## Research Journal

### August 13, 2008

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 mode converter. It was rather ugly and required significant Maple work. Recently, I've been messing around with the idea of the circularly polarized optical vortex tweezers. Using Nityan's spiral zone plate, I was able to get nice order-1 vortices. What's interesting to note is that these plates work very similarly to mode converters. The beam converges into what seems to be a HG and then into a vortex and into another HG that's orthogonal to the first one. However, when experimenting with higher-order plates, it creates several first-order singularities that don't converge into one dark core. This is similar to what happened when I tried to convert higher-order pseudo HGs. Of course, the former is unexpected while the latter was expected.

Yiwei and I have been trying to find an appropriate method to circularly polarize the laser beam. After testing every single quarter-wave plate in the lab, we stumbled upon using prisms instead (as Dr.Noe explained Khristine Horvat had done). However, after spending an hour trying to get these prisms to work at the big laser, we realized that the beam's poalrization was not at 45 degrees to the prisms and that's why we were unsuccessful. Now, we're trying to find a mechanically sound way to rotate the laser beam or prisms. My first thought was dove prism but according to a paper I found, rotated dove prisms 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 crazy running around between 1 and 4 (my usual leisure time when I do stuff like relate 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 into discussing Hamiltonians and two-state systems. For example, yesterday's discussion talked about how to find eigenvalues and eigenvectors for a standard Hamiltonian matrix (the eigenvector turns out to be [sin(theta) cos(theta)] where theta is time-dependent). This tells us that a two-state atom sinusoidally varies between its ground ([0 1]) and excited states ([1 0]), which shows that an atom spends equal amounts of time in the two states. Also, at theta=pi/6 when the eigenvector is ([1/2 sqrt{3}/2]), there is a superposition of states -- the principle that differentiates quantum mechanics from classical mechanics.

I have a setup idea to try making radially polarized light. It involves a randomly polarized laser passing through a beam splitter upon which either leg will be polarized in orthogonal directions. Both beams will then be cut in half by a glass plate (sound familiar?) in the axis parallel to the polarization direction. Then both beams will be recombined and this should give me a desired output. To test the output, I can put a polarizer in front of the beam and rotate it, which should then always give me two spots in the axis of the polarizer. For a while I was confused about why recombining the beams won't create an interference pattern that will ruin the beam but Dr.Noe mentioned that beams with orthogonal polarizations don't interfere. Hm. So what is interference?

There's been a lot of talk about Fresnel zone plates recently so Victor and I looked at a bunch of sites about them together. There's been research going on at Harvard about zone plate tweezers! Now, that's cool. Meanwhile, the open-cavity has fixed itself. Strange. More opportunely placed dirt?

We derived a bunch of cool equations on the board today. This reminded me of why I like physics so much... derivations! =) There's another mini-project to try out... comparing the actual intensity distribution to the theoretical one and seeing how the differences are caused by the finite widths of the slits. Fourier?

### July 2, 2008

Today's the third day with the Simons students, Yiwei (pronounced Whey-whey) and Nityan (sometimes called Nathan). We've been playing around with several ideas and Victor's settled on measuring the Rayleigh ranges of HG laser modes for a mini-project. The idea was that he'd be able to resolve the issue we had last year about whether assuming HG modes from the open-cavity would diverge at the same rate as TEM_00 modes from the same laser. However, the open-cavity is acting up again and refuses to produce any nice HG modes for poor Victor. I remember having the same problem last year but tinkering and cleaning has yielded no avail as of yet.

### June 25, 2008

Yesterday, we identified and categorized piles and piles of optics stuff 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 cylinder lenses, polarizers, and camera lenses.

This got me thinking about radially polarized light which we never got to try last year and may be a nice thing to check out for a project this year. I went and printed some papers from the SINC -- it seems there are 3 ways of creating such a beam: liquid crystal polarizer, interferometers, or fiber optics. I'm yet to really read any of this literature though so we'll see.

As for the high school students coming on Monday, here's a list of demos we're going to show them:
1. oscilloscope
2. interferometer
3. magnifying glass (inside and outside)
4. rubberband
5. rainbow glasses
6. candle lamp
7. optical vortices (gratings and phase plates)
8. pig mirage toy
9. polarizers and quarter wave-plate
10. total internal reflection in glass tank
11. quantum eraser
12. towers of hanoi (optional and purely for entertainment)

Also, here's a list of possible mini-projects they can do to get started in the lab:
1. Use the dial guage, rubberband, and interferometer to measure the wavelength of light.
2. Measure the focal length of a lens with the autocollimator
3. Play with the fiber bundle
4. Make a half-wave plate and determine what wavelength of light it works for
5. Make a white light interferometer (HARD)

Possible areas for kids to investigate as they embark on long-term projects include:
1. Optical tweezers (setup already in existence)
2. Azimuthally or radially polarized light (creation and investigation of special properties)
3. Optical vortices (creation, mathematical or computerized analysis, and implementation in various devices)
4. Pinhole dynamics (studying how light diffracts, how light's behavior changes with angular variations, etc.)
5. Photoacoustics (ask Marty)
6. Many other topics such as holography, fourier transforms, moire patterns, laser circuitry, etc.

I have to make a powerpoint presentation about Gaussian optics and tweezers for the high school kids.

P.S. Victor brought in a piece of paper with holes in it today and miraculously, it improves vision for near-sighted people (like moi)! Now, isn't that weird? Who knew paper with holes can add diopters! Turns out a lot of quacks sell it on the internet, claiming that it gives victims 20-20 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 initials and a flower on his sneakers. I also almost set my black pants on fire while wearing them (there's a little charred spot on it now)! Dr. Noe took us to Raga and we ate a delicious lunch and came back to do physics problems on the whiteboard after that.

### June 24, 2008

Today is my first day back in the lab for this summer. Currently, there is an REU student here named Will (he's from Alaska!!) and a high school student called Victor. Two more Simons students will be joining us next week on Monday (June 30th); one is a local student, and the other is from Philipps Exeter and will be leaving us once the summer ends. For now, we're all to focus on cleaning up the lab. More to 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. I recently 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 amazing and 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 very fancy 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 bounce off 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 that there 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 the heavens 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, download the 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 (trumpet music 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 parents for 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: The tweezers 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 chamber and 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 is concentrated 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 cell trapping 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 met in 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 54 pages 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 on conquering 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 incorporate into 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 the dichroic and the mirror underneath the microscope to be at the right 90-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 that it reflects the beam directly back to where it came from -- this means that the dichroic is in the right position.

