截断非傍轴矢量高斯光束的传输特性
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摘要
文章基于非傍轴矢量光束横截面上光强的严格定义〈S_z〉,采用桶中功率定义光束的束宽、远场发散角以及M~2因子。以截断非傍轴矢量高斯光束为例,对光束的传输特性进行了详细的理论分析和数值计算,并与非傍轴标量理论的结果进行了比较分析。数值计算表明,束腰半径W (0)<λ时,传输特性的矢量描述与非傍轴标量描述有显著差别。当截断参量R/ω_0<0.5时,截断高斯光束的传输特性与截断平面波的传播趋于一致;当截断参量R/ω_0>2时,过渡到自由高斯光束的传播。
Based on the rigorous definition of light intensity of nonparaxial vectorial beams in the transverse plane(〈S_z〉),beam width,far-field divergence angles and M~2 factors are defined by the power in the bucket.Taking truncated nonparaxial vectorial Gaussian beam as an example,the detailed theoretical analyses and numerical calculations about the propagation characteristics are performed,and the results are compared with those from the nonparaxial scalar theory.Numerical calculations show that when the beam waist W(0)<λ,there are obvious differences between the propagation characteristics described by nonparaxial scalar and vectorial theory.When the truncation parameter R/ω_0<0.5,the propagation characteristics of truncated nonparaxial vectorial Gaussian beams trend to those of truncated plane waves.Meanwhile,when R/ω_0>2,truncated nonparaxial vectorial Gaussian beams follow the same propagation laws of free Gaussian beams.
Based on the rigorous definition of light intensity of nonparaxial vectorial beams in the transverse plane(〈S_z〉),beam width,far-field divergence angles and M~2 factors are defined by the power in the bucket.Taking truncated nonparaxial vectorial Gaussian beam as an example,the detailed theoretical analyses and numerical calculations about the propagation characteristics are performed,and the results are compared with those from the nonparaxial scalar theory.Numerical calculations show that when the beam waist W(0)<λ,there are obvious differences between the propagation characteristics described by nonparaxial scalar and vectorial theory.When the truncation parameter R/ω_0<0.5,the propagation characteristics of truncated nonparaxial vectorial Gaussian beams trend to those of truncated plane waves.Meanwhile,when R/ω_0>2,truncated nonparaxial vectorial Gaussian beams follow the same propagation laws of free Gaussian beams.
引文
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[9]朱莉华,聂义友,吕百达.截断平顶高斯光束M2因子的比较研究[J].光子学报,2007,36(3):536-538.
[10]邓小玖,汪国安,刘彩霞,等.非傍轴矢量光束二阶矩的发散特性[J].物理学报,2009,58(12):8260-8263.
[11]邓小玖,牛国鉴,刘彩霞,等.非傍轴高斯光束传输特性的研究[J].物理学报,2011,60(9):094202-1-094202-4.
[12]牛国鉴,邓小玖,刘彩霞,等.微小孔非傍轴衍射光束传输特性的研究[J].光子学报,2010,39(10):1840-1843.
[13]王珊姗,邓小玖,刘彩霞,等.截断非傍轴标量高斯光束的传输特性[J].光子学报,2014,43(4):0426003-1-0426003-4.
[14]CHEN C G,KONKOLA P T,FERRERA J,et al.Analyses of vector gaussian beam propagation and the validity of paraxial and spherical approximations[J].J Opt Soc Am A,2002,19(2):404-412.
[15]CIATTONI A,CROSIGNANI B,PORTO P D.Vectorial free-space optical propagation:a simple approach for generating all-order nonparaxial corrections[J].Optics Communications,2000,177(1):9-13.
[16]曹清,邓锡铭,郭弘.横截面上光强的精确表述[J].光学学报,1996,16(7):897-902.
[17]邓小玖,胡继刚,刘彩霞,等.光束质量因子的研究[J].合肥工业大学学报(自然科学版),2002,25(6):1187-1190.
[2]PORRAS M A.Finiteness and propagation law of the power density second-order moment for diffracted scalar light beams[J].Optik,1999,110(9):417-420.
[3]GAO C,WEBER H.The problems with M2[J].Optics and Laser Technology,2000,32(4):221-224.
[4]周国泉,赵道木,王绍民.平面波经微小圆孔衍射的传输特性[J].光子学报,2002,31(7):874-876.
[5]DONGMEI D.Generalized M2 factor of hollow Gaussian beams through a hard-edge circular aperture[J].Physics Letters A,2005,341(14):352-356.
[6]KANG X P,LUB D.The M2 factor of nonparaxial Hermite Gaussian beams and related problems[J].Optik,2005,116(5):232-236.
[7]POYEMKIN A K,KHAZANOV E A.Calculation of the laser-beam M2 factor by the method of Moments[J].Quantum Electronics 2005,35(11):1042-1044.
[8]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[J].物理学报,2006,55(9):4569-4574.
[9]朱莉华,聂义友,吕百达.截断平顶高斯光束M2因子的比较研究[J].光子学报,2007,36(3):536-538.
[10]邓小玖,汪国安,刘彩霞,等.非傍轴矢量光束二阶矩的发散特性[J].物理学报,2009,58(12):8260-8263.
[11]邓小玖,牛国鉴,刘彩霞,等.非傍轴高斯光束传输特性的研究[J].物理学报,2011,60(9):094202-1-094202-4.
[12]牛国鉴,邓小玖,刘彩霞,等.微小孔非傍轴衍射光束传输特性的研究[J].光子学报,2010,39(10):1840-1843.
[13]王珊姗,邓小玖,刘彩霞,等.截断非傍轴标量高斯光束的传输特性[J].光子学报,2014,43(4):0426003-1-0426003-4.
[14]CHEN C G,KONKOLA P T,FERRERA J,et al.Analyses of vector gaussian beam propagation and the validity of paraxial and spherical approximations[J].J Opt Soc Am A,2002,19(2):404-412.
[15]CIATTONI A,CROSIGNANI B,PORTO P D.Vectorial free-space optical propagation:a simple approach for generating all-order nonparaxial corrections[J].Optics Communications,2000,177(1):9-13.
[16]曹清,邓锡铭,郭弘.横截面上光强的精确表述[J].光学学报,1996,16(7):897-902.
[17]邓小玖,胡继刚,刘彩霞,等.光束质量因子的研究[J].合肥工业大学学报(自然科学版),2002,25(6):1187-1190.