Research Journal

April 25th, 2005

Wow. It has been nearly god knows how many months since I have updated this journal, but the time has come. A lot has happend both with our spanner and with other events. Ani and I, in November, wrote our paper and submitted it to Siemens. We went to Carnegie Mellon University at Pittsburgh as Regional Finalists and the experience was awesome. More than the competition, we had the opportunity to meet one of the top computer science professors in the country. We also had the oppurtunity to meet another physics professor, who happend to be the head judge. He was quite knowledgeable and told us about how he would want to use an optical spanner to measure the coefficients of friction of various objects in a medium. He also proposed that we used the spanner, once working, to measure the viscosity of various liquids. After we gave our presentation, which went really well, Ani and I had to go into the back room for questioning in front of a panel of judges. I almost started laughing but I contained myself and the questioning went smoothly. Although we didn't win, Professor Lee, the computer science professor, told us he'd help us out with the creation of the interference pattern. He said that what happend was something known as catastrophic cancellation, when the computer has to perform repeated summations, and the computation somehow breaks down. The next few months were packed. Between trips to Washington DC, for the documentary I am producing with a few friends, All state, concerts, and school, I didn't have much time on my hands. But now, I have more time on my hands and started to fiddle with the interference pattern. Ani and I won at LISEF and are going to Pheonix on May 7th. Basically, I found that the way we'd been trying to graph the interference pattern is wrong. The equation we used over the summer, with the complex phase amplitude, is too complicated. I found another equation in the same paper that is a reduced version of the equation we used previously. This equation contains the Mod function, something I should have realised as reponsible for the blazing effect. Below I have attached some pictures that show what I've come up with. It seems as if the interference patter which we are looking for occurs at the Z=0 plane. So I am still trying to find a way to isolate that plane of interference.

Interference Pattern

August 31st, 2004

August is drawing to a close but our project is most definitely not, although there has been a lot of progress lately. So basically, the HeNe is our laser now. The beam is really dirty and has a lot of excess junk around it. We managed to expand the actual beam to about 6 mm and then we placed an iris right after the periscope to cut out all the junk from the beam. Another problem we had was that the Dichroic mirror was not meant for HeNe wavelength. In other words, the HeNe was reflecting off the front surface and the back surface so there were two beams that were produced and the two beams interfered too! For this reason we ordered another dichroic mirror that would be better for HeNe wavelength. The main problem is the optimization of the HeNe as it passes through a fork grating. We finally got that paper from Azure, once she came back, and have been reading it. It turns out a fork interference pattern comes from the interference of two beams that interfere at an angle theta. We are trying to plot thisby summing two waves in mathematica/maple. If we can do this than we will be able to produce CGHs that will channel the intensity to one order over the rest. This would help us greatly.

August 25th, 2004

Today was an interesting day in that Ani showed up and we started to work on the tweezers. Our main goal was to find a laser that we could use in our setup since the high power laser is basically out of the question and the diode laser could not produce sufficient vortices. Interestingly enough, we found a laser that the diode laser, which was supposed to be 25 mW, turned out to be only 11 mW. We found a HeNe laser that was 18 mW so we're going to use it. After some measurements we found that only about 1/12 of the beam that goes into the fork grating actually comes out in the +1 and -1 orders. We emailed Azure about something that she had mentioned about a fork grating that could concentrate the intensity into one order. There was also stuff about this that was mentioned in the Optical Vortices book. If this be true, then it would help us a lot in that we would no longer be dependent upon a fork grating that suppresses orders in order to do our trapping. We were set up our laser today (the 18mW one) and aligned most of the setup. Dr. Noe told us that we shouldn't just throw some stuff together, and we happen to agree with him about that, and I can definitely see how we could have been very hectic in the interest of time. For this reason we did do some reading and decided to hold off a little bit today. But as far as today is concerned we were able to align the CCD camera with the microscope such that the whole field of view is visible in the TV. This way we won't have to actually move the whole slide to see the laser in the field of view. We even found a beautiful filter to filter out the light so that the CCD isn't over exposed. Actually the field of view looks pretty BEAUTIFUL. This is really due to the fact that we do not have an IR filter anymore so all the dust and dirt that was on it is no longer visible. Our main concern right now is how to concentrate the intensity into one order. How is this possible? I also have one more side question that no one's been able to answer so far, how do Laguerre Gaussian beams propagate?