3. Tilt the dichroic to a 45-degree angle such that the beam that goes up and reflects off of the mirror above is reflected back to where the beam originally came from. This means that the dichroic is correctly angled.

4. Move the microscope till the beam that reflects off of the mirror on the stage and transmits through the dichroic hits the center of the microscope's base. This means that the microscope is positioned to receive the beam at the center of the objective.

5. Adjust the mirror below the dichroic so that it transmits the beam mentioned 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 wear safety goggles when adjusting elements at eye level.

Anyway, after all that, the thing successfully tweezed yeast cells but it didn't seem like it was really rotating. Since yeast cells aren't very absorptive, I tried copper (II) oxide -- what Padgett used. But this doesn'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 particles and circularly polarized light -- the same thing seems to be happening here). I really wish the vortex tweezer people would be more specific about how exactly this OAM thing worked...

### October 10, 2007

I'm sure everyone taking the time to read this journal will be absolutely delighted to learn that, this Saturday, I finished constructing the vortex tweezers! Does it work? I don't know. I guess I'll have to test it, 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 a summary/list of what I know and what I don't know and hope to find out. 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 shift

What 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 lens mathematically
-how to make the vortex non-astigmatic (more analysis)
-determine an ideal width to make the vortex beam before it enters the objective (6mm wide)
-what is the ideal particle size for trapping & rotation? (for trapping, 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 what we've been up to: I measured the Rayleigh range of the open cavity to be just 300mm while that of the big laser turned out to be 1100mm. As a result, I determined the appropriate mode-matching lens for the big laser to be 200mm about 700mm away from the laser (this gives the input beam a Rayleigh range of ~30mm while the ideal would be 34mm). Also, using the ABCD matrix calculations, I determined that the elliptical input beam through 2 spherical lenses cannot create a sufficient phase shift for a mode conversion. However, Marty had another idea which I should try out at some point. Construction of the vortex tweezers has begun and yesterday, I successfully got a 18mW l=1 vortex out of the big laser. The interferometer is also under construction to analyze the HG mode and the vortex. I plan to finish the tweezers as soon as I can get another 2-3 full days to spend in the lab. Meanwhile, I need to get the CuO particles soon to try out as soon as the tweezers are working. I also asked about the anti-reflection coated glass to cut the beam and Prof. John Longgin reccommended the "square window" from Edmund Scientific.

P.S. Professor Beijersbergen replied to my email! I look forward to learning some great stuff about mode converters from him.

### September 3rd, 2007

Today is Labor day & you know what that means... shopping and great deals at Macy's!! It was positively awesome!!! However, other than shopping, I also plan to get some data today. I'm measuring the laser's Rayleigh range and tracing out some profiles of the HG and Gaussian modes for comparison. I learned some great stuff by reading the Sasada paper and the accumulated Gouy phase shift paper and I plan to put that info to work after discussing it with Dr.Noe.

### August 31st, 2007

Today is officially the end of the last week of summer *tear*. As much as I love my school schedule (which has me in several periods at the same time while giving me such forbidden privileges like free periods and early dismissal), I'm still not quite inclined to leaving the comfort of the lab to the school-home-Stonybrook class-lab-homework shuttling business. I wish I had several more weeks for my project (there's still so much to do!).

Anyway, getting back to physics, I made a really nice model on Excel this morning using the ABCD matrices and q-parameters (which I think are really cool now as opposed to obscure and scary). Using that, Dr.Noe suggested that I model the required mode-matching lens depending on the Rayleigh range of the laser output. Shouldn't be too bad, methinks. After that, I also want to use that Gouy phase shift accumulation formula to figure out some stuff for the spherical mode converter idea. At some point, I would also need to move the mode converter to the big laser to start 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 of curvature and the waist size of the beam to get the position of the focus and the Rayleigh range. It was very nice to be able to visualize the beam as all the theoretical parameters changed.

Yesterday, I played around with the modes in the open-cavity laser. By cutting the Gaussian mode with a glass slide, I was able to create some cool HG modes and convert them into funky optical vortices that correspond to those described in Sasada's paper. Check out the results.

### August 29th, 2007

A bunch of theoretical investigation is going down here at the LTC. Dr.Noe, Marty, and I have been hot on the pursuit of a spherical lens mode converter configuration. Dr.Noe had a rather brilliant idea of using an elliptical input beam but it does not seem to be too practical as far as a collimated input goes. However, an input beam with a finite radius of curvature is still something to be investigated. Meanwhile, the mode converter apparatus has been affixed to a transportable rail. Yet, I am not sure if the 150mm mode-matching lens is the same one I should use. Will update soon.

### August 24th, 2007

SWEET STORY OF SUCCESS... the mode converter worked (Note the alliteration)!!! Today was a day of much strange and wonderful happenings. Perhaps I should start from the beginning...

First, I got to the lab at around 8:50 AM. I sat down at the open cavity laser and tried messing around with the alignment after adding a hair to see if I could choke out any HGs. The answer was no so I sat down to do some code for the website instead. Later, Simone joined me and we colored up the world... well just the front pages of our sites really. Then, I set up the Model 127 laser to measure the glass slide HG beam profile... and noticed something funky. The reflection off of the glass slide was creating a vortex-like beam! I tried setting up an interferometer to verify it's vorticity but Marty came in and started experimenting with the beam's polarization. Half the donut seemed to disappear at one polarization while the other half disappeared at the opposite one... this issue still remains a mystery.

After lunch, Dr.Noe and Marty helped me fix the open cavity laser modes by cleaning the output coupler. Then, we used one of my infamously thin hairs to get some really cool modes (check out pics)!! Dr.Noe suggested we try the pi mode converter first, which was relatively easy (just 2 cylindrical lenses spaced 2f apart).

