光学捕捉与柱对称矢量光束的理论研究
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摘要
自上世纪70年代美国贝尔实验室的Ashkin发现光场中的梯度力可捕获微小粒子以来,光学捕捉技术或称之为光镊已经作为一种重要的工具被广泛应用于到从原子、分子、亚微米量级到几百个微米级别的各种微观领域的研究。围绕着光学捕捉中光束与粒子的相互作用,本论文主要完成了以下工作:
1.提出了一种改进的T矩阵方法,使得计算非轴对称体和复杂形状微粒的散射场成为可能。普通的T矩阵方法只能计算轴对称型粒子,我们提出的改进T矩阵方法用表面剖分的办法对粒子的表面用一组三角形集合来近似,因此可以计算任何复杂形状微粒的散射场。
2.针对T矩阵方法,提出了散射场的快速计算算法。在散射场的计算中,T矩阵的计算涉及到矩阵的乘法和求逆,当粒子尺寸很大时,这两种矩阵运算特别是求逆将消耗大量的时间。Petrov等人提出了一种优化的矩阵求逆算法,在这种优化矩阵求逆算法的基础上,我们提出了另外的快速计算散射场的算法。我们的方法通过进行矩阵与入射场系数矢量之间的运算来得到散射场,它们之间的运算可以通过上述的优化求逆的方法进行。数值结果显示我们的方法需要的时间少于Petrov等人方法消耗时间的一半。
3.提出了用复源点球面波(CSPSW)矢量势来描述径向偏振光束(R-TEM_(01))。传统的描述多采用Lax微扰级数法来获得矢量势,其表达式随精度要求的提高而变得复杂。我们使用的CSPSW矢量势具有非常简单的数学形式,而且能准确地满足波动方程。
4.提出了五次方修正的径向偏振Laguerre-Gauss光束(R-TEM_(nl))描述方法。应用Lax微扰级数法,得到了径向偏振光场产生矢量势(通常是沿z方向)的二阶修正表达式以及由其生成的五次方修正的R-TEM_(nl),同时得到了Laguerre-Gauss光束的任意次修正表达式。
5.理论证明了径向偏振光束可以改善轴向捕捉效率。捕获光阱作用在粒子上的辐射力通常分为梯度力和散射力,后者在轴向捕捉是需要克服的,其大小依赖于Poynting矢量的纵向分量S_z。径向偏振光束的径向分量的强度在焦点附近将出现一个空洞,导致它的S_z在焦点附近为零,这很好地满足了降低散射力的要求,理论计算验证了这一点。
6.为了进一步降低散射力,我们提出用双环径向偏振光束捕捉微粒。双环径向偏振光束的内外环的瞬时偏振方向刚好相反,经过聚焦后,其横向分量的强度将产生两个环,且内环强度小于R-TEM_(01)在相应区域横向分量的强度。由于S_z正比于横向分量的强度,我们预言只要粒子的半径限制在内环区域,DR R-TEM_(01)模相对于R-TEM_(01)模可以提供更高的轴向捕捉效率。
Since Ashkin of Bell Lab demonstrated in 1970 that the gradient force in optical field can trap micro-particle,optical trapping or optical tweezer has emerge as a powerful tool with wide-reaching applications in the study of microscopic field covering from atoms,molecules,sub-micron to the dimension of the order of hundreds micron.Centered on the interaction between the trapping beam and the particle,this thesis completed the following work.
1.An improved T-matrix method is proposed,which is capable of dealing with the scattering by non-axis-symmetrical and complicated-shape particles.The new method discretizes the surface of the particle by a set of triangles.It is therefore applicable to calculating the scattering field by particles with complicated shape.
2.For T-matrix method,a technique of speeding the calculation of the scattered field is presented.In computing the scattering fields,the determination of the T-matrix involves matrix multiplication and inversion,which consumes considerable time when the size of the particle is large.Petrov et al.proposed an improved matrix inversion method.Based on this improved inversion,we present another fast technique for calculating the scattering fields.Our method obtains the scattered field by directly multiplying the matrix and the incident field coefficients,operation between which can be completed by the improved matrix inversion.Numerical results show that this technique can decrease time-consumption by more than half that of the optimized matrix inversion technique by Petrov et al.
3.Complex-source-point spherical wave(CSPSW) vector potential is introduced to describe radially polarized beam(R-TEM_(01)).The vector potential expression represented by the conventional Lax perturbative series method become rather complicated with increasing the accuracy.The CSPSW vector potential acquires very simple form in mathematics and exactly satisfies the Ho equation.
4.The method of representing a fifth-order corrected radially polarized Laguerre-Gauss beam(R-TEM_(nl)) is obtained.By using the Lax perturbative series method,we derive the vector potential expression with second-order correction from which 5th-order corrected R-TEM_(nl) is found.Meanwhile,a scalar Laguerre-Gauss wave accurate to any order is obtained.
5.The possibility of improving axial trapping efficiency by raidally polarized beams is proved theoretically.In optical trapping,radiation forces on the particle are,in general,divided into the gradient force and the scattering force,and the latter needs to be reduced as weak as possible in axial trapping and its amplitude depending on the z component S_z of Poynting vector.Radially polarized fields acquire zero radial field component near the focus,leading to a vanishing S_z near the focus.Thus the scattering force can be weakened significantly.Our calculation strongly confirms this.
6.Double-ring radially polarized beam(DR R-TEM_(01)) is suggested to further reduce the scattering force in optical trapping.The fields of inner and outer rings of a DR R-TEM_(01) are polarized in instantly opposite direction along the radius. After being focused,the beam develops two intensity rings of radial component and the inner intensity is less than that of R-TEM_(01) in the same region.Since S_zis proportional to the radial component intensity,we predict that DR R-TEM_(01) could give higher axial trapping efficiency provider that the particle size falls into the inner ring.
