## Journal## August 3, 2010Recently, I have been preparing my write-ups and presentation. This is the final week, so I need to finish up everything by Friday. We spent a lot of time as a group editing our abstracts, which we just turned in yesterday. Also, I took the rough draft I have for my report and put it up on my webpage as an html file, which was interesting because I had to learn a few new html commands. We have practice talks tomorrow and Thursday, so I've also been getting my presentation ready. Hopefully I will be able to end the REU well and give a good talk on Friday. ## July 26, 2010Today, we had several speakers come in to talk about different projects related to the realm of optical vortices. I found Kiko Galvez's talk particularly interesting, because he discussed both transverse modes and polarization states. These are two topics that I am interested in, and that I learned something about earlier in the summer. In learning about these topics, I noticed a strange similarity between types of polarization and types of transverse modes. Polarization of light can be classified as linear, circular, or elliptical. Linear and circular polarization can be considered special cases of elliptical polarization on opposite extremes. In a similar way, transverse modes can be either Hermite-Gaussian (cartesian symmetry) or Laguerre-Gaussian (circular symmetry). However, there is a third type of transverse mode called Ince-Gaussian, which has elliptical symmetry. All three of these mode classifications can be considered a basis set, from which other forms can be created. I thought it was interesting that there was at least a qualitative similarity between these two optical phenomena. Kiko touched on a few of the similarities between transverse modes and polarization in his talk, so I found it very intriguing. Many of the talks dealt with cylindrical vector beams, which I did not know much about previously. I was able to understand a bit more about them through the presentations, but I must admit that most of the talks left me curious rather than enlightened. The topic of cylindrical vector beams certainly interests me, since it deals with several concepts that I have been learning about this summer. However, I didn't understand much that was discussed about them today, so the "Optical Vortex Party" has served mainly to excite my curiosity about cylindrical vector beams rather than teach me much about them. ## July 21, 2010Today, I took a new set of data using the Fabry-Perot to compensate for frequency pulling/pushing. Again, I took data over a total change in length of 0.8000 inches in increments of 0.0250 inches. Using a standard regression, I obtained a result for the speed of light of 2.99734E8 m/s. I need to determine my uncertainty in this result. Also, while the uncertainty in the beat frequency is the same for each data point, I am plotting length vs. 1/(beat frequency), so the uncertainty in this term will be different for each data point. The paper discusses this to some degree. My next goal is to determine how accurate my result is (based on the experiment, not by using the accepted value for the speed of light). I do not have much experience doing error analysis such as this, so this will be a learning experience for me. As part of my error analysis, I will eventually take data with increasing cavity lengths (instead of decreasing lengths, as I have been doing). Hopefully this will tell me something about any backlash I am getting with my translation stage. ## July 16, 2010Yesterday, I got my original Fabry-Perot to work, which solved a lot of
my problems with the second Fabry-Perot (such as the small peaks, the
difficulty of securing
it, etc.) Now that I got a Fabry-Perot to display the modes well, I can
use that to compensate for frequency pulling/pushing. The main paper I'm
using referenced
another paper in regards to frequency pulling. The main idea is that the
beat frequency between two adjacent modes, which ideally is constant,
actually varies. This
is because the beat frequency depends on the index of refraction, which
varies quite a bit with frequency near the resonance transition of the
gain medium. So the
position of each mode under the gain curve plays a role in determining the
beat frequency. The problem I encountered is that I cannot keep the relative intensity between the two modes constant long enough to take a beat frequency reading by simply pressing on the frame myself. So I spent most of today trying to devise a method to adjust the relative intensities more efficiently. Eventually, I ended up with a setup that seems to work. I attach a rubber band to three screws so that the rubber band is stretched over a bar on the laser frame. By adjusting the middle screw, I can adjust the amount that the rubber band pushes on the frame. Ideally, once I adjust the screw, the relative intensities will not change. In practice, this seems to work reasonably well. I am excited to take data using this scheme to take frequency pulling into account and see how this affects my result. ## July 14, 2010I have been trying to get the Fabry-Perot to work for the past few days, and I have made a little progress. I switched to a different Fabry-Perot which is easier to align, and now understand how to use the driver and the oscilloscope more or less. The problem I am currently experiencing is that the peaks on the