Collins formula and propagation of Bessel-modulated Gaussian light beams through an ABCD optical system

From the Collins diffraction integral, an expression is derived for the amp litude distribution of a Bessel-modulated Gaussian light beams propagating through an optical system described by an ABCD matrix with real elements. T he amplitude distribution at the output plane is calculated as a function o f the amplitude distribution at the input plane by considering the argument of the Bessel function is linear or quadratic in the transverse coordinate . Free space propagation, Fourier and fractional Fourier transfer systems a re also treated as particular cases. (C) 2000 Elsevier Science B.V. All rig hts reserved.