THEN, we tried the pi/2 conversion. After moving the mode-matching lens and the cylindrical lenses around, we decided to change the focal length of the mode-matching lens to compensate for the slight divergence of the laser. In the end, we ended up using a 150mm lens instead of the calculated 415mm! And, as aforementioned, the converter worked!! YAY!

The most exciting part, however, was when we took a zero-order Gaussian mode, cut it with a cover slip into a HG10 and Dr.Noe fiddled it with it till we got a vortex out of the mode converter! IT WORKS! This sudden transition 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 school so that I have some fighting chance of vortex tweezing and writing a good paper on it for Intel... apparently, this is going to be a lot tougher than I thought. There are so many "little things" to do, though at the end it sounds like: I took 2 cylindrical lenses, made a vortex, put it in tweezers (this could be the beginnings for my 100-word project summary for Intel...). Anyway, now for the news.

Dr.Noe and I cleaned the Brewster window of the open cavity since excessive dirt on it seemed to be causing dramatically lower power. After this, I spent an hour taking data for the beam profile measurement of a HG10. However, for some strange reason, my data did not comply with the expected double curve. To my horror, the laser was not lasing a HG! Apparently, the cleaning removed some dirt that must have been causing the HGs and LGs before by creating an extra node... the hairless HG mystery has now been solved. Unfortunately, this also means I have to set up new HGs the old-fashioned way... with a hair... which seems to be a little trickier than I thought. I wish I'd paid more attention when Victor did this last summer.

### August 22nd, 2007

Haven't updated in a while... mainly because I've been out since Thursday =/. So, a brief summary:

Dr.Noe has mounted both cylindrical lens onto rotators for me so that I can start the cylindrical lens mode converter. Today, I aligned the open cavity so it was parallel to the surface and in lign with the holes. I then put up the components for the mode converter at relatively correct distances and... nothing happened. As I expected. So, trouble-shooting time. The biggest issue (I think) is that the laser beam is diverging rather significantly when it enters the mode-matching lens instead of being 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 the middle of the two cylindrical lenses (might be quite significant). So, the thing to do is to take measurements of the beam width at various distances to see how the beam is diverging and to predict where exactly the focus of the beam is. I plan to do this tomorrow. Also, Dr.Noe pointed out that the beam diameter that I am assuming is that of the Gaussian mode and not the HG mode. Hm. More issues that need to be examined.

Marty and I also did some more stuff on spherical mode converters yesterday. He pointed out that my idea with expanding the astigmatic beam to an isotropic one again with a 45-deg phase shift on either end might not work because the lens that would be needed to bring it back would be withing one Rayleigh range of the focus -- meaning that it may not actually work. Something that could be looked at using ABCD matrics or the ray optics program, methinks. Marty also had another idea but I shall not elaborate till I check it out in Excel... =).

### August 15th, 2007

Marty and I spent quite some time pondering the spherical mode converter yesterday. After correcting my flawed initial calculations, we found that there are two ways of achieving a pi/2 relative phase shift using 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 without having another phase shift? The solution bring us to method 2. Bring one axis almost to a focus so that it goes through a pi/4 phase shift. 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 phase shift. The net relative phase shift... pi/2!

So, the main problem is that we don't know for sure how the focal length of 1 axis changes with the tilt of the lens. Also, Marty expressed his concern that the other axis may undergo a change in focal length too. Outside, the Fresnel plates relationship of f= f_o*cos^2(theta) does not necessarily hold for spherical lenses. I suppose I will have to test this using the camera soon.

### August 14th, 2007

Dr.Noe and I accomplished quite a bit yesterday. To mount the mode-matching lens, Dr.Noe epoxied the lensholder to a short post so that I can try out the mode converter for the open cavity laser. We also went through some equations in GnuPlot to find out that (surprisingly) the beam waist of an HG mode is reached when the intensity is 2/e of the peak intensity (compare to e^-2 for a regular Gaussian beam). This doesn't seem to capture much of the intensity, hinting that the aperture of the objective may need to be much bigger than the beam waist. I will apply the equations to see what the beam waist of a LG mode is compared to it's peak intensity.

We set up the huge He-Ne laser and measured it's power to be 33.3mW (so powerful that it can burn electrical tape when brought to a focus!). I need to measure the beam width. I also should start setting up the mode converter at the open cavity laser. However, for the calculations to work out, I need to collimate it to a beam diameter of 2mm first.

### August 13th, 2007

Simons is over =(!!! This means... THREE WEEKS left before school... ew.

I found this old paper that seems to describe my entire project (except the spherical mode converter and the glass slide to make the HGs). The good part: their final LG was only 10mW and it was still enough power to achieve measurable rotation!

### August 9th, 2007

I found so many papers at the library today. Yesterday, I was thinking about the fact that radially polarized light having such a small focus can have applications in tweezers... sure enough "Radiation forces on a dielectric sphere produced by highly focused cylindrical vector beams."

Also, yesterday, Dr.Noe talked about focusing beams having skewed Poynting vectors because of the azimuthal tilt. This leads me to wonder about momentum transfer by focusing beams. I would add more except I have to go practice for Simons presentations.

### August 8th, 2007

Today was extremely productive! Dr.Noe sat down with Simone and me and we brainstormed possible project venues. He re-introduced the concept of radially and azimuthally polarized light (I remember him explaining this to me last summer but I actually understand it now). Simone was at a sad loss about which project to do because of her insistence on fractional vortices and such "murky" ideas as those proposed by the revered Berry.

Then, Dr.Noe took us the Curry Club (mmm...) and after coming back, we had a semi-list of ideas including using a Shack-Hartmann wavefront sensor on fractional vortices, measuring the OAM of fractional vortices by the razor blade method, etc. We also tried illuminating the side of the fractional charge diffraction grating that had the phase dislocation in the razor-blade method. Simone later told me that every odd mode had been a HG -- now that I think about it, that's obvious because the phase dislocation area is the same hologram as that for the HGs (a Pi phase shift between the top and bottom). The even modes were vortices with orders that were multiples of 3. It seems natural from hindsight but I could never have predicted it beforehand. Anyway, it was an interesting day.

