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About two weeks ago, I completed the calculations for Marty's question,proving that tilted lenses or mirrors can't in fact create a perfect modeconverter. It was rather ugly and required significant Maple work.Recently, I've been messing around with the idea of the circularlypolarized optical vortex tweezers. Using Nityan's spiral zone plate, I wasable to get nice order-1 vortices. What's interesting to note is thatthese plates work very similarly to mode converters. The beam convergesinto what seems to be a HG and then into a vortex and into another HGthat's orthogonal to the first one. However, when experimenting withhigher-order plates, it creates several first-order singularities thatdon't converge into one dark core. This is similar to what happened when Itried to convert higher-order pseudo HGs. Of course, the former isunexpected while the latter was expected. Yiwei and I have been tryingto find an appropriate method to circularly polarize the laser beam. Aftertesting every single quarter-wave plate in the lab, we stumbled upon usingprisms instead (as Dr.Noe explained Khristine Horvat had done). However,after spending an hour trying to get these prisms to work at the biglaser, we realized that the beam's poalrization was not at 45 degrees tothe prisms and that's why we were unsuccessful. Now, we're trying to finda mechanically sound way to rotate the laser beam or prisms. My firstthought was dove prism but according to a paper I found, rotated doveprisms introduce elliptical poalrization to a linearly polarized beam!Perhaps we can balance it by adjusting the angles of the prisms...July 10, 2008 It's been a week since I last updated because driver's ed has me crazyrunning around between 1 and 4 (my usual leisure time when I do stuff likerelate lab experiences to the entire world). Anyway, a few major things.Dr. Metcalf has been giving us a series of lectures on Quantum Mechanics.He started with some basic matrix mathematics but soon he jumped intodiscussing Hamiltonians and two-state systems. For example, yesterday'sdiscussion talked about how to find eigenvalues and eigenvectors for astandard Hamiltonian matrix (the eigenvector turns out to be [sin(theta)cos(theta)] where theta is time-dependent). This tells us that a two-stateatom sinusoidally varies between its ground ([0 1]) and excited states ([10]), which shows that an atom spends equal amounts of time in the twostates. Also, at theta=pi/6 when the eigenvector is ([1/2 sqrt3/2]),there is a superposition of states -- the principle that differentiatesquantum mechanics from classical mechanics.I have a setup idea to try making radially polarized light. It involvesa randomly polarized laser passing through a beam splitter upon whicheither leg will be polarized in orthogonal directions. Both beams willthen be cut in half by a glass plate (sound familiar?) in the axisparallel to the polarization direction. Then both beams will be recombinedand this should give me a desired output. To test the output, I can put apolarizer in front of the beam and rotate it, which should then alwaysgive me two spots in the axis of the polarizer. For a while I was confusedabout why recombining the beams won't create an interference pattern thatwill ruin the beam but Dr.Noe mentioned that beams with orthogonalpolarizations don't interfere. Hm. So what is interference?There's been a lot of talk about Fresnel zone plates recently so Victorand I looked at a bunch of sites about them together. There's beenresearch going on at Harvard about zone plate tweezers! Now, that'scool. Meanwhile, the open-cavity has fixed itself. Strange. Moreopportunely placed dirt?We derived a bunch of cool equations on the board today. This remindedme of why I like physics so much... derivations! =) There's anothermini-project to try out... comparing the actual intensity distribution tothe theoretical one and seeing how the differences are caused by thefinite widths of the slits. Fourier?July 2, 2008 Today's the third day with the Simons students, Yiwei (pronouncedWhey-whey) and Nityan (sometimes called Nathan). We've been playing aroundwith several ideas and Victor's settled on measuring the Rayleigh rangesof HG laser modes for a mini-project. The idea was that he'd be able toresolve the issue we had last year about whether assuming HG modes fromthe open-cavity would diverge at the same rate as TEM_00 modes from thesame laser. However, the open-cavity is acting up again and refuses toproduce any nice HG modes for poor Victor. I remember having the sameproblem last year but tinkering and cleaning has yielded no avail as ofyet.Meanwhile, I finally read the chapter in Siegman and the paper he wroteabout matrices for tilted lenses. Now, I have to go back and add them tomy Excel calculations. Hopefully, I'll remember what exactly I did backthen =). It may take a little more than the two minutes it would've takenme had I not been lazy