## Journal## Saturday - 22 September 2007Alas! I have data. Fortunately, it is a scan of the proper part of the plastic. Unfortunately, the proper part doesn't seem to deviate much, but I still have to plot all the numbers. They do vary, but not enough for me to see right away. Right now I'm working on my Siemens paper, trying to figure out what to write with such uncooperative data and the like. I must return to my muddle of confusion. ## Friday - 14 September 2007Alas! I have data. Unfortunately, the part of the cracked plastic I scanned did not deviate enough. When I put the plastic in the interferometer, the area of the crack that did form the vortex was not at the very beginning of the slit. So, now I have to go back and collect more data. At least I have numbers for what the plastic looks like where there is no vortex forming. Why do I keep doing these stupid things so close to deadlines? ## Saturday - 7 September 2007It has only been a week since I last came to the lab, but it feels like much longer since school has started. Because of this dreaded school, I can only come to the lab on Saturdays and holidays. Unfortunately. Progress has been very slow for me, in fact, I've taken many steps back today; my data is not good and I have to redo my surface scan. I've kept most of the setup, so all I need to do is recalibrate and make a new cracked plastic. The new one, cracked plastic L is much cleaner than B [the one I used before]. I also have a software problem: my Mathematica CD does not work and Tech Support was closed today. Alack! ## Friday - 31 August 2007Today is the last day before school starts. Ack. I feel as if I am hiting dead ends wherever I go. On the upside, my surface scan appears to be working. On the downside, I need to put it into Matlab and such. Oh dear. ## Tuesday - 28 August 2007Once again, I've been neglecting this poor journal. For the past week, or rather, the past 3 days, I have been preparing and constructing and aligning my surface scanner setup. Although it sounds simple in concept, and I have the happy fortune of following what other students in the LTC have done, it's still tedious to use a laser beam to "scan" over a cracked plastic surface. From this, I can analyze the topology and then the phase of the plastic. ## Wednesday - 22 August 2007For the past weekish, I've been assessing the usefulness of the cracked plastic pieces I made. I posted the photos of the ensuing vortices [or non-vortices: cracked plastic F showed no forks in its interferogram] on my webpage under the "Pictures" section. I'm only announcing this because I did it all by myself without any disaster. ## Friday - 17 August 2007Because I didn't update earlier in the week, I suppose I should turn this entry into a week's worth. Tuesday, Hamsa showed me a bit of Mathematica where I spent far too much time trying to graph something with polar coordinates. [It didn't work...even the example plots wouldn't graph. I have no idea what is going on [or what I'm doing wrong.]] Wednesday was spent cracking pieces of plastic. Yay. It was too hard tto get a controlled crack in the plexiglass, so Dr. Noe and I ended up cracking a CD cover. The optical quality is not so high [things are distorted when looked through], but we can bend it enough to offset the two edges of the piece so that a vortex will result. ## Friday - 10 August 2007Today is the last day of Simons. We had a little reception where every Simons student gave a 2 minute [or less] presentation on his/her project. I think I managed to get mine to under a minute [speaking lightening fast]. Even though the program is over, I'm still coming back to the lab. Tuesday. ## Thursday - 9 August 2007Today is already the second to last day of the Simons program, but I feel as if I'm only beginning to understand my project. Working on condensing my research plan into a 2 minute speech that cannot depend on jargon really helped me conceptualize it all. Hamsa, Danny, and I spent much of the day squeezing all we had to say into such a short time frame [with the help of Dr. Noe, of course]. It really doesn't help any that I'm most likely the first kid to speak because alphabetically my name is at the top of the list. The good part is that I have a nifty "optical vortex" made of cardstock that models the helical wavefront of the beam. ## Wednesday - 8 August 2007Yay. My abstract is finished with very many thanks to Dr. Noe, and it should be posted soon [I actually know how to do it now]. Dr. Noe took Hamsa and me out to lunch to discuss what I should write in my abstract. Several hours later [and a discussion on radially polarized light], the finished product was on its merry way to Ms. Kernan. Today we also tried the 1.5 charge forked grating [generously given to us by Kiko Galvez] for the first time. We could really see the discontinuities in the optical vortices of fractional charge. When we cut the beam with a razor blade, illuminating the side without the phase dislocation, we observed the same for the integral vortices. The vortices appeared as crescents which appeared to rotate. When the side with the phase dislocation was illuminated, something really cool happened: every odd numbered order was an HG-01 mode. This is because of the 180 phase dislocation of the grating. Even order vortices appeared just as they did for the side without the phase dislocation. This is because the charge of a vortex diffracted by a hologram is equal to the incident charge plus the order multiplied by the charge of the grating. So, for even order vortices, the charge is calculated to be an integer. ## Tuesday - 7 August 2007Yesterday and today have been such a flurry of activity; we were preparing for the visit of the