## Journal## Monday, August 30, 2010I'm finally able to write in my journal again! I had some technical issues but I finally have access to this system now. But for some reason, the connection is really unstable and keeps logging me out. I worked on the Gouy phashe shift values last week, and I was honestly really nervous about the outcome, expecially because I kept on getting values that did not make sense at all. But I was making a few critical mistakes (which I eventually fixed). 1. When I was calculating the Gouy phase shift of the inactive beam component from the refocusing lens to the point of vortex destruction (pvd), I calculated the Gouy phase shift for the entire distance. However, I needed to calculate separate phase shifts for the distance up to the waist, and from that point to the pvd. 2. Calculating the Gouy phase shift for the active beam component from the refocusing lens to the pvd was NOT simply the arctan(distance traveled/rayleigh range). The z in arctan(z/zr) is sometimes defined as the 'distance traveled' only because it is assumed that one is calculating the Gouy phase shift up to the waist. However, that does not hold true for my experiment, since I'm trying to calculate the value up to a point before the waist. Therefore, I had to find the phase shift from the refocusing lens to the waist, and then subtract the phase shift from pvd to the waist. As a result of discovering mistakes and fixing them for a good two hours, I got the following Gouy phase shift values: Inactive beam component: 6.04489 ~ 6.0 Active beam component: 5.84533 ~ 5.8 Soooooo the difference is about 0.2, which is pretty close to zero!!! Yay! ## Friday, August 18, 2010Last night I worked on taking pictures of the beam under four different conditions: when the refocusing lens was double-convex and not tilted, when the d-c lens was tilted, when the refocusing lens was plano-convex and not tilted, and when the p-c lens was tilted. Both lenses created vortices when tilted by a similar amount (5~6 degrees for the double-convex, and 4~5 degrees for the plano-convex). One problem I ran into while taking the pictures was a horizontal smudge of light which made it hard to examine the beam. We tried cleaning the polarizers and everything but it didn't go away. So when the intensity of the vortex is low, it is hard to make out the shape of the beam. When I increased the exposure time, the smudge became brighter also. ## Wednesday, August 16, 2010Hamsa came to the LTC today, and we talked about my experiment and kind of came to the conclusion that we will need to take pictures of the focal region with a camera when the beam is focused down by a double-convex lens and then do the same thing with a plano-convex lens. Coddington's equation says that the new focal lengths of the x and y axis will be f*cos(a) or f/cos(a) (a being the angle of tilt) but when the focal length is graphed for an increasing value of a, one focal length experiences an increase while the other decreases. This is odd because a previous student project came to the conclusion that BOTH focal lengths decrease, but the difference between the focal lengths increase because one focal length decreases faster than the other. Below are some graphs (I got the third and fourth one using Coddington's equation) A graph of changing waist sizes before the refocusing lens is tilted: A close-up of the focal region refocused by an untilted lens A graph of changing waist sizes after tilting the refocusing lens by 6.5 degrees: A close-up of the focal region refocused by a tilted lens ## Tuesday, August 15, 2010The miniproject page is looking a lot better now that I cleaned up the html and inserted the correct pictures and equations. I also started working on my report on my project, both for school and for the LTC. I have strong theoretical values to support what we observed, so all I need to do is write a good report on it. I really want to have a solid draft by the end of this week!! ## Saturday, August 14, 2010The Simons Program ended yesterday with a successful poster session and awarding ceremony. I presented my poster that showed the results of refocusing the vortex from a single lens mode converter. So this week was all about getting my abstract and poster ready for presentation. I'm glad my poster turned out nicely. I thought I would ahve a lot of trouble printing it, but luckily nothing went wrong. Marty suggested another really interesting thing on Friday - he said by tilting the refocusing lens, we may be able to move the position of a waist. This will lock the beam into a vortex, so it won't turn back into a HG even after being focused again. I decided that it would be a nice idea to find all the equipment by Friday so that I can work on it over the weekend, but I ended up building the entire setup. I also got really nice results - when the lens is turned by about 8 degrees, the beam becomes a vortex and remains a vortex. I took some pictures (uploaded to my photos page) of the results. ## Tuesday, August 10, 2010Marty found out something extremely interesting about the single lens mode converter!!! I will update in detail later today. Dr. Noe and I worked on my photos and abstract page. We explain everything in detail. Other things that happened today include losing my HG mode which I recovered by placing a hair inside the laser cavity (the farther away from the output coupler the better) and the Simons fellows visiting our lab. Ben, Pradyoth, and I each briefly explained our own experiments and showed them our setup. A lot of people didn't show up, but I understand that everyone is trying to finish their experiments by this week. ## Monday, August 9, 2010I found out today that I will not be able to build a tweezer in two weeks because the high-power laser is gone now. I