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非均匀手征分层粒子的俘获特性研究在化学工程、生物医药、光镊、微纳米加工等领域都有着重要的应用. 为了有效地俘获及操控手征分层球形粒子, 本文对椭圆高斯波束照射下手征分层球形粒子的辐射俘获力展开研究. 从广义米理论出发, 将入射椭圆高斯波束用矢量球谐函数展开, 根据波束散射理论及电磁场动量守恒定理, 得出椭圆高斯波束对手征分层球形粒子辐射俘获力的级数表达式, 并对椭圆高斯波束入射分层手征细胞时的轴向及横向俘获力进行了数值模拟, 讨论了手征参数、极化状态、束腰宽度、损耗以及最外层厚度对俘获情况的影响. 研究表明: 手征参数的引入会降低非均匀手征粒子的轴向俘获特性, 但是选择合适的极化态入射时, 可以有效地实现对非均匀手征粒子的稳定俘获. 对于内层损耗小的手征多层球形粒子, 当内层折射率大于最外层时, 最外层厚度大的非均匀手征粒子在光轴上更容易俘获; 反之内层折射率小于最外层时, 最外层厚度小的粒子在光轴上有更强的束缚; 同时与传统圆高斯波束相比, 椭圆高斯波束的强会聚性更容易实现对非均匀手征分层细胞的三维俘获, 具有良好的应用前景.Theoretical study on optical trapping of multi-layered chiral sphere has attracted more and more attention for its important applications in many frontier scientific fields such as chemical engineering, biomedicine, optical tweezers, micro/nano lithography etc. In order to trap and manipulate chiral multi-layered particles efficiently, the present paper aims at developing the theoretical research of trapping force (TF) exerted on a multi-layered chiral sphere induced by laser sheet which might have great potential to improve the light performance in optical trapping as well as capture, suspension, and high-precision delivery of chiral cells. Here, based on the Generalized Lorenz Mie theory and the completeness of spherical vector wave functions (SVWFs), the electromagnetic field of incident laser sheet are expanded in terms of SVWFs. Accordingly, by introducing the beam scattering theory and the conservation law of electromagnetic momentum (EM), the analysis of TF exerted on multi-layered chiral sphere can be analytically expressed in terms of the incident and scattering coefficients. Taking the chiral cell as an example, the TF induced by laser sheet is simulated numerically. Numerical effects of the varying chirality, polarization states, beam waist width, inner material loss and outmost size on the TF induced by laser sheet are analyzed and compared with those by circular Gaussian beam incidence in detail. It is found that the introduction of chirality parameter may reduce the axial TF exerted on chiral multi-layered cell. Thus, it is more difficult to trap and manipulate stratified chiral cells than to trap general isotropic cells. Also it is shown that the TF of chiral cells can be significantly discriminatory in nature, depending upon both the handedness of the interacting particles and the polarization of the incident light. Thus, an appropriately polarized beam should be considered in trapping chiral cells. For chiral multi-layered cells with small loss in the inner layer, when the inner refractive indices are less than the outmost refractive index, the TF of multi-layered chiral cell becomes stronger with the outmost radius decreasing. Conversely, for the inner refractive indices are greater than the outer refractive index, TF becomes weaker as the outmost radius decreases. Besides, compared with the traditional circular Gaussian beam, the strong convergence of elliptical Gaussian beam can be easier to achieve three-dimensional capture of stratified chiral cells, which may provide a recipe to understand the light interaction with more complex chiral cells with the aid of the analytical approach and could be a promising avenue for the design of optical trapping systems.
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Keywords:
- trapping force /
- laser sheet /
- multi-layered chiral cell /
- optical tweezers
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Google Scholar
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[48] 李应乐, 李瑾, 王明军, 董群峰 2013 激光与光电子学进展 50 6
Li Y L, Li Q, Wang M J, Dong Q F 2013 Laser Optoelectron. Prog. 50 6
[49] Ma N Z, Li R X 2010 International Symposium on Antennas Propagation & Em Theory Guangzhou, Novenber 29–December 2, 2010 p646
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Google Scholar
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Google Scholar
[53] Barton J P, Alexander D R, Schaub S A 1989 J. Appl. Phys. 66 4594
Google Scholar
[54] Rohrbach A, Stelzer E H K 2000 J. Opt. Soc. Am. A 18 839
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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图 1 非均匀手征分层球对椭圆高斯波束散射图
Fig. 1. Geometry for scattering of a non-uniform multi-layered chiral sphere induced by laser sheet.
图 2 手征多层球退化为各向同性多层球的辐射俘获力与实验及文献结果进行对比 (a) 单层球对比轴向俘获力
${F_z}$ ; (b) 双层球对比轴向俘获力${F_z}$ ; (c)五层球对比横向俘获力截面${C_{{\text{pr}}, x}}$ Fig. 2. Comparisons of trapping force (TF) from the theory when multi-layered chiral sphere is degenerated into stratified isotropic sphere with the results from existing references and experiments: (a) Comparisons of axial TF
${F_z}$ on a single-layered sphere; (b) comparisons of axial TF${F_z}$ on a double-layered sphere; (c) comparisons of transverse TF cross section${C_{{\text{pr}}, x}}$ on a five-layered sphere.
