Analytical propagation equation of astigmatic Hermite–Gaussian beams through a 4×4 paraxial optical system and their symmetrizing transformation |
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| Authors: | Baida Lü ,Ping Wu, |
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| Affiliation: | a Department of Applied Physics, Southwest Jiaotong University, Chengdu 610031, China;b Institute of Laser Physics and Chemistry, Sichuan University, Chengdu 610064, China;c State Key Laboratory of Laser Technology, Huazhong University of Science & Technology, Wuhan, 430074, China |
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| Abstract: | Starting from the Collins formula, a closed-form propagation equation of astigmatic Hermite–Gaussian (H–G) beams through a 4×4 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. |
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| Keywords: | Astigmatic Hermite– Gaussian beam Propagation equation Symmetrizing transformation |
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