will be measuring the intensity distribution of the vortex in far field using the pinhole method, finding the intensity distribution of the focused vortex (show the change in ellipticity from right to left), and fit the curve according to the expected intensity distribution of LG beams. Also, I will show the intensity distribution of HG mode and compare it to the expected values as well. I want to eventually relate most of these things to astigmatism and somehow figure out whether astigmatism stayed the same or decreased. ## Saturday, August 7, 2010Today I focused the beam and measured the residual astigmatism. On Friday I was trying to find a good way to measure the x and y axis of the beam. I thought I would just need to traverse the beam in the x and y direction, but the beam itself was rotated 45 degrees because the input Hermite-Gaussian beam was not tilted. I attatched the razor blade to the transition stage so that it is tilted 45 degrees. Later, when I analyzed the data, I divided the distance traveled by sqrt2 to get the real distance traversed through the beam. I did end up with an ellipse, but the difference between the waist in the x and y axis is not very big. But since the actual size of the widths themselves are small, the differences are significant. ## Thursday, August 5, 2010I realized that I can use the hyperbola graph to find the waist!! I knew the formula and that I can find the waist from knowing just one width, but the calculations turned out to be imaginary (probably because of a typing error). Anyway I found that the optimum single lens mode converter for the laser will be the apparatus with the following conditions: - f mm = 100 mm
- Rayleigh range of laser = 281.882 mm
- rayleigh range after mm lens = f cyl = 20mm
- d from laser to mm lens = 347.9mm
- d from mm lens to cl = 24.84
The resulting vortex beam was beautiful. It was actually circular. Hurray! For the rest of the day, I set up and found the intensity profile of the vortex. It took me a while to set up the transitional stage, and it also took me a long time to take the data because the vortex beam had a pretty large diameter. Dr. Noe suggested that I use a pinhole instead of a razor blade since I can show the quality of the vortex by showing a nice M-shaped intensity curve. My data points are little iffy though: the intensity didn't equal to zero at the center (probably because I didn't exactly traverse through the center) and the intensity of the laser itself seemed to increase. The 'zero' was at .14 volts but increased to .3 volts by the end. I'll analyze the data tonight and see if I need to redo it tomorrow. ... I just finished plotting the graph. The y values are just the voltages because I didn't use a resistor, and V=IR so it is proportional to the current. ## Wednesday, August 4, 2010We had an extended lunch meeting today. We went over our abstracts, and the REU students gave their practice talks. Other then that, I worked on my poster. The draft is due tomorrow, so I need to have the basic information on it by tonight. I have a lot to accomplish this week. First, I need to set up the lens to demonstrate that the beam in the near field is elliptical but circular in the far field. I can measure this experimentally by profiling the beam in the x and y axes. I can then calculate the waist positions by using matrices. When we were going over my abstract today, Marty suggested something interesting that might take my project to another level. I can address the possible disadvantages of using the single lens mode converter for optical tweezers and somehow experimentally determine how the astigmatism will affect the performance of the tweezer. Optical tweezing was my main interest before I started focusing on learning mode conversion, so I am really excited for this! I understand that I don't have too much time left, so I will spend extra hours in the lab from now on (except for tomorrow since I am planning on having dinner with my dad! :)) ## Tuesday, August 3, 2010The poster is due on Thursday and the draft for abstract is due tomorrow!!! I better work on this tonight. These are the top two things on my to-do list right now. But today was a pretty exciting day for me at lab. Twenty three high school students from a Stony Brook math camp came to visit our lab, and I got to show them my project! It was such a good feeling having something to show other people what I'm working on. I really need to get my calculation over soon so that I can start adding things to the single lens mode converter. But I still need to work on the abstract and poster first since they are due this week.. The Simons talk today was about the college admission process. The Oliver (Trey) Street, director the Honors College (and who was also a former Georgetown admissions officer), came and told us all about the secrets behind the doors of the admissions office. I learned that the things they tell us are not true many of the times. I got out of lab early today and went on a run with Sarah and Pam, then went to the gym to do some core stuff. I really need to get in shape for field hockey! But hearing what Oliver Street talked about today, I might have to compromise some of my current activities to focus on my academics because my course load is a killer in the fall term. Oh, and I figured out why Hamsa had a different focal length for the x axis!! I forgot that she was focusing on tilting the lens. Later Marty and Dr. Noe found out that it wasn't necessary after she had finished writing her paper. ## Monday, August 2, 2010Dr. Noe emailed to inform me that I can start off with a given cylinder lens and figure out the appropriate mode matching lens from there on. I spent my day calculating and setting up a single lens mode converter that suits the new waist of the