### August 7th, 2007

The Simons talks are finally over =)!!! Brad Thurow and David from the Physics Department showed some really fancy math stuff (unfortunately, my cell phone went off which was quite embarrassing). Then, Danny gave his long spiel on beam alignment and Simone did her thing on vortices (quite well, might I add). Finally, I finished off the powerpoint marathon with mode converter stuff.

Afterwards, we showed the Simons kids the lab, including the quasi-HGs, optical vortices, working tweezers, the laser light show, and the polarizers. I think it went pretty well. And, oh, I finally handed in my abstract and wrote a bunch of code to post all my abstracts on the site. Check it out. I think I'm getting better at this LINUX thing everyday :-P.

### August 3rd, 2007

Today is the REU's last day in the LTC... therefore, it is the last awesome day of their lives because now, they have the pain of parting company with the amazing moi. To this, Mallory the Marvellous says, "Y'all are nuts!"

At this point, I would like to add that my pictures link has finally come into existence after an extended period of 14 months so... you BETTER check it out. Vortices, HGs, you name it (only HGs or vortices), you'll find it in the Pictures section. For this, Simone shall forever be indebted 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 HG modes, I sort of forgot about this issue but now that Simone has taken it up, it's back to haunt me. I understand that the vortex makes a fractional number of 2*Pi rotations in a cross-section but according to Berry, these vortices don't really exist. So, then some papers say that a vortex with charge between 2 and 3 actually oscillates with a third vortex existing and annihilating at points in the beam's propagation. However, that doesn't make any sense because the OAM is not conserved. Then, Kiko brought up that there are actually a whole bunch of +1 and -1 vortices on the side that change during propagation in a fractional vortex. This is rather confusing as if all vortices are just superpositions of integral vortices, you can't create a fractional vortex by just adding a row of oppositely charged vortices on the side... Either way, this doesn't seem to conserve OAM either. Clearly, I don't know what I'm talking about in this case.

### August 1st, 2007

Oh no, it's August. Summer is more than halfway over and the weight of deadlines is upon me. Even worse, the Simons kids are coming in next week to hear us present about... probably Simone & Danny's mini-project and my non-existent one. This tells me that I have a week to put together a working mode converter (using the new lenses that Dr.Noe has ordered for this purpose), set up the 35mW laser, and re-construct my tweezers setup around it. It doesn't sound that bad I guess but I'm sure messy complications will arise (mode converter doesn't work, some focal length issue is messed up, etc,etc.).That reminds me that one of the things I need to do is measure the beam width of the huge laser. I'm also not giving up on the spherical lens mode converter idea (using equations by Beijersbergen). I have a setup in mind to induce the astigmatism and to make it isotropic again but I've no idea how to calculate the new Rayleigh range which is quite necessary for me to do the calculations.

### July 30th, 2007 Afternoon

Kiko Galvez's visit was pretty awesome! He analyzed the interferogram of the spiral that we got from the cracked piece of plastic -- it had 8 prongs and by that logic, it was a 7th order vortex!!! However, when we made the fringe pattern finer, the forks got more complex. I've taken pictures of both situations.

Unfortunately, Kiko thinks that 4mW at the sample won't be enough power to rotate the particles. He claims he used 50-100mW for just a few degrees a second! Maybe, I can eventually try out that 80mW if necessary...

After doing the math for the mode converter (based on Beijersbergen), it appears that I need a REALLY long focal length for my spherical mode-matching lens (almost a meter). It also turns out that the focal length of the mode-matching lens varies directly with the focal length of the cylindrical lens. More on this to come...

### July 30th, 2007 Morning

I'm sooo excited!! Last night, I actually read (meaning that I UNDERSTOOD) Padgett's article on Gaussian beams (the ENTIRE thing), Padgett's paper on mode converters (also the whole thing), and Beijersbergen's paper on the derivation of the equations used in the mode converter (almost the whole thing)!!! After reading these 3 articles about 6 million times, it was a very strange sensation to suddenly acquire the ability 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 I get the Gouy phase shift idea too. As soon as I read the last part of Beijersbergen, 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 has actually put vortex-based tweezers to work, showcasing OAM, using the cracked piece of plastic! I'm hoping he can clear some of my questions like how he managed to rotate particles without an integral vortex and what he did when he encountered problems with the non-uniform coverslips. 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 the Intensity and Phase Structure of Laguerre-Gaussian Laser Modes" by Padgett and Allen and "Astigmatic Laser Mode Converters and Transfer of Orbital Angular Momentum" by Beijersbergen (of which I can't find an online copy). Then I finally understood what they were trying to do and got really confused -- the cylindrical lens was being used to bring the HG01 mode to a focus at the same place as the HG10 beam (which was not affected by the cylindrical lens) but with a different Rayleigh range. This would then induce different Guoy phase shifts (Pi/2 preferrably for a LG).

Then the question was: how can you insert a lens into a converging beam without changing the focus position?? Simone and I brought up the issue with Dr.Metcalf and after some thought and one of their intense group meetings, he told us that geometric optics was misleading us and that we would have to use matrices (for which he referred us to Thien An).

The other thing that troubles me is that in the paper, the mode that is not being affected by the cylindrical lens doesn't have a huge Rayleigh range either. If, as Thien An claims, the phase shift will be the same after both modes cross their Rayleigh ranges, then there won't be any net phase change to boast of. I guess the thing to do here is to read the paper (and refer back to Beijersbergen) more this weekend and go hunting for the ray matrices. 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 and safety. I still don't really have a project but I've been trying to convert HG modes to LG modes with the cylindrical lenses. Today, I created a basic setup using a glass slide and cover slip to create a 1st-order HG mode 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't sufficient. It definitely doesn't work out to be as simple as it looks (Guoy phase shift 1 component Pi/2 relative to the other to get a LG beam). After a few appeals of 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 to finish the 7th book in a day for all practical purposes)! I still have to watch the 5th movie but back to physics...

I've been looking at using HG modes to create integral low-order optical vortices (hopefully l=2 or so) for the tweezers. At first, I thought it'd be a matter of a couple cylindrical lenses and alignment but the theory behind it, as Dr.Noe pointed out, is extremely complicated. Ian and I will hopefully be working on this...

