Research Journal

August 12, 2014

Today was our last day. It was fun to explain the project to a few people and was really interesting to see the projects of other Simons fellows. After the poster session, Dr Noé took us and our parents to lunch at the Simons cafe.

Yesterday Mr. Lipski was kind enough to coat our lenses. They came out very nice and I hope to use them soon. Yesterday was also the LTC lab tour. We each gave a short presentation and it seemed like the other students enjoyed it very much.

August 10, 2014

We concluded that the best way to go about the mirror setup was to buy lenses and have them coated. We purchased two cylindrical lenses of FL +/- 400ml, which would become +/- 100mm mirrors. After correspondence with the authors of the tunable Airy beam paper, however, we learned that mirrors of equal focal length should not be possible to align.

August 4, 2014

Today, in addition to working on my web report, I begin trying to make mirrors for generating Airy beams. I did not have to many options, so I tried using polished metal to make the cylindrical mirrors. Unfortunately the small, parallel scratches acted as many cylindrical mirrors and spread the beam in one dimension. Dr. Noé suggested I stretch mylar across something to make it a mirror. This will work very well for a convex mirror, but I still need to figure out how to do this for a concave mirror. Another option I may have is using something flexible and partially reflective, such as a polarizer, that is not really needed in the lab and to cut and bend it to shape. I would have to figure out how to hold it so that it keeps its shape.

July 31, 2014

Today I worked to solve the circular diffraction problem I was having. First I used a different laser with a smaller beam diameter. It was much harder to align than the wide-beam laser, and the resulting Airy beam had few peaks and was preserved for only a short distance away from the focal plane. I then decided to simply remove the aperture in order to avoid the undesired diffraction. The result was a much nicer, albeit not perfect, Airy beam. The peak lobe was consist across the entire beam, which helped me get much better measurements. My new deflection plot, featured in my abstract, looks a lot nicer and matches the theoretical deflection very well except for a linear component, a result of the beam path and the camera rail not being perfectly parallel. The intensity profile, however, was not great-looking. I found that by covering part of the first lens so that only half of the lenses would be hit by the beam, I was able to get a much nicer beam. Dr. Noé suggested I remove the front tube of the laser and replace the lense with a different collimating lens in order to get a smaller beam, a much more elegant solution. What remains to be done with this setup is to record the peak lobe widths as the beam propogates, and to record an intensity profile and compare it to a theoretical one.

July 30, 2014

Melia informed me of a tool called Image J which I can use to analyze pictures. I used the tool to find the full width half max of the Airy beam peak lobe at the focal plane. Based on the width, I calculated the theoretical deflection of the Airy beam. The theoretical curve was far from my actual data. However, if the width was 2 pixels narrower, I would have a good fit. Upon inspecting the images I noticed what appear to be fringes from circular interference. I analyzed the width at a bright fringe, where the peak lobe appears to be significantly wider. I plan to try to replace the current laser and iris with a laser of smaller beam diameter in order to avoid the circular interference.

A number of suggestions were made regarding how I might increase the range angles of the negative lense. I could place one or both of the two first lenses in beeswax, ridding the setup of the bulky clamps, I could place both lenses in a single "sandwich" clamp, or I could place one or both lenses on double-sided tape. For now, I have the positive lense sitting on top of double-sided tape. The negative lens now has a much greater range of motion.

I was unable to find convex cylindrical mirrors, but Professor Metcalf suggested I simply take shiny sheet metal and bend it to the correct shape. Dr. Noé said I could even get it machined at the shop. After I finish collecting and analyzing data from my lens setup I think I will attempt the same experiment with mirrors.

July 29, 2014

Dr. Cohen suggested I either use a positive lens with the same focal length as the negative lens, or switch to a single lens. Since the second lens is used in order to cancel out aberrations other than the coma, it makes sense that it should be the same focal length as the negative lens. I found a small +80mm cylindrical lens lying around on the optics table. It was difficult to collimate the beam with the two lenses of equal focal length. Eventually I was able to, but I had to tilt the second lens slightly. Dr. Cohen was right. I was able to get a much better Airy beam. Some undesireed aberrations are still present in the beam, but the peak lobe appeared unchanged over a distance of several centimeters. I was able to measure the parabolic deflection of the peak lobe by taking pictures of the beam at different distances from the focal point. Dr. Noé showed me how to create a quadratic fit for the data in a spread sheet.