oscilloscope are too small for me to use them to minimize the effects of frequency pulling/pushing. The technique is to visually determine when the peaks corresponding to each mode are at the same intensity relative to each other and to the peaks for other cavity lengths. Currently, my peaks are too small for me to have a reasonable idea of when they are of equal intensity. I put this problem aside for the time being to take some data. Although there is surely some error from frequency pulling/pushing, I obtained a reasonable result for the speed of light. I took data over a change in cavity length of 0.800 inches at increments of 0.025 inches. My result for the speed of light was 2.99E8 m/s. I am pleased with this result but hope to obtain more accurate data once I can include the Fabry-Perot into my experiment. I also hope to eventually modify the setup to be able to take data over a greater range of cavity lengths. Hopefully with these modifications I can obtain a more accurate result. ## July 12, 2010I spent most of the day working with the Fabry-Perot portion of the setup, which is used to monitor the relative intensities of the longitudinal modes to minimize the effects of frequency pulling/pushing. This is an important step to obtain accurate frequency measurements. Unfortunately, I couldn't get the Fabry-Perot to operate as it did on Friday with Sam Goldwasser. I think part of the problem is that I am unfamiliar with the scanning interferometer driver that controls the Fabry-Perot, as well as the oscilloscope used to display the modes. I attempted to find operating manuals for each online but couldn't find anything. Right now I have the output coupler on a translation stage that moves through two inches. I would like to expand my range of movement, so I eventually plan to modify the setup with a longer translation stage. Before I do that, however, I want to get accurate data with the setup I have currently. For the time being, I will be focusing my energy on understanding how to operate the Fabry-Perot. ## July 9, 2010I finally have a project to work on! I'm trying to replicate the
experiment to measure the speed of light using the longitudinal modes of a
laser (the first entry on
my ideas page). The basic theory behind this is that adjacent longitudinal
modes of a laser are separated by a frequency of c/2nL. If we know the
length of the cavity
and the beat frequency of two modes, we can calculate the speed of
light. The ## July 6, 2010I have been reading a good variety of optics papers to try to come up with ideas for a project. Many of the things I have read have the potential to make good project, and I have found several experiments that deal with topics of interest to me. These can be found on my "ideas" page. I'm not quite sure where to go from here however. I don't know how to take these ideas and design a project out of them, or whether we have the equipment at the Laser Teaching Center to reproduce something similar to the experiments I have read about. I hope I'll be able to figure all this out soon so I can get started on a project. ## June 30, 2010Today, I gave a talk to the Simons Fellow high school students on the wave nature of light. Specifically, I discussed the equation and properties of a harmonic wave, writing a harmonic wave as a complex exponential, the different forms of light waves (plane, spherical, Gaussian), interference (including the double slit experiment) and diffraction. We also had a lunch meeting today, in which Dr. Metcalf discussed several other topics related to waves. A lot of his discussion was tied into music, so I found it very interesting. We talked about why different instruments sound different from each other (a different combination of higher harmonics present) and how by the addition of higher harmonics, one can produce a periodic wave of various shapes. In addition, we discussed the superposition of two waves of close frequency, including group and phase velocities. I really enjoyed this discussion, as it was on a topic that is very interesting to me. As far as designing a project goes, I have been making a little progress this week. In reading different papers, I came across an experiment that deals with fractal modes of an unstable cavity laser. Fractals are a fascinating topic, and I am also very interested in laser modes, so naturally this experiment excited my interest. Unfortunately, I don't think I will have the means to reproduce the setup described in the paper exactly, but if I can come up with a way to modify the setup, it may prove to be a decent project. ## Week 2: June 21 – 25, 2010I spent this week researching several topics in optics in an effort to come up with a project to research for the remainder of the summer. On Monday, I decided to learn about circular polarization. This was a subject that I had heard of, but knew very little about, which prompted me to see what I could learn about it. Both circular and linear polarization are two special cases of the more general elliptical polarization. If we break up the electric field vector (complex) into x and y components (assuming we are traveling in the z direction), the mode of polarization is determined by the amplitude of each of those components as well as their relative phase. Different combinations of these factors will produce different kinds of polarizations. For instance, for linear polarization, each