setup at LOB may not be the best
- continue a search for articles and other sources which may have alternative methods of profiling a beam
- learn more about beam optics and what may cause beams to be something other than Gaussian (i.e. what gives us a flat top beam, etc).

Monday, June 15, 2009

A Refined Sense of Direction

Today (Friday) I spent the morning looking over Mittleman’s "Sensing with Terahertz Radiation" mainly as an attempt to better understand the terahertz regime. The notes that I took from the first section of the text were mainly about the history of THz, the introduction of TDS to THz and what benefits this has over CW spectroscopy, and also some other introductory facts about THz.

The next two sections that I read were about spectroscopy and imaging. Reading of typical characteristics of THz frequency (1THz corresponds to energy of 0.004eV, a temperature of 50K, and a wavelength of 0.3mm) and types of THz interactions (three distinct categories dependent on values of Q resonance) gave me a better understanding of a typical THz laser and how different samples are analyzed. These two sections also mention the practicality of THz radiation and how THz technology is sometimes the most effective technology for a given problem.

I also met with Antoine today and talked a little more about where I am at and where I might want to go next. He basically confirmed that LOB is currently using a technique to get a spatial profile but that it is probably not the best method, hence my role in determining a better method. He did not explain the method they use here too much, and I have not had ample time to look into it yet, but I do know that they use some sort of aperture that opens and closes to allow a certain fraction of light through each time it is open. He made it sound like this aperture was scanned through the waist of the beam and then a profile was made from this.

Though I do not yet understand completely the method used in LOB, I do understand that their problem is a result of diffraction. I am told that they are able to produce an image which looks Gaussian, but the “tails” of the curve are possibly not accurate due to diffraction (i.e. if you cut the tails off of a Gaussian curve maybe around were the concavity changes then that is what may limit your accuracy). I need to investigate this diffraction problem to determine whether the effect is negligible or not. In doing so, Antoine mentioned a certain convolution which might describe this effect, but I have yet to look into this.

I went to the library today and added two more books to my pile: Diffraction, Fourier Optics, and Imaging, by Okan K. Ersoy and Introduction to Fourier Optics, by Joseph W. Goodman. The plan is to read through some of the sections on diffraction and Fourier analysis.

Also, I read through some of the initial article that I was given while still in Michigan to see if I could pick up on anything that I may have missed. Simply as a note to myself, I found that they used THz-TDS to measure ionic content in living tissues (specific ions being: K+, Na+, and Ca++). Again, this was near-field THz, so they performed transverse scans over the sample and their image was 150μm by 1000μm. The article is not directly related to my task of creating a spatial profile, but I thought it would be good to re-read it since it was the one which was initially given to me for reading.

Finally, I have received the comments by John on the past couple of posts and this is something I will be looking into on Monday and should have answers to by Tuesday or Wednesday.

Friday, June 12, 2009

Two Seminars in the Morning and More About Beam Profiles in the Afternoon

I went to two seminars which the LOB hosted this morning. The first was about a new form of microscopy developed by Jerome Mertz and his group at Boston University. This type of microscopy is called “HiLo Microscopy” and is intended to remove the out-of-focus background image artifacts that are common in microscopy when using devices like the confocal microscope. In essence, his technique involved optical sectioning and compiling together two complementary images – one of which was taken with a high-pass filter and the other of which was taken with a low-pass filter.

The second talk was about collagens and a little about multiphoton microscopy, but I did not understand this talk as well as the first.

This afternoon I read into some sources a bit more, one of which was the source I mentioned in my last post by the Moscow group. My main interest in reading this was to look at different techniques that physicists are using to attain such a beam profile. The article mentions the more traditional approach of using autocorrelation functions or spatial Fourier transforms, the former is one which I am not particularly familiar with and would like to read into a bit more. This group is able to attain a pulse shape and beam profile by using measurements from two different techniques: partially overlapping time intervals which are used to understand the temporal dependence (pulse shape) AND multidirectional bands which are used to understand the spatial dependence (beam profile). The article is more about the algorithms developed to solve this problem than the actual experimental design and was therefore more helpful in understanding the mathematics rather than the design.

Another article that I skimmed through was “Spatiotemporal transformations of ultrashort terahertz pulses” by a group from the Czech Republic. The article was from 1999 and was published in the Journal of the Optical Society of America. I found this article intriguing in that it discussed how THz pulses reshape in specific optical components. For instance, a THz beam is reshaped through any focusing optics and this reshaping can be described with an ABCD transformation (something I will read about in the photonics text).

Finally, I began reading through a little of Mittleman’s text on Imaging with Terahertz at the end of the day and intend to read more of this on Friday.

