Today was my first day in the lab. I got here about 9, and Dr. Metcalf was there a few minutes later to open the door to the lab. There are 3 other high school students here. Jon and Danielle are Simons Fellows, and Ani is a commuter. We spent a good part of the morning working with different shaped lenses to analyze their focal lengths and whether they form points or lines. It was pretty sunny out, so I got a rather bad burn on the back of my neck, but it was worth it. Lunch at the SAC was good, almost Stanfordesque if not quite its equal. The Simons tour showed us the athletic center. In the afternoon we had a lecture on "A Proposed Electric Dipole Moment Measurement With Radon". The research team is attempting to show that the distance between the poles of an electron is less than the accepted epsilon value of 1 x 10-27, which would contradict the Standard Model. Either that or I didn't understand it.
I got here about the same time today, but Jon was already sitting inside, which was nice because the door was unlocked. After transcribing the notes from yesterday, Ani and Danielle got here and we started to work on determining the angular diameter of the sun (0.5 degrees). That took a few hours, largely because most of our measurements were wrong. There was a fire drill at the SAC, so we lost Jon and Danielle, but Ani was there. The SAC has really, really good tapioca pudding. Good pizza too. In the afternoon we determined the relationship between focal length and focal point diameter for the glasses and magnifying glass lenses.
Diopter = 1 inverse meter.
OH...burning holes in paper is fun. Burning holes in my hand is less fun. I've gotta be more careful with those magnifying glasses.
I got here this morning to work on coding. Danielle and Ani were on computers. Jon came in a few minutes later. I showed Danielle and Jon how to code their bios and journals, then worked on my own, which you're reading now. I had to look up how to set the anchor for the top link, but other than that it was fairly straightforward.
It's nice to have the vending machines upstairs whenever I need some quick food. Yum.
We spent the rest of the morning fixing our measurements for the diopter-focus length-focus point size relationship. The measurements now correspond much more closely to the proper line on our graph. Jon and I used some of our spare time to talk about good homestarrunner.com Strong Bad emails, which was fun. For lunch Ani and I went to the SAC while Danielle and Jon were at a lab safety requirement for Simons students.
During the afternoon Metcalf gave us a lecture on physics history that explained theories treating matter as a wave. Apparently light is a wave on Monday, Wednesday, and Friday, and a particle on Tuesday, Thursday, and Saturday. Your choice what it is on Sunday. Also, if you shove a frog through a grating it will behave like a wave, and fringes will be apparent. But that's not what the point of the talk was. The whole talk explained the idea of momentum being a constant in collisions, which leads into an introduction to laser cooling. Dr. Noe stayed afterwards so we could make a Lecture Wish list, schedule events, and discuss some ideas we had questions about or were interested in.
We need to make a shrine for Yiyi. That's just too many awards to count.
w007! I am now officially titled Penguin, master of Linux. Notice how all the linked journals look essentially the same. That's because it's all using my coding. I think that the FDA should declare Linux a controlled substance, because I'm getting addicted ^.^
So I spent most of the morning coding. Jon has started using emacs for his text editing and html coding, but I prefer the GTE (Ghetto Text Editor), known to Linux as "pico". Being able to view my source code using Mozilla really helps.
For lunch I ate pizza and soda in the conference room with Ani, Jon, Danielle, Lidiya, Yiyi, Azure, Dr. Noe, and Dr. Metcalf. There were many conclusions drawn, among them:
After lunch we were still hungry, so we went dowwn to the SAC and freeloaded some unused catering food out of the auditorium.
My afternoon has been spent programming more HTML, setting up my Weblink page with useful information for future reference and note-taking, and modifying stuff that I feel like modifying.
I'm exhausted from watching the marathon classic 13-inning Yankees-Red Sox game yesterday, but it's Friday and Fridays are awesome. :p
So anyway, I got here and the lab was open but empty, so I sat down and started to look at style sheets for HTML. It's ridiculous how much time I spend learning coding, but it'll be worth it when I'm the only one who understands how to make my web pages work, and that will really help me stayed organized during research. Which is something I need help doing...I have no organization skills.
I was reading Jon's journal and he said something about a diffraction grating that combined single-slit and multiple-slit diffraction patterns. I should ask him about that. I'm disappointed that he couldn't solve the Towers of Hanoi puzzle though. Meh. At least his inverse radius-tangent relationship is right.
At 11 we had a lecture from Dr. Metcalf. The lecture continued his explanation of laser cooling, explaining Heisenberg's derivation of the Heisenberg uncertainty principle, the concept of optical molasses having a cooling effect on particles where p is positive, the role of Doppler shifts in laser cooling, and the relationship between the value of δ in the incoming laser beam wavelength and the decay time for an excited-state electron excited by said beam. And Ani, if you say that light is a particle on Fridays again Metcalf is gonna kill you. :p
After clam chowder from the SAC, Jose taught us about CCD cameras, which Maanit Desai used in his coherent backscattering project. We used the camera to take pictures of me, but we forgot to save them so I still don't have a picture on my main page.
So, for future reference:
It was definitely a good week. I've learned more HTML, I understand Linux, and I'm able to get through a physics discussion without feeling dizzy. I still need to find out why Dr. Noe said I'm interested in laser modes, but I'm sure there's a good reason I've overlooked. I know I'm going to learn something in any case.
OK, first things first. The Laser Center was closed today because they were waxing the floors, so we spent most of the day in the library. My routine consisted of rading through articles until I recognized a word, then looking up that word and writing the definition down. Unfortunately it was very time-consuming since I don't know that many words that I haven't already found the definition of (mostly because I don't know many words to begin with). I did find the meaning of anisotropic, so now I have a slightly better understanding of the setup described in Tim Chupp's lecture.
I also understand why Dr. Noe said I'm interested in laser modes. He was talking about longitudinal laser modes, which explain why power oscillation occurs, which also makes my project idea obsolete. Back to the drawing board.
Danielle...this is not how Linux works:
danielle@laser:~$ cd publicDanielle...you have broken the first commandment of Linux according to Penguin: Never make stuff up if you have no idea what you're doing, ask Penguin instead. Never do this again, or we will laugh more. The Penguin has spoken.
