By using the expansion of the aperture function into a finte sum of complex Gaussian functions, the corresponding analytical expressions of Hermite-cosh-Gaussian beams passing through annular apertured paraxially and ...By using the expansion of the aperture function into a finte sum of complex Gaussian functions, the corresponding analytical expressions of Hermite-cosh-Gaussian beams passing through annular apertured paraxially and symmetrically optical systems written in terms of ABCD matrix were derived, and they could reduce to the cases with squared aperture. In a similar way, the corresponding analytical expres- sions of cosh-Gaussian beams through annular apertured ABCD matrix were also given. The method could save more calculation time than that by using the diffraction integral formula directly.展开更多
In this paper, an exact analytical propagation formula of Finite Olver-Gaussian Beams (FOGBs) passing through a paraxial ABCD optical system is developed and some numerical examples are performed. The propagation prop...In this paper, an exact analytical propagation formula of Finite Olver-Gaussian Beams (FOGBs) passing through a paraxial ABCD optical system is developed and some numerical examples are performed. The propagation properties of the FOGBs through general optical systems characterized by given ABCD matrix are studied on the basis of the generalized Huygens-Fresnel diffraction integral, which permits to show the behavior of this laser beams family and its properties de-pending of the laser parameters. This research is of interest to prove some investigations done in the past by other researchers.展开更多
Based on the Collins diffraction formula and by means of the expansion of a hard aperture function into a finite sum of complex Gaussian functions, two analytical approaches of the Finite Olver beams (FOBs) passing th...Based on the Collins diffraction formula and by means of the expansion of a hard aperture function into a finite sum of complex Gaussian functions, two analytical approaches of the Finite Olver beams (FOBs) passing through a paraxial ABCD optical system with a circular annular aperture or a rectangular one are developed in this paper. The propagation properties of the FOBs through an unapertured ABCD optical system or through this last with a circular (or rectangular) aperture or a circular (or rectangular) black screen are deduced, from the main results, as particular cases. Also, the characteristics of Finite ordinary Airy beam passing through the all considered optical systems are derived here that correspond to zeroth-order of the FOBs. According to the predicted formulas, computer simulation examples are given to deepen the understanding of the characteristics of the FOBs passing through some optical systems of annular aperture basis.展开更多
An orthonormal beam family of super Lorentz-Gauss （SLG） beam model is proposed to describe the higher-order mode beams with high divergence, which are generated by a high power diode laser. Here we consider the simp...An orthonormal beam family of super Lorentz-Gauss （SLG） beam model is proposed to describe the higher-order mode beams with high divergence, which are generated by a high power diode laser. Here we consider the simplest case of the SLG beams, where there are four mutually orthogonal SLG beams, namely SLG00, SLG01, SLG10, and SLGll beams. The SLG00 beam is just the Lorentz-Gauss beam. Based on the Collins integral formula and the Hermite-Gaussian expansion of a Lorentz function, an analytical expression for the Wigner distribution function （WDF） of an SLG11 beam through a paraxial ABCD optical system is derived. The properties of the WDF of an SLG11 beam propagating in free space are demonstrated. The normalized WDFs of an SLG11 beam at the different spatial points are depicted in several observation planes. The influence of the beam parameter on the WDF of an SLGI 1 beam in free space is analyzed at different propagation distances. The second-order moments of the WDF of an SLG11 beam in free space are also examined. This research reveals the propagation properties of an SLGll beam from another perspective. The WDFs of SLG01 and SLG10 beams can be easily obtained by using the WDFs of Lorentz-Gauss beam and the SLG11 beam.展开更多
本文通过对顶棚造型与线条、结构与材质以及整合附件与功能性的深入探讨,以及 A-D 柱护板外观设计策略的分析,希望提出一套综合的优化方案以加强车辆的美观度与实用性。文中研究了提升 A 柱的视觉效果与结构优化以增强安全,考虑 B 柱外...本文通过对顶棚造型与线条、结构与材质以及整合附件与功能性的深入探讨,以及 A-D 柱护板外观设计策略的分析,希望提出一套综合的优化方案以加强车辆的美观度与实用性。文中研究了提升 A 柱的视觉效果与结构优化以增强安全,考虑 B 柱外观与乘员保护的一致性和兼容性,C柱与D柱的流线性与造型协调性,以及如何在整个外观设计中实现细节特征与整体风格的融合。还分析在遵守安全规范的同时追求审美趋势,以及功能性与视觉效果整合应用的重要性。确保设计策略不仅回应了当代审美和技术要求,也提高了车辆的市场竞争力。展开更多
文摘By using the expansion of the aperture function into a finte sum of complex Gaussian functions, the corresponding analytical expressions of Hermite-cosh-Gaussian beams passing through annular apertured paraxially and symmetrically optical systems written in terms of ABCD matrix were derived, and they could reduce to the cases with squared aperture. In a similar way, the corresponding analytical expres- sions of cosh-Gaussian beams through annular apertured ABCD matrix were also given. The method could save more calculation time than that by using the diffraction integral formula directly.
