轴对称偏振光束特性的研究
|
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。
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.
(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。
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.
引文
[1] F. Gori. Polarization basis for vortex beams. J. Opt. Soc. Am. A, 2001, 18(7): 1612-1617
[2] R. Zheng, C. Gu, A. Wang, et al. An all-fiber laser generating cylindrical vector beam. Opt. Express, 2010, 18(10): 10834-10838
[3] M. P. Thirugnanasambandam, Y. Senatsky, K. Ueda. Generation of radially and azimuthally polarized beams in Yb:YAG laser with intra-cavity lens and birefringent crystal. Opt. Express, 2011, 19(3): 1905-1914
[4]张艳丽.矢量偏振光束特性及应用研究: [硕士论文].合肥:中国科学技术大学图书馆, 2006
[5] A. V. Nesterov, V. G. Niziev. Laser beams with axially symmetric polarization. J. Phys. D, 2000, 33(15): 1817-1822
[6]张艳丽,李小燕,朱健强.矢量偏振光束的产生及其高数值孔径聚焦性质.中国激光, 2009, 36(1): 129-133
[7] Jia Xinting, Li Bo, Wang Youqing, et al. Propagation properties of a cylindrically polarized vector beam. Front. Optoelectron. China, 2009, 2(4): 414-418
[8] Q. W. Zhan, J. R. Leger. Focus shaping using cylindrical vector beams. Opt Express, 2002, 10(7): 324-331
[9] Q. W. Zhan, J. R. Leger. Microellipsometer with radial symmetry. Appl. Opt., 2002, 41(22): 4630-4637
[10] S. Quabis, R. Dorn, M. Eberler, et al. Focusing light into a tighter spot. Opt. Commun., 2000, 179(1-6):1-7
[11] R. Dorn, S. Quabis, G. Leuchs. Sharper focus for a radially polarized light beam. Phys. Rev. Lett., 2003, 91(23): 233901
[12] Y. I. Salamin, C. H. Keitel. Electron acceleration by a tightly focused laser beam. Phys. Rev. Lett., 2002, 88(9): 095005
[13] D. N. Gupta, N. Kant, D. E. Kim, et al. Electron acceleration to GeV energy by a radially polarized laser. Phys. Lett. A, 2007, 368(5): 402-407
[14] Q. W. Zhan. Trapping metallic Rayleigh particles with radial polarization. Opt. Express, 2004, 12(15): 3377-3382
[15] K. S. Youngworth, T. G. Brown. Inhomogeneous polarization in scanning optical microscopy. Proc. SPIE, 2000, 3919: 75-85
[16] W. Kim, N. Park, Y. Yoon, et al. Investigation of near-field imaging characteristics of radial polarization for application to optical data storage. Opt. Rev., 2007, 14(4): 236-242
[17] V. G. Niziev, A. V. Nesterov. Influence of beam polarization on laser cutting efficiency. J. Phys. D, 1999, 32(13): 1455-1461
[18] M. Meier, V. Romano, T. Feurer. Material processing with pulsed radially and azimuthally polarized laser radiation. Appl. Phys. A, 2007, 86(3): 329-334
[19] V. G. Niziev, A. V. Nesterov. Longitudinal fields in cylindrical and spherical modes. J. Opt. A: Pure Appl. Opt., 2008, 10(8): 085005
[20] A. Hartschuh, E. J. Sánchez, X. S. Xie, et al. High-resolution near-field Raman miscropy of single-walled carbon nantubes. Phys. Rev. Lett., 2003, 90(9): 095503
[21] H. Watanabe, Y. Ishida, N. Hayazawa, et al. Tip-enhanced near-field Raman analysis of tip-pressurized adenine molecule. Phys. Rev. B, 2004, 69(15): 155418
[22] N. Hayazawa, Y. Saito, S. Kawata. Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy. Appl. Phys. Lett., 2004, 85(25): 6239-6241
[23]郑启光.激光先进制造技术.武汉:华中科技大学出版社, 2001. 96-104
[24] Q. W. Zhan. Cylindrical vector beams: from mathematical concepts to applications. Advances in Optics and Photonics, 2009, 1(1): 1-57