laser. Since the length of the cavity was different, I had to find the width of the beam to recalculate the Rayleigh range of the beam. Although I was worried because of the low intensity output of the laser, Katya showed me a way to amplify the signal (a method initially suggested by Dr. Noe). I looked up the responsivity of the laser on the Thorlabs catalogue and calculated the current. I found the waist with very little error (less than 1!!) and found the Rayleigh range, which was 1653mm. Then, using the equations given in the Photonics West paper, I calculated d1 and d2, which are the distance from the waist of laser to the mode matching lens and the distance from mm lens to the cylindrical lens, respectively. I assumed that the focal length was 20mm, which was the lowest I can find (actually, the lowest one is 19mm but the shape of the lens is weird. Also I already did all the calculations for 20mm). I plugged in different focal lengths for the mode matching lens to find the smallest d1 and d2. I got d1=~957 and d2=~209 for a mm lens focal length of 200mm. When I actually set up the mode converter, d2 was a little but longer than expected. The total distance between the mm lens and cl was supposed to be 229mm, but it turned out to be 256. Maybe the distance between mm lens and the laser is a bit off. I was setting up the matrices when I realized that Hamsa's first matrix for each beam component was different. For her beam on the x-axis, she moved around the mm lens. The final focal length of for the x-axis beam was 66. I don't really understand how/why this happened... I thought the initial beam from the laser was isotropic. So why do the two beam components need different mode-matching focal lengths? ## Saturday, July 31, 2010Yes, it's Saturday and I'm in lab working on my project. I realized that I have a ton to do before I build the slmc. I made one yesterday, but the since the length of the cavity of the laser is different from that of the paper that I read, I need to re-calculate the waist, the focal length of the lens I will use, etc etc. I tried to profile the beam from the open cavity laser today, but the intensity of light was so low that I don't think I'll have enough data to profile the beam the same way we did for our mini project. What I need to do: figure out waist and Rayleigh range of the laser, then figure out what kind of mode-matching lens I need and where I should put it, then figure out the focal length of the cylindrical lens I need ## Thursday, July 29, 2010I emailed Giovanni Milione yesterday asking about cylindrical vector beams. I read a couple of papers that caused some confusion. One paper mentioned the radial polarization of LG beams, whereas the other one talked about the azimuthal and radial indices of a LG beam. I wanted to know
- What causes the singularity in cylindrical vector beams
- What is the exact difference between LG and CVB
- Radially polarized beams can have azimuthal indices?
Giovanni responded with a really nice explanation of the differences between the concepts. LG beam is characterized by its azimuthal PHASE, whereas radial and azimuthal polarizations are independant of the azimuthally varying phase. The beams that just have the radial or azimuthal polarizations without the azimuthal phase are cylindrical vector beams. The indices of an LG beam, l and p, are sometimes referred to as azimuthal and radial indices, respectively. These have no relation to the polarization. L, or the azimuthal index, explains the azimuthal phase variation (from 0 to 2pi). P indicates the number of rings that the LG beam has. Usually, p=0 which means that the beam has a single ring. This index is referred to as the radial index. I'm glad I emailed Giovanni because his email was extremely helpful. There are so many different azimuthal and radial things related to LG and CVB... Also, I figured out the errors in my spreadsheet and fixed them. I also am now looking at how the beam waist changes as I change different parameters. ## Wednesday, July 28, 2010I finished creating an excel spreadsheet to organize the matrices. I got so confused yesterday that I sent a facebook message to Hamsa, who originally found and developed the single lens mode converter. I was so glad she replied, and was even happier when her explanations actually made sense!!! What I was uncertain about was the relationship between regular matrix optics and Gaussian optics. The complex parameter q used in Gaussian optics involves an approximation using the A, B, C, and D in the 2X2 matrices used in regular matrix optics. But when I asked Dr. Noe yesterday, he said that the regular matrix is not used in Gaussian optics. At this point I got really confused, since Hamsa's paper on the slmc definitely used matrices. Hamsa explained to me that the usages of matrix components in finding the q parameter has nothing to do with how matrices function. I need to compose a really long message thanking her now! haha. Anyway, I spent most of my time today making a spreadsheet to simulate the setup in the slmc paper. Thankfully, my resulting q values were equal to that of the paper. I had to look up formulas for computing complex numbers online, but it was definitely worth the time since it worked!! As of now, I have all the lenses mentioned in the paper in my spreadsheet, and I have an additional lens (a hypothetical one with a random focal length) that I will be using to focus down the light. What I need to do now is how the numbers I have on my spreadsheet relate to astigmatism. I understand that the beam in the vertical axis has a different waist position to that of the horizontal beam, but right now the numbers are wayyyy off. Other than making spreadsheets, we also did other exciting stuff during LTC lunch meeting. A rising junior