文摘In this paper, an exact analytical propagation formula of Finite Olver-Gaussian Beams (FOGBs) passing through a paraxial ABCD optical system is developed and some numerical examples are performed. The propagation properties of the FOGBs through general optical systems characterized by given ABCD matrix are studied on the basis of the generalized Huygens-Fresnel diffraction integral, which permits to show the behavior of this laser beams family and its properties de-pending of the laser parameters. This research is of interest to prove some investigations done in the past by other researchers.
文摘Based on the Collins diffraction formula and by means of the expansion of a hard aperture function into a finite sum of complex Gaussian functions, two analytical approaches of the Finite Olver beams (FOBs) passing through a paraxial ABCD optical system with a circular annular aperture or a rectangular one are developed in this paper. The propagation properties of the FOBs through an unapertured ABCD optical system or through this last with a circular (or rectangular) aperture or a circular (or rectangular) black screen are deduced, from the main results, as particular cases. Also, the characteristics of Finite ordinary Airy beam passing through the all considered optical systems are derived here that correspond to zeroth-order of the FOBs. According to the predicted formulas, computer simulation examples are given to deepen the understanding of the characteristics of the FOBs passing through some optical systems of annular aperture basis.
基金Project supported by the National Natural Science Foundation of China (Grant No.10974179)the Natural Science Foundation of Zhejiang Province,China(Grant No.Y1090073)
文摘An orthonormal beam family of super Lorentz-Gauss （SLG） beam model is proposed to describe the higher-order mode beams with high divergence, which are generated by a high power diode laser. Here we consider the simplest case of the SLG beams, where there are four mutually orthogonal SLG beams, namely SLG00, SLG01, SLG10, and SLGll beams. The SLG00 beam is just the Lorentz-Gauss beam. Based on the Collins integral formula and the Hermite-Gaussian expansion of a Lorentz function, an analytical expression for the Wigner distribution function （WDF） of an SLG11 beam through a paraxial ABCD optical system is derived. The properties of the WDF of an SLG11 beam propagating in free space are demonstrated. The normalized WDFs of an SLG11 beam at the different spatial points are depicted in several observation planes. The influence of the beam parameter on the WDF of an SLGI 1 beam in free space is analyzed at different propagation distances. The second-order moments of the WDF of an SLG11 beam in free space are also examined. This research reveals the propagation properties of an SLGll beam from another perspective. The WDFs of SLG01 and SLG10 beams can be easily obtained by using the WDFs of Lorentz-Gauss beam and the SLG11 beam.
文摘本文通过对顶棚造型与线条、结构与材质以及整合附件与功能性的深入探讨,以及 A-D 柱护板外观设计策略的分析,希望提出一套综合的优化方案以加强车辆的美观度与实用性。文中研究了提升 A 柱的视觉效果与结构优化以增强安全,考虑 B 柱外观与乘员保护的一致性和兼容性,C柱与D柱的流线性与造型协调性,以及如何在整个外观设计中实现细节特征与整体风格的融合。还分析在遵守安全规范的同时追求审美趋势,以及功能性与视觉效果整合应用的重要性。确保设计策略不仅回应了当代审美和技术要求,也提高了车辆的市场竞争力。
