摘要
傍轴近似常被用于光束传输理论的表达,数值计算常被用于非傍轴光束的传输特性分析。为了使一维会聚非傍轴高斯光束的传输特性更加简明,本文基于倾斜因子由观察方倾斜角余弦平方根表达的非傍轴衍射积分公式,给出了符合行波场辐射能守恒定律的一维会聚非傍轴高斯光束的焦平面光场分布表达,同时给出了焦点附近一维会聚非傍轴高斯光束的轴上点光强和相位特性表达。当一维会聚非傍轴高斯光束的最大倾斜角远大于高斯光束的远场发散角时,合理的观察方倾斜因子可将高斯光束传输特性从傍轴领域延拓到非傍轴领域。本文阐明了一维会聚非傍轴高斯光束的传输特性,并验证了用观察方倾斜角余弦平方根表达观察方倾斜因子的合理性。
Objective The theories of beam propagation characteristics are often expressed by the paraxial approximation,and the propagation characteristics of nonparaxial beams are often analyzed using numerical calculation.When analyzing the characteristics of a light field near the focus of a convergent light wave,the characteristics of a light field near the focus of paraxial convergent beams are usually expressed approximately using the Debye integral formula,and the characteristics of the light field near the focus of nonparaxial convergent beams are usually calculated using a vector diffraction integral formula.However,the physical significance of nonparaxial beam propagation is not clear enough.To clarify the propagation characteristics of a one-dimensional(1D)nonparaxial convergent Gaussian beam(GB),a new normalized inclination factor of the 1Dnonparaxial diffraction integral formula is employed to analyze the light field near the focus of a 1Dnonparaxial convergent GB.Methods According to the Huygens principle and the law of conservation of radiation energy in traveling wave field,the normalized inclination factor of the 1Dnonparaxial diffraction integral formula was expressed by the square root of the cosine of the observation side inclination angle.Then,the characteristics of the focal-plane light field and on-axis point light field of a 1Dnonparaxial convergent GB were analyzed using the new diffraction integral formula.To clarify the rationality of the new diffraction integral formula,the characteristics of the focal-plane light field and on-axis point light field of the 1Dnonparaxial convergent GB were also analyzed using the Debye diffraction integral formula,and the propagation characteristics of the GB were presented.Results and Discussions Based on the normalized inclination factor that is expressed by the square root of the cosine of the observation side inclination angle,the characteristics of the focal-plane light field of the 1Dnonparaxial convergent GB,which conform to the law of conservation of radiation energy in traveling wave field,are described.Additionally,the characteristics of the on-axis point light intensity and phase of the 1Dnonparaxial convergent GB near the focus are elucidated.When the maximal inclination angle of the 1Dnonparaxial convergent GB is much larger than the far-field divergence angle of GB,the characteristics of the light field near the focal line of the 1D nonparaxial convergent GB are very close to the propagation characteristics of GB(Figs.2--4).As the influence of the observation side inclination angle is ignored by the Debye diffraction integral formula,it is equivalent to the normalized inclination factor of the Debye diffraction integral formula being equal to one.The characteristics of the focal-plane light field and on-axis point light intensity near the focal line of the 1Dnonparaxial convergent GB that are computed using the Debye diffraction integral formula differ from the propagation characteristics of GB.Moreover,the value of the light intensity of the focal line of the 1Dnonparaxial convergent GB that is computed using the Debye diffraction integral formula is larger than the theoretical value,shown in Figs.2and 3.As an example,when the maximal inclination angle of the 1Dnonparaxial convergent GB is 1rad,the far-field divergence angle of the GB is 0.4rad,the value of the light intensity of focal line of the 1Dnonparaxial convergent GB that is computed using the Debye diffraction integral formula is 1.0443times of the value of the light intensity of the focal line of the 1Dnonparaxial convergent GB that is computed using the new diffraction integral formula.Conclusions In a two-dimensional plane,the characteristics of a light field near the focus of a 1Dconvergent GB are analyzed using a 1Ddiffraction integral formula.As the normalized inclination factor that is expressed by the square root of the cosine of the observation side inclination angle is engaged,the characteristics of the focal-plane light field of the 1Dnonparaxial convergent GB that is expressed by a new diffraction integral formula conform to the law of conservation of radiation energy in traveling wave field,the characteristics of a light field near the focal line of the 1Dnonparaxial convergent GB are reasonable.Then,the propagation characteristics of the GB are extended from the paraxial field to the nonparaxial field using the reasonable observation side inclination factor.Furthermore,the rationality of the observation side inclination factor expressed by the square root of the cosine of the observation side inclination angle is verified.
作者
郭福源
李连煌
郑华
Guo Fuyuan;Li Lianhuang;Zheng Hua(Key Laboratory of Optoelectronic Science and Technology for Medicine of Ministry of Education,Fujian Provincial Key Laboratory of Photonic Technology,Institute of Laser&Optoelectroutes Teclmology,College of Photonic and Electronic Engineering,Fujian Normal University,Fuzhou,Fujia 350007,China)
出处
《中国激光》
EI
CAS
CSCD
北大核心
2022年第3期50-56,共7页
Chinese Journal of Lasers
基金
中央引导地方科技发展专项(2020L3008)
福建省自然科学基金(2019J01269)。
关键词
衍射
光束传输
倾斜因子
非傍轴
高斯光束
聚焦
diffraction
beam propagation
inclination factor
nonparaxial
Gaussian beam
focus
