Abstract

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Optical Vortices: The Orbital Angular Momentum of Light Christopher Cepero Department of Physics, Bridgewater State College -- Bridgewater MA, 02325 Mentor: Dr. Edward Deveney Abstract It was not realized until 1992 that light could possess angular momentum – plane wave light twisted in a corkscrew.  Due to resemblance with a similar phenomenon seen in fluids, this momentum is called an Optical Vortex.  While optical vortices are still under investigation, they are already a crucial component of optical tweezers which are used in biomedical applications to trap neutral particles.  Our work centers on the first investigation of optical vortices here at BSC performing an experiment described in an American Journal of Physics (AJP) article called “Making optical vortices with computer-generated holograms.” Using software, we take analytic interference patterns to generate a holographic mask – laser light impingent on the mask ‘picks up’ angular momentum and the projections of the momentum can be measured using a modified CCD camera. Our goal in recreating this experiment is to learn more about both the theory and experimental outcomes of optical vortices. Results Our experimental procedure begins with the characterization of our optics equipment. The beam splitters and polarizers we have were manufactured for a 780nm laser., and the AJP article utilizes a 633nm He-Ne laser. Using a power meter, we measured our 633nm He-Ne laser to have a power of 0.566W. After shining it through the 50/50 beam splitter, we measured a power between 0.238W and .315W for the transmitted beam; about 60% of the initial power. The reflected beam was measured to have a power 40% the initial, at 0.120W to 0.230W. Once we characterized our equipment, we moved on to generating the orbital angular momentum. With the help of Professor Nunez from the photography department, we photographed the interference patterns and developed the film to act as our holographic mask. Methods Our experiment is a reproduction of the experiment performed in the AJP article “Making optical vortices with computer-generated holograms.” The method of creating optical vortices described in this paper involves generating an interference pattern and condensing it accurately into a 0.5cm by 0.5cm square on film. The interference pattern is created by the interference of the following two waves, and the calculation of the resulting function. Introduction When dealing with light waves, it all begins with Maxwell’s Equations: Figure 4: The film used as an optical mask. Our most recent progress has been in encoding the angular momentum from the optical mask into the laser beam. The interference pattern is approximately 0.5cm by 0.5cm, and the laser must hit the very center of the interference pattern as it is transmitted. Once it is properly centered, the angular momentum is observable in the interference pattern the laser creates. From these equations you can determine that light is an electromagnetic wave which travels at 300,000,000 m/s in a vacuum, and has the general form: Furthermore, out of Maxwell’s Equations we can derive the Poynting vector: Figure 5: The first optical vortices generated at BSC For an electromagnetic plane wave, the Poynting vector points in the direction of the waves propagation, and describes the magnitude and direction of the momentum carried in the wave. For light waves with a helical polarization, the pointing vector contains a component of the momentum in the azimuthal direction. This component of the momentum causes an angular momentum parallel to the axis of propagation. This angular momentum rotates around the beam axis, and has been dubbed an Optical Vortex. The vortex can visibly be seen when you interfere a plane wave at the center of a helical wave, while both are coherent. Current Status Now that we have successfully coded the laser beam with an angular momentum, we must cause it to interfere with another coherent laser beam, using beam splitters. Once we are able to accurately interfere the two laser beams, we will be able to image the optical vortex. • (b) • Figure 2:Interference patterns (a) m=2 and (b) m=3, generated using Maple. • Apparatus • A Class II 633nm He-Ne Laser is our light source, and a CCD camera records the images. • We use black and white film as our Holographic Mask (HM) Figure 6: Viewing the optical vortex requires basic optics equipment such as : 50/50 Beam Splitters (BS), Mirrors (M), Polarizers (P), and slits/diaphrams (S). (image from Carpentier et al.) After imaging the optical vortices, there are lots of other exciting applications and experiments this research can be applied to for future research topics. • Acknowledgements • We are very appreciative of the BSC Photography Department for their assistance with photographing and developing the film for the holographic mask. • Many thanks to Dale Smith for help with resizing the interference patterns for printing. (a) (b) • References • A.V. Carpentier et al., “Making optical vortices with computer-generated • holograms,” Am. J.Phys. 76, 916-921 (2008). • Miles Padgett, Johannes Courtial, Les Allen; “Lights Orbital Angular Momentum,” • Physics Today. 76, 35-40 (2004). Figure 1 – (a) Light wave with a helical wave front and the Poynting Vector, alongside the optical vortex. (b) Diffracted pattern caused by the holographic mask. (Images from Padgett, Courtial, Allen paper) Figure 3: Initial set-up to image the angular momentum.