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


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.

Thursday, June 4, 2009

First (real) day of work

Today (Wednesday) I spent the afternoon getting set up with my desk and new French laptop which has all the keys in different places. Yesterday does not count for work since we had a nice long picnic and then could not get our badges for lab access/cafeteria.

The rest of the day consisted of talking about THz generation and detection with Dr. Guilhem Gallot, who I will be working under for the next two months. The material we talked about helped out with my understanding how the basic laser set up of my lab works. The generation and detection works just how I mentioned in the powerpoint presentation last Friday. Generation happens with two electrodes placed on a semiconducting sheet held at a potential difference. A pulsed fs laser creates charge carriers in the semiconductor (transition from valence to conducting band). These charges accelerate from the two electrodes and we get THz radiation.

The radiation is not really "aimed" in a single direction and so a lens is used to focus the beam. Detection works in a very similar way. We have two metal electrodes set on a semiconductor (by the way, this is usually GaAs, and is typically prepared in low-temperature conditions) which look almost like an "H" with a gap in the horizontal bar connecting the two vertical bars (of the H). This is not kept at a potential difference. What we do is have a reference THz beam which is aimed directly at the incoming beam we want to measure. This whole setup is on a device which essentially steps to take a range of measurements. The measured wave and reference wave add together and we have interference. The "stepper platform" allows us to scan point-by-point what this new wave is and then the computer builds our signal for us.

Also note the detector measures a photocurrent which is amplified with a lock-in amplifier.

We also talked a little about THz spectroscopy and how we would get something such as an absorption spectrum by removing the reference spectrum from the measured. This can be used for solids, liquids, and gasses, and seems pretty straight-forward. Along with this introduction to THz spectroscopy, we mentioned the Fourier analysis which goes into the data aquisition.

Near-field was the last thing that we talked about. Basically, we use near-field to attain better spatial resolution of our sample. It works by blocking the laser with a sheet that has a pinhole aperture that allows only some of the light through. We then place the sample very close to this aperture and we use the evanescent light waves to probe the sample. The draw back to this technique is loss of a lot of the beam due to the small aperture.

Finally, we talked about what I should be doing for part of my time this summer. We mentioned using one of the three setups in the lab to try and look at cells (of what type, it was not mentioned). The idea is to deposit a layer of cells on a Si wafer and measure the absorption and transmission of THz radiation through said cells. I also am asked to look at a paper which describes a technique used for profiling a THz beam using optical transmission modulation in Si.

Right now it stands that I would like to get a lot of reading/reviewing done before getting in the lab. My main focus is on understanding techniques in the spatial profiling of the THz beam and on the Fourier analysis.


Just to make sure this is working...