component must be either in phase or pi out of phase. For circular polarization, the components must have equal magnitude and be pi/2 out of phase. I also researched laser modes because lasers are a topic I am very interested in, but I didn't know much about different modes. I learned that there are two basic types of laser modes: longitudinal and transverse. Longitudinal modes are very similar to the harmonics possible on a vibrating string. They result from the fact that a laser cavity of fixed length can support standing waves of multiple different frequencies. As long as an integer number of half-wavelengths can fit into the cavity exactly, that frequency can be supported by the cavity. The longitudinal modes, combined with the lineshape function of the laser, determine what wavelengths of light the laser can produce. In addition to longitudinal modes, lasers have different transverse modes. These are a result of a more general Gaussian solution to the wave equation. Higher order transverse modes have very interesting shapes. There are several different types of transverse modes, each with a different type of symmetry. Some examples are Hermite-Gaussian modes, Laguerre-Gaussian modes, and Ince-Gaussian modes. I find transverse modes fascinating, and would love to learn more about them by designing a project that involves transverse modes. Dr. Noe suggested that I learn more about the Gaussian shape of a laser beam before doing a project on transverse modes. I spent Thursday researching the derivation of the electric field formula for a Gaussian beam, which helped me gain insight as to the origin of many different properties of the Gaussian beam. The intensity profile of the cross-section of such a beam is a Gaussian distribution (hence the name). These beams narrow to a "waist" before spreading out again. From the electric field formula, we can determine the spot size at any point in the beam. We can also derive an expression for the spread of the beam after it passes through the waist. It turns out that the narrower the waist the more the beam diverges. Also, longer wavelengths diverge more than shorter wavelengths. On Friday I learned the matrix treatment of an optical system and how it applies to lasers. It turns out that you can easily predict how a Gaussian beam will behave in a given optical system using matrices. The matrix treatment of an optical system involves using a matrix associated with each element of the system to describe how an arbitrary light ray passes through the element. When all the matrices are combined, the resulting matrix describes the entire system. There are different forms of this matrix for translation, refraction, and reflection. Applying this to Gaussian beams, we can discover how an optical system will act on the beam. This is quite useful when trying to manipulate the beam from a laser. We find that with the right optical system, a Gaussian beam can be focused to a second waist. I definitely feel like I have a better understanding of the form and propagation of a laser beam. This will be of great use to me should I end up designing a project to study the transverse modes of a laser. I hope to have some definite idea for a project by the end of next week at the latest. ## Week 1: June 14 – 18, 2010Hello! This journal is where I will be keeping a record of my activities and progress throughout the summer here at the Laser Teaching Center. This was my first week at Stony Brook University. I arrived on campus on Monday and got settled in. The LTC group met that night for dinner to get to know each other, which was nice. The other REU students seem like a good group, so I'm looking forward to working with them for the summer. The first official day was Tuesday. After an informational meeting, we spent most of the afternoon experimenting with pinholes and magnifying glasses out in the sun. When trying to explain what was going on, I realized that my optics knowledge was a little rusty. We spent most of Wednesday inside explaining what we saw outside the day before. Much of it could be explained by considering the angle between the light rays from the top and bottom of the sun. We tend to think of the sun as approximately "infinitely" far away compared to the optical system, but in reality the angle is still important. A result of this is that lenses with a shorter focal length will be able to burn things more efficiently. This also plays a role in why the outline of a shadow is less distinct further away from the object. On Thursday, we explored some more concepts in geometric optics. One thing we discovered was that for a fixed distance between an object and image plane, there are two locations you can place the lens to produce an image. This can be shown mathematically by manipulating the thin lens equation into a quadratic form. In the afternoon on Thursday, we sat in on a presentation on a Bose-Einstein condensate experiment being conducted by another professor here. That was very interesting to me; I had very little prior knowledge about BEC's, and I felt like I gained a good basic understanding of the subject through the talk. Overall, this week has been a good start to the program. It helped me realize that there is so much out there that I don't know about yet. I'm really excited to learn more about some of the topics I was exposed to this week, and to start my own project. |