Abstract
Based on the Collins diffraction formula and by means of the expansion of a hard aperture function into a finite sum of complex Gaussian functions, two analytical approaches of the Finite Olver beams (FOBs) passing through a paraxial ABCD optical system with a circular annular aperture or a rectangular one are developed in this paper. The propagation properties of the FOBs through an unapertured ABCD optical system or through this last with a circular (or rectangular) aperture or a circular (or rectangular) black screen are deduced, from the main results, as particular cases. Also, the characteristics of Finite ordinary Airy beam passing through the all considered optical systems are derived here that correspond to zeroth-order of the FOBs. According to the predicted formulas, computer simulation examples are given to deepen the understanding of the characteristics of the FOBs passing through some optical systems of annular aperture basis.
Highlights
As is well known, the Finite Airy beam, as solution of paraxial wave equation, was firstly devoted in opticalHow to cite this paper: Hennani, S., Ez-Zariy, L. and Belafhal, A. (2015) Intensity Distribution of the Finite Olver Beams through a Paraxial ABCD Optical System with an Aperture of Basis Annular Aperture
By using the integral representation of Olver functions given by Equation (7), recalling the integral formulae as given in Equation (8) and Equation (9), and after some calculations, we find the output optical field of a Finite Olver beam passing through an ABCD optical system with a circular annular aperture as follows
Propagation of a Finite Airy Beam through a Rectangular In this case, the propagation of this beams family passing through a paraxial ABCD optical system with rectangular annular aperture is treated
Summary
The Finite Airy beam, as solution of paraxial wave equation, was firstly devoted in optical. The answer to this question will lead us to study the behavior of the FOBs propagating through an ABCD optical system with a circular annular aperture or with a rectangular one, using the generalized Huygens-Fresnel diffraction integral and the expansion of a hard aperture function into a finite sum of complex Gaussian functions. Propagation of a Finite Airy Beam through a Rectangular In this case, the propagation of this beams family passing through a paraxial ABCD optical system with rectangular annular aperture is treated This case is obtained when n = 0 and by the use of Equation (10), the output field is given by h1 =1. Equation (21) is obtained from Equation (17) and gives the output electrical field of a Finite Airy beam through an ABCD optical system truncated by a circular annular aperture.
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