单周期以上超短脉冲光束在自由空间中的矢量非傍轴传输方法

在Lax等建立的微扰法的基础上，应用傅里叶变换的方法得到了一种用于自由空间中单周期以上（即脉冲长度在一个振荡周期以上）脉冲光束的矢量非傍轴修正方法.在频域，其横向分量的一阶修正等价于Fu等所得相应结果，而在时域内则比Fu等所得结果更有利于非傍轴解析解的得出.通过量级关系证明了矢量效应在对标量傍轴光束修正中的必要性.从例子中发现，由于时空耦合的存在，超短脉冲光束中的矢量非傍轴效应会被其时间分布所影响. 关键词： 矢量 非傍轴 超短脉冲光束     

非傍轴高斯光束传输方程解的探讨

由洛伦兹规范下光场满足的矢势和标势方程出发, 探讨了初始光场具有任意对称性的一般非傍轴光束在空间的传输情况。利用角频谱并结合傅里叶变换处理得到了非傍轴光束的传输方程。利用扰动方法并结合新近似取法得到了非傍轴横向光场的扰动形式解, 该解对于近场弱非傍轴情况下的效果比强非傍轴条件下要好。给出了光束非傍轴传输高阶(八阶)修正解。对于零阶情况, 非傍轴光束退化为傍轴光束, 传输方程也相应退化为傍轴传输的模型方程。高斯解为扰动参量的零阶修正解。     

超短脉冲径向偏振光束的解析解及时空耦合效应

从超短脉冲光束的傍轴传输方程出发,运用傅里叶变换和相关数学算符的对易性,得到了超短脉冲径向偏振光束的解析表达式,该解可适用于任意脉冲驱动的径向偏振光束.基于该解析表达式并结合具体例子,讨论了超短脉冲径向偏振光束在自由空间中的传输性质.结果表明,在传输过程中时空耦合主要体现在光束边沿的脉冲延迟.这一效应导致了脉冲不同时间位置处横向光强分布随传输的变化,以及脉冲前后沿关于束腰的不对称性.本文的方法同样适用于得到超短脉冲方位角偏振光束的解析解和传输性质.     

超短脉冲径向偏振光束的解析解及时空耦合效应

从超短脉冲光束的傍轴传输方程出发, 运用傅里叶变换和相关数学算符的对易性, 得到了超短脉冲径向偏振光束的解析表达式.该解可适用于任意脉冲驱动的径向偏振光束. 基于该解析表达式并结合具体例子,讨论了超短脉冲径向偏振光束在自由空间中的传输性质. 结果表明, 在传输过程中时空耦合主要体现在光束边沿的脉冲延迟. 这一效应导致了脉冲不同时间位置处横向光强分布随传输的变化, 以及脉冲前后沿关于束腰的不对称性. 本文的方法同样适用于得到超短脉冲方位角偏振光束的解析解和传输性质.     

矢量非傍轴离轴高斯光束的传输

基于矢量瑞利-索末菲衍射积分公式，得出了波动方程的一个解，它代表矢量非傍轴离轴高斯光束，其在自由空间的传输方程表示为解析的结果.矢量非傍轴离轴高斯光束的轴上和远场公式，矢量非傍轴高斯光束的传输方程，以及傍轴的结果都可作为一般表达式的特例而得出.研究表明，f参数对光束的非傍轴特性有重要影响，而离心参数也影响非傍轴行为.与共轴情况不同的是，对离轴情况，在y方向存在场的纵向分量. 关键词： 激光光学 矢量非傍轴离轴高斯光束 瑞利-索末菲衍射积分 f参数 离轴参数     

等衍射超短脉冲厄米高斯光束在自由空间中的传输及其时空耦合效应

从超短脉冲光束的傍轴传输方程出发,得出了描述任意脉冲形式驱动的等衍射超短脉冲厄米高斯光束在自由空间中的解析表达式. 并通过例子研究了超短脉冲厄米高斯光束的传输性质. 结果表明：在传输过程中,由于群速度的空间分布不均匀性,会导致超短脉冲光束的脉冲时间延迟,并进而导致了在脉冲不同位置处光束横向分布严重偏离了厄米高斯函数. 另外,在传输过程中,发现不同阶数的脉冲厄米高斯光束会发生不同次数的极化反转. 并用脉冲光束的群-相速度差对这一现象进行了解释. 关键词： 超短脉冲 厄米高斯光束     

