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双零阶贝塞尔波束的传播及对单轴各向异性球的散射特性

李顺 李正军 屈檀 李海英 吴振森

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双零阶贝塞尔波束的传播及对单轴各向异性球的散射特性

李顺, 李正军, 屈檀, 李海英, 吴振森

Propagation of double zero-order Bessel beam and its scattering properties to uniaxial anisotropic spheres

Li Shun, Li Zheng-Jun, Qu Tan, Li Hai-Ying, Wu Zhen-Sen
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  • 基于广义洛伦兹Mie理论, 研究了单轴各向异性球形粒子对两束具有任意传播和极化方向的零阶贝塞尔波束的传播和散射特性, 并与单零阶贝赛尔波束入射单轴各向异性球形粒子时的传播和散射特性进行了对比研究. 利用球矢量波函数的正交关系及坐标旋转定理, 导出了任意传播和极化方向零阶贝塞尔波束的球矢量波函数的展开形式, 通过矢量叠加得到了总入射场的展开系数. 基于傅里叶变换方法和切向连续的边界条件, 得到了单轴各向异性球内部电磁场的球矢量波函数展开式, 并导出了散射系数解析表达式. 将零阶贝塞尔波束退化成平面波, 通过将其入射到单轴各向异性球形粒子的雷达散射截面角分布与文献结果进行对比, 验证了本文理论及程序的正确性. 数值分析了入射角、锥角及极化角等参数对雷达散射截面角分布的影响. 本文理论和数值结果希望能应用于多波束入射下各向异性粒子、生物细胞等复杂粒子体系的散射、粒径分析以及光学俘获等特性的研究中.
    Based on the generalized Lorenz Mie theory, the propagation and scattering properties of a uniaxial anisotropic spherical particle illuminated separately by double zero-order Bessel beam with arbitrary propagation direction and polarization direction are studied. The propagation and scattering characteristics are compared with those of a uniaxial anisotropic spherical particle illuminated by a single zero-order Bessel beam. Using the orthogonal relation of the spherical vector wave function and coordinate rotation theorem, the expanded forms of double zero-order Bessel beams with arbitrary propagation direction and polarization direction are derived. The analytical expressions of the expansion coefficients are derived by the integral method. The expansion coefficients of total incident field are obtained through the vector superposition principle. Based on the Fourier transform and tangentially continuous boundary conditions, the internal electromagnetic field of the uniaxial anisotropic sphere is expanded in terms of the spherical vector wave function and the scattering coefficients are derived. By comparing the angular distribution of the radar cross section of the particle illuminated by single and double zero-order Bessel beam when degenerating into plane waves with those results given by the literature, the correctness of the theory and the program in this paper are both verified. The effects of the incidence angle, conic angle and polarization angle on angle distribution of the radar cross section are numerically analyzed. The theoretical and numerical results in this paper are expected to be used to study the scattering properties, particle size analysis and optical trapping for anisotropic particles, biological cells and other particles illuminated by multi-beams.
      通信作者: 李正军, lizj@xidian.edu.cn
    • 基金项目: 陕西省自然科学基础研究计划(批准号: 2021JM-135)和国家自然科学基金(批准号: 62071359, 61801349)资助的课题.
      Corresponding author: Li Zheng-Jun, lizj@xidian.edu.cn
    • Funds: Project supported by the Natural Science Basic Research Program of Shaanxi Province, China (Grant No. 2021JM-135) and the National Natural Science Foundation of China (Grant Nos. 62071359, 61801349).
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    Durnin J 1987 J. Opt. Soc. 4 651Google Scholar

    [2]

    Garces-Chavez V, Roskey D, Summers M D, Melville H, Mcgloin D, Wright E M, Dholakia K 2004 Appl. Phys. Lett. 85 4001Google Scholar

    [3]

    Marston P L 2006 J. Acoust. Soc. Am. 120 3518Google Scholar

    [4]

    Zhang L, Marston P L 2012 J. Acoust. Soc. Am. 131 329Google Scholar

    [5]

    Milne G, Dholakia K, Mcgloin D 2007 Opt. Express 15 13972Google Scholar

    [6]

    Vahimaa P, Kettunen V, Kuittnen M 1997 J. Opt. Soc. Am. A 14 1817Google Scholar

    [7]

    Ding D, Liu X 1999 J. Opt. Soc. Am. A 16 1286Google Scholar

    [8]

    Cimár T, Kollárová V, Bouchal Z, Zemánek P 2006 New J. Phys. 8 43Google Scholar

    [9]