图 3 不同手征参数对轴向俘获力
${F_z}$ 随粒子离轴位置$d$ 变化的影响Fig. 3. Effects of chirality parameter on axial TF with the varying position
$d$ of the chiral cell off axis.
图 4 不同极化状态对轴向俘获力
${F_z}$ 随粒子离轴位置$d$ 变化的影响Fig. 4. Effects of polarization states on axial TF with the varying position
$d$ of the chiral cell off axis.
图 5 不同束腰半径对轴向俘获力
${F_z}$ 随粒子离轴位置$d$ 变化的影响Fig. 5. Effects of beam waist widths on axial TF with the varying position
$d$ of the chiral cell off axis.
图 6 内层损耗变化对轴向俘获力
${F_z}$ 随粒子离轴位置$d$ 变化的影响Fig. 6. Effects of inner material loss on axial TF with the varying position
$d$ of the chiral cell off axis.
图 7 最外层厚度变化对轴向俘获力
${F_z}$ 随粒子离轴位置$d$ 变化的影响(内层及次外层折射率小于最外层时)Fig. 7. Effects of outmost particle size on axial TF with the varying position
$d$ of the chiral cell off axis (the inner refractive index is less than the outmost refractive index case).
图 8 最外层厚度变化对轴向俘获力
${F_z}$ 随粒子离轴位置$d$ 变化的影响(内层及次外层折射率大于最外层时)Fig. 8. Effects of the outmost particle size on axial TF with the varying position
$d$ of the chiral cell off axis (the inner refractive index is greater than the outmost refractive index case).
图 9 不同束腰半径对横向俘获力随粒子离轴位置
$d$ 变化的影响 (a)${F_x}$ 随粒子离轴位置$d$ 变化; (b)${F_y}$ 随粒子离轴位置$d$ 变化Fig. 9. Effects of beam waist width on transverse TF with the varying position
$d$ of the chiral cell off axis: (a)${F_x}$ changes with the varying position$d$ off axis; (b)${F_y}$ changes with the varying position$d$ off axis. -
[1] Ashkin A 1970 Phys. Rev. Lett. 24 156
Google Scholar
[2] Ashkin A 1980 Science 210 1081
Google Scholar
[3] 蒋云峰, 陆璇辉, 赵承良 2010 物理学报 59 3959
Google Scholar
Jiang Y F, Lu X H, Zhao C L 2010 Acta Phys. Sin. 59 3959
Google Scholar
[4] 吴鹏, 韩一平, 刘德芳 2005 物理学报 54 2676
Google Scholar
Wu P, Han Y P, Liu D F 2005 Acta Phys. Sin. 54 2676
Google Scholar
[5] Ren K F, Gréha G, Gouesbet G 1994 Opt. Commun. 108 343
Google Scholar
[6] Lock J A 2004 Endocrinology 43 2532
[7] Gouesbet G, Lock J A 1994 J. Opt. Soc. Am. A: 11 2503
[8] Ren K F, Gouesbet G, Gréha G 1998 Appl. Opt. 37 4218
Google Scholar
[9] 韩一平, 杜云刚, 张华永 2006 物理学报 55 4557
Google Scholar
Han Y P, Du Y G, Zhang H Y 2006 Acta Phys. Sin. 55 4557
Google Scholar
[10] 韩国霞, 韩一平 2009 物理学报 58 6167
Google Scholar
Han G X, Han Y P 2009 Acta Phys. Sin. 58 6167
Google Scholar
[11] Onofri F, Gréha G, Gouesbet G 1995 Appl. Opt. 34 7113
Google Scholar
[12] Li H Y, Wu Z S, Li Z J 2009 Chin. Phys. Lett. 26 104203
Google Scholar
[13] Ladutenko K, Pal U, Rivera A, Rodríguez O 2007 Comput. Phys. Commun. 214 225
[14] Pei S, Pan Q, Cui F, Xu S S, Cao Z L 2018 Optik 180 379
[15] Bohren G F, Huffman D R 1983 Absorption and Scattering of Light by Small Particles (New York: Wiley)
[16] Kerker M 1969 The Scattering of Light and Other Electromagnetic Radiation (New York: Academic)
[17] Wu Z S, Wang Y P 1991 Radio Sci. 26 1393
Google Scholar
[18] 李海英, 吴振森 2008 物理学报 57 833
Google Scholar
Li H Y, Wu Z S 2008 Acta Phys. Sin. 57 833
Google Scholar
[19] Chen Z Y, Han Y P, Cui Z W, Shi X W 2015 Opt. Commun. 340 5
Google Scholar
[20] Yu M P, Han Y P, Cui Z W, Sun H Y 2018 J. Opt. Soc. Am. A 35 1504
[21] Shore R A 2015 IEEE Antennas Propag. Mag. 57 69
[22] Wang H B, Liu X Z, Gao S, Cui J, Liu H J, He A J, Zhang G T 2018 Chin. Phys. B 27 034302