Simons students to the LTC. Not only were we cleaning, organizing [and pseudo-organizing: stacking those papers in a neat pile], setting up demonstrations but we were completing our powerpoint presentations for the visitors. After a series of inconvenient and even cruelly humorous computer glitches ["computer is disconnected from internet - click link below for more information"] I finally completed my powerpoint an hour before the talks. The presentations went well; the two other physics-but-not-LTC-kids talked about their really neat projects [perhaps I'm partial to physics in general]. While showing the studens around the lab, Dr. Noe gave a light show by placing a mirror [a broken CD shard] on a speaker connected to a CD player. The music vibrated the mirror so that the laser beam incident on it moved in all sorts of strange squiggles on the wall when projected. Now I'm working on a slightly late abstract for the Simons closing ceremonies booklet. Danny and I [with much revising with Dr. Noe] have already completed an abstract for "Walking the Beam." Now I need to formulate in words what my real project is. It's harder than I'd thought. ## Friday - 3 August 2007Today was the REUs last day. They each presented their projects at the REU symposium and they were really well done. It was interesting to see how much their talks evolved just from their practice run-throughs [and lots of hard work, I heard] last night. Additionally, I've been grappling with how orbital angular momentum [OAM] is conserved in fractional vortices. I feel as if I'm missing some information. If the topological charge, l, is fractional, how then can a vortex of charge 6.3 then appear as a vortex of charge 6? The OAM per photon is l*h-bar. So what happened to that 0.3*h-bar? Once again, more thinking is necessary. And some fiddling around with cracked plastic and optical vortices of unknown fractional charge. Hamsa and I, yesterday, noticed some order 1 vortices along the radius of a cracked plastic vortex. Perhaps the forks we observed from the interferogram are an example of what that fractional vortex business is all about. Perhaps I'm just hopelessly confused. ## Wednesday - 1 August 2007Eek. It's already August. Where did the time go? Anyway, lately I've been reading papers about optical vortices, especially fractional vortices. I just read a Berry paper and understood that a "superpostion of vortices" is even weirder than it sounds. A fractional vortex appears as the nearest integral vortex except when it is a half-vortex. Then, along the axis where forked grating is shifted to accomodate the phase step, an infinite series of alternating + or - 1 vortices. Apparently, these vortices do not possess orbital angular momentum [I read that in another paper], but I think I'm misunderstanding something. As for my project, I'm thinking of one-hundred-and-one things to do to a fractional charge optical vortex. Of course, I have a few modest ideas, but they're so modest I don't even want to post them just yet. More thinking is necessary, it seems. ## Monday - 30 July 2007Today Enrique Galvez, a reseacher and professor at Colgate University came to visit the LTC and give a talk about optical vortices. He brought his daughter who is also going to be a high school senior because he picked her up from the airport [she had just arrived from Peru]. Much of what he said was really clear and understandable to me. I liked learning about how there is really no such thing as a fractional topological charge vortex; it's a superposition of other charges. After the visit/talk, I did some more reading about LG beams and vortex experiments. I hope to start my project really soon. ## Friday - 27 July 2007Today was a continuation of the oodles of reading I'm doing. However, it was interrupted [actually, I willingly wandered into Hamsa's business] by a question about mode-converters. How can a cylindrical lens change the Rayleigh range of a Gaussian beam without changing the location of the focus? According to a paper by Padgett et al. it is quite possible. Unfortunately, Hamsa and I don't know why. We brought the question to Dr. Metcalf [actually, I tagged along with Hamsa] and he told us to come to his group meeting. We went and came back stuffed with new types of information but still not much closer to the answer [i.e. very much confused]. Ah well, I suppose it's time to scrutinize the Beijersbergen paper; maybe I'll understand that. ## Thursday - 26 July 2007I'm still doing a lot of reading of papers trying to understand enough to glean a project idea out of them. Mornings I spend reading at the library [and not printing...as a Simons student, I have no printing priviledges at the library]. Afternoons I spend puttering around and helping Hamsa with whatever is the alignment-problem-of-the-day. Today the Simons students had a lecture/talk by a geophysicist who also happens to be the head of the Stony Brook Honors College. Needless to say, it was all about college admissions. If it weren't for his being an animated person and the pizza, it would have been a very pointless meeting. ## Tuesday - 24 July 2007Today, REUs who are not from the LTC came to visit the lab. Danny and I reconstructed our mini-project setup. [I recently learned "setup" is spelled without a hyphen. I don't know if I like that.] Because I was helping Hamsa realign her tweezers setup, I didn't have to present the project to the enthusiastic REUs. Unfortunately, Hamsa is really having no luck with her tweezers. First the laser was too low and then it was too high. Now she noticed her silver mirror transmitted too much light [losing her power], so I sat with a razor and detached a gold mirror [which is more reflective] from