    Taylor J M, Love G D 2009 J. Opt. Soc. Am. A 26 278Google Scholar

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    Ambrosio L A, Herández-Figueroa H E 2011 Biomed. Opt. Express 2 1893Google Scholar

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    Mishra S R 1991 Opt. Commun. 85 159Google Scholar

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    Marton P L 2007 J. Acoust. Soc. Am. 121 753Google Scholar

    [13]

    Ma X B, Li E 2010 Chin. Opt. Lett. 8 1195Google Scholar

    [14]

    Gouesbet G, Maheu B, Gréhan G 1988 J. Opt. Soc. Am. A 5 1427Google Scholar

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    Li R X, Guo L X, Ding C 2013 Opt. Commun. 307 25Google Scholar

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    Mitri F G 2011 Opt. Lett. 36 766Google Scholar

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    Cui Z W, Han Y P, Han L 2013 J. Opt. Soc. Am. A 30 1913Google Scholar

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    Klimov V 2020 Opt. Lett. 45 4300Google Scholar

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    Wang X, Wang L, Lin P 2021 J. Innovative. Opt. Health Sci. 14 2150008Google Scholar

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    Stout B, Nevière M, Popov E 2006 J. Opt. Soc. Am. A 23 1111Google Scholar

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    Wong K L, Chen H T 1992 IEE Proc. H 139 314Google Scholar

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    Qiu C W, Li L W, Yeo T S 2007 Phys. Rev. E 75 026609Google Scholar

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    Geng Y L, Wu X B, Li L W, Guan B R 2004 Phys. Rev. E 70 056609Google Scholar

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    Wang M J, Zhang H Y, Liu G S, Li Y L 2012 J. Opt. Soc. Am. A 29 2376Google Scholar

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    Yuan Q K, Wu Z S, Li Z J 2010 J. Opt. Soc. Am. A 27 1457Google Scholar

    [26]

    Wu Z S, Yuan Q K, Peng Y, Li Z J 2009 J. Opt. Soc. Am. A 26 1778Google Scholar

    [27]

    Wang J J, Chen A T, Han Y P 2015 J. Quant. Spectrosc. Radiat. Transfer. 167 135Google Scholar

    [28]

    Qu T, Wu Z S, Shang Q C, Li Z J, Bai L 2013 J. Opt. Soc. Am. A 30 1661Google Scholar

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    Zemánek P, Alexandr J, Liska M 2002 J. Opt. Soc. Am. A 19 1025Google Scholar

    [30]

    Li Z J, Wu Z S, Qu T, Li H Y, Bai L, Gong L 2015 J. Quant. Spectrosc. Radiat. Transfer. 162 56Google Scholar

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    Hulst H 1957 Phys. Today 10 28Google Scholar

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    Barton J P, Alexander D R, Schaub S A 1988 J. Appl. Phys. 64 1632Google Scholar

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    Li Z J, Wu Z S, Qu T, Shang Q C, Bai L 2016 J. Quant. Spectrosc. Radiat. Transfer. 169 1Google Scholar

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    Li M M, Yin S H, Yao B L, Lei M, Yang Y L, Min J W 2015 J. Opt. Soc. Am. B 32 468Google Scholar

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    Wu Z S, Li Z J, Li H Y, Yuan Q K, Li H Y 2011 IEEE Trans. Antennas Propag. 59 4740Google Scholar

    [38]

    李正军, 吴振森, 屈檀, 白璐, 曹运华 2014 电波科学学报 29 668Google Scholar

    Li Z J, Wu Z S, Qu T, Bai L, Cao Y H 2014 Chin. J. Radio 29 668Google Scholar

    [39]

    Li Z J, Wu Z S, Shang Q C 2015 Procedia Eng. 102 89Google Scholar

  • 图 1  双零阶贝塞尔波束离轴斜入射UA介质球的示意图

    Fig. 1.  Schematic diagram of a uniaxial anisotropic sphere illuminated by off-axis obliquely incident double zero-order Bessel beams.

    图 2  两直角坐标的旋转关系示意图

    Fig. 2.  Schematic diagram of rotation relationship between two rectangular coordinate systems.

    图 3  相同极化角下反向传播双零阶贝塞尔波束的电场强度分布 (a) ${C_1} = {C_2} = 5^\circ $; (b) ${C_1} = {C_2} = 15^\circ $; (c) ${C_1} = {C_2} = 30^\circ $

    Fig. 3.  Electric intensity distribution of back propagating double zero-order Bessel beams with identical polarization angles: (a) ${C_1} = $$ {C_2} = 5^\circ $; (b) ${C_1} = {C_2} = 15^\circ $; (c) ${C_1} = {C_2} = 30^\circ $.