For my project idea, I think I'd like to see how trapping efficiency changes as the order of the optical vortex increases (I could use the cracked plastic if I had some way of measuring the phase structure of the vortex to determine it's precise order). Then, using the HG-to-LG vortices, I'd like to actually cause the particles to rotate and then look at the trapping efficiency. This is just an idea and I'm hoping it'll give me some specific direction to follow.

### July 18th, 2007

Pizza lunch meeting with white pizza & broccoli -- yay!! Simone and Danny presented their mini-project and it looked pretty impressive. Dr.Metcalf thrust some doubt about the quasi-vortex coming out of Ian's open cavity laser. Ian and I also had a little talk about vortices. I'm really trying to understand where this OAM stuff is coming from but I'm having trouble grasping the idea.

I placed a quarter-wave plate in the tweezers (not completely aligned as circular though) and tried a saturated calcite solution in water. They rotate a little but stop right before making me too happy. Bratty little calcite particles...

I'm also taking a second look at this ray tracing software. I kind of put the index of refraction sorting idea in the back seat but I think it could still prove useful.

### July 17th, 2007

Prof. Hemmick is giving a talk today. Today, I finished re-aligning the tweezers with the linearly polarized laser and I measured the beam width to be 1mm. I need to get some anti-reflection coated lenses.

I went with Dr.Noe to crush some calcite. I hope to use circularly polarized light to cause some spin angular momentum. I'm thinking that this will help me understand more about 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 align the tweezers and measure the beam width. Unfortunately, I didn't realize that my eyes would get laser-sick so soon... I guess I'll read some papers to wile away the time.

### July 13th, 2007

Last night, I fixed both equations (and the 1st one successfully matched up with the one that Amol came up with in his paper) and graphed them on Excel. After some advice from Dr.Metcalf to increase the step size, the graphs came out to be... somewhat nice I guess. We also experimented with different types and the radar graph (suggested by Simone) was by far the most impressive-looking though rather useless. Rather interestingly, the change in the optical path length as the tilt angle increass seems parabolic since it's derivative is almost linear (notice the almost).

Also, I've a few new ideas concerning the vortices: using two pieces of cracked plastic in a row at different tilt angles, superimposing an infrared vortex with a green one, etc. I also have to arrange the cracked plastic better since it is quite volatile in its current position.

Sadly, today, the tweezers had to be taken apart... again. We were at a sad loss of mirrors for the mini-project and so the 2 tweezer mirrors were sacrificed for the sake of physics. The bright side is that this is a prime opportunity to insert the linearly polarized laser into the setup. Add a quarter-wave plate and we will then have spin angular momentum!!!

### July 12th, 2007

Yesterday, I stayed in the lab, all alone except for Simone, till ~7 working on an equation that would model the phase shift on either end of the cracked plastic depending on the tilt of the plastic and the tilt of the plastic itself. To my surprise, after using a sheet of ripped paper as a model, I realized that both cases are analogous to an extent but the equation changes significantly.

This morning, after listening to Thien An's quite excellent talk on Fabry Perots and a scintillating argument with the REUs that didn't end till the intervention of Dr.Metcalf, I graphed the equation on Excel and realized that I messed up. But everyone insisted on lunch so I tore myself away. (By the way, the hospital food is much cheaper and tastier.) On the way back, we stopped at the library and I picked up some papers about rotation of particles in tweezers and OAM in the hopes that some startling revelation will help me fix the vortex tweezers.

Now, I shall go fix my equation about the cracked plastic. Then, I'll read the papers. Then, I'll measure the thickness of the cracked plastic. At least that's the plan.

### July 11th, 2007

Yesterday was a very exciting day. Dan, Simone, and I managed to align the interferometer such that both beams were collinear. The cracked plastic (at a 15 degree tilt) produced a beautiful spiral like it was supposed to and we took pictures. Simone pulled on one of the mirrors with a rubberband and the spiral rotated. On the multi mode, I should be able to make an animated gif of the rotation... eventually. On closer inspection, the spiral is actually a little deformed -- probably owing to the deformed fork pattern produced earlier with the plane wave interferogram.

Based on this, I think I should start taking measurements with the plastic to see what really is going on. First of all, I'm going to measure the exact thickness of the coverslip. Then, I plan to see how tilting it from the plane orthogonal to the beam changes the optical path length on either side of the crack (I expect equations to go with this). With that information, I hope to calculate how much OAM the vortex has and how the tilt can be used to calibrate this quantity.

### July 9th, 2007

Today, I stared for an increased period of time at the vortex interferogram. I've been trying to trace the fringes but it just hasn't worked out as it's way too blurry in the center. BUT finally, I did get a clear interferogram. Right when I was about to trace it, something bad happened and the interferogram got misaligned :(. Then, I tried re-aligning it for about an hour but for some strange reason, the fringes got fatter and fatter... That's when the startling revelation that collinear beams don't interfere to form fringes was revealed. Goes to show how much I know about optics...

Then, I came back to the lab with Simone at ~7:30 or so to find Mallorie and Ian playing with the open cavity laser to create all kinds of modes and stuff and of course... you guessed it: an optical vortex!

### July 6th, 2007

Ian gave his talk on HeNe lasers today & then went on to talk briefly about modes. I guess I have the basics down now but I'm all the more overwhelmed by all the mathematics equations being spewed left and right. Anyway, I guess I'll have to worry about that later because of the vortices. 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 fork grating).

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 degrees at a time.

I guess there will be more to add later. Enough procrastination... back to work.

### July 5th, 2007

BNL Field trip today. It was pretty nice - I finally learned what the relativistic heavy ion collider (RHIC) is. Yay for me! Then we went and had lunch at the Wang Center and talked about weird stories.

I tried putting the optical vortex on a yeast sample. The good news: it tweezes normally. The bad news: it tweezes normally. I'm yet to see any orbital angular momentum...

### July 3rd,2007

OPTICAL VORTEX CREATED IN TWEEZERS SETUP WITH NEW PIECE OF CRACKED PLASTIC. SEEMS TO BE OF HIGH ORDER. CHECK OUT PIC IN TWEEZERS/VORTS SECTION!!