its mount. Tomorrow I need to detach a mirror from its micrometer mount so that she can reattach the gold mirror. As for my own project, I've been reading papers. I've gotten myself interested in transverse laser modes. And optical vorices [which really are Laguerre-Gaussian modes]. I'm hoping I can find something to do with them as a project; my understanding of them is so limited. ## Friday - 20 July 2007YAY! I do believe we're finished -except for the LaTeX stuff that needs to be inserted into the web page]. I suppose I shouldn't be happy until the "under construction" disclaimer is erased, but I can't help it. I intend on doing some serious optics reading next week to find a feasible project idea. ## Thursday - 19 July 2007Danny and I have nearly completed our web report for the mini-project. All we have left to do is one section, the conclusion, insert the diagrams/graphs, and edit edit edit. I understand the project so much better now, after I've written down the explanations for what Danny and I have done. Next time I believe I shall try writing it all before explaining to other people so that I know what I did. ## Wednesday - 18 July 2007Unfortunately for everyone else in the lab, today Danny and I presented our mini-project during the lunch meeting because no one else was scheduled to come. Dr. Metcalf came to the lunch talk and brought up some observations that none of us [including the rest of those who suffered through the presentation] noticed: the zig-zag plot is made up of two sets of parallel lines, and to actually align the beam, it is necessary to overshoot the target, not line the beam up with it. After the talk, I continued writing up the mini-project report that is now a posted shambles. It is an odd feeling knowing that my outline is floating around the internet all exposed. But, since it is a very low probability that someone will read it, it really does not matter the state it is in. I suppose the same holds true for this journal. Nevertheless, I am quite fond of vaguely correct grammar. ## Tuesday - 17 July 2007Today was a very fragmented day due to a Simons [and REU] talk given by Dr. Hemmick about quark-gluon plasma. He equated the forces of the universe to college students and frisbees, chess, and love. Needless to say, it was a very interesting talk; I learned a lot and promptly forgot it. In the lab, I learned more about using the computers here. I now know how to rename picture files and the like. Unfortunately, just like Dr. Hemmick's talk, I don't remember how to do it. ## Monday - 16 July 2007Danny and I only have to do our lab report. Yay. Today, with Dr. Noe nearly walking us step-by-step, Danny and I derived the recursive equations for d1 and d2. It was so much easier than the pages of calculations I did; we only needed to solve for alpha 1 and alpha 2 [the angles the mirror 1 and mirror 2 are moved, respectively]. Then, when we graphed the data using Quattro Pro, we got beautiful graphs: spirals and zig-zags. I expect those graphs to be posted soon under the mini-project section of this webpage- as soon as I figure out how to do it, I mean. The same goes for a link posted here to get there. Now that I think of it, soon will be a very loooong soon at the rate I'm learning how to use this computer. Just using Quattro Pro was something of a challenge. I can see why Dr. Noe likes it; it's so simple there isn't even a mouse. And, the program is so small it fits on a FLOPPY DISK. My powerpoint presentations for school don't even fit on a floppy. Because I told Dr. Noe I would post this bit of embarrassing information: the data Danny and I collected on Friday is moot because we stupidly forgot to measure the distances between the mirrors and pinholes. In my defence, I was going to do the measurements this morning, but Hamsa got to the lab before me and took back her mirrors [see previous entry for more on the lab's mirror shortage]. ## Friday - 13 July 2007I think I may finally be done with my mini-project today. All that is left is analyzing the data and seeing if my recursive relationship fits the data. At first, I thought that Danny and I would have no data because unfortunately we couldn't find any mirrors for our set-up. And, we needed mirrors with mirror mounts because beam alignment is based on making finite adjustments to the to the mirrors. Finally [after repeatedly refusing to interrupt her stuff], we took up Hamsa's offer to use the mirrors from her tweezers set-up; she needs to realign everything anyway because she switched out the current laser she was using for a linearly polarized one. With our laser properly misaligned, Danny and I began the process of marking and moving the mirrors. Marty suggested that we use graph paper to mark the distances the beam moves instead of measuring it with an unwieldy ruler. We did a few trials in this manner, which brings me back to the first sentence of this entry. Consequently, it's Friday the 13th. I didn't notice this until nearly half-way through the day. So much for superstition. ## Thursday - 12 July 2007Today Thien An continued her talk from Tuesday. She spoke about Fabry-Perot cavities. Unfortunately, her talk was interrupted by some rotten algebra: multiplying by the complex conjugate is definitely not the same as squaring an imaginary number. From all of the discussion, I finally understand how a cosine wave can be represented as a power of e. And, how the imaginary component must be accounted for when translating between both forms. Dr. Metcalf, who cured our confusion, said that it is necessary to multiply by the complex conjugate and divide by 2. Danny also derived a matrix that is a much neater representation of the alignment problem. However, he