    图 4  不同极化角下反向传播双零阶贝塞尔波束的电场强度分布 (a) ${C_1} = {C_2} = 5^\circ $; (b) ${C_1} = {C_2} = 15^\circ $; (c) ${C_1} = {C_2} = 30^\circ $

    Fig. 4.  Electric intensity distribution of back propagating double zero-order Bessel beams with different polarization angles: (a) ${C_1} = {C_2} = 5^\circ $; (b) ${C_1} = {C_2} = 15^\circ $; (c) ${C_1} = {C_2} = 30^\circ $.

    图 5  斜入射时反向传播双零阶贝塞尔波束的电场强度分布 (a) ${C_1} = {C_2} = 5^\circ $; (b) ${C_1} = {C_2} = 15^\circ $; (c) ${C_1} = {C_2} = 30^\circ $

    Fig. 5.  Electric intensity distribution of back propagating double zero-order Bessel beams with oblique incidence: (a) ${C_1} = {C_2} = 5^\circ $; (b) ${C_1} = {C_2} = 15^\circ $; (c) ${C_1} = {C_2} = 30^\circ $.

    图 6  斜入射时非反向传播双零阶贝塞尔波束的电场强度分布 (a) ${C_1} = {C_2} = 5^\circ $; (b) ${C_1} = {C_2} = 15^\circ $; (c) ${C_1} = $$ {C_2} = 30^\circ $

    Fig. 6.  Electric intensity distribution of non-back propagating double zero-order Bessel beams with oblique incidence: (a) ${C_1} = $$ {C_2} = 5^\circ $; (b) ${C_1} = {C_2} = 15^\circ $; (c) ${C_1} = {C_2} = 30^\circ $.

    图 7  UA介质球对单零阶贝塞尔波束的RCS角分布

    Fig. 7.  Normalized RCS of a UA dielectric sphere illuminated by single zero-order Bessel beam versus the scattering angle.

    图 8  双零阶贝塞尔波束退化成平面波入射UA介质球的RCS角分布 (a) E-plane; (b) H-plane

    Fig. 8.  Angular distribution of the RCS of a UA dielectric sphere by double zero-order Bessel beams when degenerating into plane waves: (a) E-plane; (b) H-plane.

    图 9  UA介质球对不同离轴情形入射的单零阶贝塞尔波束的RCS角分布 (a) E-plane; (b) H-plane

    Fig. 9.  Angular distribution of the RCS of a UA dielectric sphere illuminated by different off-axis incident zero-order Bessel beams: (a) E-plane; (b) H-plane.

    图 10  UA介质球对离轴入射的双零阶贝塞尔波束的RCS角分布 (a) E-plane; (b) H-plane

    Fig. 10.  Angular distribution of the RCS of a UA dielectric sphere illuminated by different off-axis incident double zero-order Bessel beams: (a) E-plane; (b) H-plane.

    图 11  UA介质球对不同入射角下双零阶贝塞尔波束的RCS角分布 (a) E-plane; (b) H-plane

    Fig. 11.  Angular distribution of the RCS of a UA dielectric sphere illuminated by double zero-order Bessel beams with different incident angles: (a) E-plane; (b) H-plane.

    图 12  双反向传输的零阶贝塞尔波束在不同锥角入射的情况下UA介质球的RCS角分布 (a) E-plane; (b) H-plane

    Fig. 12.  Angular distribution of the RCS of a UA dielectric sphere illuminated by back propagating double zero-order Bessel beams with different conic angles: (a) E-plane; (b) H-plane.

  • [1]

    Durnin J 1987 J. Opt. Soc. 4 651Google Scholar

    [2]

    Garces-Chavez V, Roskey D, Summers M D, Melville H, Mcgloin D, Wright E M, Dholakia K 2004 Appl. Phys. Lett. 85 4001Google Scholar

    [3]

    Marston P L 2006 J. Acoust. Soc. Am. 120 3518Google Scholar

    [4]

    Zhang L, Marston P L 2012 J. Acoust. Soc. Am. 131 329Google Scholar

    [5]

    Milne G, Dholakia K, Mcgloin D 2007 Opt. Express 15 13972Google Scholar

    [6]

    Vahimaa P, Kettunen V, Kuittnen M 1997 J. Opt. Soc. Am. A 14 1817Google Scholar

    [7]

    Ding D, Liu X 1999 J. Opt. Soc. Am. A 16 1286Google Scholar

    [8]