[25] Y. Mushiake, K. Matsumura, N. Nakajima. Generation of radially polarized optical beam mode by laser oscillation. Proc. IEEE, 1972, 60(9): 1107-1109
[26] A. A. Tovar. Production and propagation of cylindrically polarized Laguerre-Gaussian laser beams. J. Opt. Soc. Am. A, 1998, 15(10): 2705-2711
[27] A. V. Nesterov, V. G. Niziev, V. P. Yakunin. Generation of high power radially polarized beam. J. Phys. D, 1999, 32(22): 2871-2875
[28] R. Oron, S. Blit, N. Davidson, et al. The formation of laser beams with pureazimuthal or radial polarization. Appl. Phys. Lett., 2000, 77(21): 3322-3324
[29] M. A. Ahmed, J. Schulz, A. Voss, et al. Radially polarized 3kW beam from a CO2 laser with an intracavity resonant grating mirror. Opt. Lett., 2007, 32(13): 1824-1826
[30] S. Quabis, R. Dorn, G. Leuchs. Generation of a radially polarized doughnut mode of high quality. Appl. Phys. B, 2005, 81(5): 597-600
[31] G. Machavariani, Y. Lumer, I. Moshe, et al. Efficient extracavity generation of radially and azimuthally polarized beams. Opt. Lett., 2007, 32(11): 1468-1470
[32] G. Machavariani, Y. Lumer, I. Moshe, et al. Spatially-variable retardation plate for efficient generation of radially and azimuthally polarization beams. Opt. Commun., 2008, 281(4): 732-738
[33] V. G. Niziev, R. S. Chang, A. V. Nesterov. Generation of inhomogeneously polarized laser beams by use of a Sagnac interferometer. Appl. Opt., 2006, 45(33): 8393-8399
[34] K. J. Moh, X. C. Yuan, J. Bu, et al. Generating radial or azimuthal polarization by axial sampling of circularly polarized vortex beams. Appl. Opt., 2007, 46(30): 7544-7551
[35]庄杰佳,赵润乔,叶桂木等.径向偏振分布激光场的理论分析和实验论证.物理学报, 1985, 34(6): 752-759
[36]种兰祥,李建郎.基于内腔布儒斯特双轴锥棱镜的掺镱光纤激光器的径向偏振莫振荡.光子学报, 2008, 37(3): 430-434
[37] J. Li, K. Ueda, M. Musha, et al. Radiaaly polarized and pulsed output from passively Q-switched Nd: YAG ceramic microchip laser. Opt. Lett., 2008, 33(22): 2686-2688.
[38] T. Moser, H. Glur, V. Romano, et al. Polarization-selective grating mirrors used in the generation of radial polarization. Appl. Phys. B, 2005, 80(6): 1-7
[39] T. Moser, J. Balmer, D. Delbeke, et al. Intracavity generation of radially polarized CO2 laser beams based on a simple binary dielectric diffraction grating. Appl. Opt., 2006, 45(33): 8517-8522
[40] I. Moshe, S. Jackel, A. Meir. Production of radially or azimuthally polarized beams in solid-state lasers and the elimination of thermally induced birefringence effects. Opt Lett., 2003, 28(10): 807-809
[41] G. Machavariani, Y. Lumer, I. Moshe, et al. Birefringence-induced bifocusing forselection of radially or azimuthally polarized laser modes. Appl. Opt., 2007, 46(16): 3304-3310
[42] K. Yonezawa, Y. Kozawa, S. Sato. Compact laser with radial polarization using birefringent laser medium. Jpn. J. Appl. Phys., 2007, 46(8): 5160-5163
[43] M. Endo. Azimuthally polarized 1 kW CO2 laser with a triple-axicon retroreflector optical resonator. Opt. Lett., 2008, 33(15): 1771-1773
[44] J. F. Bisson, J. Li, K. Ueda, et al. Radially polarized ring and arc beams of a neodymium laser with an intra-cavity axicon. Opt. Express, 2006, 14(8): 3304-3311
[45] Y. Kozawa, S. Sato. Generation of a radially polarized laser beam by use of a conical Brewster prism. Opt. Lett., 2005, 30(22): 3063-3065