非傍轴矢量高斯光束的传输

运用非傍轴光束传输的矢量矩理论，对非傍轴矢量高斯光束的传输特性进行了系统的研究.结果表明，基于二阶矩定义的横向光束宽度在光束传播过程中满足简单的双曲线变化规律，并且给出了光束传输因子的解析表达式.就高度非傍轴情形，进一步给出了简洁的计算公式，在高斯光源线度趋向零的极限情形下，横向的最大发散角为90°.同时，还推广到了傍轴情形，得到了与原有傍轴公式稍有区别的结果，而且光束传输因子始终保持略大于1最后，对非傍轴矢量高斯光束和非傍轴标量高斯光束的传输进行了比较，结果显示对于线度在两个波长范围之内的高斯光源发散 关键词： 矢量高斯光束 光束传输 非傍轴 二阶矩     

自由空间中超短脉冲光束的非傍轴效应分析

在应用时间与空间傅里叶变换的基础上, 运用泰勒展开的方法, 得出了一种对多周期超短脉冲光束进行非傍轴修正的方法, 并将其应用于脉冲高斯光束．与数值结果的比较表明, 对于束宽在波长量级的脉冲光束, 二阶修正已经很接近非傍轴精确解, 并在例子中观察到：由于超短脉冲光束中时空耦合效应的存在, 脉冲的时间分布将会影响修正的空间分布．     

非傍轴双曲余弦-高斯脉冲电磁光束远场特性

利用矢量瑞利-索末菲衍射积分公式,推导出了非傍轴部分空间相干部分光谱相干双曲余弦-高斯(ChG)脉冲电磁光束在自由空间传输时交叉谱密度矩阵的远场解析公式,并用来表示脉冲电磁光束的光谱密度(光强)和偏振度。结果表明,对非傍轴远场部分空间相干部分光谱相干ChG脉冲电磁光束,其非傍轴性主要由参数f, f决定,而离心参数、脉冲宽度和时间相干长度影响其非傍轴行为。非傍轴部分空间相干部分光谱相干高斯-谢尔模型脉冲电磁光束的远场传输可作为特例处理。     

矢量非傍轴双曲余弦-高斯光束

 引入了矢量非傍轴双曲余弦-高斯(ChG)光束概念。使用矢量瑞利-索末菲衍射积分公式推导出了矢量非傍轴ChG光束在自由空间传输的解析公式。矢量非傍轴ChG光束轴上和远场的解析式以及傍轴结果作为一般传输公式的特例给出。研究表明,对矢量非傍轴ChG光束,其非傍轴性主要由f参数决定,但偏心参数会影响其横向光强剖面形状和非傍轴行为。     

Propagation properties of vectorial elliptical Gaussian beams beyond the paraxial approximation

Starting from the vectorial Rayleigh diffraction integral formula and without using the far-field approximation, a solution of the wave equation beyond the paraxial approximation is found, which represents vectorial non-paraxial elliptical Gaussian beams in free space. The far-field expressions for non-paraxial Gaussian beams and elliptical Gaussian beams can be regarded as special cases treated in this paper. Some basic propagation properties of vectorial non-paraxial elliptical Gaussian beams, including the irradiance distribution, phase term, beam widths and divergence angles are studied. Numerical results are given and illustrated.     

Analytical vectorial structure of non-paraxial nonsymmetrical vector Gaussian beam in the far field

Based on the vectorial structure of non-paraxial electromagnetic beam and the method of stationary phase, the analytical TE and TM terms of non-paraxial nonsymmetrical vector Gaussian beam in the far field are presented. According to the analytical electromagnetic fields of the TE and TM terms, the energy flux distributions of the whole beam, its TE and TM terms are investigated. Moreover, the influences of non-symmetries on the energy flux distributions of the whole beam, its TE and TM terms are also analyzed, respectively. This research reveals the internal vectorial structure of non-paraxial laser beam in the far field and is useful to the propagation of non-paraxial laser beam.     

