Cross-correlation measurements and the topological charge of a Laguerre-Gaussian beam

Benjamin Perez-Garcia; Dorilian Lopez-Mago; Hipolito Garcia-Gracia; Jorge A. Garza-Alanis; Raul I. Hernandez-Aranda; Julio C. Gutiérrez-Vega

doi:10.1117/12.2062246

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17 November 2014 Cross-correlation measurements and the topological charge of a Laguerre-Gaussian beam

Benjamin Perez-Garcia, Dorilian Lopez-Mago, Hipolito Garcia-Gracia, Jorge A. Garza-Alanis, Raul I. Hernandez-Aranda, Julio C. Gutiérrez-Vega

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Proceedings Volume 9194, Laser Beam Shaping XV; 919403 (2014) https://doi.org/10.1117/12.2062246
Event: SPIE Optical Engineering + Applications, 2014, San Diego, California, United States

Abstract

We study both theoretically and experimentally the cross-correlation function of single-ringed Laguerre-Gaussian (LG) beams, which allows us to determinate the topological charge of the beam by performing power measure-ments only. We employ a superposition of two exact copies of the original LG beam whose centroids are displaced from each other. The behaviour of the auto-correlation is studied as a function of the displacement between these two copies of the beam for different topological charges. Our results indicate that the auto-correlation is described by a polynomial function of the displacement parameter, and the number of zeros of this polynomial maintains a one to one correspondence with the topological charge. A detailed description of the experiment to perform these measurements is also provided, our experimental findings are in excellent agreement with the theory. This technique offers an alternative for measuring the content of orbital angular momentum in a beam without the need of a camera.

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Benjamin Perez-Garcia, Dorilian Lopez-Mago, Hipolito Garcia-Gracia, Jorge A. Garza-Alanis, Raul I. Hernandez-Aranda, and Julio C. Gutiérrez-Vega "Cross-correlation measurements and the topological charge of a Laguerre-Gaussian beam", Proc. SPIE 9194, Laser Beam Shaping XV, 919403 (17 November 2014); https://doi.org/10.1117/12.2062246

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