Hmm..what else happened today...oh, I read in Physics Today that the fine-structure constant (of which I only know 1 ⁄ 137.035) was brought into question in 1999, but has since been brought back out of question. Something about quasars and quantum physics and stuff. Ani solved the Towers of Hanoi in something like 7 minutes, partially because he developed these basic algorithms for moving the smallest x rings as stacks. Reminds me of Tyson Mao, on of my RA's from EPGY last year.
Further investigation into what longitudinal laser modes actually are has led me to the following finding:
Taken from Laser Machining Processes on the Columbia University website. Surely laser cavity is also very important for a laser in many other aspects, for example, its dimension decides the longitudinal laser modes. Then what is a laser mode? Generally speaking light modes means possible standing EM waves in a system. The number of modes in this meaning is huge. Laser mode means the possible standing waves in laser cavity. We see that stimulated lights are transmitted back and forth between the mirrors and interfere with each other, as a result only light whose round trip distance is integer multiples of the wavelength l can become a standing wave. That is: m = 2L/(c/f) =2L/l , or f = m c/(2L), D f = c/(2L) Where L is the length of cavity, c is the light speed in laser cavity, f is the frequency of standing wave, l is the wavelength, m is an integer, D f is the frequency difference between two consecutive modes. The number of longitudinal modes may be very large, it can also be as small as only a few (below 10). If we intersect the output laser beam and study the transverse beam cross section, we find the light intensity can be of different distributions (patterns). These are called Transverse Electromagnetic Modes (TEM). Three indices are used to indicate the TEM modes, TEMplq, where p is the number of radial zero fields, l is the number of angular zero fields, and q is the number of longitudinal fields. We usually use the first two indices to specify a TEM mode, like TEM00, TEM10, etc. Clearly, the higher the order of the modes the more difficult it is to focus the beam to a fine spot. That is why some times TEM00 mode or Gaussian beam is preferred. |
Yeah...that answers a lot of my questions. Plus that links to a fairly extensive glossary of basic laser terms - all nice things to have in my weblinks - and the very next page I found was Alex Ellis's, which has a good deal of information on transverse modes and multi-modes. Internet 1, Physics Library 0.
I finished the notes from Alex's page today. I'm going to lay off the multi-modes until after I grasp the TEM and LG modes.
Today Kiko Galvez visited us. He is a professor at Colgate University and has access to lasers more powerful than what is found here in the Laser Teaching Center. As a result the optical traps he worked with were significantly more powerful and sophisticated than the ones created here. In the afternoon, after pizza, he gave us a presentation on "Light Beams in High-Order Modes: Optical Phases in New Landscapes", which was interesting to say the least. Galvez was combining non-collinear donut and HG00 beams to create a spiral, among other things, but the work involved Gouy phase shifts, dove prisms, and multiple interferometers operating one within the other. Galvez also demonstrated how dual-slit and single-slit diffraction gratings combine to produce an even-odd pattern from the dual slit result being limited by the single slit envelope...at least that's what I got from what he was showing us. Most of the talk was devoted to laser modes work, which is my thing,. so it was definitely a good day. Plus I got to gorge myself on pizza :p
I'm not going to be here tomorrow, but I've already told Dr. Noe a number of times, so telling him again is more likely to get on his nerves. I'll just tell someone to remind him tomorrow in case he asks where I am. See ya on Monday, people.
This week was just as much fun as my first one, but in just three working days I've accomplished so much more. It's hard to work without knowing what I'm interested in, but that's not a problem anymore. Turns out Dr. Noe knew I was interested in laser modes before I realized it. Thanks for pointing me in the right direction. Alex's page was really helpful, and I still have more stuff there to look at when I progress further. That's a great addition to my weblinks, which have really grown in the area of laser modes. I found a good glossary to put in there also.Reading and studying a lot have helped me to understand the topic of a lecture when I walk in, so I can follow the speaker at least most of the way through, and in some cases all the way through. Life is good :)
Ah, the start of another week at the Laser Teaching Center. And today is Yaagnik's first day with us. He'll probably be up to speed pretty soon. There's also some CSS in our journals, someof which is original, and for some people borrowed from Azure if they don't know any CSS yet.
So basically, we spent most of the morning going over a good part of the information that we've accumulated during the first two weeks. Ani tried to convince us that (-1)^h=0, but eventually he realized his error. After much work we managed to recall the series expansions for sine and cosine. It is most definitely Monday today.
Yaagnik didn't come to lunch today, he went with some of the others, so the four of us went to the SAC as usual. I saw Victor Simoes, who's working as a Simons Fellow somewhere else on campus. I've noticed that the price of junk food there is much cheaper than the price of healthy food, which would explain why the lower classes have worse nutrition than the upper classes as a general rule: They can't afford healthy food. But that's social science, not physics.
My weblinks continue to grow. I've found another glossary as well as a useful site on Helmholtz resonators, which we studied earlier. This information has to come in handy sooner or later, at least for someone. I wish I had remembered it quicker this morning, maybe that would have saved some time in our explanations. At least I didn't mix up the exponents in the series expansions.
In the afternoon I took a lot of notes on coherence of light, which will lead into longitudinal modes and holography, an area I hope to learn more about. I also looked at a blown-up cross-section of a laser in the dark, which was an experience that I imagine would be similar to group hallucinations.
A lot of people's fire alarms went off last night in the dorms, so everyone who is staying here for the summer is extremely tired. So this morning we went to the aftermath of a freshman orientation session and grabbed some leftover food. Yum.
Metcalf gave us a lecture having to do with MOTs, mostly focusing on the angular momentum of a photon. It is a vector quantity with its direction defined by the polarization of the particle. I think I got all the stuff written down in my notebook.
Great site: Practical Holography is a resource I must add to my weblinks ASAP. I've also added some coding references in case I confuse myself. Even a penguin needs some assistance!
So that's why e^(i*π)+1=0:
Jon, Yaagnik, Lidiya and I also did some writing on the board and found:
If the discriminant is 0, then there is only 1 image of an object that can be formed by a magnifying glass. This relationship can be expressed as d=4f. We therefore get:
That's a pretty nice thing to remember...could save me time in the future.
I got to the lab today, and much to my chagrin remembered that yesterday's journal was only half finished. Half-empty, that is. As you can see, that day's entry has now been finished...so down to business now.
