光镊的理论模型及纳米颗粒的操纵
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摘要
在微/纳尺度上操纵颗粒和测量微小力学量,能帮助我们从单分子层次了解DNA弹性和蛋白折叠等生物大分子的力学信息,从单颗粒层次上研究流体动力学作用,以及研究微/纳尺度上组装和传动微型机器。在众多的微/纳操纵技术中,光镊技术具有纳米级位移和飞牛量级测量精度的独特优势,广泛应用于单分子、胶体和纳米科学等领域。
在各种应用中,最常用光镊的方式为基于高数值孔径物镜的单光束梯度力阱,实现远场操纵微粒。为了更好的理解和运用光镊技术,理论研究光阱对微粒的俘获机理和光阱参数对光阱力的影响,对于完善光镊理论模型,提升现有光镊性能并付诸于实际应用具有重要的意义。当微粒尺度小到纳米尺度,光阱难以束缚它。光镊操纵纳米颗粒不仅是对光镊设备性能的挑战,而且在纳米流变学、纳米组装、胶体体系和表面增强拉曼散射信号上有着重要应用。
本论文主要研究了矢量光线追迹的RO模型和矢量衍射-矩量法的EM模型,利用矢量衍射理论,分析了在光阱中纳米颗粒的辐射力与光镊参数的关系,并从实验上探索三维操纵纳米颗粒。在低信噪比情形下,我们研究了自相关函数标定颗粒的光阱刚度,它适用于标定纳米颗粒的光阱刚度。
关于RO模型的理论研究中,本论文应用矢量光线追迹方法,统一分析三维方向上光阱力,简化了RO模型的计算。结合空间矢量和矩阵的计算方法,它能有效地分析偏振光束对颗粒的光阱力,弥补传统RO模型的不足。在此基础上,我们分析了玻璃-水界面球差引起的矢量光线追迹,利用坐标旋转的方法,实现对任意形状颗粒的光阱力及应力张量和力矩的计算。对于长杆状颗粒,球差并不随俘获深度增大时降低光阱对它的轴向俘获力,不规则颗粒在光阱作用的力矩下,自动调整到颗粒长轴与光轴平行的方位,这一方法拓展了传统RO模型的适应范围。
有关光镊的EM模型的理论研究中,本论文提出了矢量衍射-矩量法的EM模型。这一模型分成聚焦光束的场分布、电磁散射后总场的分布和计算辐射力三个独立的部分。这一模型在改变参数时,能减少计算工作量,例如改变入射激光光束截面和物镜数值孔径等参数,无需计算反映微粒特性的矩阵元。通过模拟计算,得出在光阱中无法稳定俘获较大尺度的高折射率颗粒的结论。基于这一理论计算平台中,通过Rayleigh近似我们直接计算了纳米颗粒的辐射力,并研究纳米颗粒的辐射力与各参数的关系,得出在短波长、高数值孔径物镜和最佳光束分布时光阱俘获纳米颗粒的力最大。通过这些理论模拟,为我们三维操纵纳米颗粒的实验提供理论依据。
根据前述辐射力的理论分析,本论文提出暗场照明光镊,实现实时观察三维主动操纵纳米颗粒。根据观察的需要,我们采用横向激光暗场照明,实现宽视场、实时和长时间观察纳米颗粒,并动态观察三维操纵纳米颗粒过程。由于观察和操纵纳米颗粒在俘获深度的相互限制,我们引入机械筒长失配的球差补偿,在较大俘获深度上的增强光阱力,实现在光学显微镜下清晰观察三维操纵直径70nm的颗粒。
由于纳米颗粒的光阱力很弱,容易受到外界噪声的影响,它的刚度测量上需要尽可能降低这方面的影响。我们研究了自相关函数测量纳米颗粒的光阱刚度,作为方法的验证,在滤波和引入外界噪声等方面比较了功率谱法和自相关函数标定刚度的差异,具体分析了导致差异的原因。刚度标定的方法在光镊应用中非常重要,如何实现原位和实时标定刚度,不仅能简化实验过程,还能准确反映测量中瞬时的力学信息。
本论文从理论上较系统地研究RO模型和EM模型,建立一套在微／纳米尺度上计算光阱力的方法。理论方法的建立有助于我们更好地理解微粒在光阱中的行为,指导实验设计和分析实验中遇到的问题。实验研究中我们提出暗场照明光镊并实现纳米粒子的俘获,分析了自相关函数标定刚度与实验各因素的关系。这些研究将拓展光镊应用于纳米领域。
Manipulation of particle on the micro/nano scale conveys the information of mechanical characteristics of signal molecules, such as researches on DNA elasticity, protein folding etc. The manipulation also facilitates the investigations of hydrodynamic interaction at the single particle level and assembling micro/nano machine. Among many technologies of manipulation, optical tweezers as a non-contact trap way have unique advantages:nanometer resolution on displacement and femtonewton resolution on force. This technology is widely applied in single molecules, colloid and nanotechnology fields.