### July 1st, 2007

The good news is that Simone and I re-aligned the entire tweezers setup this morning before lunch! That has to be a record so we treated ourselves to some Chinese poker after lunch =). The bad news is that it isn't tweezing yet. The focus isn't quite on the same plane as the cells which should be a simple aligning of the 3rd lens issue but it nevertheless is an issue which is no fun =(.

After lunch, we tried to create an optical vortex but it just doesn't seem to be happening. Not to mention the issue that I might not have enough power with a vortex for trapping. I wish I had that 80mW laser... except it wouldn't matter since I can't make a vortex anyway. Whatever... back to vortex land. If I ever get a vortex through 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 tracing idea. The Harvard website (which I will post a link to as soon as I figure out how to) has a lot of information about light propogation through tissues and even provides the indices of refraction of various intracellular parts and a basic formula to approximate the index of refraction of other parts. THe paper that Dr.Noe had sent me earlier about ray tracing in a standard cell involves ray tracing through multiple layers in a similar fashion. I'd really like to create an even more detailed model and then observe the difference for a cancerous cell. Urszula said she is willing to send me cancerous neurons and kidney cells, etc. but I'd need an exact model of exactly how a cancerous cell differs from a regular cell in terms of index of refraction, etc. Maybe I should 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 was quite enlightening and reinforced the idea that I don't know much about tweezers. Apparently, there are many, much more accurate ways to calculate the drag force. One is to, of course, use a flow chamber - one powered by gravity by establishing a tilt on the chamber I presume. The other is called the power spectra method. A quadrant diode is place above the tweezers to collect the scattered light from the particle to observe the Brownian motion. This is then used to figure out the corner frequency and then substituted into a variety of equations including Langevir -stating that the net force is equal to zero - to figure out the trap stiffnesss and trapping efficiency. Pretty neat but I don't know if we'll be able to get a quadrant diode. Another way, suggested by Dan, is to video tape the particle motion as it leaves the trap and to create a position-time graph using a program and to calculate the max drag velocity by taking a derivative when the particle leaves the trap. Interesting but I don't really 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 a Simons Fellow which means that other than the joy of seeing the tweezers again, I also get the happy prospect of \$!

The 2 other Simons people here are Simone and Dan and they're both pretty cool. The REUs are Mallorie, Christina, Dan, and Ian and I'm hoping that Dan will be able to use his prior tweezer experience to help me around a little this summer. Speaking of which, I'm not totally sure what I'm going to do. I had a whole list of ideas coming back from ISEF but unfortunately I seem to have misplaced them in my head. I'll try to update my list of potential ideas today. According to my teacher, I have to have the first draft of my research paper in by the first day of school. This makes me sweat.

### September 26th, 2006

Alright, I'm back! School in junior year is harder than ever and Calc 3 eats up my Tues, Wed, and Thurs afternoons.

Shock of the day: THE TWEEZERS ARE GONE!! I met Tobi who said that he is working on rebuilding the setup to try and get it to work again... =( =( =(!!! More to come on this...

### August 30th, 2006

Today's my last summer day here... but I'll be back on Wednesday when school and Calc 3 classes start (gasp). I REALLY hope that I haven't actually forgotten as much math as I seem to have. Anyway, the tweezer has been fixed... but not successfully. The field of view is way too small and stray reflections from the laser are ruining the viewing zone =(. I theorize that the the magnification is messed up (when I put the hair on the slide, it was much thinner than it had been before but the ratio of its thickness to the diameter of the field of view stayed the same). Also, I think there's a better chance of me finding the laser spot if the field of view was bigger.

The cracked plastic is making a beautiful donut that I love =) and I've centered and aligned it to death so as soon as the tweezer starts working, I'm ready to see some spinning yeast cells! Also, Dr. Noe talked to us about circular polarization and wave plates yesterday (I need to know this so that I can make birefringent calcite particles spin with circularly polarized light and to expand my vortex knowledge). I was a litle confused but after reading the section about polarization in Elementary Wave Optics, I get it pretty well. Also, eventually, I can use those wave plates to measure the torque applied on my particles from the donut/vortex beam.

### August 23rd, 2006

Today, was find-out-how-bad-a-situation-my-tweezers-were-actually-in day. The laser had the WEIRDEST non-Gaussian beam profile. So obviously, its not very regular and ideal for tweezing. But I got rid of some of the ugly stuff with an iris and Dr.Noe suggested that I spatially filter the beam to soften out the irregularities. Then Dr.Noe asked about the non-collimated light coming out of the lens telescope and that sent him to look at the non-focused-at-infinity CCD camera. I shan't describe in detail but a lot of changes occurred (involving epoxy lol) and the setup is now in some sort of a fixed-up mess. Re-alignment? Oh, yes... Well, I can't complain and I can't say I mind much =o]. Besides, Dr.Noe, talks of buying a new objective (60x, NA=0.85, distance>2mm) - yyyyaaaayyyy!!!

### August 18th, 2006

Haven't updated in ever sooo long so here goes...

Karen actually managed to tweeze yeast cells with Marty's help the night before the REU presentations! Unfortunately, I wasn't there so it took me a few days after that to actually tweeze myself. But it happened (in all 3 dimensions!!!) and I was very excited. So... the next step was sticking in an optical vortex. Unfortunately, it wasn't as simple as "plug in the cracked plastic".

First problem, I couldn't find the vortex. Dr.Noe suggested that I might need more distance to actually see it so I reflected the beam onto a wall but still saw nothing except the slit in the plastic. Disappointed, I was about to walk out the room when I noticed strange shapes on the heat gun. So I caught the light with a white plate and saw singularities! Weird ones too... Then I looked at the other wall to find even more stray reflections... except these were spirals... spirals of light!! So I got excited and tried playing more with the plastic. Suddenly, the spirals disappeared! But then I found the vortex! Or at least a perfect dougnut shaped beam... I realized that this was because I had positioned only half the beam onto the crack whereas before I'd placed the entire beam on the crack. So then Victor suggested I test whether it was actually a vortex by placing it through an interferometer but what we didn't know was the tedious alignment issue that came with that. So, naturally, being an impatient person, I decided it would be easier to tell if it was a vortex by actually sending the beam into my wonderful tweezers and seeing if the particles rotate. But the doughnut beam seemed to be missing the lenses and to adjust, I made the fatal mistake of moving the optical elements. There went weeks of alignment work down the drain. Wow, that was stupid. So now, I'm trying to re-align the setup and hopefully steal some of Marty's help =).