Today was the BNL trip for Simons students, so Jon and Danielle were gone for a good part of the day. I spent the beginning of the morning struggling with HTML hex codes. Even with my newly found resources, it was a good amount of time before I figured out why the hex code wasn't working (I checked another resource and found the proper code). My style sheets are working a bit better, but they still aren't fully functioning. I can get around the broken parts though.
Important things I've found today:
In the afternoon Jose gave us a talk about how a laser works and different laser modes. Because I've been doing my reading, I understood the talk and actually knew about a lot of the stuff that he was explaining.
Ani: "I've always wanted to memorize the lanthanoids". Me too, Ani...me too.
Happy birthday Pat!
This morning me, Danielle, Ani, and Yiyi went to the SAC for food for about an hour, then I went back and fixed the style sheets. That's right, now everything is colored without me having to use a bunch of different tags, and when you hover the mouse over a link or text it changes color! w007! I put in background music, but I'm not sure if it's working...I'll have to go home to check because I don't have speakers hooked up in the lab.
Note from bathroom: λ sucks, θ rules...and ψ rulz!
For lunch we had pizza and had lunch with a former Ward Melville student. Ani commented that "physics has been very good to me". We all stated 6 different areas of interest within optics, while Dr. Metcalf tried to cause trouble 6 different ways. I got stuck at three or four for a while. Later, Dr. Noe put some CoffeeMate in a fishtank and showed the difference between scattering and multiple scattering, as well as the polarization shifts due to cavity expansion and mode switching that are observed in a HeNe laser. He brought up a project idea for me involving a heat-feedback system to stabilize a laser, which I am now very, very interested in. So for tomorrow, I'll try to find some information on heat-feedback systems, fix any CSS that might still be broken, and then maybe talk to Dr. Noe about moving forward with this project idea.
Last night I got a copy of Newton's Principia, which is definitely awesome. I also spent some time thinking about what Dr. Noe as talking about. I think that if I put a polarizer in the beam's path, and I have some sort of laser I can program and some sort of power sensor, I can program the heater to heat the laser to a temperature where the polarized beam is as close to zero intensity as possible, which would mean that no light is passing through the polarizer. Therefore, all the light would be polarized perpendicularly to toe orientation of the polarizer. It must therefore be light in a single mode, because any adjacent modes would pass through the polarizer and be detected.
This morning we went to an information session that Dr. Rafailovich had invited the Simons students to, but we quickly found that it was directed toward the Garcia students, so we didn't stay there very long. Yiyi says that anyone with a 6th-grade reading level can understand the Intel paperwork, so I'm not too concerned about dealing with that when it comes up.
Dr. Noe: "What are you smiling about?"
Danielle: "Linux."
Lunch was good, except for a brief rice shower from someone, but I'm not going to talk about that because it probably wouldn't be appreciated by said person. In other news, I talked to Mrs. Schoch and gave her an update on the situation in the lab. She said that sometime later on when my project is actually under way, she'll come in and take pictures and stuff, which I think is cool. Pictures are definitely useful for PowerPoint presentations, probably for posterboards also.
So I went and talked to Dr. Noe about the project. He said that the problem with the idea is that the heater can't sense what side of the gain curve, so any deviation from the mode would have an equal chance of being made worse. That's not good. So I need to figure out some other way to do this...which means I need to go learn more about longitudinal modes and the differences between ones that are adjacent to one another.
What else did I do today? Well, I took the "h4" tags out and replaced them with "p" tags that I defined in my CSS. I also defined quote tags that I then implemented in certain points throughtout this page.
As far as physical work, well, today I started that too. You know, I mean actually moving stuff around. As in stuff that I'll probably use in my project. We cut a square of Polaroid and put it in a rotation stage, then put the stage on a stand. That's about 3 minutes of work plus looking for stuff, but it's still progress. Tomorrow I'll...wait, tomorrow's Saturday...that's my birthday! w007! So I'll be 15, and I'll add the photodiode and the HeNe laser to the setup, and then we'll really start working.
I've finally achieved my goal of getting a project idea. That and learning CSS have me pleased at the moment. Now that the idea is in place, I can start ot move forward with my research...and that is definitely a good thing. See you all on Monday.
So the morning went well today (I got an email from China that I was waiting for). People were their usual (albeit slightly sleepy) selves, with the usual ribbing about the usual topics at the usual times. Dr. Noe got here about 10 and talked to us (minus Danielle, who was in the library) about our progress and about how different topics are interconnected.
About noon I realized that I hadn't eaten since lunch on Sunday, which prompted an intense, overpowering urge to eat anything edible in sight. Unfortunately, I was alone in experiencing this insatiable craving for all things palatable, and as a result had to wait until after 2 in the afternoon before I could appropriately deal with the situation at the SAC. In the meantime, we built a Michelson interferometer. Fun stuff.
After lunch, I returned to the lab (or cave, depending on your perspective) and proceeded to try and get a hold of a computer. It took a really, really long time, but apparently I succeeded, because there is an entry here. Unfortunately there isn't much coding for me to do at the moment. Hopefully soon I'll find it appropriate to start learning LaTeX, because I want something to do besides read. Typing and coding is more interesting than leafing through journals. Not that I don't like journals...but I don't like finding one relevant article after reading through 5 journals, only to find that I can't begin to understand what the article is talking about. Well, I'll talk more tomorrow, but right now Jon is on my back and I've got to go. See ya, folks.
I got here expecting to find nothing, but instead I found Azure working with Paint and a polarizer set up already for me. Good stuff. It seems that Paint on Windows 95 doesn't use Ctrl-A for Select All, opting to use Ctrl-L instead. Ctrl-A does some toggle thing with the color box. This seemed to frustrate Azure on a number of occassions. Those Windows people...they'll never learn. But I use a Mac!
So after checking email, Xanga, etc, I went with Ani and Azure to go get free food at the SAC, only to find that we were late today. Apparently our amazing hobo senses didn't come through in the clutch this time. Oh well. I got apple pie from the vending machine though. Good stuff. After that I went back and started working.
