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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 sqrt{3}/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 sure if the 150mm mode-matching lens is the same one I shoulduse. Will update soon.August 24th, 2007 SWEET STORY OF SUCCESS... the mode converter worked (Note thealliteration)!!! Today was a day of much strange and wonderfulhappenings. Perhaps I should start from the beginning...First, I got to the lab at around 8:50 AM. I sat down at the opencavity laser and tried messing around with the alignment after adding ahair to see if I could choke out any HGs. The answer was no so I sat downto do some code for the website instead. Later, Simone joined me and wecolored up the world... well just the front pages of our sitesreally. Then, I set up the Model 127 laser to measure the glass slide HGbeam profile... and noticed something funky. The reflection off of theglass slide was creating a vortex-like beam! I tried setting up aninterferometer to verify it's vorticity but Marty came in and startedexperimenting with the beam's polarization. Half the donut seemed todisappear at one polarization while the other half disappeared at theopposite one... this issue still remains a mystery.After lunch, Dr.Noe and Marty helped me fix the open cavity laser modesby cleaning the output coupler. Then, we used one of my infamously thinhairs to get some really cool modes (check out pics)!! Dr.Noe suggested wetry the pi mode converter first, which was relatively easy (just 2cylindrical lenses spaced 2f apart).THEN, we tried the pi/2conversion. After moving the mode-matching lens and the cylindrical lensesaround, we decided to change the focal length of the mode-matching lens tocompensate for the slight divergence of the laser. In the end, we ended upusing a 150mm lens instead of the calculated 415mm! And, asaforementioned, the converter worked!! YAY!The most exciting part, however, was when we took a zero-order Gaussianmode, cut it with a cover slip into a HG10 and Dr.Noe fiddled it with ittill we got a vortex out of the mode converter! IT WORKS! This suddentransition from theory to practical-ness astounds me beyond measure.August 23rd, 2007 I made a plan of all the stuff that I have to accomplish before schoolso that I have some fighting chance of vortex tweezing and writing a goodpaper on it for Intel... apparently, this is going to be a lot tougherthan I thought. There are so many "little things" to do, though at the endit sounds like: I took 2 cylindrical lenses, made a vortex, put it intweezers (this could be the beginnings for my 100-word project summary forIntel...). Anyway, now for the news.Dr.Noe and I cleaned the Brewster window of the open cavity sinceexcessive dirt on it seemed to be causing dramatically lower power. Afterthis, I spent an hour taking data for the beam profile measurement of aHG10. However, for some strange reason, my data did not comply with theexpected double curve. To my horror, the laser was not lasing aHG! Apparently, the cleaning removed some dirt that must have been causingthe HGs and LGs before by creating an extra node... the hairless HGmystery has now been solved. Unfortunately, this also means I have to setup new HGs the old-fashioned way... with a hair... which seems to be alittle trickier than I thought. I wish I'd paid more attention when Victordid this last summer.August 22nd, 2007 Haven't updated in a while... mainly because I've been out sinceThursday =/. So, a brief summary:Dr.Noe has mounted both cylindrical lens onto rotators for me so that Ican start the cylindrical lens mode converter. Today, I aligned the opencavity so it was parallel to the surface and in lign with the holes. Ithen put up the components for the mode converter at relatively correctdistances and... nothing happened. As I expected. So, trouble-shootingtime. The biggest issue (I think) is that the laser beam is divergingrather significantly when it enters the mode-matching lens instead ofbeing collimated. This leads to two issues: the Rayleigh range changes(may not be as significant) and the focus of the beam may not be in themiddle of the two cylindrical lenses (might be quite significant). So, thething to do is to take measurements of the beam width at various distancesto see how the beam is diverging and to predict where exactly the focus ofthe beam is. I plan to do this tomorrow. Also, Dr.Noe pointed out that thebeam diameter that I am assuming is that of the Gaussian mode and not theHG mode. Hm. More issues that need to be examined.Marty and I also did some more stuff on spherical mode convertersyesterday. He