Non-Linear Effects in Optical Systems by Lie Algebra and Symplectic Mapping
Non-Linear Effects in Optical Systems by Lie Algebra and Symplectic Mapping作者机构：Centro de Física Aplicada y Tecnología Avanzada/Secretaría de Desarrollo Institucional Universidad Nacional Autónoma de México Queretaro México
出 版 物：《Journal of Modern Physics》 (现代物理（英文）)
年 卷 期：2022年第13卷第11期
页 面：1314-1323页
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
主 题：Symplectic Mapping Geometrical Optics Non-Linear Effects
摘 要：The use of signals of different frequencies determines the geometrical deviation with respect to the optical axes of a given beam. This angle can be determined by Sympletic Map (SM), a powerful and simple mathematical tool for the characterization and construction of images in Geometrical Optics. The Sympletic Map constitutes a Lie Group, with an algebra associated: the Lie Algebra. In general, the SM can be expressed as an infinite series, where each term corresponds to different contributions produced by the optical devices that constitute the optical system (lenses, apertures, bandwidth cutoff, etc.). The level of correction to be performed on the image to recover the original object is clear and controllable by SM. This formalism can be extended easily to physical optics to describe diffraction and interference phenomena.
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