Here is the current setup:

The distance between the middles of the first two lenses is 2.5cm. The tilt angle of the first lense is 12 degrees. The beam hits only the right side of the first lens. Due to the small size of the positive lens, most but not all of the beam lands on the right side of the second lens. In order to adjust the angle of the beam so that it will land on the camera, the last lens is offset so that the light hits it on the right side as well.

July 28, 2014

Dr. Cohen realized that the camera was washing out. By placing a neutral density filter (ND=3) in front of the camera and changing the exposure time and the pixel clock, i was able to get the beam to appear correctly on the camera. Instead of black on a white background it now appears white on a black background. Features of the beam can now be seen at the focal point. I found a measuring tool in the camera viewer. I now just have to find the units per pixel for the camera and I will be able to measure distances in the image. The Airy beam still doesn't look quite right and the peak lobe does not remain clearly visible across as long a distance from the focal point as it should.

July 24, 2014

Today I made a number of changes to my set up. I replaces the spherical lens with convex cylindrical lens. As a result, the pattern became much clearer and bore a closer resemblance to the 1D beam in the paper. I also began using an aperture in front of the laser, since I was unable to resolve the pattern near the focal length of the lens. With a smaller, weaker beam, I was able to see the pattern closer to the focal point. At the focal point, I still can not make out the lobe of highest intensity. I used a "hood," a cylinder of black paper on the camera in an effort to block out ambient light. I also tried using a neutral density filter of a density of 1. It proved to filter out too much light, as the remaining light was not enough to be picked up by the camera. The beam does appear to be curving, but I will have to find a method of counting pixels to determine the displacement of the most intense lobe.

July 23, 2014

I recorded the Airy beam at various distances from the focal point. It does appear to be curving. An issue I am running into is that at the focal point the beam appears to be a single rectangle. I am unable to see the separate lobes with the camera. I will try fiddling around with camera settings, lighting and beam brightness.

July 22, 2014

Today I found an interesting article that explains that a high-powered airy beam can be used to create a plasma channel and detect gas composition at different locations. The curvature of the beam makes it possible to pinpoint one location. I have notice in my setup that the two cylindrical lenses, which are set to focus the light horizantally, also seem to focus the light vertically. I have moved my entire setup to a rail, and I am currently trying to capture the deflection of the beam by moving the camera along the rail and taking pictures near the focal point of the Fourier lens at measured distances apart. In my set of pictures, the peak lobe clearly moves. However, it is not yet clear if it moves due to parabolic deflection, or because the rail and the beam are not parallel. Also, in the original artical, a curve in one direction, then the other was observed. In other words, the vertex of the parabola was at the Fourier plane. My beam only "moved" in one direction. I will test it again along a longer distance.

July 21, 2014

Based on Gullstrand's Equation:

one can determine that if

the light should be collimated, as the focus will be at infinity. Using this derived equation, I was able to determine the focal length of the concave lense. I placed the convex lense in front of the laser, and then moved the concave lense until I observed collimated light. The spot of light appeared to be the same size about two meters away, the furthest distance I could reach. The value I determined for the focal length was 7.9 cm.

I set up the laser, lenses and camera in order to generate and record a 1-D Airy beam.

First, I set up only the laser and the two cylindrical lenses. I tilted the concave lense in order to create a coma and spaced the two lenses approximately 3 cm away from each other. I then adjusted the convex lens until the beam appeared collimated. Next, I added a convex lens in or to bring the beam into the far-field. I recorded the beam close to its focal point. I moved the camera back and forth slightly and saved a number of images. Here are two of them.

July 18, 2014

Today, using a laser, a screen and a positive cylindrical lens of known cylindrical lens, I attempted to find the focal length of a negative cylindrical lens. I placed one lens in front of the laser, the second lens in front of the first, and the screen at the focal point of the light. I hoped to determine the focal length of the negative lens using Gullstrand's Equation . I later switched the two lenses and ran into a problem. The distance at which the screen had to be placed so that the light was focused changed significantly. According to Gullstrand's Equation, the placement of the object does not affect the focal length.

On a separate note, Dr. Noé pointed out that the two-lens system operates much like an alternating-gradient(AG) lens. In an AG lens, four magnets are placed at four corners. The poles of the magnets are alternated so that the magnets across from each other are of the same pole. This creates a magnetic field which points inward along one axis and outward along the other. When a particle beam passes through the AG lens it is focused due to the force exerted on a charged particle in a magnetic field. Like a cylindical lens, it will focus (or defocus) in one plane. Unlike a cylindrical lens, it will also defocus (or focus) in the perpendicular plane.