pointed out that my idea with expanding the astigmatic beamto an isotropic one again with a 45-deg phase shift on either end mightnot work because the lens that would be needed to bring it back would bewithing one Rayleigh range of the focus -- meaning that it may notactually work. Something that could be looked at using ABCD matrics or theray optics program, methinks. Marty also had another idea but I shall notelaborate till I check it out in Excel... =).August 15th, 2007 Marty and I spent quite some time pondering the spherical modeconverter yesterday. After correcting my flawed initial calculations, wefound that there are two ways of achieving a pi/2 relative phase shiftusing tilted lenses. One is to bring one axis to a focus and not the other-- problem: how do you bring the focus back to an isotropic beam withouthaving another phase shift? The solution bring us to method 2. Bring oneaxis almost to a focus so that it goes through a pi/4 phaseshift. Bringing it back to an isotropic beam using a diverging lens(tilted at the same angle & with the same f) will cause another pi/4 phaseshift. The net relative phase shift... pi/2!So, the main problem is that we don't know for sure how the focallength of 1 axis changes with the tilt of the lens. Also, Marty expressedhis concern that the other axis may undergo a change in focal lengthtoo. Outside, the Fresnel plates relationship of f= f_o*cos^2(theta) doesnot necessarily hold for spherical lenses. I suppose I will have to testthis using the camera soon.August 14th, 2007 Dr.Noe and I accomplished quite a bit yesterday. To mount themode-matching lens, Dr.Noe epoxied the lensholder to a short post so thatI can try out the mode converter for the open cavity laser. We also wentthrough some equations in GnuPlot to find out that (surprisingly) the beamwaist of an HG mode is reached when the intensity is 2/e of the peakintensity (compare to e^-2 for a regular Gaussian beam). This doesn't seemto capture much of the intensity, hinting that the aperture of theobjective may need to be much bigger than the beam waist. I will apply theequations to see what the beam waist of a LG mode is compared to it's peakintensity.We set up the huge He-Ne laser and measured it's power to be 33.3mW (sopowerful that it can burn electrical tape when brought to a focus!). Ineed to measure the beam width. I also should start setting up the modeconverter at the open cavity laser. However, for the calculations to workout, I need to collimate it to a beam diameter of 2mm first.August 13th, 2007 Simons is over =(!!! This means... THREE WEEKS left beforeschool... ew.I found this oldpaper that seems to describe my entire project (except the sphericalmode converter and the glass slide to make the HGs). The good part: theirfinal LG was only 10mW and it was still enough power to achieve measurablerotation!August 9th, 2007 I found so many papers at the library today. Yesterday, I was thinkingabout the fact that radially polarized light having such a small focus canhave applications in tweezers... sure enough "Radiation forces on adielectric sphere produced by highly focused cylindrical vector beams."Also, yesterday, Dr.Noe talked about focusing beams having skewedPoynting vectors because of the azimuthal tilt. This leads me to wonderabout momentum transfer by focusing beams. I would add more except I haveto go practice for Simons presentations.August 8th, 2007 Today was extremely productive! Dr.Noe sat down with Simone and me andwe brainstormed possible project venues. He re-introduced the concept ofradially and azimuthally polarized light (I remember him explaining thisto me last summer but I actually understand it now). Simone was at a sadloss about which project to do because of her insistence on fractionalvortices and such "murky" ideas as those proposed by the revered Berry.Then, Dr.Noe took us the Curry Club (mmm...) and after coming back, wehad a semi-list of ideas including using a Shack-Hartmann wavefront sensoron fractional vortices, measuring the OAM of fractional vortices by therazor blade method, etc. We also tried illuminating the side of thefractional charge diffraction grating that had the phase dislocation inthe razor-blade method. Simone later told me that every odd mode hadbeen a HG -- now that I think about it, that's obvious because the phasedislocation area is the same hologram as that for the HGs (a Pi phaseshift between the top and bottom). The even modes were vorticeswith orders that were multiples of 3. It seems natural from hindsight butI could never have predicted it beforehand. Anyway, it was an interestingday.August 7th, 2007 The