In various applications, optical tweezers, a single-beam gradient force trap, are based on a high numerical aperture objective and used to manipulate particle in far field. To apply optical tweezers better, theoretical investigation between parameters and forces is significant in comprehending mechanism of trap and improving optical tweezers model. From theoretical analyses, we can improve the performance of optical tweezers, which is very important in application. When the particle is reduced to nano-size, optical trap can hardly hold it. Manipulating nanoparticle is not only a challenge for optical tweezers but also has important applications in nanorheoloy, nano-assembling, colloid and surface-enhanced Raman scattering.
In this thesis, we applied a vectorial ray-tracing method in ray-optics (RO) model and combined the vectorial diffraction (VD) and moment of method (MOM) in electromagnetic (EM) model for calculating forces. Using VD theory, we analyzed the relations between the radiation forces on nanoparticles and parameters of optical trap. Under the theoretical guidance, we explored experimentally manipulating nanoparticles in three dimensions. Meanwhile, we demonstrated that the stiffness of nanoparticles can be calibrated by a method using autocorrelation function (ACF) for system with low signal-noise ratio.
With our presented vectorial ray-tracing method, the analysis of optical forces in three dimensions are unified, it simplifies the calculation in RO model. The ray-tracing is implemented by spatial vectors and rotation matrixes. It is appropriate to calculate optical forces from focused polarized beam, and avoids the defects in traditional RO model. Based on vectorial ray-tracing and rotating coordinate system, the forces of arbitrary shape particle can be calculated in the case of sphere aberration in a glass-water interface. The optical forces, tensor and torque of spheroid particles have been simulated. For a rod particle, the axial optical force decreases little with trap depth increasing. The irregular particle in an optical trap will adjust itself to align its long axis parallel to optical axis. The vectorial ray-tracing extends traditional RO model in applications.
Our EM model of VDMOM is divided into three parts of calculation:field distribution of focused beam, total field after electromagnetic scattering and radiation forces. When some parameters, such as beam profile and objective numerical aperture (NA), are changed, this model avoids repetitive calculation of matrix elements, which originates from characteristics of particle. Our simulation results demonstrated that an optical trap can't hold a micro-sized particle with high refractive index in the axial direction. When particle size is reduced to nano-size, the trap can hold nanoparticle stably. With Rayleigh approximation, we have investigated the relation between radiation forces on nanoparticles and parameters of the optical trap. To obtain maximum force, the parameters should be selected at short wavelength, high NA, optimal beam profile. This simulation results will help us to manipulating nanoparticles in three dimensions in the following experiments.
To observe nanoparticles in a conventional microscope and manipulate them, we presented a dark-field-illumination optical tweezers, in which the direction of a lateral illumination laser was perpendicular to the optical axis of the microscope. The manipulation of nanoparticles can be monitored in wide field, real time and long time. Due to the mutual constraint of trap depth between observation and optical trap, the mismatch tube length was introduced to compensate the spherical aberration in the glass-water interface. This method enhanced the trapping forces at a large depth, and facilitated us to clearly observe the manipulation process of 70-nm particle in three dimensions.
Since the trapping forces are weak, the trapped nanoparticle will be affected by circumstance noises. To decrease this influence, we presented ACF for the calibration of stiffness. For testing its validity, we compared the differences between power spectrum method and ACF in the cases of filter and introduced noises, and detailed the reasons on their differences. Calibrating stiffness is very important in applications. How to calibrate stiffness in situ and in real time not only simplifies the process of experiments but also help us to accurately measure the temporary information on force.
