Vol. 43

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues
2015-08-09

The Fractional Fourier Transform of Hypergeometric-Gauss Beams through the Hard Edge Aperture

By Jun Qu, Mengyao Fang, Ji Peng, and Wei Huang
Progress In Electromagnetics Research M, Vol. 43, 31-38, 2015
doi:10.2528/PIERM15070705

Abstract

Based on the Collins integral formula and Lohmann optical system, we expand the hard edge aperture into complex Gauss function and derive an approximate analytic expression of intensity distribution theoretically for Hypergeometric-Gauss beams through the fractional Fourier transform (FRT) optical systems with hard edge aperture. The influences of FRT order, aperture size and other optical parameters on the light intensity distribution of Hypergeometric-Gauss beams passing through the FRT optical systems are discussed in detail. The results show that the FRT is an excellent beam-shaping method.

Citation


Jun Qu, Mengyao Fang, Ji Peng, and Wei Huang, "The Fractional Fourier Transform of Hypergeometric-Gauss Beams through the Hard Edge Aperture," Progress In Electromagnetics Research M, Vol. 43, 31-38, 2015.
doi:10.2528/PIERM15070705
http://www.jpier.org/PIERM/pier.php?paper=15070705

References


    1. Renn, M. J., et al., "Laser-guided atoms in hollow-core optical fibers," Physical Review Letters, Vol. 75, 3253-3256, 1995.
    doi:10.1103/PhysRevLett.75.3253

    2. Cai, Y., X. Lu, and Q. Lin, "Hollow Gaussian beams and their propagation properties," Optics Letters, Vol. 28, 1084-1086, 2003.
    doi:10.1364/OL.28.001084

    3. Paterson, L., et al., "Controlled rotation of optically trapped microscopic particles," Science, Vol. 292, 912-914, 2001.
    doi:10.1126/science.1058591

    4. MIshra, S. and S. K. Mishra, "Focusing of dark hollow Gaussian electromagnetic beams in a plasma with relativistic-ponderomotive regime," Progress In Electromagnetics Research B, Vol. 16, 291-309, 2009.
    doi:10.2528/PIERB09061705

    5. Alkelly, A. A., H. Al-Nadary, and I. A. Alhijry, "The intensity distribution of hollow Gaussian beams focused by a lens with spherical aberration," Optics Communications, Vol. 284, 322-329, 2011.
    doi:10.1016/j.optcom.2010.08.040

    6. Sodha, M. S., S. K. Mishra, and S. Misra, "Focusing of a dark hollow Gaussian electromagnetic beam in a magnetoplasma," Journal of Plasma Physics, Vol. 75, 731-748, 2009.
    doi:10.1017/S0022377809007922

    7. Kotlyar, V. V., et al., "Hypergeometric modes," Optics Letters, Vol. 32, 742-744, 2007.
    doi:10.1364/OL.32.000742

    8. Karimi, E., et al., "Hypergeometric-gaussian mode," Optics Letters, Vol. 32, 3053-3055, 2007.
    doi:10.1364/OL.32.003053

    9. Ozaktas, H. M. and D. Mendlovic, "Fractional Fourier transforms and their optical implementation. II," Journal of the Optical Society of America A, Vol. 10, 2522-2531, 1993.
    doi:10.1364/JOSAA.10.002522

    10. Lohmann, A. W., "Image rotation, Wigner rotation, and the fractional Fourier transform," Journal of the Optical Society of America A, Vol. 10, 2181-2186, 1993.
    doi:10.1364/JOSAA.10.002181

    11. Mendlovic, D., H. M. Ozaktas, and A. W. Lohmann, "Graded-index fibers, Wigner-distribution functions, and the fractional Fourier transform," Applied Optics, Vol. 33, 6188-6193, 1994.
    doi:10.1364/AO.33.006188

    12. Zhang, Y., et al., "Beam shaping in the fractional Fourier transform domain," Journal of the Optical Society of America A, Vol. 15, 1114-1120, 1998.
    doi:10.1364/JOSAA.15.001114

    13. Wang, F., Y. Cai, and Q. Lin, "Experimental observation of truncated fractional Fourier transform for a partially coherent Gaussian Schell-model beam," Journal of the Optical Society of America A, Vol. 25, 2001-2010, 2008.
    doi:10.1364/JOSAA.25.002001

    14. Zhou, G., R. Chen, and X. Chu, "Fractional Fourier transform of Airy beams," Applied Physics B, Vol. 109, 549-556, 2012.
    doi:10.1007/s00340-012-5117-3

    15. Zhou, G., "Fractional Fourier transform of a higher-order cosh --- Gaussian beam," Journal of Modern Optics, Vol. 56, 886-892, 2009.
    doi:10.1080/09500340902783816

    16. Namias, V., "The fractional order Fourier transform and its application to quantum mechanics," IMA Journal of Applied Mathematics, Vol. 25, 241-265, 1980.
    doi:10.1093/imamat/25.3.241

    17. Erdélyi, A. and H. Bateman, "Tables of integral transforms,", 1954.

    18. Wen, J. J. and M. A. Breazeale, "A diffraction beam field expressed as the superposition of Gaussian beams," The Journal of the Acoustical Society of America, Vol. 83, 1752-1756, 1988.
    doi:10.1121/1.396508

    19. Ding, D. and X. Liu, "Approximate description for Bessel, Bessel-Gauss, and Gaussian beams with finite aperture," Journal of Optical Society of America A, 1286-1293, 1999.
    doi:10.1364/JOSAA.16.001286

    20. Cai, Y. and L. Hu, "Propagation of partially coherent twisted anisotropic Gaussian Schell-model beams through an apertured astigmatic optical system," Optics Letters, Vol. 31, 685-688, 2006.
    doi:10.1364/OL.31.000685

    21. Zheng, C., "Fractional Fourier transform for a hollow Gaussian beam," Physics Letters A, Vol. 355, 156-161, 2006.
    doi:10.1016/j.physleta.2006.02.025