Research Journal

September 9, 2008

So about a week ago I started writing up a report on the research that I did this summer. Overall, I believe that the results I got for the fractional vortices matched the predictions made by the simulations that I ran using Mathematica. If the intensity measurements do indeed match up, the I should be able to use Mathematica to calculate and graph the phase distribution of the fractional vortices; I am expecting that this will clearly show that there is a non integer phase shift as one moves around the ventral axis. If all of the math works out, then I am effectively done with measurements and lab work and all I need to do now is work on completing the paper so that I can enter it in Intel STS for sure and hopefully in Siemens if I can finish it in time.

Links:

• Intel STS
• Siemens Competition

August 25, 2008

So for the past few weeks I've been continuing my work with spiral zone plates and the interferometer. I've been trying to make some second order vortices, however, the singularities do not seem to converge and what we end op with is 2 first order singularities. It seems that slight imperfections in the gating and the laser beam play a much larger role for second order vortices than they do for first.

What I've spent more time on, however, are fractional vortices. I've been trying to produce fractional vortices using the spiral zone plates, something that I do not think has been done before. The advantage of producing fractional vortices with spiral zone plates is that they should theoretically be able to be produced for a very specific topological charge.

Today I managed to get what I think are relatively decent results. I was able to see what appeared to be line singularity of the fractional vortex and in the interferometer it appeared as a series of alternating forks, meaning that there is indeed some phase activity there. What I found was that when the "freezing" lens was placed a little bit beyond the focus, you ended up with a spiral. The dark spiral arms, which placed in the interferometer, appeared to be a twisted up singularity. The lines produced by the interferometer were broken and cut along the dark regions of the spiral. When placed exactly at the focal point, however, this "spiral singularity" appeared to unravel and become much straighter, forming a line that retained the interferometric structure of the initial spiral. All of these measurements were done using a spiral zone plate designed to produce a vortex with a topological charge of 1.4. Although I ran out of time today, hopefully I'll be able to do measurements for a range of spiral zone plates and see how the fractional vortex evolves.

I have also thought of a few other ideas for the spiral zone plates. First, would it be possible to pass a beam through multiple plates to get better higher order vortices. For example, could I create a true 2nd order vortex by passing a first order vortex through another forst order plate of the same handedness. Second, could I create fractional vortices or at least fractional angular momentums by interfering two vortices with opposite handedness where one vortex is dimmer than the other.

Links:

• Optical vortices evolving from helicoidal integer and fractional phase steps by M V Berry

August 8, 2008

Today was actually a very successful day. I was able to create a much better looking vortex and build an interferometer around my setup that gave me some very good results. I started of by trying to improve the vortex. This task was rather tedious as it involved making very small and precise changes to the position of the last lens in the setup. This lens was responsible for "freezing" the vortex at the focus where it formed and projecting it onto a screen. Once I had a good vortex, I then began the process of building an interferometer, something much more complicated that it sounds. The interferometer was to consist of two beam splitters and two mirrors that would effectively interfere the vortex with a gaussian beam , yielding a forked diffraction pattern if all was done correctly. First I had to collimate the vortex beam. Because the beam was based on diffraction, every time I tried to collimate it using a standard 2 lens setup, the vortex that was easily visible with only one lens would vanish, leaving me with a spiral pattern. I solved this by realizing that when the beam was collimated, the spiral fringe patterns were able to once again interfere with the vortex, causing it to dissolve. I fixed this by placing an iris in between the two collimating lenses, cutting off the spiral fringe patterns.

I also encountered problems when setting up the interferometer itself. The gaussian beam that I was interfering the vortex beam with had to be the same size as the vortex beam, meaning that I had to shrink that beam. The mirrors had to be extremely precisely aligned so that the vortex and the gaussian beam would actually interfere. This involved tediously aligning the mirrors, checking the beam at different points, and then realigning the mirrors. By the end of the day, however, it was all worth it. I ended up with a working interferometer that I was able to use to get forked interference patterns. This meant that the vortices I were making were indeed vortices and were not fractional but order one. Having been working on these vortices all week, this was quite an achievement.

In other news, I have been reading up on some articles about fractional vortices, which actually look rather interesting. Based on what I've read, I might actually be able to make them using specially designed spiral plates. If so, I might be able to run some experiments using them which would hopefully prove rather interesting.