Simons talks are finally over =)!!! Brad Thurow and David from thePhysics Department showed some really fancy math stuff (unfortunately, mycell phone went off which was quite embarrassing). Then, Danny gave hislong spiel on beam alignment and Simone did her thing on vortices (quitewell, might I add). Finally, I finished off the powerpoint marathon withmode converter stuff.Afterwards, we showed the Simons kids the lab, including the quasi-HGs,optical vortices, working tweezers, the laser light show, and thepolarizers. I think it went pretty well. And, oh, I finally handed in myabstract and wrote a bunch of code to post all my abstracts on thesite. Check it out. Ithink I'm getting better at thisLINUX thing everyday :-P.August 3rd, 2007 Today is the REU's last day in the LTC... therefore, it is the lastawesome day of their lives because now, they have the pain of partingcompany with the amazing moi. To this, Mallory the Marvellous says, "Y'allare nuts!"At this point, I would like to add that my pictures link has finallycome into existence after an extended period of 14 months so... you BETTERcheck it out. Vortices, HGs, you name it (only HGs or vortices), you'llfind it in the Pictures section. For this, Simone shall forever beindebted to me (her pictures on her Simons ppt). Thank you very much.August 2nd, 2007 Nagging Question: What is a fractional vortex?? When I moved on to HGmodes, I sort of forgot about this issue but now that Simone has taken itup, it's back to haunt me. I understand that the vortex makes a fractionalnumber of 2*Pi rotations in a cross-section but according to Berry, thesevortices don't really exist. So, then some papers say that a vortex withcharge between 2 and 3 actually oscillates with a third vortex existingand annihilating at points in the beam's propagation. However, thatdoesn't make any sense because the OAM is not conserved. Then, Kikobrought up that there are actually a whole bunch of +1 and -1 vortices onthe side that change during propagation in a fractional vortex. This israther confusing as if all vortices are just superpositions of integralvortices, you can't create a fractional vortex by just adding a row ofoppositely charged vortices on the side... Either way, this doesn't seemto conserve OAM either. Clearly, I don't know what I'm talking about inthis case.August 1st, 2007 Oh no, it's August. Summer is more than halfway over and the weight ofdeadlines is upon me. Even worse, the Simons kids are coming in next weekto hear us present about... probably Simone & Danny's mini-project and mynon-existent one. This tells me that I have a week to put together aworking mode converter (using the new lenses that Dr.Noe has ordered forthis purpose), set up the 35mW laser, and re-construct my tweezers setuparound it. It doesn't sound that bad I guess but I'm sure messycomplications will arise (mode converter doesn't work, some focal lengthissue is messed up, etc,etc.).That reminds me that one of the things Ineed to do is measure the beam width of the huge laser. I'm also notgiving up on the spherical lens mode converter idea (using equations by Beijersbergen). I have a setup inmind to induce the astigmatism and to make it isotropic again but I've noidea how to calculate the new Rayleigh range which is quite necessary forme to do the calculations. July 30th, 2007 Afternoon Kiko Galvez's visit was pretty awesome! He analyzed the interferogramof the spiral that we got from the cracked piece of plastic -- it had 8prongs and by that logic, it was a 7th order vortex!!! However, when wemade the fringe pattern finer, the forks got more complex. I've takenpictures of both situations.Unfortunately, Kiko thinks that 4mW at the sample won't be enough powerto rotate the particles. He claims he used 50-100mW for just a few degreesa second! Maybe, I can eventually try out that 80mW if necessary...After doing the math for the mode converter (based on Beijersbergen),itappears that I need aREALLY long focal length for my spherical mode-matching lens (almost ameter). It also turns out that the focal length of the mode-matching lensvaries directly with the focal length of the cylindrical lens. More onthis to come...July 30th, 2007 Morning I'm sooo excited!! Last night, I actually read (meaning that IUNDERSTOOD) Padgett's article on Gaussian beams (the ENTIRE thing),Padgett's paper on mode converters (also the whole thing), andBeijersbergen's paper on the derivation of the equations used in the modeconverter (almost the whole thing)!!! After reading these 3 articles about6 million times, it was a very strange sensation to suddenly acquire theability to just