### July 31st, 2006

Ouch, tough day... the laser's only giving out about 3mW instead of 20!! Bunch of measurements, not-working elements... ugh. I had to stay till 7 all alone in the big lab (even Dr.Noe left!!!) to finish taking measurements and I don't even know if we need them!!! Grrrr.......

### July 28th, 2006

Wow... we've gotten a lot of work done! We selected cylindrical lenses to adjust the curvature of the elliptical beam and spherical lenses to resize the beam. Since the lens labels can't be trusted, we went outside to measure the focal lengths ourselves and sure enough, some were labelled wrongly but we fixed that. Then we setup the actual tweezers and are now working on aligning the optical elements (VERY TEDIOUS AND ANNOYING might I add). Things are looking good. I decided to start looking into what I'm going to do after making the inverted tweezers. I looked into what Dr. Noé was talking about (sending an optical vortex into the tweezers) and I found this link talking about different methods of using optical vortices to trap and manipulate particles in an optical tweezers setup. Hopefully I can find some interesting idea for a project.

### July 26th, 2006

OMG. Today, Karen and I figured out an inverted optical tweezer layout but apparently we don't need most of the stuff anymore because Dr.Metcalf gave us this HUGE ALREADY-INVERTED MICROSCOPE!! YAY!!!

### July 25th, 2006

Today, was picture day!! And I was sooo sure it was tomorrow... oh well. Dr.Metcalf made us stand outside with fake smiles for about 6 shots. Amazing fun. Marty didn't make it so he's going to be Photoshop-ed (I know it's not a word) in. After that, we basically prepped for the REU tour - we set up some Brownian motion slides to show off our wonderful jiggling yeast cells. I also lit up the old lamp - ahhh, i remember staring at that lamp for oh-sooo long when I first came here and I had nooo idea what to do. Fond memories, lol.

I also looked at some caustic stuff since Dr. Noé keeps bringing it up but they don't really have much on Wikipedia about it... Then, we tried to start planning out the tweezer setup and to fix our magnification controversy by measuring the diffraction grating on those 3D glasses (finally managed to understand what Dr. Noé was saying the other day about the lenses) but all of a sudden, I felt really sick and I didn't do anything for the rest of the day... ugh, worst headache ever!!

### July 24th, 2006

Not a very eventful day... I got off to an amazing start this morning at the SincSite when I was doing my math homework... I finished 2 whole problem sets between the weekend and this morning - thats gotta be a record! Then after that, I guess I just kind of died out. Dr. Noé talked to Karen and I about the lens magnification and I lost him pretty quickly. So once he was gone, I bombarded Karen with questions and successfully confused her too. So after an extensive conversation about the lenses, we're both kind of like... what? After lunch, Karen and I tried to observe some Brownian motion and we were relatively successful... =). Then, a bunch of us went outside with Dr. Noé and burnt paper... oh, and did physics, lol. Yet again, I was reminded that the angular size of the sun is 1/100th of a radian... I don't think I'm ever going to forget that in my life ;).

### July 21st, 2006

We set up the microscope today!! My major accomplishment of the day was when I managed to clamp a fiber optic cable in front of the high intensity light source and clamp the other end of the cable so that it hit the mirror on the microscope. It required some severe mechanical knowledge about posts, screws, etc. that I didn't have so though the setup was quite simple, it took me a long time!

We also took some measurements on the camera lens and stuff. Then, we cut people's hair and compared their thickness under the microscope. Apparently, Krish has the thickest hair and Matt has the thinnest. Mine was not all that bad after all! Wow. Anyway, so now it seems that I've got basic microscope skills ... maybe, lol.

### July 20th, 2006

First, I'd like to announce that I'm writing this journal from home... that's right - I downloaded SSH Client (finally!). Yesterday I changed my journal's font, background color, etc. I'm so excited!! Anyway, back to physics ...

Today, Karen and I worked on setting up the CCD camera and the microscope lens. We connected the monitor and measured the magnification from the camera to the monitor using a 1.4mm slit and a fiber optic cable. Then, Karen taught me some basic lens stuff like f-number and concave/convex stuff. Mike taught Scott, Victor and I matrices. We learned how to add and multiply matrices and to apply them to ray optics. I'm still reading the paper Inexpensive optical tweezers for undergraduate laboratories . Tomorrow, I hope that we can finish setting up the microscope for the traditional "optical tweezers".

### July 19th, 2006

SO MUCH happened today... it was crazy. For once we were all working! So it seems that I have a project... I'm now working with Karen to build an inverted-optical tweezer setup. We cleaned out a working space and took apart old slides and cleaned them (years and years of parafilm and goo, yuck). Karen explained how optical tweezers worked - it helped that I'd already had a little intro from Ursula in a group meeting before. Then I spent the rest of the morning learning basic vector stuff like dotproducts and cross-products from Karen. After that, we had the group meeting (w/ delicious pizza from Dr. Noé as usual =D). He told us about how optical vortices could be used to block out incoming light from a star so that the less intense light from a planet can be viewed. That was cool. Then, he went on to talk about how the sonoluminescence bubble is actually a form of an acoustic tweezer since it attracts the bubble to the center, the point of highest intensity by sound waves. So, if the point of highest intensity was shifted, theoretically, we should be able to move the bubble. I think I'd like to do something with that after I finish up the project with Karen... maybe I can even make an inverted acoustic-tweezer setup or something... I've to say - today was the best day so far in terms of getting stuff done and ideas floating around =).

### July 18th, 2006

Alright, more ideas galore!

Dr. Noé wants me to do something more mathematical so I was thinking "back to optical vortices". Stephanie was talking about some connection with astronomy and we'll be discussing that in group tomorrow ...

Dr. Noé told me that perhaps I should try continuing Shriya's work with the piggy. When you raise the mirror lid, you see more images that alternate in the direction that they phase - obviously something to do with reflection off of the concave mirrors.