July 17, 2014

This morning we looked at diffraction patterns resulting from a laser shined through circular, square and triangular apertures. The circular diffraction pattern was a bull's eye pattern, with a bright, circular spot in the middle and alternating dark and light rings around the spot. Shining light through the square aperture resulted in a diffraction pattern consisting of a a bright square in the middle with four bright streaks starting at each side of the square. The streaks were composed of alternating light and dark bands.

July 16, 2014

This morning we gave small presentations about our plans for projects. Afterwards, we had our pizza lunch. Dr. Schneble gave an interesting talk about his work with Bose-Einstein condensates that, among other things, further explained laser cooling, which we had first learned about from Dr. Metcalf. Afterwards, we were given a tour of the lab. Creating a BEC requires quite an intricate contraption. it is no wonder that it took over a year and a half to get it working. After we returned to the lab,I stumbled across an interesting photo with an explanation of caustics. I continued to read about aberrations.

July 15, 2014

I found out how to us Matlab based on Rachel's SLM guide I began learning about aberrations using Wikipedia, Hyperphysics,, Principles of Optics by Born & Wolf, and Useful Optics by Welford.

Aberration Types:

Comatic Aberration:

Comatic Aberration

The image appears to have a "tail."



Curvature of Field:

Spherical Aberration:

An ideal wavefront from a lens is a part of a sphere with its center at the focus. When this doesn't happen, the rays do not all meet at the focal point.

Perturbation (aberration) is given by a function:

Each term includes an aberration coefficient and represents one of the five aberrations. "α" is the field coordinate, a concept I do not fully understand. "ρd" is the distance from the axis at the pupil. "θ" is the angle at which the aberration is present, with reference to an origin.

My current understanding is that the Airy beam is created using a comatic aberration. "Copies" of the object (a Gaussian beam) appear, giving it its "tail". Doing this in two dimensions gives you the intensity distribution of the Airy beam.

July 14, 2014

Today we spoke about our interessts in optics. Dr. Noé suggested I take a look at Jeffrey Davis' work and at a paper which explains how a number of lenses can be used to generate an Airy beam. I found this article very exciting, as the only means of generating Airy beams I had known of was using an SLM. The authors of the paper used the aberrations of lenses in order to create Airy beams.

July 11, 2014

This morning, we estimated the speed of the Earth. We used the approximate average distance from the Sun to the Earth, the approximate time to complete an orbit, and our knowledge of Kepler's law: a line from the Earth to the Sun sweeps out equal areas during equal amounts of time. We calculated the Earth's average speed to be 30,000 m/s. Afterwards, we attended an AMO talk. A representative of SAES getters presented a variety of vacuum pumps that his company makes. To reach ultra-high vacuum, one must use a getter - a material which will absorb certain gases. Afterwards, I read an article which detailed the tweezing of mutliple particles with different refractive indices using a single, self-reconstructing Bessel-beam. This is pretty exciting.

July 10, 2014

Today I read an entry by a former LTC student about an interesting phenomenon involving a fiber optic in the lab. When a laser was shined into the fiber at an angle, the light leaving the fiber was a hollow beam. I wonder what is at play here. I began to read a paper by Kogelnik and Li which explains lasers in general. They show how matrices can be used to calculate the output characteristics of a ray of light passing through an optical device, such as a lens. I also found out that an approximation of a Bessel beam can be generated simply by focusing a Gaussian beam through an axicon lens, though an ideal Bessel beam would require an infinite amount of energy. On Dr. Goldwasser's website, I found a link to a brief guide on building laser microphones. A microphone can be built by simply bouncing light of the vibrating surface and onto a photodetector, but it seems that buy bouncing to beams of the same surface and interfering them, on can reduce noise and get a more consistent signal. I learned that Bessel and Airy beams are not the only propogation-invariant beams. Mathieu and Weber beams also nondiffracting. Like Airy beams, they can accelerate parabolically.