Vectorial structures of non-paraxial linearly polarized Gaussian beam and their beam propagation factors

Based on the vectorial structure of non-paraxial electromagnetic beam and non-paraxial vectorial moment theory, the relationship of the beam waists, the divergence angles and the beam propagation factors among non-paraxial linearly polarized Gaussian beam, its TE and TM terms have been presented, respectively. The analytical beam propagation factors are given and further discussed at the highly non-paraxial case. The maximum divergence angles in the x-direction of non-paraxial linearly polarized Gaussian beam, its TE and TM terms are all 54.7°, and those in the y-direction are limited to be 63.4°, 67.7° and 39.2°, respectively. As TE and TM terms are orthogonal and can be detached at the far field, the potential applications of the isolated TE and TM terms are deserved further investigation.     

Propagation properties of a non-paraxial hollow Gaussian beam

Based on the non-paraxial vectorial moment theory of beam propagation, the analytical expressions of the M² factors for a non-paraxial hollow Gaussian beam (HGB) have been derived. The analytical formulae are further simplified for paraxial and highly non-paraxial cases. The beam waists, the divergence angles and the beam propagation factors are also depicted as functions of the parameter w₀. The divergence angles will not exceed the maximum value of 90°. When w₀ is within the scale of one time of light wavelength, the TE polarization results in the different beam propagation factors in the two transverse directions and the beam propagation factors first increase and then decrease. When w₀ is large enough, the beam propagation factors are determined only by the beam order.     

超短脉冲Bessel 光束和空间诱导色散效应

 给出了含时的波动方程的一族特解－超短脉冲Bessel光束，其脉冲光束的空间和时间部分可以做分离变量，空间部分在传输过程中保持Bessel光束不变，而时间脉冲部分的传输行为类似于在普通色散介质中的传输，此效应被称之为空间诱导色散效应。     

Propagation properties of high order axially symmetric polarized beams

The paraxial and non-paraxial propagation properties of high order axially symmetric polarized beams are theoretically studied. The mathematical expressions of the propagation fields for such beams are derived based on vectorial Rayleigh–Sommerfeld formulas. Simulation results are presented for different dimensionless perturbation parameters, which shows the beam propagation intensity distribution and evolution behavior are affected largely by the polarization property of such beams, especially in the non-paraxial regime.     

等束腰宽度超短脉冲光束传输的脉冲修正方法

利用角谱分析和傅里叶变换的方法,得到一种描述几个周期的等束腰宽度脉冲光束传输的脉冲修正方法。以准单色光束传输的结果为出发点,通过对准单色光束的解进行泰勒级数展开,得到了一种相对简单的修正方法,可以精确的描述具有任意时间波形和横向光束分布的不短于一个周期的超短脉冲光束的传输行为。给出等束腰宽度超短脉冲的近似解,具体研究高斯脉冲光束的传输特性,分析几种不同的频谱对脉冲光束传输行为的影响。     

Influence of cladding layer field of slab waveguide on M~2 factor

Based on the theory of semiconductor laser pattern and the non-paraxial vectorial moment theory of light beam propagation, the beam quality factor M2 of TEo propagating mode is analyzed and calculated. The result shows that when both core layer and cladding layer are considered, M2>1 is always obtained. Moreover, by analyzing the characteristic of real beams, this result is generalized to the multilayer isotropic linear slab waveguides.     

Investigation in the far field characteristics of TM polarized Gaussian beam from the vectorial structure

Based on the vectorial structure of electromagnetic beam and the method of stationary phase, the analytical TE and TM terms of TM polarized Gaussian beam, the rigorous solution of Maxwell's equations for a confocal resonator, have been presented in the far field. Then in terms of the vectorial structure, TM polarized Gaussian beam is compared with Gaussian TEM₀₀ mode. The TE term is located at the y-axis, and the TM term the x-axis. At the non-paraxial case, the whole beam spot is elliptical, and the long axis is located at the y-axis. Moreover, the whole beam spot of TM polarized Gaussian beam is smaller than that of Gaussian TEM₀₀ mode. At the paraxial case, the whole beam spot is circular, and TM polarized Gaussian beam reduces to be Gaussian TEM₀₀ mode.