Marty suggested that I could use his setup from last spring to do a really simple experiment. He had shot a laser beam through a material that had sound waves passing through it and due to the Doppler effect, the light wave's frequence was either increased or decreased depending on whether the light beam travelled away from or towards the direction of the sound beam. Marty thought that perhaps I could use a polarized light beam and measure the angle of polarization of the outcoming light to calculate the deviation of the polarization in the medium.

Other than that, we had a really extensive talk about photodetectors and all. We did a couple derivations. It was pretty cool. Can't wait for the lunch meeting tomorrow... I just might get a project!! =)

### July 17th, 2006

I did a bunch of reading over the weekend - I'm getting desperate to find a project!! So here goes:

(1) First I found a paper on creating a new optical grating that is less sensitive to polarization and its application in an optical communications device. But that project is apparently too complicated so I won't bother getting into that.

(2) I read about this really neat idea about finding small leaks in plastic packages by using a laser beam and analyzing the reflected light! I don't know how people think of these things! Check out the paper: Terahertz technique for detection of microleaks in the seal of flexible plastic packages Better leak-detection technology has applications in a range of fields. For example, it can be used in refrigerators to avoid the leakage of refrigerant fluid (which is both expensive and harmful to the environment -- check out article .

(3) Surface profiling using laser beams and the phase shift that results! Yet another idea like the leak-detection... how do you think of stuff like that?? Seems quite interesting - check out the paper: Surface profiling using phase shifting Talbot interferometric technique

(4) Also, I've been thinking... maybe I should try building a set of acoustic tweezers - not totally sure how feasible this is but it'll give me a start on something. Look at paper: A theoretical study of the feasibility of acoustic tweezers

(5) To be honest, I haven't really looked into this last idea but it involves stuff that I might know a little about... maybe. Karen and Scott were telling me a little about Moire interferometry and I think by now I've got the "phase-shift" idea down. I'll probably skim over this paper after lunch but I'll put it up for now anyway: Phase-shifting moire interferometry based on a liquid crystal phase modulator

So that's all for today, folks!

### July 13th, 2006

So I think I might have the hang of how optical vortices work. I decided to start looking at possible projects involving these vortices. I found Amol Jain (Simons fellow from last year -- check out web page ) had also worked with optical vortices to improve high speed data transfer. I began reading his paper - apparently, communications are carried out through a modulated binary system depending on light characteristics like frequency, amplitude, etc. The orbital angular momentum of an optical vortex shows even more states and so information can be modulated in a higher base and data transfer will becom faster. This sounds pretty interesting but Amol seems to have already constructed and analyzed such a data sorter so I'm not really sure where I can go from that...

Dr. Noé mentioned another topic today about phase contrast microscopy. He suggested creating a phase plate using a material with varying thickness - this would cause the light passing through to come out of it at varying phases. This is supposed to help view transparent objects such as cells without using dye. It sounds cool - I'll have to look more into it ( Brief Explanation from Wikipedia ).

The group meeting took place today and we had a guest speaker, Urszula, talk about constructing and operating a set of optical tweezers. It looks pretty neat but it's definitely not for me. Maybe I could analyze or mathematically model optical tweezers but setting the thing up sounds pretty tedious. I was also disappointed that we ran out of pineapple pizza before I even got to try a slice! And it was my suggestion to get them too! Grrr...

I've started a tradition to do something mystical everyday till I find a project... Today, I shall meditate and let my breathing flow so that my mind can freely discover a project... At least, I hope I will stop hiccupping. =)

### July 13th, 2006

Still looking for ideas... I re-thought the optical tweezers - maybe I will look more into it after all. I looked at Yiyi Deng's journal - seems kinda interesting.

### July 10th, 2006

I haven't updated this thing in a while so this might be long... Here goes!

Last week, I was looking into optical vortices. Apparently, they have applications in optical tweezers. I wasn't really sure what they were and Maaneli suggested that I do a project creating acoustical vortices. Then these would lead to acoustical tweezers. He said that sound particles have more momentum than photons so acoustical tweezers would be able to move larger particles than optical tweezers. That sounded really neat so I decided I would start reading about optical vortices. I found a paper "Introduction to the atoms and angular momentum of light special issue" by L Allen but I soon realized it was the wrong place to start (too complex!). Then, on Dr. Noé's suggestion, I read the article on Wikipedia about the vortices by Azure and started to get an idea of what they were. But I have to say I made the most headway this morning when I went to the SincSite.

I found a whole bunch of helpful illustrations and explanations of vortices and orbital angular momentum and possible projects involving these (all of which I will post on my Ideas section). So a brief overview on what I think is going on with the whole optical vortex/orbital angular momentum/etc. thing:

Light has two factors: spin and orbital angular momentum. Spin is the circular polarization. The orbital angular momentum is the spinning of the light in a corkscrew fashion. When light hits a particle (as in the optical tweezers) it transfers both energy and orbital angular momentum so the particle starts spinning (transfer of torque to an electric dipole?) -- hence, the name optical spanners. When light is travelling in a corkscrew fashion, its polarization or spin is constantly changing to opposite ends and this happens while the light wave is in a single period. The orbital angular momentum of light can be used to transmit information (possible project). Also, the Heisenberg Uncertainty Principle states that any object's momentum and position cannot be known at the same time - this relates the photon's orbital angular momentum and position - another possible project?

Since this stuff is REALLY confusing & I probably have some concept wrong, I'll mostly be working to understand this stuff better for the next couple days. Till then!

P.S. I've really improved at hearts! =)

### June 27th, 2006

Stephanie's lecture on complex numbers today. It was pretty interesting and I got an overview into all that complex number stuff that I never learned =). The highlight of the day was when Maaneli brought in a whole container of liquid nitrogen. We exploded a happy ball (Dr. Noé wasn't too pleased) and froze soda (ew, disgusting - I'm not drinking soda for a while now). Then, Mike decided to risk his life and stick a balloon in. The thing shrunk like a withered leaf! And then when he took it out, it became normal again! And most amazingly, the thing didn't explode! Weird. Then I went upstairs and had a chat with Rebecca who was stuck all alone in her room. I've decided on my three most important goals for the summer but I have to go so I won't bother sharing, lol.

 Mike Kornhausermkornhau (a) rochester.edu Home  Laser Teaching Center