Propagation of Bessel and Bessel-Gaussian beams through an unapertured or apertured misaligned paraxial optical systems

Propagation of Bessel and Bessel-Gaussian beams through an unapertured or apertured misaligned paraxial optical system is investigated. Analytical formulas for Bessel and Bessel-Gaussian beams propagating through an unapertured misaligned paraxial optical system are derived based on the generalized diffraction integral formula for treating the propagation of a laser beam through a misaligned paraxial optical system in the cylindrical coordinate system. By expanding the hard aperture function into a finite sum of complex Gaussian functions, some approximate analytical formulas are derived for Bessel and Bessel-Gaussian beams propagating through an apertured misaligned paraxial optical system. Some numerical examples are illustrated. The present analytical formulas provide a convenient and effective way for studying the propagation and transformation of Bessel and Bessel-Gaussian beams through an unapertured or apertured misaligned paraxial optical system. (C) 2007 Elsevier B.V. All rights reserved