Analytical propagation equation of astigmatic Hermite-Gaussian beams through a 4 x 4 paraxial optical system and their symmetrizing transformation

Starting from the Collins formula, a closed-form propagation equation of astigmatic Hermite-Gaussian (H-G) beams through a 4 x 4 paraxial optical system is derived, which permits us to calculate the irradiance distribution at any propagation plane and to study the symmetrization of astigmatic standard and elegant H-G beams. A detailed symmetrizing transformation of astigmatic H-G beams through a three-cylindrical-lens mode converter is illustrated both analytically and numerically. It is found that in accordance with the second-order moments characterization, there are two types of beam symmetrization. The transformation of standard H-G beams through the three-cylindrical-lens mode converter belongs to the perfect symmetrization, whereas the transformation of elegant H-G beams is the imperfect one. (C) 2003 Published by Elsevier Science Ltd.