[46] A. M. Ahmed, A. Voss, M. M. Vogel. Multilayer polarizing grating mirror used for the generation of radial polarization in Yb: YAG thin-disk lasers. Opt. Lett., 2007, 32(22): 3272-3274
[47] K. Duan, B. Lü. Nonparaxial diffraction of vectorial plane waves at a small aperture. Optics and Laser Technology, 2005, 37(3):193-197
[48] K. Duan, B. Lü. A comparison of the vectorial nonparaxial approach with Fresnel and Fraunhofer approximations. Optik, 2004, 115(5): 218-222
[49] K. Duan, B. Lü. Propagation properties of vectorial elliptical Gaussian beams beyond the paraxial approximation. Optics and Laser Technology, 2004, 36(6): 489-496
[50] B. Lü, K. Duan. Nonparaxial propagation of vectorial Gaussian beams diffracted at a circular aperture. Opt. Lett., 2003, 28(24): 2440-2442
[51] G. Zhou, X. Chu, L. Zhao. Propagation characteristics of TM Gaussian beam. Optics and Laser Technology, 2005, 37(6): 470-474
[52]周国泉.任意线偏振高斯光束的非傍轴传输.物理学报, 2005, 54(10): 4710-4717
[53] C. G. Chen, P. T. Konkola, J. Ferrera, et al. Analyses of vector Gaussian beam propagation and the validity of praxial and spherical approximatioins. J. Opt. Soc. Am. A, 2002, 19(2): 404-412
[54] A. Ciattoni, B. Crosignani, P. D. Porto. Vecotrial free-space optical propagation: a simple approach for generating all-order nonparaxial corrections. Opt. Commun., 2000, 177(1): 9-13
[55] M. Lax, W. H. Louisell, W. B. McKnight. From Maxwell to paraxial wave optics. Phys. Rev. A, 1975, 11(4): 1365-1370
[56]吕百达.激光光学—光束描述、传输变换与光腔技术物理. (第3版).北京:高等教育出版社, 2003. 7-9
[57]杨儒贵.电磁场与电磁波. (第2版).北京:高等教育出版社, 2007
[58] G. P. Agrawal, D. N. Pattanatak. Gaussian beam propagation beyond the paraxial approximation. J. Opt. Soc. Am A, 1979, 68(4): 575-578
[59] A. Wünsche. Transition from the paraxial approximation to exact solutions of the wave equation and application to Gaussian beams. J. Opt. Soc. Am A, 1992, 9(5): 765-774
[60] S. Seshadri, R. Virtual. Source for a Hermite-Gauss beam. Opt. Lett., 2003, 28(8): 595-597
[61] R. K. Luneburg. Mathematical Theory of Optics. Berkeley: University of California Press, 1966
[62] P. Varga, P. T?r?k. Exact and approximate solutions of Maxwell’s equations for a confocal cavity. Opt. Lett., 1996, 21(19): 1523-1525
[63] P. Varga, P. T?r?k. The Gaussian wave solution of Maxwell’s equations and the validity of scalar wave approximation. Opt. Commun., 1998, 152(1-3): 108-118
[64] L. Mandel, E. Wolf. Optical Coherence and Quantum Optics. Cambridge: Cambridge University Press, 1995
[65] Y. Zhang, L. Wang, C. Zheng. Vector propagation of radially polarized Gaussian beams diffracted by an axicon. J. Opt. Soc. Am. A, 2005, 22(11): 2542-2546
[66]刘普生,吕百达.非傍轴矢量高斯光束的圆屏衍射.物理学报, 2004, 53(11): 3724-3728
[67]邓小玖,李怀龙,刘彩霞等.矢量衍射理论的比较研究及标量近似的有效性.量子电子学报, 2007, 24(5): 543-547
[68] I. S. Gradshteyn, I. M. Ryzhik. Table of Integrals, Series, and Products. New York: Academic Press, 1994
[69] D. Deng. Nonparaxial propagation of radially polarized light beams. J. Opt. Soc. Am. B, 2006, 23(6): 1228-1234
[70] M. Born, E. Wolf著.光学原理.杨葭荪等译.北京:电子工业出版社, 2005
[71] K. Duan, B. Lü. Nonpraxial analysis of far-field properties of Gaussian beams diffracted at a circular aperture. Opt. Express, 2003, 11(13): 1474-1480
[72]郁道银,谈恒英.工程光学.北京:机械工业出版社, 2001