before. Also, I've been reading about makingradially polarized light with fiber optics. Apparently, I'll need afew-mode fiber like what Victor used, which means that I'll be using abeam with a shorter wavelength in a single-mode fiber that's designed fora longer wavelength. However, before I put the beam into the few-modefiber, it'll have to go through a meter-long single-mode fiber! The tiltbetween the two fibers is supposed to help me select the radiallypolarized beam. This will be hard because all the modes exiting thefew-mode fiber will be annular (radial, azimuthal, or hybridpolarizations) and it will not be easily apparent which is the one I'mlooking for. To top things off, I have no idea how to set up a fiber. I'llhave to read a lot more about this. On an ambitious note, if I can getthings working, maybe I can work with Yiwei (since she's interested inOT) to put a radially polarized beam into the tweezers to make a reallytight focus. However, this may require more power as the efficiency of thecoupled fibers is very low according to the authors of the paper I'mreading. More to come.June 25, 2008 Yesterday, we identified and categorized piles and piles of opticsstuff that Dr.Noe picked up from RVSI. Some of the stuff is really strange(7 cases of fancy plexiglass?) and some of the stuff is REALLY cool(liquid crystal polarizer). There was a whole bunch of nice cylinderlenses, polarizers, and camera lenses.This got me thinking about radially polarized light which we never gotto try last year and may be a nice thing to check out for a project thisyear. I went and printed some papers from the SINC -- it seemsthere are 3 ways of creating such a beam: liquid crystal polarizer,interferometers, or fiber optics. I'm yet to really read any of thisliterature though so we'll see.As for the high school students coming on Monday, here's a list ofdemos we're going to show them:1. oscilloscope2. interferometer3. magnifying glass (inside and outside)4. rubberband5. rainbow glasses6. candle lamp7. optical vortices (gratings and phase plates)8. pig mirage toy9. polarizers and quarter wave-plate10. total internal reflection in glass tank11. quantum eraser12. towers of hanoi (optional and purely for entertainment)Also, here's a list of possible mini-projects they can do to getstarted in the lab:1. Use the dial guage, rubberband, and interferometer to measure thewavelength of light.2. Measure the focal length of a lens with the autocollimator3. Play with the fiber bundle4. Make a half-wave plate and determine what wavelength of light itworks for5. Make a white light interferometer (HARD)Possible areas for kids to investigate as they embark on long-termprojects include:1. Optical tweezers (setup already in existence)2. Azimuthally or radially polarized light (creation and investigationof special properties)3. Optical vortices (creation, mathematical or computerized analysis,and implementation in various devices)4. Pinhole dynamics (studying how light diffracts, how light'sbehavior changes with angular variations, etc.)5. Photoacoustics (ask Marty)6. Many other topics such as holography, fourier transforms, moirepatterns, laser circuitry, etc.I have to make a powerpoint presentation about Gaussian optics andtweezers for the high school kids.P.S. Victor brought in a piece of paper with holes in it today andmiraculously, it improves vision for near-sighted people (like moi)! Now,isn't that weird? Who knew paper with holes can add diopters! Turns out alot of quacks sell it on the internet, claiming that it gives victims20-20 vision! So if you're reading this, don't fall for it!P.P.S. We burned paper in the sun today. I also burned Will's initialsand a flower on his sneakers. I also almost set my black pants on firewhile wearing them (there's a little charred spot on it now)! Dr. Noe tookus to Raga and we ate a delicious lunch and came back to do physicsproblems on the whiteboard after that.June 24, 2008 Today is my first day back in the lab for this summer. Currently, thereisan REU student here named Will (he's from Alaska!!) and a high schoolstudent called Victor. Two more Simons students will be joining us nextweek on Monday (June 30th); one is a local student, and the otheris from Philipps Exeter and will be leaving us once the summerends. For now, we're all to focus on cleaning up the lab. Moreto come in the next few days...March 26, 2008 Today is the last day of Spring Break, and I figured it would be an appropriate time to re-introduce myself to Linux and my long-lost journal. First, the good news. Irecently got back from Washington DC (with a luxurious stay at the St. Regis Hotel) after being selected as an Intel STS Finalist!! This has been one of the most amazingand humbling experiences of my life up to this point. Dr.Noe came to the gala reception and we had quite a blast checking out "the future of the country" over some veryfancy food. Flush from this excitement, I returned home to hear that I got accepted to MIT!! I'll