assumed that the sum of the angle of the two mirros is always 0. I suppose this is true if it's a paraxial approximation, but I still think it may be assuming a lot. Maybe it's because it's so clean and simple while my work is clumsy and cumbersome. ## Wednesday - 11 July 2007I tried the new method today to create some calculations descibing what is happening with the mirrors. It seems very long-winded [I opted for rewriting all the algebra], but the solution is simple. It depends on both angles [mirror 1 and mirror 2] as well as on the distances between the pinholes and the mirrors. Everything is measurable which is much better than yesterday's calculation. However, one angle must be greater than another for the recursive relationshp to work; I had to assume some things, and that makes me uncomfortable with my work [I'm none too good with math-y things]. Maybe I derived a general equation that can be used both for properly aligning the beam and misaligning it. If angle 1 > angle 2, the beam converges onto the two pinholes; if angle 1 < angle 2, it diverges instead [which is NOT what someone would want]. ## Tuesday - 10 July 2007It turns out that the method I was using woked. It also turns out that it is based on some distance that is apparent on the diagram but is near impossible to measure in real life. So, I've gone back to using Dr. Noe's idea [I think I understand it better now]. I did way too much algebra but it seems to be working. I now have to"move" mirror 2 some angle to get d2 [the distance from the beam to pinhole 2] to equal zero. Then, it's back to moving mirror 1 to see if there is a recursive relationship amongst my math. ## Monday - 9 July 2007Danny and I have made progress. I was doing some "figuring" today, and I am on the trail of finding a relationship between the distances the beam moves and the angles the mirrors are turned. Later, though, Dr. Noe elaborated on his idea of using matrices to write the equations. It has to do with the translation matrix and the reflection matrix and creating iterations based on what the beam is doing. On another note, I still have no idea what to do for my main project. I have some inklings, but not many. ## Thursday - 5 July 2007After touring Brookhaven Labs [BNL] which was very interesting and enormous in size [thousands of acres], Danny and I finally demystified the mirror 2 problem. Actually, it was more Danny following through on one of his original ideas to treat the angles the two mirrors are moved as independent. My idea of treating them as dependent did not work in the extreme case [I was the graphing-paper sketcher for both cases]. The only problem with Danny's solution is that the "resultant" angles of the two mirrors does not coincide with the mirror 1 "component" before mirror 2. Mirror 2 should not be affecting the angle of mirror 1 before that point. ## Tuesday - 3 July 2007Tomorrow is already the Fourth of July and Danny and I have made very little progress on our mini-project so far. The project consists of mathematically representing how to align a laser beam that is rotated 180 degrees by two mirrors and must pass through two pinholes. So far, we've only managed to figure out the distance the beam needs to be moved by mirror 2 to align it with the second pinhole. Then we get stuck or rather, we go back to the beginning. I feel a bit like we're going in circles and surprised how irritating this simple project can be. ## Monday - 2 July 2007Today was the first without any talks in the moning. Instead, I spent my time helping Hamsa re-align her optical tweezers set-up while contemplating potential mini-project ideas. Dr. Noe gave Danny and me a brief lesson on diffraction that was really helpful. To continue in the vein of alignment, this afternoon Dr. Noe assigned Danny and me a deceptively easy task: we had to send a laser beam, using two mirrors, though a pinhole and into a photodetector. The challenge was that we could only move the mirrors. After a time [and the help of Hamsa and Mallory] I think we got it. We only have to show Dr. Noe tomorrow. ## Friday - 29 June 2007Unfortunately I am having some trouble adhering to Dr. Noe's request to update this journal daily. At this point, I don't remember what I did yesterday; I only remember I learned a lot about something. Today Mallory gave her lecture on polarized light which was very enLIGHTening [bad puns are always funny]. Dr. Noe and the rest asked Hamsa, Danny, and me [the 3 high school students] about what would happen if circularly polarized light was sent through a linear polarizer. Eventually we came to the correct conclusion that the light would become linearly polarized [because either the x or y component is eliminated]. We played around with some of the polarizers after lunch. It's ironic how the linear polarizer is circularly shaped and the circular polarizer is rectangularly shaped. When using them one must speak precisely or who knows what will happen. ## Wednesday - 27 June 2007Hi. Warning: If you're reading this right now you should seriously be considering an alternative activity; this journal will most probably be boring. After receiving my ID card at the Administration building (which is shamefully mispelled), I got to listen to a talk today on optical tweezers by a woman named Urszula (I can't seem to remember her last name). It was terribly fascinating, but a bit over my head. Hamsa then presented some of her powerpoint about her work on optical tweezers, too. Alas, I've no idea what to do for my main project or even my mini-project. I'm still teaching myself some optics (by physics textbook). Dr. Noe suggested something about rubberbands and interferometers. I guess I'll see tomorrow.
Simone Agha |