in high school(I forgot his name) came to explain to us an experiment he was doing. He was trying to create visually-observable waves by blasting different frequencies of light into a huge tube partially filled with microbeads. During his talk, we found out that the waves of microbeads he was observing were extremely narrowly spaced out through the cavity compared to the theoretical values. (Theoretical value was 2m, his observation was maximum 2cm.) Dr. Noe said it may be because of the high frequencies made from the sound generator, since the frequencies generated may not be entirely pure. The student did not have a vast understanding of physics since he didn't take a physics course yet, but he definitely had a lot of enthusiasm for what he was doing. I really respect him for his confidence in his work and his positive attitude. We also proofread the abstracts written by the REU students. We discussed each and every sentence carefully. I got a general sense of how an abstract should be written. Hopefully I'll have something significant to write about in my abstract as well... ## Tuesday, July 27, 2010We spent most of our time last week writing our mini-project report and making a powerpoint presentation for the Optical Vortex Party we had on Monday. I had a really stress-free weekend, so I am ready to give my all to designing and executing my project this week. Yesterday, we had a lot of people come present their works on topics related to optical vortices. Giovanni Milione from City College of NY and Kiko Galvez from Colgate University gave talks introducing optical vortices and vector beams. I learned a lot about polarized light. I never really looked into compination of different polarized modes to create different kinds of vector beams. It's a little hard for me to visualize how certain parts of a doughnut shaped vector beam could have different polarizations at different parts, but I can kind of see how it works. High school students participating in research programs at City College of NY also came to present their works. I was surprised at how many high school students were working on projects related to circular vector beams! Some of them were funded by the army (!!) to study optical vortices. The Poincare Sphere seemed lika a cool concept. Heather was trying to explain it to me a few weeks ago when I asked her about her experiment, and I did not understand it at all at the time. After Giovanni's explanation, It makes more sense now. The equator of the sphere represents linearly polarized light (HG), and the poles are the circularly polarized light (LG). Light represented in places between the poles and the equator will look something like HG with the sides filled in (kind of like LG modes). One interesting thing I learned that might be related to my project was the fact that when radially polarized beams are focused down, they do not maintain their doughnut-like shape. However, azimuthally polarized beams still have a singularity when focused down. I thought the vortices created from the single lens converter were azimuthally polarized, but maybe I'm wrong. LG beams have both radial and azimuthal indices, so maybe they have both. So that means that if I were to focus down a LG beam, it will not have a hole in the middle. But is LG beam a vector beam? After the "party", Dr. Noe treated us to some really good Chinese food. It was one of the best meals I had in a while. The food I'm craving the most right now is dwenjangchige and yeulmu kimchi. And Gyeranmari. I just found out that the radially polarized LG beam is the type of LG beam used in tweezing, accelerating, and etc. I'm reading a paper called "Propagation properties of radially polarized partially coherent LG (0,1)* beams." They mention this in their introduction. One question is, what do they mean by 'partial coherence'? ## Wednesday, July 21, 2010Former members of the LTC, Rebekah Schiller and Greg Caravelli, shared their experiences as high school teachers today. They were both researchers before they became high school teachers, but they both found teaching students a worthwhile experience. It felt a bit weird hearing them talk about teaching high school students since I am a high school student myself, but I was able to relate to what they were saying in their talks. They reminded me of some of the teachers I have met at Choate who really invest much of their time in teaching students and helping students understand the material. Looking back, I would like to thank them a lot. :) I read more papers on Gaussian beams today. I can't believe I was trying to understand everything back at school. There was a lot to know before I even attempted to understand some of the papers I read in the Spring term. So far, I read the two papers and one power point presentation to learn about Gaussian beams (uploaded in my References page) and these three works are working like a dream team for me. Each paper leaves out some information that confuses me, but when I look for the information in the other two papers, I can find it. My summer reading book arrived (finally) after a three week's waiting. I have so much reading to do, both for school and for lab. Plus, we have that mini project write up that is not going well at all because we've spent so much time fitting the erf curves to our data. And I have to start working out for field hockey preseason, too. Apparently I have to run two miles in 16 minutes. I should have listened when a wise senior told me that junior summer is no joke. ## Tuesday, July 20, 2010I just learned that the 2 x beam radius (or the diameter) is not the
distance from a zero-intensity point to the zero-intensity point across