August 24th, 2004

In the past ten days I aligned the interferometer, among other things. I can tell that it is not perfectly aligned because the vortex does not totally disappear; however, the alignment is very close. It is in fact close enough to demonstrate the principle being illustrated. As the beams get closer and closer in line with each other the stripes that form as a result of interference get larger and larger. In theory they should get to a point where the whole beam is gone, but that has not yet been achieved. I have come as close as producing a stripe that takes up half the beam. It was also very interesting to watch the beam in space through the liquid nitrogen vapor. The interference pattern could be seen in the whole beam, as expected. More results and pictures can be seen in my OAM Sorter page.

Friday came with an unexpected turn of events. Ani asked me to work with him on the Optical Tweezers. Since I would not be able to compete in Siemens as a junior alone and I have also been interested in optical tweezers, I enthusiastically accepted his offer. He hasn't been in the lab yet this week but there have been a few developments since. We needed a more powerful laser. We asked Dr. Noe about it but he told us to email Dr. Winters to ask about safety considerations. She responded saying that it's a big step to turn the Laser Teaching Center into a high powered laser lab and that appropriate safety measures are necessary (goggles, barriers, power supplies, etc.). So as of now it doesn't look like we'll get the laser in time, and we are considering using the 30 mW HeNe laser. It should be enough power, but might kill cells that we would try to trap. We can still trap polystyrene spheres. I'm still waiting for Ani to get back so that we can start to work on our project.

August 14th, 2004

Its proving to be a very hard task, aligning the interferometer. I cannot figure out which beam is cockeyed. So to solve this problem I got a bucket of Liquid Nitrogen. I put it in a coffee can and tried to use the vapor to see the beam. I could see the beam, but it is still not aligned. This afternoon I'm going to try to align the laser and the interferometer without any aides.

August 13th, 2004

My head is throbbing right now. I really do not know why. I have made a lot of progress on my project this week. I built the setup, now all that is needed is alignment. The beam from the HeNe laser is allowed to expand for about a meter before it passes through the forked grating, where an array of optical vorices present themselves. They are then reflected into the first beamsplitter in the Mach Zehnder Interferometer. Before passing through the beamsplitter, though, the array of vortices is filtered such that only one order passes through. In the arms of the Interferometer, the beams are rotated such that there is an angle difference between the two beams of 180 degrees. Now, when the recombine, the interfere, constructively or destructively depending upon their lvalue. If l is even the beams interfere constructively because they are completely in phase even with a 180 degree rotation. If l is odd, however, they are completely out of phase with each other and therefore destructively intefere. In this manner, different orders of Laguerre Gaussian Modes behave differently in the interferometer. My major problem at the moment is alignment. I need to align them pefectely so that the two beams are completely colinear. The slightest deviation can cause a problem.

August 9th, 2004

The lab seems empty today. Friday, I started to set up. Since I do not have so many resources, I am planning to build 2 interferometers that are fixed. I also think I may build one interferometer on a movable platform, or something of that sort, so that I can move it around to different locations. That way, I should be able to predict where each order of the Laguerre Gaussian mode would go in the sorting scheme.

August 4th, 2004

This journal updating is no longer weekly. It is sporadic, at best. I spent the morning preparing for the Simons tour. After lunch, I read in the Feynman Lectures about vector calculus. It helped me broaden my understanding of the "del" and the paraxial wave equation. I am planning to ask Dr. Noe about the beam splitters and prisms tommorow, so that hopefully I can begin 'constructing' my sorter. I also found a neat site with all of George Sudarshan (a friend and the discoverer/theorizer of the tachyon) publications on it!