Catch-up Day

I spent the day today (Wednesday) updating my blog from Tuesday and trying to understand the article on “THz Beam Profiler… in Si” a little bit better. I also looked over a few sources to try and find articles relating to beam profiling. One article which looked promising was: “New possibilities for measuring a pulse shape or a laser-radiation beam profile,” by a group at Moscow State University. There is nothing much more to report than video chatting with Dr. Yalisove this afternoon to catch up and try to coordinate a time to talk each week.

Wednesday, June 10, 2009

THz Beam Profiler Using Optical Transmission Modulation in Si

I met with Antoine for a little bit today (Tuesday) and we talked about where I am and where I am headed. It looks like the next couple of weeks will be a lot of reading. He wants me to have a solid understanding of what I am working with before actually doing anything in the lab -- which I think is a good plan.

I spent the morning reading an article by Yeubin Wang, et al, about periodic optical delay based on a tilted parabolic generatrix helicoid reflective mirror. Some notes that I took on this article inclde what an optical delay line (ODL) is and a little bit about what other types of ODL there are (ranging from linearly scattering retroreflectors to multipass cavities). From what I understand, in a very general sense, an ODL is used to lengthen the path length of light, as this will alter the phase of the light and will in turn have an effect on diffraction and interference.

More importantly, I spent the better part of the day re-reading an article from a Japanese group for which the title of today's post is named after. This article describes a new (2001) technique for spatially profiling a THz beam with the Si wafer technique that I mentioned a little in Thursday's post (and which John commented on). After talking to Antoine early in the day about this technique and re-reading the article, I understand it much better now.

The setup is rather simple (and I am trying to get a sketch to upload and it is not working). We split the beam form our Mode-locked Ti:Sapphire laser and send part to the emitter and part to the detector (which both have similar setups to what I have described before with GaAs and metallic strips). The THz radiation is then focused using parabolic mirrors onto an n-type Si wafer with charge carrier density 5.6 x 10^14 cm^-3 and thickness of about .5mm, which seems to be located at the focal distance from the parabolic mirrors.

As John mentioned in his response post, this THz radiation should penetrate the Si sample, and indeed most of it will. The reason for this is that the THz radiation will have energy of a few meV and thus cannot move electrons up to the conduction band. Also keep in mind that there will be some reflection off of the surface of the Si wafer.

In order to attain a profile of this beam, this group has come up with a technique in which a CW laser diode of 820nm is placed on a translational stage and aimed directly at the spot where the THz beam is incident on the Si wafer. The angle of incidence is 35 degrees and the beam is first passed through an optical chopper which is running at 450Hz chopping frequency.

The photons of this 820nm laser have enough energy to excite the electrons of the Si wafer into the conduction band. What this does (as John alluded to in his last post) is creates a semi-localized point on the wafer which is a semi-metal. This in turn makes that point more reflective to the THz beam and so at that point there is a loss of total power of THz signal which passes through the wafer.

Since the laser diode is on a translational stage, we are able to scan the laser across the area of the Si wafer. By taking measurements of how the total power of the THz signal changes with the location of the incident 820nm laser, we can build up a profile of the THz beam.

The group that used this technique report using this for three different frequencies of THz (or near THz) radiation. For each case, they report Gaussian beams (with some variation in x- and y- width).

The few physical problems with this setup are that there may be some sort of Fabry-Perot effect with the THz signal and also diffusion of charge carriers near the localized metallic point. Other problems with this technique are that I have not found any sources which cite this one, suggesting that this technique maybe has not been used much.

My goal is to be able to recreate this setup and try to get a profile of our THz signal. There is also the possibility of using another method if an easier one comes about. As of now it looks like this is the way to go for profiling my THz beam.

Monday, June 8, 2009

Ray, Wave, and Beam Optics

I spent this afternoon reading through some of Saleh's "Fundamentals of Photonics" text in preparation to the lab work I will soon be doing. I made it through (skimming most of it) the first three chapters, which dealt with ray optics (chapter 1), wave optics (chapter 2), and beam optics (chapter three). I personally found chapters 2 and 3 most useful in answering pre-existing questions that I had.

In chapter 2, I made special note of the Fourier analysis which allows us to expand an arbitrary function of time to a superposition of harmonic functions dependent on frequency. This superposition is characteristic of frequency (as already noted), amplitude, and phase. I also found very useful the temporal, spatial, and spectral sketches of a pulsed wave.

I found especially helpful in chapter 3 the discussion of Gaussian beams, as I am under the impression that our THz beam is of this nature. Things to look into more from here include Gouy effect and Laguerre-Gaussian beams.

Though there is not necessarily a lot for me to write about today, I feel as though taking the time to read over some very basic optical principles and more importantly some material I had not yet been exposed to really helped a lot today. The text seems very accessible and extremely comprehensive.