the beam, but it is the distance from the 1/e My dad just gave me a 45 min lecture on quantum mechanics! I just reviewed over my notes to see if I understand everything, and so far I do. We didn't discuss anything in great depth yet, so maybe I should read about how the Laguerre and Hermite polynomials are related. ## Monday, July 19, 2010We took more data today and structured our report for the mini project. I have to read and learn more about Gaussian beams to get to know them better.. ## Sunday, July 18, 2010I couldn't upload a journal on Friday because I was sick for the rest of the day, but here's what we did. We took some more data and made graphs (just as we did for the past two days.) We then plotted the different waist of the beam at different distances. Although it resembled a hyperbola, I just got an email from Ben saying that something seems wrong. I'm guessing that we have a lot of error in our data, but we really tried our best to minimize the error. Here is the graph we have so far. We haven't worked on fitting the hyperbola to the points yet, so ignore the red line for now. The 'distance' we measured was the distance from the laser to the razor blade. I wonder if there is a more accurate way to measure it since we literally took a yard stick and measured the distance between the laser and razor blade. We also started working on our report. We put the document on Google Docs, which is a great application that allows many people to edit the document at once. When we are finished with the document, we will upload it to each one of our accounts. ## Thursday, July 15, 2010We were taking data for various distances today. Instead of taking note of what we thought was the 'starting point' and the 'ending point' to calculate the width, we measured the intensities at various points. We then calculated theoretical Gaussian values and plotted the integrated values. This process was relatively simple, but we were devastated when the resulting graph from the theoretical values did not form an erf curve. We were not able to figure out what we were doing wrong! I finally figured out that we had the WRONG FORMULA! I was questioning the formula but my colleagues convinced me that it was right. The reason for this confusion was that the first cell of theoretical Gaussian values (from few days ago) had the wrong formula, and that was where we copied the formula from. But that data turned out right because the formula was right from second cell on. Dr. Noe gave a helpful advice on how to find the width. The width in the final Gaussian formula IS the width that we are looking for! So far, we are doing pretty well with minimizing the error. Ben calculated some parameters to 1/1000 of the accuracy in order to lower the error sum! By the end of the day we were really tired from doing all a lot of work on exel. Tomorrow, we should finish taking data and wrap up the analysis and work on writing the report. ## Wednesday, July 14, 2010We worked more on our mini project (which became official
today) and took data to measure the diameter of the beam. But
Dr. Marty Cohen came and told us that since Gaussian beams don't have
a distinct starting point and an ending point, we cannot measure the
exact diameter of the beam. What we CAN do is measure the 50%
intensity points, or find the points where intensity goes to
e ## Tuesday, July 13, 2010The Simons fellows went on a field trip to Brookhaven National Lab today. We saw PHENIX, a part of RHIC, the heavy ion collider of BNL. It was really cool since I have seen ALICE before, but I didn't really understand what was going on at the time. But today the lecture on ATLAS (and a little explanation about ALICE) helped me understand what the physicists are doing in these facilities. The lecture on supercomputers was also absolutely fascinating!!! What I need to do today: organize lab notebook! ## Monday, July 12, 2010We measured the intensity of light while we gradually blocked portions of light by moving a raser blade through the laser beam. Our data looked pretty 'erfy'! By using the method that Dr. Noe taught us, we came up with a Gaussian function of which the integral graph fits the data points. Gaussian Function with error of 9637.028 (as low as we can get it) ^{-2(x-93)2/642}Gaussian function with error of 2981.149 (as low as we can get it) ^{-2(x-30)2/182}## Friday, July 09, 2010Astigmatism is the propagation of light in two orthogonal directions that have different focal points. Using an olive bottle, which is a cylindrical lens, we can focus light, but the focus will be a line instead of a point. Below is a picture of astigmatism - the bottle has a short focal length, so when the screen is moved away from the bottle, the light will disperse into a straight line. Extending on what we were working on yesterday, we were thinking about the intensity of light at radius r will be with respect to the width. The Gaussian function is ^{-r2/w2}and since r=sqrt(x ^{-(x2+y2)/w2}which is ^{-x2/w2} x e^{-y2/w2}So whether we are measuring the intensity profile in a line down the center or in a line a bit off the center, we will see graphs with the same Gaussian shape. A student who had done a research on a similar topic had measured the width of the beam for different distances between the screen and the laser. Pradyoth said the graph looked like a hyperbola since the graph was curved near the origin and became a staight line as it went to infinity. So to learn more about hyperbolas, we derived the formula of a hyperbola using the definition (the differences of distance from two foci stays the same). The calculation wasn't hard but it became pretty messy because we wanted to isolate y on one side. ## Thursday, July 08, 2010Dr. Noe and Sam came to join us during lunch and taught us how to think like physicists. We estimated different orders of magnitudes, and using that, we calculated the image sizes of the sun and