The REU tour came through today. I was showing them how adjacent longitudinal modes in a short-cavity laser are perpendicular to one another, but the polarizer was at the wrong angle so it wasn't working at first. Rita told me that the photodiode in my setup can determine what side of the gain curve the laser was erring on because it uses derivatives. That's something I need to do follow-up research on. If that's true and I can somehow integrate that into the system, I can save a lot of time that would otherwise be used to work around that fact.
Danielle was doing her "shooting-myself-in-the-head" gesture during lunch until we pointed out that after the first gesture, she would in effect be prevented from repeating it because it's simulating shotting yourself in the head, which leads to death, and ignoring that fact removes all meaning from the gesture. Besides, her gesture doesn't really get the point across that well.
Taken from Azure's journal:
This is what a normal person sees:
This is what physicists see...
So that's what she was doing earlier in the morning. It actually looks pretty realistic. And that is the top of a building, in case you were wondering what the picture is of.
At 3 pm there was a MOTs lecture with Dr. Metcalf. It appears now that the actual concept of the MOT is much simpler than the concepts required in order to understand the MOT. The entire structure as a whole is quite elegant.
Today was the tour of the CMM. It was rather interesting after one considers that I'm not much of a bio person. I liked all the high-tech equipment they had, I liked the CCD camera I saw, and I liked that a lot of the labs there used Macs. Plus they gave us food, which made the whole trip worth it. Yes, I'm sure, I would be a great hobo.
I was looking at the Fabry-Perot interferometer setup, and I think I figured out how to get around the whole gain curve problem. If the Fabry-Perot is set up so that when the desired longitudinal mode is reached it is midway between in phase and out of phase, then the intensity of that beam could be used as a point of reference. If the laser starts to slip into another mode with a higher frequency, the Fabry-Perot setup will change in one direction and result in a higher or lower intensity from the resulting beam; however, slipping toward a lower frequency mode will cause the OPPOSITE phemomena to happen. This setup allows the photodiode to send information to the heater based only on the intensity of the measured beam. How would a project like this have any use in a real life application? If a transparent photodiode is used in a Fabry-Perot setup with highly reflective mirrors, and the interferometer setup uses a reference point close to maximum intensity, the longitudinal mode could be regulated with minimal intensity loss. How intense the beam can remain would depend on how close to maximum intensity the Fabry-Perot could be set up for without compromising the operation of the setup. Now I need to go talk to Dr. Noe and make sure I have the right idea.
Lidiya's Fourier talk at 3 was interesting, but I don't think I understood it because it was all formulas and I couldn't remember what the different variables stood for. Oh well.
Once again there was no free food at the SAC. I'm starting to worry that our source of hobo activity has dried up. There's got to be free food somewhere, there's just got to be...
Well, today is Thursday, so light is a particle and we had lunch with Metcalf in the conference room, as usual (Dr. Noe wasn't there because he's away for the rest of the week). The pizza didn't taste quite as good for some reason, but I did make a breakthrough. Or, maybe not a breakthrough, but at least an important step. I decided to go in a slightly different direction: To lock the HeNe into a multimode where both modes are equal intensity. This can be accomplished with a polarizing beam splitter and two photodiodes, preferably transparent or semi-transparent ones, but I don't know if we have photodiodes like that. If thephotodiodes are transparent and we can recombine the beam using an interferometer-like setup with equal path length, then there will only minimal power loss. And that isn't even necessary if the application of the system allows the beam to exit the application intact. The key will be the feedback system: I need to combine elements of a basic on/off feedback system (akin to the one used in an oven) and a proportional feedback system (an example being driving a car: if you go off-line a bit, you turn the wheel a bit to correct it). The feedback shouldn't be so strong that you continually hop back and forth trying to correct errors, but it shouldn't take so long to take effect that the laser goes way out of whack before anything is done to correct it. That will be a challenge, but I'm looking forward to it.
I need to remember to bookmark OptoSigma because I need a polarizing cube beamsplitter and they make one for 632.8 nm HeNe lasers that costs under $200. Good stuff.
Jose's talk on laser diodes was interesting. I didn't realize why the beam from the diode diverges so rapidly until now.
Ani (speaking to Danielle): You need to exaggerate a bit, like, if you said that these 6 guys were blocking the lane and it was like the Berlin Wall of swimming pools...
I read Victor Kim's abstract, and his project sounded eerily similar to mine. Then Dr. Metcalf said that Victor Kim never actually made much progress on his project. That's good for me, because now I don't have to alter the project...hopefully.
In the afternoon I got another piece of the puzzle that is my project: I borrowed a polarizing beamsplitter setup from Metcalf's lab. Good stuff. We also looked at screensavers and I read some basic electronics stuff out of a textbook.
My project really shouldn't be changing that much after this. I think that by now I've finally focused on a particular idea, I have an idea of a setup for my project, and I'm starting to get the materials I need. Next week the goal is to get everything set up and understood in time for Laser Sam. Adios, amigos.
It's that time again...reading time. Take a wild guess what I did today. That's right, I read. Well, that's not all I did (I did have lunch look at some infrared imaging, and watch Ani fiddle with the optical tweezers setup), but that's most of what I did. Since I haven't actually taken any sort of course dealing with electricity and electronics, I figured that would be a good thing to know about when constructing these circuits. So I spent most of the day reading from Sam's Laser FAQ and looking at physics textbooks to learn about that sort of stuff. I found out that I actually did know a little bit, but that I still didn't actually know that much. So in conclusion, it was a good idea, and I learned plenty of cool stuff that I didn't know this morning.
Danielle, you can't walk on mercury. The result would be like trying to walk on water: you would sink down until your body displaces an amount of mercury whose mass is equal to the mass of your body.
Funny how every time you start to think you might possibly be getting smarter, something comes along to remind you how wrong you are.
This morning I was working on deciphering the schematics I found yesterday, so that hopefully I can understand how they work when Laser Sam comes. Then Dr. Noe came and asked me to make some measurements to determine the intensity profile of a TEM00 beam from a HeNe. That's where everything went wrong. I'll just summarize and say that nobody should ever allow me near a multimeter again without specifically instructing me on what to do. It was pretty bad. Eventually, after many tries and plenty of constructive criticism from Dr. Noe, I managed to get a couple sets of readings. Unfortunately the whole thing took three hours, so by the time I finished the two sets, I had to leave for lunch. Lunch was good today. On the way back, Yaagnik disappeared for a few minutes. Everyone else assumed that he went through Harriman, but I'm taking the Calvin-and-Hobbes approach and concluding that his gravity bill payment was a few minutes overdue, which would account for the brief disappearance.
