Fractional Fourier transform of double-half inverse Gaussian hollow beams

In this paper, we study an appropriate mathematical model of dark-hollow beam by concerning double-half inverse Gaussian hollow (DHIGH) beams passing through fractional Fourier transform (FRFT) optical systems. Based on Collins integral formula and using the expression of the hard-edged aperture fun...

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Bibliographic Details
Published in:Optical and quantum electronics 2018-02, Vol.50 (2), p.1-12, Article 92
Main Authors: Saad, F., Ebrahim, A. A. A., Khouilid, M., Belafhal, A.
Format: Article
Language:English
Subjects:
Apertures
Beams (radiation)
Characterization and Evaluation of Materials
Computer Communication Networks
Computer simulation
Electrical Engineering
Fourier transforms
Gaussian beams (optics)
Integrals
Lasers
Mathematical analysis
Mathematical models
Optical Devices
Optical properties
Optics
Photonics
Physics
Physics and Astronomy
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Summary:In this paper, we study an appropriate mathematical model of dark-hollow beam by concerning double-half inverse Gaussian hollow (DHIGH) beams passing through fractional Fourier transform (FRFT) optical systems. Based on Collins integral formula and using the expression of the hard-edged aperture function into a finite sum of complex Gaussian functions, analytical expressions for the propagation properties of DHIGH beams through the FRFT optical systems without and with apertures have been derived in detail. Some numerical simulations are given to illustrate the normalized intensity distribution of DHIGH beams in a FRFT system by studying the important factors of both incident beams order and the FRFT order. Our results obtained by using an approximate analytical formula, are in a good agreement with those obtained by using numerical integral method. The results show that the FRFT optical system is a convenient way for DHIGH beams shaping.
ISSN:0306-8919
1572-817X
DOI:10.1007/s11082-018-1367-6