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.
Monday, June 8, 2009
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).
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.
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.
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.
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