And then, suddenly, I figured out how to work the whole measurement thingamajig, and by the end of the day my measurements of the beam were fairly close to a Gaussian...but not quite there. I'm gonna fix that tomorrow.
Oh, I'm getting the new TBS CD today! :) But that's not important for the lab. What is important is that Dr. Noe had some ideas about why my beam measurements might have been wrong, which leads into a bunch of other cool things I can do. Unfortunately, it involves calculus. -Not- cool stuff. I really need to learn some calculus.
So I made some more measurements and all of sudden my new graph is really, really accurate: A full order of magnitude more accurate than the previous graph. Good stuff.
Laser Sam is coming tomorrow: Hopefully I can figure out those circuits and then talk to him about setting a modified version of that up. If his site is right, he's never done it before, so maybe he's been thinking about doing that, which would be REALLY good stuff.
Pizza and Laser Sam in one day...yes, it's true. Today must be a good day.
This morning I tried to take the off-center measurements for the beam width/intensity figures, but the setup got knocked off-center and created a nice little platoon of problems to begin assaulting my patience. My patience decided to take cover in a shrubbery. (I took a break)
At noon we assembled for the LTC picture. I can guarantee that my eyes will be closed in whatever picture we end up using.
Laser Sam arrived right after we got back from the picture, and soon afterwards we ate lunch. Azure used my graph in her presentation (I got cited!) and I showed Sam everything on Quattro Pro.
One more thing: We were using a laser that Sam brought which required a good deal of power. The whole setup used a magnet to stabilize itself. You can alter the fields using other magnets, which changes the output. So Metcalf tried to alter the field, the magnet got a bit too close, stuff fell apart and we got our hands off the optical table VERY quickly. That was definitely something I'll remember.
Today was my best lab day of the year. I took the elusive set of measurements for the "beam-width effect on intensity profile" mini-project, and to my surprise the measurements weren't that difficult to get. The alignmemt was still a royal pain, but at least I figured it out. Now to analyze the data...
But that's not the really cool thing I did today. What WAS really cool was aligning an open-cavity laser by eye at different distances. Around 60 cm we lost the TEM00 mode and the cavity stopped lasing, probably because we were approaching a singularity. From 50 cm we could isolate the TEMO0 mode and split it with a hair. As the cavity length decreased, higher-level modes appeared, and changing the angle of the mirror very slightly could alter the orientation and strength of these different modes. We got some pretty cool shapes from the whole setup. Maybe early next week I can recreate the setup and take some cool pictures. Afterwards, Laser Sam certified me as a Laser Aligner, as a joke. Good stuff.
The hospital has a great cafeteria.
Well, I'm less confused about stuff now...am I? Somehow I still don't seem to know what I'm doing. Dr. Noe seems to though...I should probably ask him what exactly it is that he's thinking of, because I have all these pieces in front of me and I can't see how they all fit together. Stupid brain, work! Meh. Until next week, people, keep being people.
My brain is seriously not working today. That is not good. Maybe it's because I got kicked in the head yesterday. Brain, work! *hits head* Much better...
OK, so the weekend was quite excellent, wot wot, down to business. The first thing I found today was on Alex Ellis's page. Something about astigmatic mode converters, when he mentioned using a circular absorber in a open-cavity HeNe to ccreate an LG mode. Good stuff. Suddenly the light bulbs in my head are turning on. Using the circular absorber with our OC to create LG modes, then using that LG to create some exotic laser modes. Hehe. This is definitely awesome.
So the first problem to tackle is how to align the OC as well as possible. I did it by hand last time, but that wasn't at the maximum distance, so I only had a passable HG00, not a near-perfect one, which is what I'm looking for. Luckily for me, Sam strikes again: He linked to a page from Middlebury College where they go over the procedure for aligning the OC as part of a lab assignment.
But then my thoughts turned to the astigmatic mode converter. Alex has already figured out how the thing works, but he didn't really seem to go that much farther in that report. So maybe I can take his work and actually analyze the beam. The problem is that he never got a perfect LG beam, he only got 93%. Of course, I have no idea how well the circular absorber works...but I would expect it ot be better than 93%. So it will depend on whether I can figure out exactly what a circular absorber is, and whether I can use it. If the answers to those questions are yes, then circular absorber it is. If not, I'll try the astigmatic mode converter approach instead. Since Alex did manage to leave behind all the measurements needed for recreating the beam, I can go forward from there.
But suddenly, from the depths of my mind (actually Dr. Noe reminded me, but yeah...) came an old thought: That whole thing I was doing last week. So I went and plotted the data I hadn't plotted yet, spent a couple hours fiddling with Quattro Pro to get all the scaling to align (Dr. Noe helped, it was cool) all my data, and BAM! instant results! Turns out that the scaled graphs have widths that are almost exactly the same (about 2% off or so), which is within the range allowed for by any expected error in my measurements. The results prove that you can calculate the width of a laser beam without going through the center. As I usually say...good stuff.
Simons tour today. Repeat: Simons tour today. All hands on deck.
The equation for the Gaussian intensity distribution is
where I is the intensity at that point, I0 is the maximum intensity on that plane, r is the distance from the center of the beam, and w0 is the width of the beam.
I was trying to explain why taking different cross-sections of a sphere doesn't maintain width. I think I need to work on my math some more.
This morning I didn't do that much. My brain is not working today.
This afternoon was decidedly better. I went to the board after lunch and figured out the equation that defines amplitude for the hemisphere, then used the equation to show that width is not constant in different cross-sections of the same sphere. Good stuff. The laser is warming up, so tomorrow I'll take more measurements for width at a longer distance to verify the manufacturer's provided width values. Next week: LaTeX to write up this summer's findings.
Work, work, and more work. That's what it takes to align these mirrors. But I got them aligned eventually...I think. I got the 25-inch measurements, and not only are they my most accurate to date, but they also managed to verify the divergence figures that we already had. Good stuff...even though I skipped lunch to get it done, it was worth it. And that's saying something.