    Cimár T, Kollárová V, Bouchal Z, Zemánek P 2006 New J. Phys. 8 43Google Scholar

    [9]

    Taylor J M, Love G D 2009 J. Opt. Soc. Am. A 26 278Google Scholar

    [10]

    Ambrosio L A, Herández-Figueroa H E 2011 Biomed. Opt. Express 2 1893Google Scholar

    [11]

    Mishra S R 1991 Opt. Commun. 85 159Google Scholar

    [12]

    Marton P L 2007 J. Acoust. Soc. Am. 121 753Google Scholar

    [13]

    Ma X B, Li E 2010 Chin. Opt. Lett. 8 1195Google Scholar

    [14]

    Gouesbet G, Maheu B, Gréhan G 1988 J. Opt. Soc. Am. A 5 1427Google Scholar

    [15]

    Li R X, Guo L X, Ding C 2013 Opt. Commun. 307 25Google Scholar

    [16]

    Mitri F G 2011 Opt. Lett. 36 766Google Scholar

    [17]

    Cui Z W, Han Y P, Han L 2013 J. Opt. Soc. Am. A 30 1913Google Scholar

    [18]

    Klimov V 2020 Opt. Lett. 45 4300Google Scholar

    [19]

    Wang X, Wang L, Lin P 2021 J. Innovative. Opt. Health Sci. 14 2150008Google Scholar

    [20]

    Stout B, Nevière M, Popov E 2006 J. Opt. Soc. Am. A 23 1111Google Scholar

    [21]

    Wong K L, Chen H T 1992 IEE Proc. H 139 314Google Scholar

    [22]

    Qiu C W, Li L W, Yeo T S 2007 Phys. Rev. E 75 026609Google Scholar

    [23]

    Geng Y L, Wu X B, Li L W, Guan B R 2004 Phys. Rev. E 70 056609Google Scholar

    [24]

    Wang M J, Zhang H Y, Liu G S, Li Y L 2012 J. Opt. Soc. Am. A 29 2376Google Scholar

    [25]

    Yuan Q K, Wu Z S, Li Z J 2010 J. Opt. Soc. Am. A 27 1457Google Scholar

    [26]

    Wu Z S, Yuan Q K, Peng Y, Li Z J 2009 J. Opt. Soc. Am. A 26 1778Google Scholar

    [27]

    Wang J J, Chen A T, Han Y P 2015 J. Quant. Spectrosc. Radiat. Transfer. 167 135Google Scholar

    [28]

    Qu T, Wu Z S, Shang Q C, Li Z J, Bai L 2013 J. Opt. Soc. Am. A 30 1661Google Scholar

    [29]

    Zemánek P, Alexandr J, Liska M 2002 J. Opt. Soc. Am. A 19 1025Google Scholar

    [30]

    Li Z J, Wu Z S, Qu T, Li H Y, Bai L, Gong L 2015 J. Quant. Spectrosc. Radiat. Transfer. 162 56Google Scholar

    [31]

    Hulst H 1957 Phys. Today 10 28Google Scholar

    [32]

    Barton J P, Alexander D R, Schaub S A 1988 J. Appl. Phys. 64 1632Google Scholar

    [33]

    Li Z J, Wu Z S, Qu T, Shang Q C, Bai L 2016 J. Quant. Spectrosc. Radiat. Transfer. 169 1Google Scholar

    [34]

    Bolton H C 1959 Mathematical Gazette 43 157Google Scholar

    [35]

    Li Z J, Wu Z S, Huan L, Li H Y 2011 Chin. Phys. B 20 081101Google Scholar

    [36]

    Li M M, Yin S H, Yao B L, Lei M, Yang Y L, Min J W 2015 J. Opt. Soc. Am. B 32 468Google Scholar

    [37]

    Wu Z S, Li Z J, Li H Y, Yuan Q K, Li H Y 2011 IEEE Trans. Antennas Propag. 59 4740Google Scholar

    [38]

    李正军, 吴振森, 屈檀, 白璐, 曹运华 2014 电波科学学报 29 668Google Scholar

    Li Z J, Wu Z S, Qu T, Bai L, Cao Y H 2014 Chin. J. Radio 29 668Google Scholar

    [39]

    Li Z J, Wu Z S, Shang Q C 2015 Procedia Eng. 102 89Google Scholar

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出版历程
  • 收稿日期:  2022-03-18
  • 修回日期:  2022-05-25
  • 上网日期:  2022-09-21
  • 刊出日期:  2022-09-20

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