[73]梅掌荣,赵道木,顾菊观.矢量可控空心光束的非傍轴传输.光学学报, 2009, 29(6): 1675-1679
[74] Z. Mei, D. Zhao. Nonparaxial analysis of vectorial Laguerre-Bessel-Gaussian beams. Opt. Express, 2007, 15(19): 11942-11951
[75] K. Duan, B. Lü. Vectorial nonparaxial propagation equation of elliptical Gaussian beams in the presence of a rectangular aperture. J. Opt. Soc. Am. A, 2004, 21(9): 1613-1620
[76]曹清,邓锡铭,郭弘.横截面上光强的精确表述.光学学报, 1996, 16(7): 897-902
[77] J. W. Goodman. Introduction to Fourier optics. New York: McGraw-Hill, 1996
[78]吕乃光.傅里叶光学. (第2版).北京:机械工业出版社, 2006
[79] G. Zhou. Analytical vectorial structure of Laguerre-Gaussian beam in the far field. Opt. Lett., 2006, 31(17): 2616-2618
[80] G. Zhou, X. Chu, J. Zheng. Composition of Airy disc. Chin. Opt. Lett., 2008, 6(6): 395-397
[81] G. Wu, Q. Lou, J. Zhou. Analytical vectorial structure of hollow Gaussian beams in the far field. Opt. Express, 2008, 16(9): 6417-6424
[82] G. Zhou. The analytical vectorial structure of a nonparaxial Gaussian beam close to the source. Opt. Express, 2008, 16(6): 3504-3514
[83] P. C. Chaumet. Fully vectorial highly nonparaxial beam close to the waist. J. Opt. Soc. Am. A, 2006, 23(12): 3197-3202
[84] R. Martínez-Herrero, P. M. Mejías, A. Carnicer. Evanescent field of vectorial highly non-paraxial beams. Opt. Express, 2008, 16(5): 2845-2858
[85] W. H. Carter. Electromagnetic Field of a Gaussian Beam with an Elliptical Cross Section. J. Opt. Soc. Am., 1972, 62(10): 1195-1201
[86] H. Guo, J. Chen, S. Zhuang. Vector plane wave spectrum of an arbitrary polarized electromagnetic wave. Opt. Express, 2006, 14(6): 2095-2100
[87] R. Martínez-Herrero, P. M. Mejías, S. Bosch, A. Carnicer. Vectorial structure of nonparaxial electromagnetic beams. J. Opt. Soc. Am. A, 2001, 18(7): 1678-1680
[88] G. Zhou. Analytical vectorial structure of controllable dark-hollow beams in the far field. J. Opt. Soc. Am. A, 2009, 26(7): 1654-1660
[89] D. Deng, Q. Guo. Analytical vectorial structure of radially polarized light beams. Opt. Lett., 2007, 32(18): 2711-2713
[90] Y. Zhang, B. Wang, X. Li, J. Zhu. Analytical vectorial structure of an apertured hollow Gasussian beam in the far field. Optik, 2010, 121(7): 652-657
[91] G. Zhou, X. Chu, J. Zheng. Analytical structure of an apertured vector Gaussian beam in the far field. Opt. Commun., 2008, 281(8): 1929-1934
[92] A. E. Siegman. New developments in laser resonators. Proc. SPIE, 1990, 1224:2-14
[93]杨国光等.微光学与系统.杭州:浙江大学出版社, 2008
[94] M. A. Porras. Non-paraxial vectorial moment theory of light beam propagation. Opt. Commun., 1996, 127(1-3): 79-95
[95] X. Kang, B. Lü. The M 2 factor of nonparaxial Hermite-Gaussian beams and related problems. Optik, 2005, 116(5):232-236
[96]周国泉,赵道木,王绍民.平面波经微小圆孔衍射的传输特性.光子学报, 2002, 31(7): 874-876
[97]邓小玖,胡继刚,刘彩霞,王建国.光束质量因子的研究.合肥工业大学学报, 2002, 25(6): 1187-1190
[98]周国泉.非傍轴矢量高斯光束的传输.物理学报, 2005, 54(4): 1572-1577
[99]康小平,吕百达.非傍轴矢量拉盖尔-高斯光束的二阶矩表示.物理学报, 2006, 55(9): 4563-4568
[100]冯国英,周寿桓.激光光束质量综合评价的探讨.中国激光, 2009, 36(7): 1643-1653
[101] X. Kang, B. Lü. Vectorial nonparaxial flattened gaussian beams and their beam quality in terms of the power in the bucket. Opt. Commun., 2006, 262(1): 1-7
[102] X. Kang, Z. He, B. Lü. Far-field properties and beam quality of vectorial Hermite-Laguerre-Gaussian beams beyond the paraxial approximation. Optics and Laser Technology, 2007, 39(5): 1046-1053