1.提出了一种改进的T矩阵方法,使得计算非轴对称体和复杂形状微粒的散射场成为可能。普通的T矩阵方法只能计算轴对称型粒子,我们提出的改进T矩阵方法用表面剖分的办法对粒子的表面用一组三角形集合来近似,因此可以计算任何复杂形状微粒的散射场。
2.针对T矩阵方法,提出了散射场的快速计算算法。在散射场的计算中,T矩阵的计算涉及到矩阵的乘法和求逆,当粒子尺寸很大时,这两种矩阵运算特别是求逆将消耗大量的时间。Petrov等人提出了一种优化的矩阵求逆算法,在这种优化矩阵求逆算法的基础上,我们提出了另外的快速计算散射场的算法。我们的方法通过进行矩阵与入射场系数矢量之间的运算来得到散射场,它们之间的运算可以通过上述的优化求逆的方法进行。数值结果显示我们的方法需要的时间少于Petrov等人方法消耗时间的一半。
3.提出了用复源点球面波(CSPSW)矢量势来描述径向偏振光束(R-TEM_(01))。传统的描述多采用Lax微扰级数法来获得矢量势,其表达式随精度要求的提高而变得复杂。我们使用的CSPSW矢量势具有非常简单的数学形式,而且能准确地满足波动方程。
4.提出了五次方修正的径向偏振Laguerre-Gauss光束(R-TEM_(nl))描述方法。应用Lax微扰级数法,得到了径向偏振光场产生矢量势(通常是沿z方向)的二阶修正表达式以及由其生成的五次方修正的R-TEM_(nl),同时得到了Laguerre-Gauss光束的任意次修正表达式。
5.理论证明了径向偏振光束可以改善轴向捕捉效率。捕获光阱作用在粒子上的辐射力通常分为梯度力和散射力,后者在轴向捕捉是需要克服的,其大小依赖于Poynting矢量的纵向分量S_z。径向偏振光束的径向分量的强度在焦点附近将出现一个空洞,导致它的S_z在焦点附近为零,这很好地满足了降低散射力的要求,理论计算验证了这一点。
6.为了进一步降低散射力,我们提出用双环径向偏振光束捕捉微粒。双环径向偏振光束的内外环的瞬时偏振方向刚好相反,经过聚焦后,其横向分量的强度将产生两个环,且内环强度小于R-TEM_(01)在相应区域横向分量的强度。由于S_z正比于横向分量的强度,我们预言只要粒子的半径限制在内环区域,DR R-TEM_(01)模相对于R-TEM_(01)模可以提供更高的轴向捕捉效率。
Since Ashkin of Bell Lab demonstrated in 1970 that the gradient force in optical field can trap micro-particle,optical trapping or optical tweezer has emerge as a powerful tool with wide-reaching applications in the study of microscopic field covering from atoms,molecules,sub-micron to the dimension of the order of hundreds micron.Centered on the interaction between the trapping beam and the particle,this thesis completed the following work.
1.An improved T-matrix method is proposed,which is capable of dealing with the scattering by non-axis-symmetrical and complicated-shape particles.The new method discretizes the surface of the particle by a set of triangles.It is therefore applicable to calculating the scattering field by particles with complicated shape.
2.For T-matrix method,a technique of speeding the calculation of the scattered field is presented.In computing the scattering fields,the determination of the T-matrix involves matrix multiplication and inversion,which consumes considerable time when the size of the particle is large.Petrov et al.proposed an improved matrix inversion method.Based on this improved inversion,we present another fast technique for calculating the scattering fields.Our method obtains the scattered field by directly multiplying the matrix and the incident field coefficients,operation between which can be completed by the improved matrix inversion.Numerical results show that this technique can decrease time-consumption by more than half that of the optimized matrix inversion technique by Petrov et al.
3.Complex-source-point spherical wave(CSPSW) vector potential is introduced to describe radially polarized beam(R-TEM_(01)).The vector potential expression represented by the conventional Lax perturbative series method become rather complicated with increasing the accuracy.The CSPSW vector potential acquires very simple form in mathematics and exactly satisfies the Ho equation.
4.The method of representing a fifth-order corrected radially polarized Laguerre-Gauss beam(R-TEM_(nl)) is obtained.By using the Lax perturbative series method,we derive the vector potential expression with second-order correction from which 5th-order corrected R-TEM_(nl) is found.Meanwhile,a scalar Laguerre-Gauss wave accurate to any order is obtained.
5.The possibility of improving axial trapping efficiency by raidally polarized beams is proved theoretically.In optical trapping,radiation forces on the particle are,in general,divided into the gradient force and the scattering force,and the latter needs to be reduced as weak as possible in axial trapping and its amplitude depending on the z component S_z of Poynting vector.Radially polarized fields acquire zero radial field component near the focus,leading to a vanishing S_z near the focus.Thus the scattering force can be weakened significantly.Our calculation strongly confirms this.
6.Double-ring radially polarized beam(DR R-TEM_(01)) is suggested to further reduce the scattering force in optical trapping.The fields of inner and outer rings of a DR R-TEM_(01) are polarized in instantly opposite direction along the radius. After being focused,the beam develops two intensity rings of radial component and the inner intensity is less than that of R-TEM_(01) in the same region.Since S_zis proportional to the radial component intensity,we predict that DR R-TEM_(01) could give higher axial trapping efficiency provider that the particle size falls into the inner ring.
引文
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