laser beams on our retina. Assuming that the focal length of the eye lens is 1/50m, the size of the sun would be f*theta, theta being 1/100. The resulting size is .2 microns. On the other hand, lasers diverge at an angle of 1/1000 (given that the size of the spot is 1cm when the actual laser is 10m away) so the resulting image of a laser is .02 microns. After lunch, I joined Heather and Katya rummage through some optical devices when Dr. Noe called Ben, Pradyoth, and me over to think about what would happen to the diameter of a laser beam if we double the distance from the image. We predicted that when the distance from the laser is zero, it would start at a certain point and have a certain possible slope. Using a crude measuring method, we found that the diameter approximately doubles as distance from the screen doubles. But in order to get the best fitted line, we went through a more complex process of calculating the square of the difference of estimated and measured values. Below is the resulting graph of the best fitted line. ## Wednesday, July 07, 2010It's so hot in my room right now! The RAs decided that it's kind of dangerous to restrict us to our rooms for the night, so they are letting people sleep in the lounge, but I have a fan so I think I'll survive. Still, it's a pain using my computer because it gets extremely hot in this weather. Ok so back to the journal. Today's lunch meeting featured Laser Sam, who has the FAQ webpage which is apparently often found in the top ten results on Google when people search for something related to lasers. He introduced various types of lasers (diode, gas, liquid, and solid state) and their properties. I had very little background knowledge of lasers so most of the things he talked about were intriguing. For example, I had no idea green laser beams are created by high power diodes pumping solid state lasers. The frequency of the laser beam, which is initially infrared, is doubled in the process and therefore becomes the green beam with 532nm of wavelength. According to this site the FDA restricts the output of the green lasers to be under 5mW (I think Sam mentioned it too.) As Dr. Metcalf has mentioned today, what does the FDA have anything to do with lasers? Lasers are definitely not food, so maybe they can be considered as.. drugs? I have no idea. Other things I learned from the talk today were: - Diode lasers can be almost every color except green-yellow (500nm to 620nm.)
- Gas lasers create light from electrical excitation. The beam qualities in these lasers are high, almost producing Gaussian beams.
- Lasers are stabilized to reduce variation in output and create an absolute frequency reference. There are many stabilization techniques including dual mode polarization stabilization (the most common) and external reference stabilization (the most effective technique.)
Sam also mentioned the Fabry-Perot interferometer which can be used to find wavelengths of light by interfering beams, each resulting from reflecting between two reflective surfaces. I didn't quite understand the two frequency lasers though. I think it had something to do with this interferometer. Also, I have a couple vague ideas about what I want to do for my project that I will post on my ideas page. ## Tuesday, July 6, 2010Today we had our first Simons lunch meeting. Dr. Simmerling talked about his studies on HIV protease and DNA damage repairing by using computational chemistry. I actually read a review article written by him, so I was mostly familiar with what he was talking about. He seemed really enthusiastic about what he was doing, and he also encouraged us to find something we are passionate about. Other than that I read a couple articles and found that a quasi-Bessel beam can be created by focusing a Laguerre-Gaussian beam (or just a Gaussian beam) with an axicon. Then I read the Wikipedia page for Bessel beams and saw that they also mentioned it. So I searched for papers on topics related to that and found a paper on diffracting LG beams using helical axicons. Helical axicons were described as a combination of an axicon and a spiral phase plate. Also, high-order Bessel beams are also characterized by vortices, which is interesting. Overall, I guess today was a very uneventful day. I'm excited for the lunch meeting tomorrow because someone's supposed to come and to a lot of demonstrations, which are always extremely exciting. ## Monday, July 5, 2010We learned how to use Gnuplot today, but unfortunately Ben will probably be the only one to use the program on his PC since the program doesn't run on Windows or Mac. I arrived late today so I missed the first part of Gnuplot experimentation. Ben and Pradyoth were plotting an ellipse which has a focus that is infinitely far away from the other focus. The shape of the ellipse, if stretched even more, will eventually form a straight line. Similar plotting strategies were used to plot the osculating circle and parabola. Dr. Noe introduced some different things to notice about orbits today, such as what happens if a parabola osculates with an ellipse. We initially got a parabola that crossed the ellipse twice, which Dr. Noe pointed out to be wrong. Later we found out that there was a problem with miscalculation while taking the second derivative of the function of ellipse. A really interesting fact that I learned today was that the parabolic motions (usually free falling with a positive horizontal speed) are actually elliptical. One of the foci is the same as the 'parabola' but the other foci can be considered as the center of Earth. We thought it would be interesting to find the focal length of the parabola in terms of the variables used in the equation for the ellipse. So here's what we did (keep in mind that we considered the vertically-stretched