Later in the afternoon we went to the SAC and emptied Lidiya's entire meal card because it's expiring tonight. Good stuff...really good stuff.
An interesting week, once again. The REU students are gone now, which isn't good, but I think I understand a lot more about Gaussian beams after this week. The measurements are basically done...now I've got to start doing everything else again. Ah, the beauty of deadlines...
Feels weird not having any REU students here...like something is missing.
Dr. Noe came in this morning and announced that he had a "plan" for me. Good stuff. The main part of the plan involves a massive web report detailing all the work I've done so part, plus some measurements I'm going to make dealing with the centers of Lidiya's Airy pattern and of optical vortices. Ya, it's a lot of stuff, a lot of math I don't know yet, but that's part of the challenge. Besides, I get to use LaTeX at last...
Didn't get much done today though. I aligned the setup for my long-distance measurements after much difficulty with small, dirty mirrors. I also inserted a 33K resistor after finding that the 100K gave me voltage readings that were too high for measurements (the photodetector uses a 12V battery and I don't want the readings to approach that). The fringes of the beam are very wide and some of the beam is diffracting when it reaches the edges of the photodetector. It's a pretty cool effect when the lights are out, but I'm not sure how it will affect my measurements. I decided to take the measurements in the dark (using a flashlight to read the multimeter display) because that way I don't need to put any paper around the photodetector. The tape I was using to roll the paper was reflecting a lot of light, which isn't desirable. So measurements are going to be interesting. Ooh, drama...
And just in case I forgot how little I know, another case of Monday-thin-lens-forgetfulness managed to remind me that I know nothing.
Early in the moning Dr. Noe and I finished aligning the 93.5" setup, and I began taking measurements of the beam. This beam was much wider. Unfortunately, it took me ages to find out because when I plugged the data into the spreadsheet on Quattro Pro, I messed up one letter and ended up using intensity in place of detector position when calculating the line of best fit. The result was a really funky-looking graph with two peaks over the points where the intensity is equal to 1/e^2 times the maximum intensity. It was a nice graph, but not what I was looking for. It took me more than an hour to realize what I had done wrong, but eventually, after I figured it out, I corrected the error and found that Dr. Noe was right: A Gaussian intensity profile graphed on a logarithmic scale produces a parabola.
This morning I finished analyzing all the data by creating and recreating graphs of just about everything. After Dr. Noe checked them, I added some new calculations for width and mapped them against the spotsize graph. It appears that the beam diverges slightly faster than specifications, which is due partially to the smearing caused by the pinhole I had over the photodiode, but mostly due to the fact that the laser doesn't have to meet specifications exactly. All the information was copied over to a floppy before lunch. The floppy drive on the DOS computer is broken so I had to use pliers to remove the disk.
The next order of business is to analyze the center of an Airy disk, which Lidiya said is near-Gaussian but which Dr. Noe says is a Bessel function. A Bessel function of the first kind, Jn(x), is defined as the solution to the Bessel differential equation,
Here is a graph of Jn(x) for n={0, 1, 2, 3, 4, 5}.
Oh, actually, before that I'm creating a web report on the beam profile of a HeNe laser. This will contain my work so far, and eventually the work I'm doing the rest of the summer will be added as well.
I finished the web report by 11 this morning. Looking at the source code for the main projects page helped me figure out how to make nice, readable tables. Good data helped also. The presentation went well. Dr. Metcalf mentioned that if you take cross-sections using a razor blade at intervals of 1 micron, the resulting graph is an integral, which is pretty cool. I'd like to do that in the future as well. But Mrs. Schoch is coming tomorrow...I have to get ready for that first.
I can't believe I didn't remember to write this formula down here:
When scanning on-axis (centered), y=0, so the equation can be written as:
When scanning off-axis, y≠0, so the equation becomes:
where K is a constant equal to y2.
The reason that my off-axis intensity profile can measure width across the center is because:
It took me ages to realize that, but somehow Dr. Noe has managed to drill that fact into my head. That doesn't work with a hemisphere or just about any other curve.
In other unrelated news, the Karo-syrup-refraction-in-a-fishtank demonstration is starting to turn into a biology experiment gone bad. There is definitely something growing in there. Maybe we should take a sample down to CMM so they can analyze it or something.
The Airy disk I'm going to look at next week should look something like this:
Just for the sake of linking to it from my journal, here is my beam report.
Mrs. Schoch came to visit today. I showed her the beam report which she says is mostly good but needs a few small fixes in terms of organization and references. Most of my references will be to papers containing the equations I mention in the beam report...that reminds me, I need to add these extra equations into the report, because they ARE relevant.
Anyway, I was leafing through Fundamentals of Photonics by B.E.A. Saleh and M.C. Teich, just because it was sitting on the table...and wow. Just wow. It's like equation heaven, except that in heaven I don't think they have to worry about Gaussian optics and things like that. But back to the point. Under intensity in Chapter 3.1.B, the first sentence is:
The optical intensity I(r)=|U(r)|2 is a function of the axial and radial distances z and ρ=(x2=y2)1/2,
I(ρ, z)=I0[(W0)/W(z)]2exp[-(2ρ2/W2(z)],
where I0=|A0|2.
Yup...it's heavy stuff. But Gaussian optics is the most interesting physics I've ever come across. Sure, maybe I really don't know any calculus at all, but if someone explains a concept I think I can understand what they're talking about. I eventually understood that integral thing that Dr. Metcalf was describing yesterday, so that's an example. And finally I know that exp means e^, so that's another thing. I'll grasp calculus by next year, and that's soon enough.
It's funny how just a couple of days can turn what appeared to be very little progress into a completed web report. I'm still not sure exactly how it happened. The whole week was a big blur to me. Hopefully I managed to take enough of it in as it went by...
From Fundamentals of Photonics:
The total optical power carried by the beam is the integral of the optical intensity over a transverse plane (say at a distance z),
∫ | 1 | |
I(ρ, z)2πρdρ | ||
0 |
which gives
P=½I0(πW02)
This morning Yaagnik and Jon got some liquid nitrogen to use for aligning their interferometers. Fun quickly followed...although we did have to be careful not to get any of it on the optical table. Using the nitrogen fog we were able to see the beam pretty well, but I'm not sure how much that helped with aligning everything.