[103]康小平,何仲,吕百达.矢量非傍轴厄米-拉盖尔-高斯光束的光束质量.物理学报, 2006, 55(9): 4569-4574
[2] R. Zheng, C. Gu, A. Wang, et al. An all-fiber laser generating cylindrical vector beam. Opt. Express, 2010, 18(10): 10834-10838
[3] M. P. Thirugnanasambandam, Y. Senatsky, K. Ueda. Generation of radially and azimuthally polarized beams in Yb:YAG laser with intra-cavity lens and birefringent crystal. Opt. Express, 2011, 19(3): 1905-1914
[4]张艳丽.矢量偏振光束特性及应用研究: [硕士论文].合肥:中国科学技术大学图书馆, 2006
[5] A. V. Nesterov, V. G. Niziev. Laser beams with axially symmetric polarization. J. Phys. D, 2000, 33(15): 1817-1822
[6]张艳丽,李小燕,朱健强.矢量偏振光束的产生及其高数值孔径聚焦性质.中国激光, 2009, 36(1): 129-133
[7] Jia Xinting, Li Bo, Wang Youqing, et al. Propagation properties of a cylindrically polarized vector beam. Front. Optoelectron. China, 2009, 2(4): 414-418
[8] Q. W. Zhan, J. R. Leger. Focus shaping using cylindrical vector beams. Opt Express, 2002, 10(7): 324-331
[9] Q. W. Zhan, J. R. Leger. Microellipsometer with radial symmetry. Appl. Opt., 2002, 41(22): 4630-4637
[10] S. Quabis, R. Dorn, M. Eberler, et al. Focusing light into a tighter spot. Opt. Commun., 2000, 179(1-6):1-7
[11] R. Dorn, S. Quabis, G. Leuchs. Sharper focus for a radially polarized light beam. Phys. Rev. Lett., 2003, 91(23): 233901
[12] Y. I. Salamin, C. H. Keitel. Electron acceleration by a tightly focused laser beam. Phys. Rev. Lett., 2002, 88(9): 095005
[13] D. N. Gupta, N. Kant, D. E. Kim, et al. Electron acceleration to GeV energy by a radially polarized laser. Phys. Lett. A, 2007, 368(5): 402-407
[14] Q. W. Zhan. Trapping metallic Rayleigh particles with radial polarization. Opt. Express, 2004, 12(15): 3377-3382
[15] K. S. Youngworth, T. G. Brown. Inhomogeneous polarization in scanning optical microscopy. Proc. SPIE, 2000, 3919: 75-85
[16] W. Kim, N. Park, Y. Yoon, et al. Investigation of near-field imaging characteristics of radial polarization for application to optical data storage. Opt. Rev., 2007, 14(4): 236-242
[17] V. G. Niziev, A. V. Nesterov. Influence of beam polarization on laser cutting efficiency. J. Phys. D, 1999, 32(13): 1455-1461
[18] M. Meier, V. Romano, T. Feurer. Material processing with pulsed radially and azimuthally polarized laser radiation. Appl. Phys. A, 2007, 86(3): 329-334
[19] V. G. Niziev, A. V. Nesterov. Longitudinal fields in cylindrical and spherical modes. J. Opt. A: Pure Appl. Opt., 2008, 10(8): 085005
[20] A. Hartschuh, E. J. Sánchez, X. S. Xie, et al. High-resolution near-field Raman miscropy of single-walled carbon nantubes. Phys. Rev. Lett., 2003, 90(9): 095503
[21] H. Watanabe, Y. Ishida, N. Hayazawa, et al. Tip-enhanced near-field Raman analysis of tip-pressurized adenine molecule. Phys. Rev. B, 2004, 69(15): 155418
[22] N. Hayazawa, Y. Saito, S. Kawata. Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy. Appl. Phys. Lett., 2004, 85(25): 6239-6241
[23]郑启光.激光先进制造技术.武汉:华中科技大学出版社, 2001. 96-104
[24] Q. W. Zhan. Cylindrical vector beams: from mathematical concepts to applications. Advances in Optics and Photonics, 2009, 1(1): 1-57
[25] Y. Mushiake, K. Matsumura, N. Nakajima. Generation of radially polarized optical beam mode by laser oscillation. Proc. IEEE, 1972, 60(9): 1107-1109