read... almost as if they were written in English(gasp). But now I actually know what modes are (about time...) and I think Iget the Gouy phase shift idea too. As soon as I read the last part ofBeijersbergen, I'm ready to put my revelations to the test experimentally.On a different note, today, I'm expecting a visit from Kiko Galvez,someone who hasactually put vortex-based tweezers to work, showcasing OAM, using thecracked piece of plastic! I'm hoping he can clear some of my questionslike how he managed to rotate particles without an integral vortex andwhat he did when he encountered problems with the non-uniformcoverslips. I'm looking forward to talking to another tweezers person.July 27th, 2007 Last night, I read and re-read the paper "An Experiment to Observe theIntensity and Phase Structure of Laguerre-Gaussian Laser Modes" by Padgettand Allen and "Astigmatic Laser Mode Converters and Transfer ofOrbital Angular Momentum" by Beijersbergen (of which I can't find anonline copy). Then I finally understood what they were trying to do andgotreally confused -- the cylindrical lens was being used to bring the HG01mode to a focus at the same place as the HG10 beam (which was not affectedby the cylindrical lens) but with a different Rayleigh range. This wouldthen induce different Guoy phase shifts (Pi/2 preferrably for a LG).Then the question was: how can you insert a lens into a converging beamwithout changing the focus position?? Simone and I brought up the issuewith Dr.Metcalf and after some thought and one of their intense groupmeetings, he told us that geometric opticswas misleading us and that we would have to use matrices (for which hereferred us to Thien An).The other thing that troubles me is that in the paper, the mode that isnot beingaffected by the cylindrical lens doesn't have a huge Rayleigh rangeeither. If, as Thien An claims, the phase shift will be the same afterboth modes cross their Rayleigh ranges, then there won't be any net phasechange to boast of. I guess the thing to do here is to read the paper (andrefer back to Beijersbergen) more this weekend and go hunting for the raymatrices. Then, on Monday, I'll see what I can do experimentally.July 26th, 2007 Laser Sam visited yesterday and today and gave his speil on lasers andsafety. I still don't really have a project but I've been trying toconvert HG modes to LG modes with the cylindrical lenses. Today, I createda basic setup using a glass slide and cover slip to create a 1st-order HGmode tilted at 45 degrees. Then, I sent it through 2 cylindrical lenses(f=70mm) separated by 98.8mm. And... nothing happened.Maybe the problem is that the HG approximation isn'tsufficient. It definitely doesn't work out to be as simple as itlooks (Guoy phase shift 1 component Pi/2 relative to the other to get a LG beam). After a few appealsof help to Berjeinbergen, Ian, and Simone, I've given up... till tomorrow.July 23rd, 2007 Back to the lab after super-Harry Potter weekend (yes, I managed tofinish the 7th book in a day for all practical purposes)! I still have towatch the 5th movie but back to physics...I've been looking at using HG modes to create integral low-orderoptical vortices (hopefully l=2 or so) for the tweezers. At first, Ithought it'd be a matter of a couple cylindrical lenses and alignment butthe theory behind it, as Dr.Noe pointed out, is extremely complicated. Ianand I will hopefully be working on this...For my project idea, I think I'd like to see how trapping efficiencychanges as the order of the optical vortex increases (I could use thecracked plastic if I had some way of measuring the phase structure of thevortex to determine it's precise order). Then, using the HG-to-LGvortices, I'd like to actually cause the particles to rotate and then lookat the trapping efficiency. This is just an idea and I'm hoping it'll giveme some specific direction to follow.July 18th, 2007 Pizza lunch meeting with white pizza & broccoli -- yay!! Simone andDanny presented their mini-project and it looked prettyimpressive. Dr.Metcalf thrust some doubt about the quasi-vortex coming outof Ian's open cavity laser. Ian and I also had a little talk aboutvortices. I'm really trying to understand where this OAM stuff is comingfrom but I'm having trouble grasping the idea.I placed a quarter-wave plate in the tweezers (not completely alignedas circular though) and tried a saturated calcite solution in water. Theyrotate a little but stop right before making me too happy. Bratty littlecalcite particles...I'm also taking a second look at this ray tracing software. I kind ofput the index of refraction sorting idea in the back seat but I think