The most recent set of images can be found at: http://laser.physics.sunysb.edu/~nityan/data/interferometer_image/inter.html

Note: The interference pattern was very faint. Although easily visible with the naked eye, the camera had trouble taking pictures and in some pictures the vortex may not be easily distinguishable. The last five pictures on the page seem to have the best forks.

August 5, 2008

Today was a big day as I finally started putting together an experiment. Having worked with theory all this time, I'll finally be able to start testing that theory and hopefully find some new and interesting results. Over the weekend I took a series of pictures of spiral zone plates that I had created on the computer using Mathematica and Photoshop. Using a film camera and black and white film, I photoreduced the spiral plate prints while retaining a workable resolution. I then took the negatives to CVS for 1 hour photo processing. While the guy at CVS managed to destroy a couple of the negatives, the rest of them turned out all right (although the contrast could have been higher). All this meant that I came in on Monday with a set of properly sized, high-resolution spiral zone plates.

Now what is the point of making spiral zone plates, you may ask. Spiral zone plates are actually a variation on the normal zone plate, which uses fresnel zones to ensure that only light that constructively interferes at a given focus will be allowed through the grating. Similarly, spiral zone plates use fresnel zones to interfere light. The spiral part, however, means that the zones do not form circles around the center, but instead spiral around it. In this way, the light coming to the focal point from a spiral plate will have a phase shift as theta (the angle around the center) increases. When the zone plate is correctly calculated, this phase shift will be an integer multiple of theta, forming an optical vortex with a rotating wave front. Depending on how the zone plate is constructed, multiple order vortices can be formed as well as fractional orders.

Coming into the lab today, I almost immediately set to work trying to get the zone plates to work. My basic setup consisted of a laser, the light from which I then collimated and magnified by 4 times using two lenses. This beam was then passed through the spiral plate, from which the vortex was to be formed. Because the vortex would only truly appear at the focal points of the plate, I used a lens with a very short focal length at the appropriate distance from the primary focal point of the plate to "force" the vortex to propagate and prevent it from interfering with the other light. By noon I had some rather decent vortices that were fairly circular and consistent and also curved around a razor blade that I split the beam with. After lunch, I tried to redo the setup using a more powerful HeNe laser. The only problem with this was that the longer cavity meant that the new laser would produce more spatial modes, which would negatively impact the vortex. By the end of the day, I had a much brighter laser and a much more robust and versatile setup that would still produce optical vortices. Unfortunately, I have been unable to successfully filter out all of the spatial modes, and the vortex quality isn't quite as good as it was with the smaller laser.

Tomorrow I plan on filtering out the spatial modes completely, and taking some measurements of the vortices, hopefully using an interferometer, to establish their orders and purity.

For the time being, pictures can be found at: http://laser.physics.sunysb.edu/~nityan/data/data.html

July 28, 2008

So it's been a really long time since I've updated my journal. Recently, however, I've been doing quite a bit of work reading articles and trying to understand them in order to solidify my project. There have actually been several very interesting ones that I have come upon.

First, there was a rather interesting article on fractal zone plates, in which the authors claimed that by using fractal patterns in their zones, they could actually produce images with a much better depth of field and significantly less chromatic aberrations than the traditional zone plate. This would be extremely important in any type of imaging using zone plates such as future telescopes. It would be interesting to do some type of analysis of other fractal designs to see if further improvements could be made.

Another rather interesting article was one on the use of diffractive optics to make optical vortices. It has been known that gratings of Archimedes' Spiral could be used to make vortices. The group that wrote the paper, however, found that other types of gratings could also produce vortices with unique and interesting properties.

Finally, the diffraction and interference of light plays in extremely important role in Solar Coronagraphs. In the making of these coronagraphs, the sun in literally blocked out with a plate, leaving only the corona exposed. The only problem is that light from the sun diffracts around the obstruction and forms a diffraction pattern. By perfecting the technology used in coronagraphs, not only will we be able to do better research with regards to the sun, but the technology might one day advance to the point where we could use to search for exoplanets.