Google Scholar
[23] Schut T C B, Hesselink G, de Grooth B G, Greve J 1991 Cytomety 12 479
Google Scholar
[24] Rohrbach A, Stelzer E 2001 J. Opt. Soc. Am. A: 18 839
[25] Ermutlu M E, Sihvola A H 1994 Prog. Electromagnet. Res. 9 87
Google Scholar
[26] Ren W 1994 Prog. Electromagnet. Res. 9 103
Google Scholar
[27] Simpson S H, Hanna S 2011 Phys. Rev. A 84 053808
Google Scholar
[28] Cooray M F R, Ciric I R 1993 J. Opt. Soc. Am. A: 10 1197
[29] Jaggard D L, Liu J C 1999 IEEE Trans. Antennas Propag. 47 1201
Google Scholar
[30] Yan B, Liu C H, Zhang H Y, Shi Y 2015 Opt. Commun. 338 261
Google Scholar
[31] Wang W J, Sun Y F, Zhang H Y 2017 Opt. Commun. 385 54
Google Scholar
[32] Gao X, Zhang H 2017 Optik 129 43
Google Scholar
[33] Zheng M, Zhang H Y, Sun Y F, Wang Z G 2015 J. Quant. Spectrosc. Radiat. Transfer 151 192
Google Scholar
[34] Li L W, Dan Y, Leong M, et al. 1999 Prog. Electromagnet. Res. 23 1203
[35] Shang Q, Wu Z, Qu T, Li Z, Bai L 2016 J. Quant. Spectrosc. Radiat. Transfer 173 72
Google Scholar
[36] Ren K F, Grehan G, Gouesbet G 1994 J. Opt. 25 165
Google Scholar
[37] Ren K F, Gérard G 1993 Part. Part. Syst. Char. 10 146
Google Scholar
[38] Naqwi A A, Liu X Z, Durst F 1992 Part. Part. Syst. Char. 9 44
Google Scholar
[39] Naqwi A A, Liu X Z, Franz D 1990 Part. Part. Syst. Char. 7 45
Google Scholar
[40] Rockwell D, Magness C, Towfighi J, Akin O, Corcoran T 1993 Exp. Fluids 14 181
Google Scholar
[41] Adrian R J 1984 Appl. Opt. 23 1690
Google Scholar
[42] Gréhan D G, Gouesbet G, Naqwi D A, Durst F 1993 Part. Part. Syst. Char. 10 332
Google Scholar
[43] Doicu D I A, Ebert D I F, Schabel D I S 1996 Part. Part. Syst. Char. 13 79
Google Scholar
[44] 郭红莲, 曹勤红, 任东涛, 刘国琴, 段建发, 李兆霖, 张道中, 韩学海 2003 科学通报 48 6
Guo H L, Cao Q H, Ren D T, Liu G Q, Duan J F, Li Z L, Zhang D Z, Han X M 2003 Chin. Sci. Bull. 48 6
[45] Wang W, Shen J Q 2018 J. Quant. Spectrosc. Radiat. Transfer 212 139
Google Scholar
[46] Shen J Q, Liu X, Wang W, Yu H T 2018 J. Opt. Soc. Am. A. 35 8
Google Scholar
[47] 李应乐, 李瑾, 王明军, 董群峰 2014 中国科学: 物理学 力学 天文学 5 7
Li Y L, Li Q, Wang M J, Dong Q F 2014 Sci. Chin. -Phys. Mech. Astron. 5 7
[48] 李应乐, 李瑾, 王明军, 董群峰 2013 激光与光电子学进展 50 6
Li Y L, Li Q, Wang M J, Dong Q F 2013 Laser Optoelectron. Prog. 50 6
[49] Ma N Z, Li R X 2010 International Symposium on Antennas Propagation & Em Theory Guangzhou, Novenber 29–December 2, 2010 p646
[50] Li R X, Ren K F, Han X 2013 J. Quant. Spectrosc. Radiat. Transfer 126 69
Google Scholar
[51] Ren K F, Gréhan G, Gouesbet G 1994 J. Opt. Soc. Am. A 11 2072
[52] Gouesbet G, Grehan G, Maheu B 1988 Appl. Opt. 27 4874
Google Scholar
[53] Barton J P, Alexander D R, Schaub S A 1989 J. Appl. Phys. 66 4594
Google Scholar
[54] Rohrbach A, Stelzer E H K 2000 J. Opt. Soc. Am. A 18 839
[55] Harada Y, Asakura T 1996 Opt. Commun. 124 529
Google Scholar
[56] Schut T C, Hesselink G, Grooth B G 1991 Cytometry 12 479
Google Scholar
[57] Nemoto, Togo H 1998 Appl. Opt. 37 6386
Google Scholar
[58] Nahmias Y K, Gao B Z, Odde D J 2004 Appl. Opt. 43 3999
Google Scholar
[59] Drezek R, Dunn A, Richards-Kortum R 1999 Appl. Opt. 38 3651
Google Scholar
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