Fractional Fourier transform for a hollow Gaussian beam

Zheng, Chongwei

doi:10.1016/j.physleta.2006.02.025

Cited by 55 publications

(21 citation statements)

References 20 publications

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“…The central peak gradually becomes symmetrical double-peaks with an increasing beam order n, and the hollow size increases with an increasing beam order. There is an excellent agreement between the above results and the transmission characteristics of FRT for the hollow Gauss beams [21].…”

Section: Numerical Resultssupporting

confidence: 75%

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

Qu¹,

Fang²,

Ji³

et al. 2015

PIER M

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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 beamshaping method.

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Section: Numerical Resultssupporting

confidence: 75%

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

Qu¹,

Fang²,

Ji³

et al. 2015

PIER M

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“…[18][19][20][21][22][23] Recently, much work has been done concerning their FrFT for various types of beams that frequently used in modern optics. [24][25][26][27][28][29][30][31][32][33][34] However, to the best of our knowledge, no results have been reported until now about the propagation properties of the newly proposed HsG beams in the FrFT optical system.…”

Section: Introductionmentioning

confidence: 95%

Fractional Fourier transform of hollow sinh-Gaussian beams

2014

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Abstract. The analytical expression for hollow sinh-Gaussian (HsG) beams propagating through a paraxial ABCD optical system is derived and used to investigate its propagation properties in a fractional Fourier transform (FrFT) optical system. Several influence parameters of both the HsG beams and the FrFT optical system are discussed in detail. Results show that the FrFT optical system provides a convenient way for modulating HsG beams: HsG beams maintain their dark-centered distribution when the fractional order p is low, and low-ordered HsG beams lose their original dark-centered distribution more quickly than high-ordered ones when the value of p increases. Eventually all HsG beams' intensities evolve into peak-centered distributions with some side lobes located sideways. Furthermore, our results also show that HsG beam intensity distribution versus the fractional order is periodical and the period is 2. The results obtained in this work are valuable for HsG beam shaping. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

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“…Since then, the FrFT has been found important applications in signal processing, optical image encryption, beam shaping and beam analysis [14][15][16][17][18]. Recently, the FrFT of various beams has been widely investigated, such as the flattened Gaussian beams [19], elliptical Gaussian beams [20], partially coherent Gaussian Schell beams [21,22] [23,24], Lorentz-Gauss beams [25], and Ince-Gauss beams [26,27]. However, to the best of our knowledge, the propagation characteristics of the Airy beams have not been studied through an ABCD system [28] with a hard-edge rectangular aperture.…”

Section: Introductionmentioning

confidence: 99%

Propagation of Airy beams through a hard-edged aperture

Deng

2012

Appl. Phys. B

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Based on the fact that a hard-edged aperture function can be expanded into a finite sum of complex Gaussian functions, we obtain the analytical formula for the propagation of the Airy beams in free space and through the fractional Fourier transformation (FrFT) system. According to the derived formulas, the propagation properties of the Airy beams in free space and through the FrFT plane with a hardedged aperture are illustrated numerically.

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Fractional Fourier transform for a hollow Gaussian beam

Cited by 55 publications

References 20 publications

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

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

Fractional Fourier transform of hollow sinh-Gaussian beams

Propagation of Airy beams through a hard-edged aperture

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