Fresnel diffraction by circular aperture of gaussian beams in     gradient index media

E. Acosta; Carlos C. Gomez-Reino; R. M. Gonzalez

doi:10.1117/12.22167

1 July 1990 Fresnel diffraction by circular aperture of Gaussian beams in gradient index media

E. Acosta, Carlos C. Gomez-Reino, R. M. Gonzalez

Proceedings Volume 1319, Optics in Complex Systems; (1990) https://doi.org/10.1117/12.22167
Event: 15th International Optics in Complex Systems, 1990, Garmisch, Germany

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

Citation Download Citation

E. Acosta, Carlos C. Gomez-Reino, and R. M. Gonzalez "Fresnel diffraction by circular aperture of Gaussian beams in gradient index media", Proc. SPIE 1319, Optics in Complex Systems, (1 July 1990); https://doi.org/10.1117/12.22167

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available