[26] A. A. Tovar. Production and propagation of cylindrically polarized Laguerre-Gaussian laser beams. J. Opt. Soc. Am. A, 1998, 15(10): 2705-2711
[27] A. V. Nesterov, V. G. Niziev, V. P. Yakunin. Generation of high power radially polarized beam. J. Phys. D, 1999, 32(22): 2871-2875
[28] R. Oron, S. Blit, N. Davidson, et al. The formation of laser beams with pureazimuthal or radial polarization. Appl. Phys. Lett., 2000, 77(21): 3322-3324
[29] M. A. Ahmed, J. Schulz, A. Voss, et al. Radially polarized 3kW beam from a CO2 laser with an intracavity resonant grating mirror. Opt. Lett., 2007, 32(13): 1824-1826
[30] S. Quabis, R. Dorn, G. Leuchs. Generation of a radially polarized doughnut mode of high quality. Appl. Phys. B, 2005, 81(5): 597-600
[31] G. Machavariani, Y. Lumer, I. Moshe, et al. Efficient extracavity generation of radially and azimuthally polarized beams. Opt. Lett., 2007, 32(11): 1468-1470
[32] G. Machavariani, Y. Lumer, I. Moshe, et al. Spatially-variable retardation plate for efficient generation of radially and azimuthally polarization beams. Opt. Commun., 2008, 281(4): 732-738
[33] V. G. Niziev, R. S. Chang, A. V. Nesterov. Generation of inhomogeneously polarized laser beams by use of a Sagnac interferometer. Appl. Opt., 2006, 45(33): 8393-8399
[34] K. J. Moh, X. C. Yuan, J. Bu, et al. Generating radial or azimuthal polarization by axial sampling of circularly polarized vortex beams. Appl. Opt., 2007, 46(30): 7544-7551
[35]庄杰佳,赵润乔,叶桂木等.径向偏振分布激光场的理论分析和实验论证.物理学报, 1985, 34(6): 752-759
[36]种兰祥,李建郎.基于内腔布儒斯特双轴锥棱镜的掺镱光纤激光器的径向偏振莫振荡.光子学报, 2008, 37(3): 430-434
[37] J. Li, K. Ueda, M. Musha, et al. Radiaaly polarized and pulsed output from passively Q-switched Nd: YAG ceramic microchip laser. Opt. Lett., 2008, 33(22): 2686-2688.
[38] T. Moser, H. Glur, V. Romano, et al. Polarization-selective grating mirrors used in the generation of radial polarization. Appl. Phys. B, 2005, 80(6): 1-7
[39] T. Moser, J. Balmer, D. Delbeke, et al. Intracavity generation of radially polarized CO2 laser beams based on a simple binary dielectric diffraction grating. Appl. Opt., 2006, 45(33): 8517-8522
[40] I. Moshe, S. Jackel, A. Meir. Production of radially or azimuthally polarized beams in solid-state lasers and the elimination of thermally induced birefringence effects. Opt Lett., 2003, 28(10): 807-809
[41] G. Machavariani, Y. Lumer, I. Moshe, et al. Birefringence-induced bifocusing forselection of radially or azimuthally polarized laser modes. Appl. Opt., 2007, 46(16): 3304-3310
[42] K. Yonezawa, Y. Kozawa, S. Sato. Compact laser with radial polarization using birefringent laser medium. Jpn. J. Appl. Phys., 2007, 46(8): 5160-5163
[43] M. Endo. Azimuthally polarized 1 kW CO2 laser with a triple-axicon retroreflector optical resonator. Opt. Lett., 2008, 33(15): 1771-1773
[44] J. F. Bisson, J. Li, K. Ueda, et al. Radially polarized ring and arc beams of a neodymium laser with an intra-cavity axicon. Opt. Express, 2006, 14(8): 3304-3311
[45] Y. Kozawa, S. Sato. Generation of a radially polarized laser beam by use of a conical Brewster prism. Opt. Lett., 2005, 30(22): 3063-3065
[46] A. M. Ahmed, A. Voss, M. M. Vogel. Multilayer polarizing grating mirror used for the generation of radial polarization in Yb: YAG thin-disk lasers. Opt. Lett., 2007, 32(22): 3272-3274