itcould still prove useful.July 17th, 2007 Prof. Hemmick is giving a talk today. Today, I finished re-aligning thetweezers with the linearly polarized laser and I measured the beam widthto be 1mm. I need to get some anti-reflection coated lenses. I went withDr.Noe to crushsome calcite. I hope to use circularly polarized light to cause some spinangular momentum. I'm thinking that this will help me understand moreabout light torque in general.July 15th, 2007 It's 7:00 right now and I watch the minutes tick by as I wait for 8:35(and my train) to approach. I decided to stay longer in the lab to alignthe tweezers and measure the beam width. Unfortunately, I didn't realizethat my eyes would get laser-sick so soon... I guess I'll read some papersto wile away the time.July 13th, 2007 Last night, I fixed both equations (and the 1st one successfullymatched up with the one that Amol came up with in his paper) and graphedthem on Excel. After some advice from Dr.Metcalf to increase the stepsize, the graphs came out to be... somewhat nice I guess. We alsoexperimented with different types and the radar graph (suggested by Simone) wasby far the most impressive-looking though rather useless. Ratherinterestingly, the change in the optical path length as the tilt angle increassseems parabolic since it's derivative is almost linear (notice the almost).Also, I've a few new ideas concerning the vortices: using two pieces ofcracked plastic in a row at different tilt angles, superimposing aninfrared vortex with a green one, etc. I also have to arrange the crackedplastic better since it is quite volatile in its current position.Sadly, today, the tweezers had to be taken apart... again. We were at asad loss of mirrors for the mini-project and so the 2 tweezer mirrors weresacrificed for the sake of physics. The bright side is that this is aprime opportunity to insert the linearly polarized laser into thesetup. Add a quarter-wave plate and we will then have spin angularmomentum!!!July 12th, 2007 Yesterday, I stayed in the lab, all alone except for Simone, till ~7working on an equation that would model the phase shift on either end ofthe cracked plastic depending on the tilt of the plastic and the tilt ofthe plastic itself. To my surprise, after using a sheet of ripped paper asa model, I realized that both cases are analogous to an extent but theequation changes significantly.This morning, after listening to Thien An's quite excellent talk onFabry Perots and a scintillating argument with the REUs that didn't endtill the intervention of Dr.Metcalf, I graphed the equation on Excel andrealized that I messed up. But everyone insisted on lunch so I tore myselfaway. (By the way, the hospital food is much cheaper and tastier.) On theway back, we stopped at the library and I picked up some papers aboutrotation of particles in tweezers and OAM in the hopes that some startlingrevelation will help me fix the vortex tweezers.Now, I shall go fix my equation about the cracked plastic. Then, I'llread the papers. Then, I'll measure the thickness of the crackedplastic. At least that's the plan.July 11th, 2007 Yesterday was a very exciting day. Dan, Simone, and I managed to alignthe interferometer such that both beams were collinear. The crackedplastic (at a 15 degree tilt) produced a beautiful spiral like it wassupposed to and we tookpictures. Simone pulled on one of the mirrors with a rubberband and thespiral rotated. On the multi mode, I should be able to make an animatedgif of the rotation... eventually. On closer inspection, the spiral isactually a little deformed -- probably owing to the deformed fork patternproduced earlier with the plane wave interferogram.Based on this, I think I should start taking measurements with theplastic to see what really is going on. First of all, I'm going to measurethe exact thickness of the coverslip. Then, I plan to see how tilting itfrom the plane orthogonal to the beam changes the optical path length oneither side of the crack (I expect equations to go with this). With thatinformation, I hope to calculate how much OAM the vortex has and how thetilt can be used to calibrate this quantity.July 9th, 2007 Today, I stared for an increased period of time at the vortexinterferogram. I've been trying to trace the fringes but it just hasn'tworked out as it's way too blurry in the center. BUT finally, I did get aclear interferogram. Right when I was about to trace it, something badhappened and the interferogram got misaligned :(. Then, I triedre-aligning it for about an hour but for some strange reason, the fringesgot fatter and fatter... That's when the startling revelation