July 9, 2014

Today, after learning about resonance and photon energy, we listened to a discussion about laser cooling. Dr. Metcalf clarified concepts of temperature and order of magnitude, and then explained essentially how atoms are cooled. In one dimension, two lasers pointing in opposite directions point towards the sample. Atoms move quite quickly and will only absorb light of a certain frequency. As a result of this and the doppler effect, atoms will be affected differently by a laser depending on their velocity relative to the laser. Therefore, two lasers at the right frequency will always oppose the motion of the atom, imparting momentum to the atom when the atom moves against the direction of the beam, and leaving the atom unaffected when it is moving away. Due to discrete nature of atomic energy levels, when an atom absorbs or emits photons, the change in the atom's momentum is not smooth. This imposes a recoil limit on laser cooling which prevents the cooling of atoms below a certain temperature.

I found an article detailing the generation of Ince-Gauss beams.

July 8, 2014

Today I continued reading about different beam modes and conversions between them. I do not yet have a good understanding of the math behind them. A Gaussian beam has an intensity profile that follows a Gaussian function, with the highest intensity at its center. Hermite-Gaussian beams are defined by the product of a Gaussian function and a Hermite polynomial. They have rectangular coordinates. Laguerre-Gauss beams are radially symmetric. They have OAM and are "empty" at the center. Ince-Gauss beams are written in elliptical coordinates. The intensity distributions therefore appear as ellipses and hyporbolae. An Airy beam is a non-diffracting beam that appears to curve.

July 7, 2014

I found two more very interesting projects by LTC students. One explains how optical vortices can be used to transfer data. Since optical vortices can have an infinite number of different states, data could be sent much faster than with binary fiber optics. A second article details how an improvised sensor was used in order to measure the angle of an optical vortex wavefront. Instead of a Shack-Hartmann wavefront sensor, an expensive array of small lenses, a single, moveable pinhole was used. I also explored an imaging technique called optical coherence tomography (OCT). In OCT, low-coherence light is pointed at a sample or living subject. Interferometry is then used to estimate the depths of different layers in the sample. This is done by splitting the light and reflecting one beam from the sample and the other from a moving mirror. Due to the low coherence of the light, it will only properly interfere when the distances from the mirror and the sample layer are the same. OCT can also be implemented by measuring the intensity as a function of frequency instead of as a function of the position of the mirror, but I do not understand how the sensor works.

July 3, 2014

Today we continued reading articles and finding topics of interest. I found an interesting article that demonstrates the use of a laser vibrometer as a microphone. It works by interfering one beam directly from a laser and one which has been reflected from the vibrating surface. The authors used a photo-EMF sensor and a pulsed laser, instead of a lower-powered, continuous one, to detect vibrations as small as 75 pm. I am not entirely sure what a photo-EMF sensor is or why it seems to be less sensitive than a photodetector. I found an article that explains laser vibrometry in general. I read about STED microscopy here. One laser beam is used to excite molecules in a specimen, causing them to flouresce. A second, doughnut-mode laser is used to deplete molecules before they flouresce, leaving only the molecules at the middle of the beam to flouresce. I also read an article by a past LTC student about optical tweezers. By taking advantage of the the momentum of light, the refractive index of a particle, and a laser beam's Gaussian profile, she was able to trap particles. Light from the center of the beam would refract outward upon hitting the particle due to the particle's spherical shape and refractive index, imparting momentum onto the particle and causing it to move inward to the center of the beam. Light located closer to the edge of the beam has the opposite effect, but is of lower intensity due to the beams Gaussian profile. By inverting the tweezers, the student was able to use the scattering force, which acts in the direction the beam travels, to counteract the force of gravity.

July 2, 2014

Today, after some final changes to our slides, we had our presentations in the conference room. Afterwards, Libby showed us how to log onto and use the LTC server. We spent the rest of our time reading through papers and previous projects. I found a few projects and topics I would like to look into further. A previous LTC student was able to use thin film interference in order to find variations of depth in a soap film. The technique was used to model and observe fluid vortices. I also found an article about different transverse laser modes. I was not aware these could be achieved and would like to learn more about them.

June 30, 2014

Our first day at Simons began with an introductory breakfast where we met our mentors, Melia and Dr. Noé. After the meal, we went to the Laser Teaching Center where we discussed a variety of optical phenomena. We were shown a pig toy, a sort of lidded bowl with a reflective inside and a hole at the top of the lid, and tasked with determining its mechanism. We learned that the bowl and lid are parabolic and nearly identical, and thus are able to produce an image of the toy's contents right above the opening in the lid. We also learned the differences between a reflecting telescope and a refracting telescope. After lunch, we discussed focal length and magnification of lenses and explored this by burning paper using light from the sun. We talked about small angle approximation and unit prefixes. Later, we experimented with polarizers and were shown an interferometer.