ellipse.) First, we found the coordinates for the foci by using the formula for finding the distance between two points. Then, by equating the first derivative of the ellipse equation to zero, we found the coordinates for the maximum point of the ellipse. The distance between THOSE two points, the top focus and the maximum point of ellipse, is just the subtraction of the y coordinates because they are both on the primary axis. The distance is therefore b+k-sqrt(b^2 - a^2), which is also equal to 1/(4A) in which A is the A in a equation for a parabola, y=Ax^2. The variables b, k, and a are all parts of the ellipse equation. In order to verify that the ellipse with a focus at that point will osculate with the parabola, we plugged in numbers for the variables a, b, h, and k. a and b are the variables in the denominator of the ellipse formula, and h and k are the variables subtracted from x and y, respectively.... I think it'll be just easier if I link the equation that I'm talking about here, except the equation in this article doesn't have h or k. Anyway, we set k and h to zero to simplify the coordinates for the foci, and then had a=3 and b=5. So after a few lines of calculation, A (as in y=Ax^2 in the parabola) was 1/4, which gave a graph similar to the osculating parabola we found for the ellipse. So that was the major thing we did today, and I'm very pround of us because we worked on it for some time outside lab and discovered something new. I guess we are slowly beginning to understand parabolas and ellipses better? :) ## Saturday, July 3, 2010I was completely wrong. The special lens wasn't a Fresnel lens at all. It was a plano-convex lens with a really gradual curvature. The focus created with the light coming in an angle theta will create a focus below the focus on the principle axis. By using small angle approximation and trig, we can predict how big the image can be. Image - that was the other thing. The reason the focus is so big is that the focus is not actually a point, but it is an inverted image. Another thing that I was wrong about was the parabolic mirror. The focal point at 1/4a can't be proved by the relationship with the oscalating circle, but we can show the r=1/2a relationship after proving that the focus is at 1/4a. Yesterday, we got the Stirling engine to start. I'm really glad we were able to solve the problem without opening the motor cavity! Pradyoth polished the surface of the mirror by the metal polish that Dr. Noe brought, and we also lubricated the turning parts of the motor. It worked for a good 30 minutes until it started to slow down and finally stopped. We thought the problem was due to the contamination of the surface of the mirror again, but it might also have been because the cooler part also heated up too much from being in the heat. Also, the mirror problem and the pinhole problem can be explained by the same principle. That was why the reflection from the mirror seemed bigger when projected onto a screen far away. It was NOT because of dispersion, and NOT because the ray from left part of the sun met the left part of the mirror (all of which seemed like the obvious reasons why this happens.) So basically I was wrong about everything. I think. Maybe I'm wrong about this too. For now, I think I will enjoy the birth of America and rest for a couple days. My mom is leaving Monday morning, so I will return to campus then and go to lab (if anyone shows up) or do some research in my room. ## Thursday, July 1, 2010I finally leanrned how to explain the pin-hole effect and the 'special lens' convergence! The lens, although it looks very flat, has a focus because it is a Fresnel lens, which, instead of having a thick bulge, has spicky patterns that has the same effect as a plano-convex lens. The good thing about this lens is that the lens takes up less space than a regular convex lens. Apparently it was developed for usage in lighthouses, which I saw at Fire Island the day before I came to Stony Brook. The holes on aluminum plates, which resulted in the same spot size regardless of the size of the hole, were acting as pin holes in a pin-hole camera. So the light rays from the top of the sun would reach the bottom of the light spot, and the rays from the bottom would reach the top. When Dr. Noe ran his finger from bottom up, a shadow appeared on the light spot from top to bottom. One more question that we weren't able to come up with a definite solution for: why is the focused light spot from the 'special lens' so large? One way to think of it is that since the focal length is so large, the f number is also large (even the diameter of the lens is larger) so the focused beam can't be as concentrated in a small area as a beam from a magnifying lens would be. Or, since the spikes on the glass create some error, that may have increased the focused spot. Earlier in the day, Katya taught us how to prove Snell's law by using Fermat's principle as well as a couple lens formulas and matrix optics. We all spent a few hours probing about why 1/f equals 2/R in order to prove that a parallel light ray coming in wil bisect the radius. Then we pondered on what would happen to a parabola. By using the definition of a parabola, which is that the distance from the focus to a point on the curve should equal to the distance from that point to the directrix, and by using the fact that R=1/(2a) when R is the radius of a oscalating circle, we can prove that the focal length is 1/4a. When we went over the matrix after lunch, I finally understood that the papers were talking about when they expressed a light ray using matrix. They were trying to represent the propagation of a light ray, and as Katya said, this method is good because we don't have to visualize the light ray itself. I did a little research on creating