In this thesis, the RO and EM models have been investigated systematically. Calculating optical forces in the miro-/nano-scale has been detailed. The researches on theoretical methods are the foundations of understanding the particle's behaviors in an optical trap and designing our experiments. In our experiments, the nanoparticles have been manipulated in three dimensions, and this process can be observed in wide field. The calibrating stiffness of ACF was analyzed in detail. Those researches will extend the applications of optical tweezers in nanotechnology field.
在各种应用中,最常用光镊的方式为基于高数值孔径物镜的单光束梯度力阱,实现远场操纵微粒。为了更好的理解和运用光镊技术,理论研究光阱对微粒的俘获机理和光阱参数对光阱力的影响,对于完善光镊理论模型,提升现有光镊性能并付诸于实际应用具有重要的意义。当微粒尺度小到纳米尺度,光阱难以束缚它。光镊操纵纳米颗粒不仅是对光镊设备性能的挑战,而且在纳米流变学、纳米组装、胶体体系和表面增强拉曼散射信号上有着重要应用。
本论文主要研究了矢量光线追迹的RO模型和矢量衍射-矩量法的EM模型,利用矢量衍射理论,分析了在光阱中纳米颗粒的辐射力与光镊参数的关系,并从实验上探索三维操纵纳米颗粒。在低信噪比情形下,我们研究了自相关函数标定颗粒的光阱刚度,它适用于标定纳米颗粒的光阱刚度。
关于RO模型的理论研究中,本论文应用矢量光线追迹方法,统一分析三维方向上光阱力,简化了RO模型的计算。结合空间矢量和矩阵的计算方法,它能有效地分析偏振光束对颗粒的光阱力,弥补传统RO模型的不足。在此基础上,我们分析了玻璃-水界面球差引起的矢量光线追迹,利用坐标旋转的方法,实现对任意形状颗粒的光阱力及应力张量和力矩的计算。对于长杆状颗粒,球差并不随俘获深度增大时降低光阱对它的轴向俘获力,不规则颗粒在光阱作用的力矩下,自动调整到颗粒长轴与光轴平行的方位,这一方法拓展了传统RO模型的适应范围。
有关光镊的EM模型的理论研究中,本论文提出了矢量衍射-矩量法的EM模型。这一模型分成聚焦光束的场分布、电磁散射后总场的分布和计算辐射力三个独立的部分。这一模型在改变参数时,能减少计算工作量,例如改变入射激光光束截面和物镜数值孔径等参数,无需计算反映微粒特性的矩阵元。通过模拟计算,得出在光阱中无法稳定俘获较大尺度的高折射率颗粒的结论。基于这一理论计算平台中,通过Rayleigh近似我们直接计算了纳米颗粒的辐射力,并研究纳米颗粒的辐射力与各参数的关系,得出在短波长、高数值孔径物镜和最佳光束分布时光阱俘获纳米颗粒的力最大。通过这些理论模拟,为我们三维操纵纳米颗粒的实验提供理论依据。
根据前述辐射力的理论分析,本论文提出暗场照明光镊,实现实时观察三维主动操纵纳米颗粒。根据观察的需要,我们采用横向激光暗场照明,实现宽视场、实时和长时间观察纳米颗粒,并动态观察三维操纵纳米颗粒过程。由于观察和操纵纳米颗粒在俘获深度的相互限制,我们引入机械筒长失配的球差补偿,在较大俘获深度上的增强光阱力,实现在光学显微镜下清晰观察三维操纵直径70nm的颗粒。
由于纳米颗粒的光阱力很弱,容易受到外界噪声的影响,它的刚度测量上需要尽可能降低这方面的影响。我们研究了自相关函数测量纳米颗粒的光阱刚度,作为方法的验证,在滤波和引入外界噪声等方面比较了功率谱法和自相关函数标定刚度的差异,具体分析了导致差异的原因。刚度标定的方法在光镊应用中非常重要,如何实现原位和实时标定刚度,不仅能简化实验过程,还能准确反映测量中瞬时的力学信息。
本论文从理论上较系统地研究RO模型和EM模型,建立一套在微／纳米尺度上计算光阱力的方法。理论方法的建立有助于我们更好地理解微粒在光阱中的行为,指导实验设计和分析实验中遇到的问题。实验研究中我们提出暗场照明光镊并实现纳米粒子的俘获,分析了自相关函数标定刚度与实验各因素的关系。这些研究将拓展光镊应用于纳米领域。
Manipulation of particle on the micro/nano scale conveys the information of mechanical characteristics of signal molecules, such as researches on DNA elasticity, protein folding etc. The manipulation also facilitates the investigations of hydrodynamic interaction at the single particle level and assembling micro/nano machine. Among many technologies of manipulation, optical tweezers as a non-contact trap way have unique advantages:nanometer resolution on displacement and femtonewton resolution on force. This technology is widely applied in single molecules, colloid and nanotechnology fields.