[47] K. Duan, B. Lü. Nonparaxial diffraction of vectorial plane waves at a small aperture. Optics and Laser Technology, 2005, 37(3):193-197
[48] K. Duan, B. Lü. A comparison of the vectorial nonparaxial approach with Fresnel and Fraunhofer approximations. Optik, 2004, 115(5): 218-222
[49] K. Duan, B. Lü. Propagation properties of vectorial elliptical Gaussian beams beyond the paraxial approximation. Optics and Laser Technology, 2004, 36(6): 489-496
[50] B. Lü, K. Duan. Nonparaxial propagation of vectorial Gaussian beams diffracted at a circular aperture. Opt. Lett., 2003, 28(24): 2440-2442
[51] G. Zhou, X. Chu, L. Zhao. Propagation characteristics of TM Gaussian beam. Optics and Laser Technology, 2005, 37(6): 470-474
[52]周国泉.任意线偏振高斯光束的非傍轴传输.物理学报, 2005, 54(10): 4710-4717
[53] C. G. Chen, P. T. Konkola, J. Ferrera, et al. Analyses of vector Gaussian beam propagation and the validity of praxial and spherical approximatioins. J. Opt. Soc. Am. A, 2002, 19(2): 404-412
[54] A. Ciattoni, B. Crosignani, P. D. Porto. Vecotrial free-space optical propagation: a simple approach for generating all-order nonparaxial corrections. Opt. Commun., 2000, 177(1): 9-13
[55] M. Lax, W. H. Louisell, W. B. McKnight. From Maxwell to paraxial wave optics. Phys. Rev. A, 1975, 11(4): 1365-1370
[56]吕百达.激光光学—光束描述、传输变换与光腔技术物理. (第3版).北京:高等教育出版社, 2003. 7-9
[57]杨儒贵.电磁场与电磁波. (第2版).北京:高等教育出版社, 2007
[58] G. P. Agrawal, D. N. Pattanatak. Gaussian beam propagation beyond the paraxial approximation. J. Opt. Soc. Am A, 1979, 68(4): 575-578
[59] A. Wünsche. Transition from the paraxial approximation to exact solutions of the wave equation and application to Gaussian beams. J. Opt. Soc. Am A, 1992, 9(5): 765-774
[60] S. Seshadri, R. Virtual. Source for a Hermite-Gauss beam. Opt. Lett., 2003, 28(8): 595-597
[61] R. K. Luneburg. Mathematical Theory of Optics. Berkeley: University of California Press, 1966
[62] P. Varga, P. T?r?k. Exact and approximate solutions of Maxwell’s equations for a confocal cavity. Opt. Lett., 1996, 21(19): 1523-1525
[63] P. Varga, P. T?r?k. The Gaussian wave solution of Maxwell’s equations and the validity of scalar wave approximation. Opt. Commun., 1998, 152(1-3): 108-118
[64] L. Mandel, E. Wolf. Optical Coherence and Quantum Optics. Cambridge: Cambridge University Press, 1995
[65] Y. Zhang, L. Wang, C. Zheng. Vector propagation of radially polarized Gaussian beams diffracted by an axicon. J. Opt. Soc. Am. A, 2005, 22(11): 2542-2546
[66]刘普生,吕百达.非傍轴矢量高斯光束的圆屏衍射.物理学报, 2004, 53(11): 3724-3728
[67]邓小玖,李怀龙,刘彩霞等.矢量衍射理论的比较研究及标量近似的有效性.量子电子学报, 2007, 24(5): 543-547
[68] I. S. Gradshteyn, I. M. Ryzhik. Table of Integrals, Series, and Products. New York: Academic Press, 1994
[69] D. Deng. Nonparaxial propagation of radially polarized light beams. J. Opt. Soc. Am. B, 2006, 23(6): 1228-1234
[70] M. Born, E. Wolf著.光学原理.杨葭荪等译.北京:电子工业出版社, 2005
[71] K. Duan, B. Lü. Nonpraxial analysis of far-field properties of Gaussian beams diffracted at a circular aperture. Opt. Express, 2003, 11(13): 1474-1480
[72]郁道银,谈恒英.工程光学.北京:机械工业出版社, 2001
[73]梅掌荣,赵道木,顾菊观.矢量可控空心光束的非傍轴传输.光学学报, 2009, 29(6): 1675-1679
[74] Z. Mei, D. Zhao. Nonparaxial analysis of vectorial Laguerre-Bessel-Gaussian beams. Opt. Express, 2007, 15(19): 11942-11951