rings by transforming LG modes. In the journal article that I read, transformation of LG modes using an axicon-involved apparatus will result in an annulus that will conserve higher azimuthal indices. While other methods of mode conversions have a harder time keeping the high azimuthal index because the mode purity is degraded so easily, this method has fewer problems with that. I think there is another paper published in 2007 on a similar topic but with a different apparatus, so I think I will download and read that. ## Wednesday, June 30, 2010Today was full of eye-opening experiences. First, Vince gave a lecture on the topic "light as a wave." Basically, throughout the lecture, my mind was repeating the following procedure: I would understand (or think that I was understanding) a certain topic, and Dr. Noe or Dr. Metcalf would throw out a question that sounds really confusing, but only because I was not fully understanding what they were asking for. Then we would eventually get the answer and everything would suddenly make sense again. For example, when we found an expression in terms of exponents to describe cosine, Dr. Metcalf asked why terms that include imaginary numbers lead to a real number. It all had to do with expressing the two exponents in terms of complex conjugates. Also, when we were going over finding the difference in wavelength of the two beams at a constructive point in Young's double slit experiment, I knew what I had to do in order to prove it the conventional way, but wasn't sure exactly how I was supposed to reach that conclusion. I guess the physics course that I took freshmen year is too vague in mind right now! But the proof using binomial and small angle approximation was mind-blowing. It was incredible how everything worked out perfectly!! During the lunch meeting, Dr. Metcalf gave a lecture on combining harmonic waves to describe how instruments sound different when playing the same pitches. It was an issue that I have never pondered on before. In fact, addition of higher harmonics to the fundamental form of harmonics can construct different sounding pitches as it becomes more and more similar to a square wave. Using beat is a specific way of creating sounds using harmonic wave combination: to make a sound of a pitch 200Hz, an oboe would produce 1000Hz and 1200Hz since the difference in frequency is the resulting pitch. Maybe the frequencies aren't exact but it's really cool that this happens! I found a paper that mentions the nonlinearity of reeds in wind instruments. In the afternoon, Dr. Noe showed us what we can do with lenses and mirrors using sunlight. We tested converging and diverging lenses as well as what Dr. Noe called a 'special lens' that made a focus with a pretty big diameter. The focus was similar in size to the light shined through a hole in an aluminum pan when from the same distance as the focal length of the lens. Since we didn't have much time to work on the problems today, I think that's what we'll start with tomorrow. ## Tuesday, June 29, 2010Heather gave a talk on different math concepts, most of which we learned in calculus (or other previous math courses.) But I'm really glad we had an opportunity to go over all of these things because I forgot the specifcs of things such as general terms for sine and cosine in terms of Taylor series. But now they are fresh in my mind again! One thing I wasn't so sure about was the wave equation. I understand the general concept of it and what it is aiming for in terms of using differential equation, but I can't visualize exactly how it would be utilized. Some concepts sounded familiar but were things that I have never learned them in depth before, such as Euler's formula and Bessel functions. When the undergraduate students left to listen to their lunch meeting, we tagged along to listen. The professor introduced some simple physics experiments and concepts. One experiment that caught my attention was the sugar water refraction apparatus, which was very similar to the math project I did in the Spring. As the density of sugar water is greater in deeper water, when light is shined from the botton towards the surface in an angle, the light ray will become more horizontal as it propagates through the water. In my project I had struggled to understand the proof of Snell's law using Enterprise Integration. I didn't know any multivariable part of the proof, so I just understood the very basics of Euler's formula and skipped the rest of the multivariable part. I hope I learn it next year in math class because it seems really interesting!! For the rest of the day at the lab, I spent most of my time reading magazines. I didn't fully understand the theories behind the experiments, but I got a general sense of what people do in real optics labs. I also noticed that the magazines that aimed at a broader audience, such as Nature, spoke more of the profitability and the potentials of a certain research. It makes sense since the more general audience include people who are looking for things to invest in. Anyway I really liked the magazine articles. ## Monday, June 28, 2010The first day of Simons Program at the Laser Teaching center was interesting and fun. I visited the lab with Dr. Noe and two other Simons fellow students who will be working in the same lab. We looked at things such as the pig toy, magnifying glasses, and the film case (sliding down a paper between the eye and the film case will create a shadow that moves upward.) While having lunch with Dr. Noe, we talked about potential mini projects that might lead to our main projects. After that we looked at the undergraduates setting up an interferometer in the lab and listened to a lecture on writing in lab notebooks. Everything seems intense but I will hopefully get used to things. :) |