More research this morning...
The Airy pattern is created by having the beam pass through a circular pinhole, which results in a Fraunhofer diffraction pattern. Here is a page explaining Fraunhofer diffraction for a circular aperture.
I(r)∝ |
|
2 |
is the description of the intensity profile of the Airy pattern, where J1(x) is a Bessel function of the first kind. (Notice that I've finally figured out vertical fractions! They're a real pain to create though...tables and special CSS and way too much coding).
The Bessel differential equation is:
x2 |
|
† |
|
†(x2-m2)y=0 |
OK, good, so now I know how to code vertical fractions without having to refer back to the source code I learned it from. This will help because now I won't have the funky LaTeX text that doesn't work well with my regular font. Plus I can go back and rewrite the LaTeX equations from my beam report in HTML so that they look natural.
This morning I got to work on setting up and aligning the Gaussian intensity profile setup using two mirrors for a total distance of ~400 cm. Using a 1.8MΩ resistor I took the intensity measurements at increments of 5μm. Then I went to get lunch. Mmm...turkey bacon swiss melt...
Dr. Noe, Yaagnik, and Ani used the interferometer setup on Jon's side of the table to show cavity expansion. As different longitudinal modes swept across the gain curve, the fringes of the interference pattern changed, sometimes going from in focus to out of focus, sometimes moving in and out...it was very interesting. One of the coolest things I've seen all summer.
My graph of the intensity profile @ ~400cm is nearly Gaussian, except for a minor aberration near the top of the curve. which is probably due to imperfections on the surfaces of the mirrors I was using. In any case, the aberration doesn't affect the curve all that much. I added the width figure to the spotsize graph and then used my data points to determine what the correct beam width at d=0 is. The manufacturer specifications say that, at d=0, the beamwidth is 0.35mm; I found it to be 0.31mm. All my measurements and calculations from today have been put into an updated version of my beam report.
Today I spent the entire day converting my pages to XHTML. It was very time-consuming...for example, there were 900 XHTML errors in my journal after I specified XHTML Transitional as my DOCTYPE. But I've almost finished converting all my pages: The only ones that need work are my fortune page and my contact page. Everything else is finished...I think.
Using a 50 micron pinhole I created an Airy pattern with the HeNe beam. The pattern is extremely clean as far as I can tell. Unfortunately since to day is my last day here this summer I won't be able to make intensity profiles of it any time soon, but it's a nice pattern to see nonetheless. I now understand how Lidiya was able to isolate the Airy disk: Since the first ring around the Airy disk is virtually 0 intensity (and theorietically it IS 0 intensity), there is no diffraction around the edges of the second aperture if it is set up correctly.
Using some liquid nitrogen I was also able to view the Airy pattern through the fog in three-dimensional space, which was absolutely amazing. At some points I was able to see a half-dozen maxima on all sides. The demonstration is an excellent way to see beam propagation in 3-D space.
Dr. Noe took us to an Indian restaurant today for lunch. Indian food is relatively spicy, and although this fare was relatively mild as far as Indian cuisine is concerned (or at least I think it was), the tastes were stillmore than agreeable. I definitely need to get my hands on some more of that, particularly the chicken curry that I had.
So, in conclusion, I'm leaving after today, bound for band camp, plenty of drumming, and an opportunity to lose some brain cells through unsafe exposure to videogames. Oh, yeah, and the fact that I need to prep for school, organize all my activities for the fall, prepare for fall concerts, etc...it will still be very busy even with my absence from the LTC. It was a very good summer. I'm looking forward to coming back during the year and next summer, maybe even as a Simons Fellow or something else in the future. We'll see what happens. Bye.
Finally, over two months later, I find myself back at the lab. It's been a long time...8 weeks of school, the entire marching band season (well, almost) is already over. But it still feels nice and comfortable here. Dr. Noe has been sending me emails on a fairly regular basis, some with links to information, others with questions regarding when I'll get back, and others still with updates on what's been happening in the lab. I've even seen some pictures from the trip he and Azure took to see Professor Galvez at Colgate.
The other week I took a trip to the physics library to do some reading. It was worth every minute. I'm trying to figure out what is SUPPOSED to happen with Michelson fringes when the cavity expands. My first thoughts about the subject were wrong. Right now I'm thinking that the fringes fade in and out as the difference in path length in terms of λ as λ changes. It's confusing to me...which is why I have a problem thinking about it. Every time I come up with an idea it makes sense to me until I ask why what I'm thinking is true.
That sort of thinking is troubling, but not as troubling as this.
Jan isn't here today. I spent time using a sodium lamp with the Michelson setup. The fringes were initially hard to get, but after a little while everything was sorted out. Then Azure (who I haven't seen in over two months) popped in. Hooray! After that brief interruption I got back to work and started writing down the readings on the micrometer which resulted in max/min fringe contrast. Going in the direction of increasing micrometer numbers (i.e. 400, 401, 402, etc), I was only able to obtain a few readings before finding that beyond a certain point the micrometer would not decrease the path length any further. This was very confusing until Dr. Noe pointed out that the lever arm itself was stuck. Reomving the lever arm solved the problem. There are a couple of pictures of the sodium fringes - I'm not sure if they're up yet.
Today was very productive. Jan and I built a Michelson, used the short-cavity laser to create an interference pattern that fades in and out as the cavity expands, and then hooked up a CCD camera with a neutral-density filter so that we can take pictures of the fringes at specific time intervals and analyze them on the computer. For less than 4 hours of time in the lab, that's an awful lot of progress.
Wow, it's been a full month since my last entry. So much has happened...PSAT results, quarter grades, and of course a whole bunch of research. To recap:
I've also worked on the sodium fringes some more, and Dr. Noe was kind enough to post the graph that was made of my data, which can be seen below.
![]() |
So anyway, this has been quite the afternoon. Jan got here not long after I did. It turns out that we had made a few (OK, a lot) of mistakes. Actually, I'm lying in parentheses there, we didn't make a lot of mistakes, but the ones that were made messed a lot of other stuff up. The result was lots of confusion which is only beginnig to be cleared up. At least this means I won't run out of work on this project anytime soon ;) Hasta la vista.