Here it is

August 2nd, 2004

I spent last week reading more about LG modes and their role in my project. I am planning to build a device which will sort a beam of photons based on their orbital angular momenta. In an LG mode, the orbital angular momentum is quantized in l units of h "bar." Using this information and a cascade of Mach-Zehnder interferometers I am planning to sort the beam. The basic principle that I am working off of is that a beam with an even l, when rotated, will interfere constructively with the non-rotated beam. However an a beam with an odd l value, when rotated will interfere destructively with the original beam. Right now, I am concentrating on producing the beam which I plan to send through the cascade of interferometers. I am planning to use the open cavity HeNe laser and place a cross-hair in the cavity so that the laser would oscillate in high order HG modes, which I would then convert to LG modes using a mode converter. If that works, which I hope it will, I plan to start the construction of the beam sorter.

July 23rd, 2004

I've decided to update this journal weekly, instead of daily. I also underwent a brief stage where I thought I would pursue a project with adaptive optics. Adaptive Optics (AO) deals with aberrated wave fronts that result from turbulence in our atmosphere. To correct these aberrated wave fronts AO systems rely on deformable mirrors, mirrors whose membranes change. AO systems typically include wavefront sensors, deformable mirrors, and computers to deform the mirrors in realtime. For this reason the computers need to be extremely powerful. AO systems therefore, tend to be extremely expensive so it was unrealistic for me to pursue such a project. Today, I began to look into another topic of great interest. It deals with the sorting of photons based on their orbital angular momenta. The setup involves the use of several Mach-Zehnder Interferometers and dove prisms to sort the light. This experiment also requires the usage of Laguerre-Gaussian modes and the interpretation of patterns formed by interference. I think I will study the theory more and then eventually build this setup and investigate. Measuring the Orbital Angular Momentum of a Single Photon

July 17th, 2004

After building a Michaelson Interferometer, which was very interesting, I began to read about adaptive optics. I came across this wonderful paper about imaging extra solar planets by aligning the wave fronts through a whole apparatus. Since it is all theoretical, I may try to set it up, then continue and try to take the experiment further.

July 16th,2004

I read a lot about astronomy and spectroscopy today. I'm thinking of going into spectroscopy of either stellar bodies or possibly atoms. I also read about interferometers today...

July 15th,2004

I read this morning about laser cooling, and after the pizza lunch, I began to think about astronomy and spectroscopy. I thought about pursuing a topic in the spectroscopy of accretion disks of black holes or extra solar bodies. Since I do have a much bigger background in astronomy than I do in laser cooling, I might be able to apply what I know about spectroscopy to stellar spectroscopy.

July 14th,2004

I read more on MOT systems in the morning and am looking more into the magnetism part. Jose's talk was very interesting and I learned a lot about laser modes and Gaussian beams. More to come...

July 13th, 2004

Professor Metcalf gave a talk in this morning about MOT systems, at least about the magnetic part of it. He also began to explain the optics involved and left off there to pick up soon. I spent some time reading about the basics behind MOT systems, about optical pumping, potential wells, and a little bit of saturated spectroscopy. Some of it was cleared up when I went to the Francium Lab with Yiyi and Azure. I'm planning to read more on MOT systems and find an aspect of it that can be researched.

July 12th, 2004

Today was my first day back from Europe. I caught up with some stuff in the morning when everyone explained to me basically what they did the last few weeks: like listen to Professor Metcalf's talks. I went out to lunch with Dr. Noe, Yiyi, Rita, James, and Azure, and discussed some Laser Cooling. After setting up my journal and all, I had a small talk with Dr. Noe about what I should focus on. I'm leaning towards concentrating on one element of the MOT, since the actual construction of a MOT is a very large project that cannot be done in one summer. I plan to start looking into seperate elements of MOT systems and concentrate my focus.
Yaagnik Kosuri
April 2004
Laser Teaching Center