Links:

• Article 1: White-light imaging with fractal zone plates
• Article 2: An experimental study of anomalous behavior of spectra near phase singularity

July 17, 2008

So it's been a while since my last journal entry. I have been working on a program in Mathematica to try and simulate the fresnel diffraction pattern that is produced by light passing through a zone plate. The good news is that I think all of the math is finally correct and will yield the correct diffraction patterns. The bad news is that the math, especially the integrations, are extremely complicated and my poor computer takes a tremendous amount of time to complete each calculation. To produce a single two dimensional graph of the intensity pattern from one ring, I had to leave my computer running all night. I am currently trying to redo the same graph with a slightly larger domain, and after almost three hours my computer has still not produced anything. Oh well...

In other news, I'm planning to start doing some experiments with zone plates on Monday, starting with measurements to make sure that my model is accurate. Hopefully I'll be able to extend my model to photon sieves and then do some stuff there.

July 10-11, 2008

The journal entry for July 10-11, 2008 can be found here as a pdf file.

July 9, 2008

Today we had a presentation by Dr. Anand Sivaramakrishnan on adaptive optics. He started out by talking about traditional ground-based Astronomy where the images produced were not diffraction limited but were instead limited by the atmosphere. Distortions and non-homogeneities in the atmosphere, such turbulence, wind currents and moisture lead to parallel wave fronts from distant stars being warped and bent, effectively preventing the light from coming to a single focus in the telescope.

Adaptive optics work to correct the wave front, allowing light to come to a precise focus. Images that Dr. Sivaramakrishnan showed us of Adaptive Optics corrected images vs. non-corrected images were striking. The most basic adaptive optics system that Dr. Sivaramakrishnan talked about was of a basic feedback mechanism. When the light from the source comes into the telescope, it is reflected off of a deformable mirror and onto a beam splitter. Half the light goes through to a photodetector that will form the image and half the light reflects into a wave front sensor. This sensor will analyze the bent wave front and send an electrical signal to the piezoelectric crystals in the mirror. The mirror will then bent to counteract the wave front distortions, correcting the atmospheric disturbances that would otherwise show up in the image.

July 8, 2008

The journal entry for July 8, 2008 can be found here as a pdf file.

July 3, 2008

Today Dr. Metcalf continued his presentation on Quantum Mechanics, and started exploring the world of Quantum Mechanics using matrices in order to bypass the Schroedinger Equation and the complicated mathematics associated with it. The general premise was that any system could be described using matrices. The properties of the system itself could be described using a state vector, and any observable characteristics of the system could be produced using an operator matrix. These operator matrices would have the property that AV = kV, where A is the operator, V is the state vector, and k is an eigenvalue of matrix A which represents the observable result. For example, the Hamiltonian operator yields the energy of the state vector; HV = eV, where e is the energy. These operator matrices also have the special property that they must be Hermitian so that the transpose of the matrix is equal to the complex conjugate of the matrix; this restriction means that the eigenvalues of the matrix will be real numbers. In this way, any quantum mechanical system can be described using state vectors that represent the system and operators that give the properties of the system.

July 2, 2008

Today we had a couple of presentations on physics. The first was given by Dr. Metcalf and was on the basic ideas behind quantum mechanics discussed from a perspective that did not use advanced mathematics or the Schroedinger Equation. We reviewed imaginary numbers and matrices and began talking about the idea that particles only have a certain set of discrete states that they can occupy. We did not finish the presentation but will continue tomorrow.

The second presentation was given by Dominik Schneble and was about his work on Bose Einstein Condensates. The presentation included laser cooling, evaporative cooling, the basic ideas behind a BEC, and some new work on forming a lattice out of laser light so that each point in the lattice may only be occupied by one particle. In this way a perfect lattice could theoretically be formed, with none of the breaks or other imperfections that appear in crystalline lattices. The presentation was rather interesting, although complicated.

July 1, 2008

Today was spent mainly doing background research and exploring subfields in optics. I looked at several interesting properties of light including total internal reflection, evanescent waves (which are emitted during TIR and exhibit exponential decay), optical vortices (light with angular momentum), magnetic induction and transmitting energy using light waves, and metamaterials (which can bend light around object, effectively cloaking them). Outside of the lab, there was a lecture on lab safety which I slept through.

June 30, 2008

Today was my first day of the Simons Program and my first real day in the lab. Dr. Noe gave us an introduction to the different aspects of the lab and the computer systems. Following that, Yiwei and I proved the Law of Reflection and Snell's Law using some calculus and continued reviewing optics. We went outside for about half an hour to burn holes in paper using a magnifying glass and to try to get a heat transfer engine to work. The heat transefer engine didn't work.