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

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