be heading to the Campus Preview Weekend in April with Simone to bounceoff of their bubble-wrapped walls and to listen to number theory talks over pizza =). Finally, it seems that I will be returning to the lab this summer (especially now thatthere is a distinct possibility that I will get my driver's license in the upcoming months) to partake in more optics stuff and to help out the new kids... more to come.November 15, 2007 Hello world! Apparently this is what I am supposed to say when using MikTeX for the first time. Well, I didn't -- I said "I hope this works." And it did. Thank theheavens for LaTeX. These last few weeks have been a long and hard lesson on computer code for an ignorant soul like me. I actually had to learn how to use LaTeX, downloadthe program and find commands, convert pictures to different formats and place them in the paper, etc. etc. in a very short space of time. Oh boy.As you can see, I haven't updated my journal in a month. However, I do have a good reason: I've been tying up loose ends in my project for the INTEL STS PAPER (trumpetmusic in the background). I would like to deeply thank Dr.Noe for his long nights correcting my writing in the lab, Marty for reading and commenting on my paper, my parentsfor putting up with me (this is a big job), Danny's mom for driving me home at 3am, and Simone for moral support. So, a brief summary of what I actually got done: Thetweezers are working now. I did see some high-speed rotation of CuO but unfortunately, they're not getting trapped. Instead, they get pushed up to the top of the chamberand then escape. This is probably because I'm using a fake HG which makes my beautiful OV relatively fake -- though it looks like a ring, you can see that the intensity isconcentrated in two spots when the beam focuses. Yet, since CuO particles DID rotate, I did get some torque calculations. And the tweezers did some great yeast celltrapping which Dr.Noe had me show off at random times. Mode converter work has also been underway. I wrote out some generalized equations for conditions that need to be metin the converter (now termed SLMC for "single-lens mode converter" =P) and plugged them into Mathematica for simplification -- my "simplified solutions" turned out to be 54pages long!!! In fact, the program refused to process it after a while. Needless to say, that didn't go into my paper but is a frustrating problem that I plan onconquering in the very near future. Clearly, some simplification is necessary but I didn't get a chance to look into this yet.Apparently, a new undergrad Dan Steck will be investigating the effect of tilt on the effective focal length of lenses and I plan on working with him on that to incorporateinto the mode converter calculations. At some point, I shall work on all this but currently, I'm on break =).October 14, 2007 Yesterday, Dr.Noe and I worked on the tweezers, trying to adjust thedichroic and the mirror underneath the microscope to be at the right90-degree angle. A brief summary of the methods: 1. Remove the objective and place a flat mirror on the stage. 2. Make the dichroic perperdicular to the beam's propagation so thatit reflects the beam directly back to where it came from -- this meansthat the dichroic is in the right position. 3. Tilt the dichroic to a 45-degree angle such that the beamthat goes up and reflects off of the mirror above is reflected back towhere the beam originally came from. This means that the dichroic iscorrectly angled. 4. Move the microscope till the beam that reflects offof the mirror on the stage and transmits through the dichroic hits thecenter of the microscope's base. This means that the microscope ispositioned to receive the beam at the center of the objective. 5. Adjust the mirror below the dichroic so that it transmits the beammentioned in Step 4 to the CCD element of the camera. 6. Turn the illumination light on, place a sample slide on the stage,and you're set to begin! Note: Don't forget to block the beam when it's not in use & to wearsafety goggles when adjusting elements at eye level.Anyway, after all that, the thing successfully tweezed yeast cells butit didn't seem like it was really rotating. Since yeast cells aren't veryabsorptive, I tried copper (II) oxide -- what Padgett used. But thisdoesn't really work because the particles seem to repel the beam=/. Everytime, I crossed a particle or came near it, it rotated away(which really reminded me of my brief experiment with calcite particlesand circularly polarized light -- the same thing seems to be happeninghere). I really wish the vortex tweezer people would be more specificabout how exactly this OAM thing worked...October 10, 2007 I'm sure everyone taking the time to read this journal will beabsolutely delighted to learn that, this Saturday, I finished constructingthe vortex tweezers! Does it work? I don't know. I guess I'll have to testit, won't I? More to come after college apps (Oct. 15)...September 27th, 2007 I'm back