The goal for tomorrow will be to read a little more about the Gouy effect and Laguerre-Gaussian beams, re-read articles from last week, and meet with Dr. Gallot or Antoine to see if I am headed in the right direction.

Saturday, June 6, 2009

THz Beam Propagation Measured Through 3D Amplitude Profile Determination

Which was the name of the article which I spent some time today reading about. I spent all of today reading through this article from a group at Oklahoma state from 2003, another article from a Japanese group in 2001, and various online sources.

The 2003 article is an account of how this group tried to measure a THz beam using a 3D amplitude profile determination technique. I found this useful in helping me tie in all of the information that I have been reading about. I reviewed material on Gaussian beams, complex EM wave representation, beam width and radius of curvature. The article was useful most in the sense that I was able to read of exact experimental design, why certain things were used, and what results were found using said methods. Also, the critical angle for GaAs interface which is ~16 degrees, which is consistent with what I have already read/heard.

The method used for this experiement involved measuring r_s and r_p, which are the Fresnel reflection coefficients. Recall the Brewster angle, or the angle at which there is zero reflection for the P waves, which was utilized in this setup. From the article, "beams with arbitrary spatial variations can be described mathematically as a superposition of Hermite-Gauss modes for Cartesian symmetry or Laguerre-Gauss modes for cylindrical symmetry." This 2003 group used the Laguerre-Gauss technique because of beam shape. I think that I will be using this same sort of approach for my work.

The article had much more in it to offer, but for lack of my own comprehension, I will talk about it next week after catching up on reading this weekend.

In terms of reading, Dr. Gallot has lent me a monograph by Mittleman, which is essentially "the" book on THz and also Antoine has leant me a book on photonics. I would like to skim through both of them either by Sunday or Monday. On that same note, we have a cocktail party at ENSTA in Paris on Monday so I will just do work out of the apartment (no point in spending two hours going to and from work to stay there for a few hours).

Finally, one more thing which occurred on Friday was a talk given by Dr. Steven Girvin from Yale about "Quantum Money, Information and Computing". It ended up being a pretty interesting talk (and actually answering some questions I had from last semester).

Gaussian Wave Profiles and Si Wafers

This is from Thursday, June 4th, as I am late on updating for that date.

Today I spent the morning with Antoine, which is a student who I will be working under for this project. We went over some basic things such as how data is collected and how everything is analyzed. This included looking at sample signals on his computer and getting a feel for what data collection might be like. We spent more time with the mathematics, though.

The basis of what we talked about was the Fourier transform and what certain results might occur when performing a FT on certain functions (for instance the cosine function). This included how we are able to combine and separate out the frequencies when we do spectroscopy. From what I understand, a FT on f(t) will give us F(freq), which is an integral along the real axis of f(t)*exp(-2*pi(*nu*t)dt.

We also talked about different convolutions involving Gaussian curves enveloping sine/cosine signals. We may understand a convolution to be the integral of the product of two functions after one is reversed and shifted (wiki definition). This is useful in understanding how to get a spatial profile of the beam and why we may get a certain thing. Basically, most laser beams have a Gaussian distribution of intensity or electric field amplitude as a function of distance for the center of a cross-sectional disk of the beam. Within this distribution are the sine/cosine waveforms which describe the propagation of the actual THz signal. One characteristic of the THz signal is that we are limited to frequency by the closeness of the Gaussian beam width and actual THz beam width. This limits us to a 5fs pulse, and that seems to be the limit as of now (though research on this is needed to confirm). Finally, we typically experience a THz signal which has frequency bandwidth greater that the maximum frequency, which is not very common.

It was next possible to look at sources of THz radiation and another review of how we create/analyze the beam.

From Antoine, I was told that my focus should be on three things:

1. Determining the shape of the beam
2. Trying out a technique involving (I think) a non-THz laser and a Si wafer (which I will mention soon)
3. Using a speaker to measure the beam's spatial dimensions

The technique that we talked about with the Si wafer is that a THz radiation is incident on a thin Si wafer. The semiconductor is changed to a metal (because of the excitation of electrons to the conduction band) and the light passes though. What I need to investigate is what happens if a laser pointer shines a dot on this disc. From what I understand, we expect the THz radiation to come out of the other side of the wafer at only the point where the laser pointer (again, different than THz, I think). This results in a thinner beam with diameter approximately the size of the laser pointer beam.

The last thing that we mentioned together was the use of a speaker to move a set of reflecting mirrors back and forth to let the computer sample the beam point-by-point. We only mentioned this and I did not look it up yet, so that is one thing I need to do.

Finally, I had a chance to go into the lab today and look at a sample of data off a Si wafer. What we saw was a time-domain profile of the wave reference beam and then the reflected (and flipped) wave off the surface of the sample.

Other news for the day: I got my badge and spent the rest of the day reading over material.