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Volume 28 Issue 6
Sep.  2013
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Article Navigation >  LASER TECHNOLOGY  > 2004 >  28(6): 670-672

Citation:
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Validity of the Fresnel approximation for hard-edged diffracted beams

  • 1.

    Institute of Laser Physics and Chemistry, Sichuan University, Chengdu 610064, China;

  • 2.

    Department of Physics and Chemistry, Zigong College, Zigong 643000, China;

  • 3.

    National Laboratory of Laser Technology, HUST, Wuhan 430074, China

  • Received Date: 2003-10-20
    Accepted Date: 2004-03-15
  • The diffraction of Gaussian beams at an square aperture is studied based on the Kirchhoff and Fresnel diffraction integrals.Detailed numerical results are presented and compared.It is shown that for a given waist width w0(w0≥λ,λ is wavelength),the valid range of the Fresnel diffraction integral depends on the truncation parameter.Otherwise,if the waist width w0 is comparable to or evenless than the wavelength λ,the Kirchhoff diffraction integral should be used.
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  • [1] 吕百达.激光光学[M].成都:四川大学出版社,1992.53.
    [2]

    NEMOTO S.Nonparaxial Gaussian beams[J].Appl Opt,1990,29:1940～1946.
    [3]

    AGRAWAL G P,PATTANAYAK D N.Gaussian beam propagation beyond the paraxial approximation[J].J O S A,1979,69:575～578.
    [4]

    DUAN K L,LÜ B D.Nonparaxial analysis of far-field properfies of Gaussian beams diffracted by an aperture[J].Opt Expr,2003(11):1474～1479.
    [5]

    BORN M,WOLF E.Principles of optics[M].7th ed,Cambridge:Cambridge University Press, 1999.478.
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Validity of the Fresnel approximation for hard-edged diffracted beams

  • 1. Institute of Laser Physics and Chemistry, Sichuan University, Chengdu 610064, China;
  • 2. Department of Physics and Chemistry, Zigong College, Zigong 643000, China;
  • 3. National Laboratory of Laser Technology, HUST, Wuhan 430074, China
  • Received Date: 2003-10-20
  • Accepted Date: 2004-03-15
  • Available Online: 2004-11-25

Abstract: The diffraction of Gaussian beams at an square aperture is studied based on the Kirchhoff and Fresnel diffraction integrals.Detailed numerical results are presented and compared.It is shown that for a given waist width w0(w0≥λ,λ is wavelength),the valid range of the Fresnel diffraction integral depends on the truncation parameter.Otherwise,if the waist width w0 is comparable to or evenless than the wavelength λ,the Kirchhoff diffraction integral should be used.

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