傍轴TM高斯光束近场的矢量结构特性

基于电磁光束的矢量结构理论、傍轴近似和数学技巧,分析了共焦腔在近场的麦克斯韦方程组的精确解,即TM（横磁）高斯光束的矢量结构特性,导出了矢量结构TE项和TM项的解析表达式．描绘了TE项和TM项以及整个光束在近场的幅度分布和位相分布,揭示了傍轴TM高斯光束的矢量结构组成．这一研究有助于深化对傍轴激光束的内在矢量本性和传输特性的认识．     

Nonparaxial propagation of a super-Lorentz－Gauss SLG01 mode beam

Based on the vectorial Rayleigh--Sommerfeld integral formulae, this paper derives the analytical nonparaxial propagation equation of a super-Lorentz--Gauss (SLG) SLG₀₁ mode beam in free space. The far field expression and the scalar paraxial result are treated with special cases of the general formulae. According to the obtained analytical representation, the nonparaxial propagation properties of the SLG₀₁ mode beam are illustrated and analysed with numerical examples. This research provides an approach to investigate the propagation of the SLG₀₁ mode beam within the framework of the nonparaxial regime.     

M2 factor of four-petal Gaussian beam

Based on the second-order moments, this paper derives an analytical expression of the M^2 factor of four-petal Gaussian beam. The results show that the M^2 factor is only determined by the beam order n. The corresponding numerical calculations are also given. As the beam order increases, the augment of M^2 factor is disciplinary. As the expression of M^2 factor is expressed in series form and becomes more complicated, a new concise formula of M^2 factor is also presented by using curve fitting of numerical calculations. When 3 ≤ n ≤ 200, the maximum error rate of fitting formula will not exceed 2.6% and the average error rate is 0.28%. This research is helpful to the applications of four-petal Gaussian beam.     

Characteristics of paraxial propagation of a super Lorentz—Gauss SLG01 mode in uniaxial crystal orthogonal to the optical axis

Analytical propagation expression of a super Lorentz-Gauss（SLG） 01 mode in uniaxial crystal orthogonal to the optical axis is derived.The SLG 01 mode propagating in uniaxial crystal orthogonal to the optical axis mainly depends on the ratio of the extraordinary refractive index to the ordinary refractive index.The SLG 01 mode propagating in uniaxial crystals becomes an astigmatic beam.The beam spot of the SLG 01 mode in the uniaxial crystal is elongated in the x-or y-direction,which is determined by the ratio of the extraordinary refractive index to the ordinary refractive index.With the increase of the deviation of the ratio of the extraordinary refractive index to the ordinary refractive index from unity,the elongation of the beam spot also augments.In different observation planes,the phase distribution of an SLG 01 mode in the uniaxial crystal takes on different shapes.With the variation of the ratio of the extraordinary refractive index to the ordinary refractive index,the phase distribution is elongated in one transversal direction and is contracted in the other perpendicular direction.This research is beneficial to the practical applications of an SLG mode.     

Characteristics of paraxial propagation of a super Lorentz-Gauss SLG₀₁ mode in uniaxial crystal orthogonal to the optical axis

Analytical propagation expression of a super Lorentz-Gauss(SLG) 01 mode in uniaxial crystal orthogonal to the optical axis is derived.The SLG 01 mode propagating in uniaxial crystal orthogonal to the optical axis mainly depends on the ratio of the extraordinary refractive index to the ordinary refractive index.The SLG 01 mode propagating in uniaxial crystals becomes an astigmatic beam.The beam spot of the SLG 01 mode in the uniaxial crystal is elongated in the x-or y-direction,which is determined by the ratio of the extraordinary refractive index to the ordinary refractive index.With the increase of the deviation of the ratio of the extraordinary refractive index to the ordinary refractive index from unity,the elongation of the beam spot also augments.In different observation planes,the phase distribution of an SLG 01 mode in the uniaxial crystal takes on different shapes.With the variation of the ratio of the extraordinary refractive index to the ordinary refractive index,the phase distribution is elongated in one transversal direction and is contracted in the other perpendicular direction.This research is beneficial to the practical applications of an SLG mode.     

部分相干洛伦兹-高斯光束在湍流大气中的峭度参数

基于广义惠更斯-菲涅耳衍射积分公式和洛伦兹函数的厄米-高斯展开,导出了部分相干洛伦兹-高斯光束在湍流大气中经傍轴ABCD光学系统的峭度参数的解析表达式,对该峭度参数进行了数值计算。结果表明:空间相干长度和结构常数对峭度参数的影响与部分相干洛伦兹-高斯光束本身的光束参数有关;当空间相干长度小于光束参数时,其影响显著;当洛伦兹部分的光束参数较大或高斯部分的光束参数较小时,结构常数的影响较明显且随传输距离的增大而增强。