[75] K. Duan, B. Lü. Vectorial nonparaxial propagation equation of elliptical Gaussian beams in the presence of a rectangular aperture. J. Opt. Soc. Am. A, 2004, 21(9): 1613-1620
[76]曹清,邓锡铭,郭弘.横截面上光强的精确表述.光学学报, 1996, 16(7): 897-902
[77] J. W. Goodman. Introduction to Fourier optics. New York: McGraw-Hill, 1996
[78]吕乃光.傅里叶光学. (第2版).北京:机械工业出版社, 2006
[79] G. Zhou. Analytical vectorial structure of Laguerre-Gaussian beam in the far field. Opt. Lett., 2006, 31(17): 2616-2618
[80] G. Zhou, X. Chu, J. Zheng. Composition of Airy disc. Chin. Opt. Lett., 2008, 6(6): 395-397
[81] G. Wu, Q. Lou, J. Zhou. Analytical vectorial structure of hollow Gaussian beams in the far field. Opt. Express, 2008, 16(9): 6417-6424
[82] G. Zhou. The analytical vectorial structure of a nonparaxial Gaussian beam close to the source. Opt. Express, 2008, 16(6): 3504-3514
[83] P. C. Chaumet. Fully vectorial highly nonparaxial beam close to the waist. J. Opt. Soc. Am. A, 2006, 23(12): 3197-3202
[84] R. Martínez-Herrero, P. M. Mejías, A. Carnicer. Evanescent field of vectorial highly non-paraxial beams. Opt. Express, 2008, 16(5): 2845-2858
[85] W. H. Carter. Electromagnetic Field of a Gaussian Beam with an Elliptical Cross Section. J. Opt. Soc. Am., 1972, 62(10): 1195-1201
[86] H. Guo, J. Chen, S. Zhuang. Vector plane wave spectrum of an arbitrary polarized electromagnetic wave. Opt. Express, 2006, 14(6): 2095-2100
[87] R. Martínez-Herrero, P. M. Mejías, S. Bosch, A. Carnicer. Vectorial structure of nonparaxial electromagnetic beams. J. Opt. Soc. Am. A, 2001, 18(7): 1678-1680
[88] G. Zhou. Analytical vectorial structure of controllable dark-hollow beams in the far field. J. Opt. Soc. Am. A, 2009, 26(7): 1654-1660
[89] D. Deng, Q. Guo. Analytical vectorial structure of radially polarized light beams. Opt. Lett., 2007, 32(18): 2711-2713
[90] Y. Zhang, B. Wang, X. Li, J. Zhu. Analytical vectorial structure of an apertured hollow Gasussian beam in the far field. Optik, 2010, 121(7): 652-657
[91] G. Zhou, X. Chu, J. Zheng. Analytical structure of an apertured vector Gaussian beam in the far field. Opt. Commun., 2008, 281(8): 1929-1934
[92] A. E. Siegman. New developments in laser resonators. Proc. SPIE, 1990, 1224:2-14
[93]杨国光等.微光学与系统.杭州:浙江大学出版社, 2008
[94] M. A. Porras. Non-paraxial vectorial moment theory of light beam propagation. Opt. Commun., 1996, 127(1-3): 79-95
[95] X. Kang, B. Lü. The M 2 factor of nonparaxial Hermite-Gaussian beams and related problems. Optik, 2005, 116(5):232-236
[96]周国泉,赵道木,王绍民.平面波经微小圆孔衍射的传输特性.光子学报, 2002, 31(7): 874-876
[97]邓小玖,胡继刚,刘彩霞,王建国.光束质量因子的研究.合肥工业大学学报, 2002, 25(6): 1187-1190
[98]周国泉.非傍轴矢量高斯光束的传输.物理学报, 2005, 54(4): 1572-1577
[99]康小平,吕百达.非傍轴矢量拉盖尔-高斯光束的二阶矩表示.物理学报, 2006, 55(9): 4563-4568
[100]冯国英,周寿桓.激光光束质量综合评价的探讨.中国激光, 2009, 36(7): 1643-1653
[101] X. Kang, B. Lü. Vectorial nonparaxial flattened gaussian beams and their beam quality in terms of the power in the bucket. Opt. Commun., 2006, 262(1): 1-7
[102] X. Kang, Z. He, B. Lü. Far-field properties and beam quality of vectorial Hermite-Laguerre-Gaussian beams beyond the paraxial approximation. Optics and Laser Technology, 2007, 39(5): 1046-1053
[103]康小平,何仲,吕百达.矢量非傍轴厄米-拉盖尔-高斯光束的光束质量.物理学报, 2006, 55(9): 4569-4574
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |