【作者】 贾信庭；

【导师】 王又青；

【作者基本信息】 华中科技大学 ， 光学工程， 2011， 博士

【摘要】 作为一种空间非均匀偏振分布的光束,轴对称偏振光束由于在现代光学应用中发挥出独特的优势而受到越来越广泛地关注。本论文系统地研究和分析了轴对称偏振光束的矢量特性、偏振特性、传输特性、非傍轴行为、矢量结构以及光束质量评价等。论文的主要研究内容包括:(1)研究了非傍轴和傍轴近似下的轴对称偏振光束在自由空间中的传输特性。基于矢量瑞利-索末菲衍射积分公式,推导出自由空间中的轴对称偏振拉盖尔-高斯光束的电场解析式,径向偏振光束、角向偏振光束和傍轴近似下的传输光场可以看作该解析式的特例统一处理。分析表明,束腰宽度与波长的比值和光束阶数这两个参数均对径向偏振光束和角向偏振光束的非傍轴行为产生了重要的影响。当束腰宽度与波长的比值变小、光束阶数增大时,径向偏振光束和角向偏振光束的非傍轴性变得更加明显。随着束腰宽度与波长比值的增加、光束阶数的减小和传输距离的增大,自由空间中的径向偏振光束电场的纵向分量相对横向分量可以逐渐被忽略。(2)探索了非傍轴和傍轴范畴下的径向偏振光束和角向偏振光束经圆孔光阑衍射的传输特性。基于矢量瑞利-索末菲衍射积分公式,推导出径向偏振和角向偏振拉盖尔-高斯光束经圆孔光阑衍射的电磁场解析式,自由空间和傍轴近似下的传输光场可以作为该解析式的特例统一处理。分析表明,径向偏振光束的磁场矢量呈现角向偏振分布,而角向偏振光束的磁场矢量呈现径向偏振分布。经圆孔光阑衍射的径向偏振光束和角向偏振光束的非傍轴性不仅取决于束腰宽度与波长的比值和光束阶数这两个参数,而且还与截断参数有关。同时光束的衍射效应也需要被考虑,它随着光阑孔径的减小而变得更加明显。随着束腰宽度与波长比值的增加、光束阶数的减小和截断参数的增大,经圆孔光阑衍射的径向偏振光束电场的纵向分量相对横向分量可以逐渐被忽略。(3)描述了矢量径向偏振光束和矢量角向偏振光束在源区附近的传输特性,使用角谱表示法将径向偏振光束和角向偏振光束的传输波和倏逝波分离出来,在没有做任何近似处理下,推导出源区的径向偏振和角向偏振拉盖尔-高斯光束的传输波和倏逝波的电场解析式。结果表明,束腰宽度、光束阶数和传输距离共同决定了倏逝波的行为。当束腰宽度与波长的比值较小、光束阶数较大时,倏逝波对源区附近的径向偏振光束和角向偏振光束的贡献很大。光束阶数的不同取值对电场的横向分量和纵向分量的倏逝波轮廓都没有影响。随着束腰宽度与波长比值的增加、光束阶数的减小和传输距离的增大,倏逝波的贡献可以逐渐被忽略。倏逝波对径向偏振光束的影响比它对角向偏振光束的影响更大。(4)探索了自由空间中轴对称偏振光束在远场的矢量结构和光束质量。基于矢量角谱表示法,将轴对称偏振拉盖尔-高斯光束的电磁场划分为横向电场和横向磁场两个部分,即TE项和TM项,并且使用稳相法推导出轴对称偏振光束的TE项和TM项在远场的电磁场解析式。采用推广后的桶中功率(PIB)参数评价轴对称偏振光束的远场光束质量。研究表明,轴对称偏振光束的TE项、TM项、总的能流分布以及远场光束质量受到束腰宽度与波长的比值、光束阶数和电场矢量与径向之间的夹角这三个参数的影响。随着束腰宽度与波长比值的增大、光束阶数的减小以及电场矢量指向角向,轴对称偏振光束具有更加紧密的能流分布、更大的PIB值、更高的能量集中度和更好的远场光束质量。自由空间中非傍轴的角向偏振光束比径向偏振光束在远场具有更高的能量集中度和更好的光束质量。(5)研究了轴对称偏振光束经圆孔光阑衍射的远场矢量结构和远场光束质量。根据矢量角谱表示法,将受硬边光阑衍射的轴对称偏振拉盖尔-高斯光束的电磁场分解为TE项和TM项两个部分,并且使用稳相法推导出轴对称偏振光束经圆孔光阑衍射的TE项和TM项在远场的电磁场解析式。采用推广后的PIB参数衡量经圆孔光阑衍射的轴对称偏振光束的远场光束质量。分析表明,圆孔光阑的存在并没有改变轴对称偏振光束的矢量结构和偏振特性。束腰宽度与波长的比值、光束阶数、截断参数和电场矢量与径向之间的夹角这四个参数共同决定了轴对称偏振光束通过圆孔光阑衍射后的远场矢量结构和远场光束质量。随着束腰宽度与波长比值的增大、光束阶数的减小、截断参数的增大以及电场矢量指向角向,经圆孔光阑衍射的轴对称偏振光束具有更加紧密的能流分布、更大的PIB值、更高的能量集中度和更好的远场光束质量。在非傍轴范畴下,受硬边光阑衍射的角向偏振光束比径向偏振光束在远场具有更高的能量集中度和更好的光束质量。更多还原

【Abstract】 As a nonuniform polarization, the cylindrically polarized vector beams have drawn growing attention due to their unique adavantages in the application of modern optics. The vectoriality, polarization properties, propagation properties, nonparaxial behavior and beam quality of the cylindiraclly polarized vector beams are extensively studied in the thesis. The main contents of this thesis are included as follow:(1) The nonparaxial and paraxial propagation properties of the cylindrically polarized beams in free space are investigated. On the basis of the vectorial Rayleigh-Sommerfeld formulas, the analytical expressions for the electric field of the cylindrically polarized Laguerre-Gaussian beams (LGBs) propagating in free space are derived. The radially polarized, azimuthally polarized and paraxial cases can be viewed as the special cases of the general result. The analyses show that both the ratio of waist width to wavelength and the beam order play an important role in the nonparaxial behavior. As the ratio of waist width to wavelength decreases and the beam order increases, the nonparaxiality of the radially and azimuthally polarized beams becomes more obvious. The longitudinal component of the electric field of the radially polarized beams compared with the transverse component can be increasingly neglected with the increasing ratio of waist width to wavelength, the decreasing beam order and the increasing propagation distance.(2) The nonparaxial and paraxial propagation properties of the radially and azimuthally polarized beams diffracted at a circular aperture are studied. The analytical expressions for the electromagnetic fields of the apertured radially and azimuthally polarized LGBs are obtained based on the vectorial Rayleigh-Sommerfeld formulas. The general result can reduce to the unapertured and paraxial cases. The analyses indicate that the magnetic field of the radially polarized beams takes on azimuthal polarization, and the magnetic field of the azimuthally polarized beams takes on radial polarization. The nonparaxiality of the apertured radially and azimuthally polarized beams depends on the ratio of waist width to wavelength, the beam order and the truncation parameter. In addition, the beam diffraction effect should be considered, and it increases as the aperture radius decreases. The longitudinal component of the electric field of the apertured radially polarized beams compared with the transverse component can be increasingly neglected with the increasing ratio of waist width to wavelength, the decreasing beam order and the increasing truncation parameter.(3) The propagation properties of the radially and azimuthally polarized vector beams close to the source are described. The contribution of the propagating and evanescent waves to the radially and azimuthally polarized beams is separated by the vector angular spectrum method, and the analytical expressions for the propagating and evanescent waves of the radially and azimuthally polarized LGBs in the source region are derived without any approximation. The results show that the waist width, the beam order, and the propagation distance affect the behavior of the evanescent waves. The contribution of the evanescent waves to the radially and azimuthally polarized beams close to the source becomes more obvious with the smaller ratio of waist width to wavelength and the larger beam order. The beam order has no influence on the profiles of the evanescent waves of the transverse and longitudinal components of the electric field. The effect of the evanescent waves can be increasingly neglected with the increasing ratio of waist width to wavelength, the decreasing beam order and the increasing propagation distance. Moreover, the contribution of the evanescent waves to the radial polarization is much stronger than it to the azimuthal polarization.(4) The vectorial structure and beam quality of the cylindrically polarized beams in the far feild are investigated. In terms of the vector angular spectrum method, the electromagnetic fields of the cylindrically polarized LGBs can be expressed as a sum of the transverse electric (TE) term and the transverse magnetic (TM) term. The analytical electromagnetic expressions for the TE and TM terms of the cylindrically polarized beams in the far field are given by the method of stationary phase. The beam quality of the cylindrically polarized beams in the far feild is measured by the power in the bucket (PIB) beyond the paraxial approximation. The results indicate that the energy flux distributions of the TE term, the TM term, the whole beam, and the far-field beam quality depend on the the ratio of waist width to wavelength, the beam order and the angle between the electric field vector and the radial direction. As the ratio of waist width to wavelength increases, the beam order decreases and the electric field vector points to the azimuthal direction, the cylindrically polarized beams has the more compact energy flux distribution, the larger value of PIB, the better energy focusability and the better far-field beam quality. The azimuthal polarization compared with the radial polarization has the better energy focusability and the better beam quality in the far field beyond the paraxial approximation.(5) The far-field vectorial structure and beam quality of the cylindrically polarized beams diffracted at a circular aperture are studied. The electromagnetic fields of the apertured cylindrically polarized LGBs can be decomposed into the TE and TM terms by the vector angular spectrum method. The analytical electromagnetic expressions for the TE and TM terms of the apertured cylindrically polarized beams in the far field are obtained based on the method of stationary phase. The far-field beam quality of the apertured cylindrically polarized beams is measured by the PIB in the nonparaxial regime. The analyses show that the circular aperture does not change the vectorial structure and polarization properties of the cylindrically polarized beams. The ratio of waist width to wavelength, the beam order, the truncation parameter and the angle between the electric field vector and the radial direction have a great impact on the far-field vectorial stucture and beam quality. As the ratio of waist width to wavelength increases, the beam order decreases, the truncation parameters increases and the electric field vector points to the azimuthal direction, the apertured cylindrically polarized beams has the more compact energy flux distribution, the larger value of PIB, the better energy focusability and the better far-field beam quality. In the nonparaxial regime, the apertured azimuthally polarized beams compared with the apertured radially polarized beams have the better energy focusability and the better beam quality in the far feild.更多还原