thatcollinear beams don't interfere to form fringes was revealed. Goes to showhow much I know about optics...Then, I came back to the lab with Simone at ~7:30 or so to findMallorie and Ianplaying with the open cavity laser to create all kinds of modes and stuffand of course... you guessed it: an optical vortex!July 6th, 2007 Ian gave his talk on HeNe lasers today & then went on to talk brieflyabout modes. I guess I have the basics down now but I'm all the moreoverwhelmed by all the mathematics equations being spewed left andright. Anyway, I guess I'll have to worry about that later because of thevortices. I wonder how Amol and Victor figured it out. So here's my list of stuff to do for now: 1. Trace plane wave interference pattern. 2. Compare the interference pattern of a regular vortex (from forkgrating). 3. Does it make a difference if vortex is linearly polarized? 4. Try using polystyrene beads in the tweezers instead of yeast cells. 5. See how vortex morphs as cracked plastic is rotated a few degreesat a time. I guess there will be more to add later. Enoughprocrastination... back to work.July 5th, 2007 BNL Field trip today. It was pretty nice - I finally learned what therelativistic heavy ion collider (RHIC) is. Yay for me! Then we went andhad lunch at the Wang Center and talked about weird stories. I tried putting the optical vortex on a yeast sample. The goodnews: it tweezes normally. The bad news: it tweezes normally. I'm yet tosee any orbital angular momentum...July 3rd,2007 OPTICAL VORTEX CREATED IN TWEEZERS SETUP WITH NEW PIECE OF CRACKEDPLASTIC. SEEMS TO BE OF HIGH ORDER. CHECK OUT PIC IN TWEEZERS/VORTSSECTION!!July 1st, 2007 The good news is that Simone and I re-aligned the entire tweezers setupthis morning before lunch! That has to be a record so we treated ourselvesto some Chinese poker after lunch =). The bad news is that it isn'ttweezing yet. The focus isn't quite on the same plane as the cells whichshould be a simple aligning of the 3rd lens issue but it nevertheless isan issue which is no fun =(.After lunch, we tried to create an opticalvortex but it just doesn't seem to be happening. Not to mention the issuethat I might not have enough power with a vortex for trapping. I wish Ihad that 80mW laser... except it wouldn't matter since I can't make avortex anyway. Whatever... back to vortex land. If I ever get a vortexthrough that thing, I'm taking the day off, Simons or not ;).June 28th, 2007 So, I've been really thinking about this cell sorting & ray tracingidea. The Harvard website (which I will post a link to as soon as I figureout how to) has a lot of information about light propogation throughtissues and even provides the indices of refraction of variousintracellular parts and a basic formula to approximate the index ofrefraction of other parts. THe paper that Dr.Noe had sent me earlier aboutray tracing in a standard cell involves ray tracing through multiplelayers in a similar fashion. I'd really like to create an even moredetailed model and then observe the difference for a cancerouscell. Urszula said she is willing to send me cancerous neurons and kidneycells, etc. but I'd need an exact model of exactly how a cancerous celldiffers from a regular cell in terms of index of refraction, etc. Maybe Ishould email the guy at Harvard. More on that to come.June 27th, 2007 Today, Urszula came in to give a talk on optical tweezers. It wasquite enlightening and reinforced the idea that I don't know much abouttweezers. Apparently, there are many, much more accurate ways to calculatethe drag force. One is to, of course, use a flow chamber - one powered bygravity by establishing a tilt on the chamber I presume. The other iscalled the power spectra method. A quadrant diode is place above thetweezers to collect the scattered light from the particle to observe theBrownian motion. This is then used to figure out the corner frequency andthen substituted into a variety of equations including Langevir -statingthat the net force is equal to zero - to figure out the trap stiffnesssand trapping efficiency. Pretty neat but I don't know if we'll be able toget a quadrant diode. Another way, suggested by Dan, is to video tape theparticle motion as it leaves the trap and to create a position-time graphusing a program and to calculate the max drag velocity by taking aderivative when the particle leaves the trap. Interesting but I don'treally know how to make such a program.June 26th, 2007 Well, it's practically been a year! It's good to be back. Now I'm aSimons Fellow which means that other than the joy of seeing the tweezersagain, I also get the happy prospect of $! 2b1af7f3a8