任意线偏振高斯光束的非傍轴传输

Nonparaxial propagation of Gaussian beam in arbitrary linearly polarized state

运用非傍轴光束传输的矢量矩理论,对任意线偏振高斯光束的非傍轴传输进行了系统的研究,给出了定量计算偏振对束腰、横向远场发散角和光束传输因子贡献的解析通式.并对高度非傍轴和傍轴两种极端情形,简化了相应的计算式.在高斯光源线度趋向于零的极限情形下,两个横向的最大发散角均为90°,与偏振态无关.在高度非傍轴情形下,可以通过所给出的解析通式设计高斯光源的半宽度与激射光波长之比值以及线偏振态来达到所期望的光束传输特性.对于傍轴情形,不同偏振对束腰和横向远场发散角稍有影响,但这种影响一般可以忽略不计;而光束传输因子却始终保持不变,与偏振态无关.若介于这两种极端情形之间,则可以根据高斯光源的半宽度之值和所期望的计算精度,确定解析式中级数的项数进而确定任意线偏振高斯光束的非傍轴传输特性.

By applying the vectorial moment theory of nonparaxial beam propagation, the nonparaxial propagation of Gaussian beam with arbitrary linearly polarized state has been systemically investigated. Universal analytical expressions of the beam waist, far field divergence angle and beam propagation factor have been presented, which allow calculating the quantitative contribution of polarization. The formulae can be further simplified in the highly nonparaxial case and paraxial case. As the dimension of Gaussian light source tends to zero, the two transverse maximum divergences are 90~ and independent of the polarized state. For the highly nonparaxial case, the anticipated beam propagation ~harecterlstics can be obtained by designing the half width of Gaussian light source and the linearly polarized state. When extending to the paraxial case, the effect of polarization can usually be neglected as its contribution to the beam waist and divergence angle is very slight. The beam propagation factor, however, keeps invariant and is independent of the polarized state. When the value of the half width of Gaussian light source is in between the above cases, the item number of series required to calculate is decided by the half width of Gaussian light source and the expected calculation accuracy. Then, the nonparaxial propagation of Gaussian beam with arbitrary linearly polarized state can be determined.