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Proceedings Paper

Fresnel diffraction by circular aperture of gaussian beams in gradient index media
Author(s): E. Acosta; Carlos C. Gomez-Reino; R. M. Gonzalez
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Paper Abstract

The intensity distribution of a gaussian beam propagating through GRIN media that has been truncated by a centered circular aperture is calculated by Fresnel-Kirchoff theory. On axis intensity is evaluated. 1 MATHEMATICAL TREATMENT AND DISCUSSION. The circular aperture in an opaque screen is located at z r is the radial coordinate. In the z half-space the medium has a refractive index profile given by 2 2 2 2 n (r (z)r ). For the z half-space the medium is considered to be homogeneous with n''l. The diffracted field in the z region when a gaussian beam source at z0 in the z region is evaluated in terms of Bessel functions. The beam at z can be represented in terms of its waist size and its half-width w(z0) and curvature radius R(z0) at the aperture plane. The Huygens-Fresnel diffraction formula with the Fresnel approximation can be evaluated as an infinite sum yielding: S 2 Akwn iknHr 2 J(aa) 00 01 1 1 2 n u(r w(z )JexP[ 2H JJ : exp(a C) (1) 1 0 1 n 2n! (aa) where H(z) and H2(z) are respectively the axial and the field rays1 a and C intensity distribution in the diffraction pattern is given by I(r This treatment predicts for the on axis intensity: I 2 2 nH 1 I I a 1 ia ki 1 0 2 I (z)cx . coshi

Paper Details

Date Published: 1 July 1990
PDF: 1 pages
Proc. SPIE 1319, Optics in Complex Systems, (1 July 1990); doi: 10.1117/12.22167
Show Author Affiliations
E. Acosta, Univ. of Santiago de Compostela (Spain)
Carlos C. Gomez-Reino, Univ. of Santiago de Compostela (Spain)
R. M. Gonzalez, Univ. of Santiago de Compostela (Spain)

Published in SPIE Proceedings Vol. 1319:
Optics in Complex Systems
F. Lanzl; H.-J. Preuss; G. Weigelt, Editor(s)

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