after quite a while, yet again. Apparently, I am to make asummary/list of what I know and what I don't know and hope to findout. So... here we go.What I know:-how to make optical tweezers-how to make a quasi-HG-how to make a mode converter to convert the aforementioned HG into a vortex-how to make a vortex with just one cylindrical lens-how to analyze beam propagation using ABCD matrices-how to calculate Gouy phase shiftWhat I hope to find out (soon):-how the focus of a lens is changed as a function of its tilt angle-how exactly the optical vortex is formed with 1 cylindrical lensmathematically-how to make the vortex non-astigmatic (more analysis)-determine an ideal width to make the vortex beam before it enters theobjective (6mm wide)-what is the ideal particle size for trapping & rotation? (fortrapping, it seems to be larger but is it smaller for rotation?)And... is that it?September 16th, 2007 Since I haven't updated in a while, here's a brief summary of whatwe've been up to: I measured the Rayleigh range of the open cavity to bejust 300mm while that of the big laser turned out to be 1100mm. As aresult, I determined the appropriate mode-matching lens for the big laserto be 200mm about 700mm away from the laser (this gives the input beam aRayleigh range of 30mm while the ideal would be 34mm). Also, using theABCD matrix calculations, I determined that the elliptical input beamthrough 2 spherical lenses cannot create a sufficient phase shift for amode conversion. However, Marty had another idea which I should try out atsome point. Construction of the vortex tweezers has begun and yesterday, Isuccessfully got a 18mW l=1 vortex out of the big laser. Theinterferometer is also under construction to analyze the HG mode and thevortex. I plan to finish the tweezers as soon as I can get another 2-3full days to spend in the lab. Meanwhile, I need to get the CuO particlessoon to try out as soon as the tweezers are working. I also asked aboutthe anti-reflection coated glass to cut the beam and Prof. John Longginreccommended the "square window" from Edmund Scientific.P.S. Professor Beijersbergen replied to my email! I look forward tolearning some great stuff about mode converters from him.September 3rd, 2007 Today is Labor day & you know what that means... shopping and greatdeals at Macy's!! It was positively awesome!!! However, other thanshopping, I also plan to get some data today. I'm measuring the laser'sRayleigh range and tracing out some profiles of the HG and Gaussian modesfor comparison. I learned some great stuff by reading the Sasada paper andthe accumulated Gouy phase shift paper and I plan to put that info to workafter discussing it with Dr.Noe.August 31st, 2007 Today is officially the end of the last week of summer *tear*. As muchas I love my school schedule (which has me in several periods at the sametime while giving me such forbidden privileges like free periods andearly dismissal), I'm still not quite inclined to leaving the comfort ofthe lab to the school-home-Stonybrook class-lab-homework shuttlingbusiness. I wish I had several more weeks for my project (there's still somuch to do!).Anyway, getting back to physics, I made a really nice model on Excelthis morning using the ABCD matrices and q-parameters (which I think arereally cool now as opposed to obscure and scary). Using that, Dr.Noesuggested that I model the required mode-matching lens depending on theRayleigh range of the laser output. Shouldn't be too bad, methinks. Afterthat, I also want to use that Gouy phase shift accumulation formula tofigure out some stuff for the spherical mode converter idea. At somepoint, I would also need to move the mode converter to the big laser tostart working on that.August 30th, 2007 Dr.Noe and I spent the morning decoding Steck's notes on Gaussian beams-- q-parameters and ABCD matrices. We got some very nice results(hamsa7.wq1) in the sense that we were able to manipulate the radius ofcurvature and the waist size of the beam to get the position of the focusand the Rayleigh range. It was very nice to be able to visualize the beamas all the theoretical parameters changed.Yesterday, I played around with the modes in the open-cavity laser. Bycutting the Gaussian mode with a glass slide, I was able to create somecool HG modes and convert them into funky optical vortices that correspondto those described in Sasada's paper. Check out theresults.August 29th, 2007 A bunch of theoretical investigation is going down here at theLTC. Dr.Noe, Marty, and I have been hot on the pursuit of a spherical lensmode converter configuration. Dr.Noe had a rather brilliant idea of usingan elliptical input beam but it does not seem to be too practical as faras a collimated input goes. However, an input beam with a finite radius ofcurvature is still something to be investigated. Meanwhile, the modeconverter apparatus has been affixed to a transportable rail. Yet, I amnot sur


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