Well, it's been a long time. Only working here one day a week does that, I guess. The project has made good progress. Jan and I have 480 pictures of the interferogram, each somewhere around 320 kilopixels. We also have (in addition to that and the sodium work) stuff in Mathematica that converts each picture to a plot showing average intensity of all pixels distance x from the center versus distance from center. Currently we're working on an algorithm to do this for 80 pictures at a time, because otherwise somebody would have to sit at the computer forever to get all the data conversion done. Jan left early today to go to his friend's thesis defense, so I'm here by myself at the moment (Dr. Noe isn't in today). Hey, at least I get a chance to update this.
More news as it comes, folks.
Buenas tardes. It's been a while.
The algorithm was completed not long after my last update. It was also streamlined to make everything run faster. Using the algorithm, the data was processed and as a result was more easily analyzed. Basically at that point the project was completed.
So I prepared a board to practice presenting with and did a few small presentations, leading up to the KPHS science fair (which I won), and then the more important fair, LISEF Round 1, in which I failed to advance to Round 2 but did have a very good time at. It was nice...basically all the judges understood what I was saying, and the questions they asked me tended to be thoughtful ones.
Congratulations to everyone from the LTC who moved on to Round 2. And Jon, your project should have moved on also, just bad luck, I guess.
Rob Hupcher and Zach Ingbretsen were supposed to visit the LTC today, but the visit has been postponed until a later date.
I forgot to congratulate Azure in my journal...congratulations (about next summer)! It sounds like you're going to have a lot of fun.
Things are pretty quiet at the moment (because nobody's here). Something to talk about...oh, I went to Chicago a couple weeks ago (which is why I wasn't here on the 17th) to visit colleges. The University of Chicago was really impressive, and I also liked Notre Dame. The one thing that surprised me was how good the food was at both places. The quality and variety was very good, especially considering the low cost. In a few weeks I'll take another trip up to Boston, and then I should be done looking.
It's beginning to look more and more like Zach and Rob will be able to come next week, which will be nice.
But that's not the important thing that's happened over the last week. My Simons letter came - I got accepted!
I'm going to Boston for two days in a couple of weeks, to finish my college visits. With that out of the way, I'll be free to focus on...tests. Wonderful.
Other random news - I just realized that my school doesn't have an engineering club, or do anything of or related to robotics competitions...really science outside of research group and the classroom is minimal at best. I have Fridays free all year, every year. Hmm. Sounds like a plan.
I meant to update last week, but I (and everyone else) was at URECA for the day, so it was basically impossible. Whatever.
The lab has been fairly busy, with many people visiting plus URECA, and of course I've been busy also. AP tests, the SAT, a backlog of assignments to work on, and no computer (I need to get my hard drive replaced) have kept me somewhat occupied. This should all sort itself out by next week.
My project for this year is starting to take shape. Last summer I had ideas about building a dual-mode-stabilized short-cavity HeNe by splitting the modes according to polarization and then using a feedback system to thermally stabilize the laser. My research advisor at school, Mrs. Schoch, is worried tht the project is too similar to other projects which have been done. Although I'm not sure how many times this has been done, I know that mode-stabilized lasers can be bought as it is, so I'm looking for some application I can further explore using the laser. This will necessitate not interrupting the beam emitted via the output coupler, so I will need to construct a system using the much weaker beam emitted via the high reflector.
What else...oh, I've suddenly found myself very, very interested in Zeeman splitting for no apparent reason. Well, maybe there is a reason, but I haven't realized what my reason is yet.
This diagram of a proposed stabilized HeNe is of value: (Thank you Laser Sam!)
My computer is now back and healthy and operating, although without all the important files I had forgotten to back up. Of course, that latter part of the situation is entirely my fault. Nothing I can do about that. Oh well. At least now I can check my email and do work and that sort of thing.
This week is Azure's last in the lab - she's leaving for Rochester (home) on Tuesday - so we've decided to wrap things up by having her teach me as much calculus as she can in 5 minutes. We did chain rule, trig rules, partial derivatives, and multiple partial derivatives in that amount of time. It was awesome.
Azure is no longer on campus, which feels strange - it means 1 less familiar face in the lab - but also means I'll spend less time talking about things other than physics and more time doing what I'm actually here for, so it's not really a terrible tradeoff.
For the moment, I'm looking at a site that Dr. Noe mirrored some time ago about HeNe stabilization with an iodine cell. It's interesting stuff and although the site doesn't do an awful lot of explaining, it's still very useful. Being able to see pictures of the setup is particularly helpful.
Azure's calc help from last week has come in handy, and my new knowledge made it much less confusing when Dr. Noe talked about the small angle approximation and series expansion for sinθ. Woo-hoo! Less confusion! Now maybe after tonight's concert (school orchestra) I can get some sleep without stressing over work.
I need to look for a RadioShack electronics kit - Azure, you have one - which would be useful for learning what I need to know (with circuitry, that is) for the feedback system project. Dr. Noe says he may be able to get one by next week, which would be VERY good. Good stuff.
I got my SAT scores back: 800V, 800M, 700W. Overall I'm very, very pleased, as I was certainly not expecting an 800V. But enough about SATs.
Although I did spend some time this afternoon searching for food (no, just because I've gone a couple of weeks without using this page as a food blog doesn't mean I stopped eating - I had research during lunch at school today and needed to find myself something to eat), I made decent enough progress today. Dr. Noe gave me Stephanie Lim's paper on HeNe polarization fluctuation, and her laser turns out to be my laser. Because she has ALL the specifications for the laser, I can now include them when I write the final copy of my paper for ISR early next month.
More importantly, my upcoming project is starting to gather some steam. I've spent most of today studying the op-amp, which will be an integral part of my circuit. This background research involved the usual: reading papers, searching for pages whcih explain the function of an op-amp, studying diagrams, et cetera.
A not-so-random side-note: Today in physics (we're in the modern unit) we were studying matter waves, which prompted the question of whether matter waves are EM waves. One source which I found said that they are not EM waves because matter waves need a medium to travel through; however, I found no other source which mentioned that, so I am still trying to confirm that matter waves are not EM waves.
References from the Lim paper: