Simone Agha, Herricks High School, New Hyde Park, NY; Harold Metcalf and John No�, Laser Teaching Center, Department of Physics and Astronomy, Stony Brook University.Optical vortices are an unusual form of light with fascinating physical and mathematical properties. A laser beam containing an optical vortex appears as a doughnut shaped spot of light with a dark center. Not apparent to the eye is the fact that the phase of the light beam varies with the clock or azimuthal angle. A consequence of this is that the center of the beam (the hole of the doughnut) contains a phase singularity; it is this singularity which causes the intensity of the light to be zero. The phase variation is described by the complex factor eil where is the azimuthal angle and l is called the topological charge. Normally l is an integer so that the phase returns to its original value as increases by 2, one complete revolution. When l is fractional, the beam contains a superposition of vortices [1]. A special case is the half-integer vortex which contains an infinite series of �1 charge vortices along the axis of the phase dislocation (the phase "jumps" by between revolutions) [1, 2]. The goal of this project is to analyze the phase distributions of vortices of non-integral topological charge, and thus determine the locations of the superimposed integer vortices within. An optical vortex of arbitrary fractional charge can be created by means of a simple spiral phase plate made from a piece of cut or cracked plastic, while a half-integer vortex can be produced in an existing computer-generated holographic diffraction grating. Phase distributions obtained from interferograms will be compared to computer simulations to determine the structure of the vortices produced by these two methods. We thank the Simons Foundation for its support and Prof. Kiko Galvez of Colgate University for providing the computer-generated holograms. [1] M. V. Berry, "Optical vortices evolving from helicoidal integer and fractional phase steps," J. Opt. A: Pure Appl. Opt. 6, 259-268 (2004). [2] S. Baumann, E. J. Galvez, "Non-integral vortex structures in diffracted light beams," Proceedings of SPIE 6483, 6483OT (2007).
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