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The optical Airy transform and its application in generating and controlling the Airy beam
Optics Communications, 2012We propose an optical Airy transform in this paper, and obtain the analytical expressions for the Airy transform of fundamental Gaussian beams and finite energy Airy beams. The setup for performing the optical Airy transform is presented. The Airy transform for Gaussian beams and finite energy Airy beams are theoretically calculated and analyzed.
Yunfeng Jiang, Xuanhui Lu
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Production of Airy-related beams by an Airy transform optical system
Optical and Quantum Electronics, 2019Based on the process of Huygens–Fresnel diffraction integral, we investigate theoretically the characteristics of fields generated by diffracted controllable dark-hollow beams (CDHBs) through an Airy transform optical system. It is shown that the CDHB is transformed into Airy-related beams and the dark central spot is converted into peak intensity. The
Abdelmajid Belafhal
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Optical and Quantum Electronics, 2020
In this paper, we investigate the transformation of a higher-order cosh-Gaussian beam into an Airy-related beam by an Airy transform optical system. Based on the Huygens-Fresnel integral diffraction, the analytical expression of the generated curved beam is derived.
Abdelmajid Belafhal
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In this paper, we investigate the transformation of a higher-order cosh-Gaussian beam into an Airy-related beam by an Airy transform optical system. Based on the Huygens-Fresnel integral diffraction, the analytical expression of the generated curved beam is derived.
Abdelmajid Belafhal
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Realization and measurement of Airy transform of Gaussian vortex beams
Optics and Laser Technology, 2021Abstract Airy transformation is a useful technique to modulate amplitude and phase of a light beam, which has important applications in particle trapping/manipulation, optical communications and optical imaging. However, most of the studies only focused on the Airy transform of Gaussian beams and other vortex-free beams in the past.
Rui-Pin Chen, Guoquan Zhou
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Optical and Quantum Electronics, 2019
In the present work, we investigate theoretically the transformation of a double-half inverse Gaussian hollow (DHIGH) beam into a superposition of finite Airy beams by using an optical Airy transform system. The analytical expression of the generated finite Airy beam is derived by means of the generalized Huygens–Fresnel integral diffraction. Numerical
Abdelmajid Belafhal
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In the present work, we investigate theoretically the transformation of a double-half inverse Gaussian hollow (DHIGH) beam into a superposition of finite Airy beams by using an optical Airy transform system. The analytical expression of the generated finite Airy beam is derived by means of the generalized Huygens–Fresnel integral diffraction. Numerical
Abdelmajid Belafhal
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Propagation properties of finite cosh-Airy beams through an Airy Transform Optical System
Optical and Quantum Electronics, 2019In this paper, we have derived the analytical expression for a diffracted finite cosh-Airy beam by an Airy Transform Optical System (ATOS). The obtained output field is expressed as a superposition of finite Airy modes with different weights and decay factors.
Abdelmajid Belafhal
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Investigation on Airy transform of Four-Petal Gaussian beams
Optical and Quantum Electronics, 2020The transformation of Four-petal Gaussian (FPG) beam by an Optical Airy Transform System (OATS) is examined theoretically. The generalized expression of the output generated field is performed for an arbitrary beam order N. In particular, we derived alternative closed-form output field expressions for three lower beam orders N = 1, 2 and 3.
Abdelmajid Belafhal
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Laplace transforms of Airy functions
Journal of Physics A: Mathematical and General, 1982Analytic expressions, involving gamma, incomplete gamma and degenerate hypergeometric functions, are obtained for the Laplace transforms of Airy functions, which arise in the theory of electron tunnelling from solids.
Davison, S. G., Glasser, M. L.
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Hacettepe Journal of Mathematics and Statistics, 2015
In this note, we introduce the fractional Airy transform using the higher order derivatives of the Airy function and the Airy polynomials. Then, we show that the new integral transform is coincided to the natural Airy transform in particular case of the scaling parameter. Some properties of this transform are also given.
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In this note, we introduce the fractional Airy transform using the higher order derivatives of the Airy function and the Airy polynomials. Then, we show that the new integral transform is coincided to the natural Airy transform in particular case of the scaling parameter. Some properties of this transform are also given.
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