In various applications, optical tweezers, a single-beam gradient force trap, are based on a high numerical aperture objective and used to manipulate particle in far field. To apply optical tweezers better, theoretical investigation between parameters and forces is significant in comprehending mechanism of trap and improving optical tweezers model. From theoretical analyses, we can improve the performance of optical tweezers, which is very important in application. When the particle is reduced to nano-size, optical trap can hardly hold it. Manipulating nanoparticle is not only a challenge for optical tweezers but also has important applications in nanorheoloy, nano-assembling, colloid and surface-enhanced Raman scattering.
In this thesis, we applied a vectorial ray-tracing method in ray-optics (RO) model and combined the vectorial diffraction (VD) and moment of method (MOM) in electromagnetic (EM) model for calculating forces. Using VD theory, we analyzed the relations between the radiation forces on nanoparticles and parameters of optical trap. Under the theoretical guidance, we explored experimentally manipulating nanoparticles in three dimensions. Meanwhile, we demonstrated that the stiffness of nanoparticles can be calibrated by a method using autocorrelation function (ACF) for system with low signal-noise ratio.
With our presented vectorial ray-tracing method, the analysis of optical forces in three dimensions are unified, it simplifies the calculation in RO model. The ray-tracing is implemented by spatial vectors and rotation matrixes. It is appropriate to calculate optical forces from focused polarized beam, and avoids the defects in traditional RO model. Based on vectorial ray-tracing and rotating coordinate system, the forces of arbitrary shape particle can be calculated in the case of sphere aberration in a glass-water interface. The optical forces, tensor and torque of spheroid particles have been simulated. For a rod particle, the axial optical force decreases little with trap depth increasing. The irregular particle in an optical trap will adjust itself to align its long axis parallel to optical axis. The vectorial ray-tracing extends traditional RO model in applications.
Our EM model of VDMOM is divided into three parts of calculation:field distribution of focused beam, total field after electromagnetic scattering and radiation forces. When some parameters, such as beam profile and objective numerical aperture (NA), are changed, this model avoids repetitive calculation of matrix elements, which originates from characteristics of particle. Our simulation results demonstrated that an optical trap can't hold a micro-sized particle with high refractive index in the axial direction. When particle size is reduced to nano-size, the trap can hold nanoparticle stably. With Rayleigh approximation, we have investigated the relation between radiation forces on nanoparticles and parameters of the optical trap. To obtain maximum force, the parameters should be selected at short wavelength, high NA, optimal beam profile. This simulation results will help us to manipulating nanoparticles in three dimensions in the following experiments.
To observe nanoparticles in a conventional microscope and manipulate them, we presented a dark-field-illumination optical tweezers, in which the direction of a lateral illumination laser was perpendicular to the optical axis of the microscope. The manipulation of nanoparticles can be monitored in wide field, real time and long time. Due to the mutual constraint of trap depth between observation and optical trap, the mismatch tube length was introduced to compensate the spherical aberration in the glass-water interface. This method enhanced the trapping forces at a large depth, and facilitated us to clearly observe the manipulation process of 70-nm particle in three dimensions.
Since the trapping forces are weak, the trapped nanoparticle will be affected by circumstance noises. To decrease this influence, we presented ACF for the calibration of stiffness. For testing its validity, we compared the differences between power spectrum method and ACF in the cases of filter and introduced noises, and detailed the reasons on their differences. Calibrating stiffness is very important in applications. How to calibrate stiffness in situ and in real time not only simplifies the process of experiments but also help us to accurately measure the temporary information on force.
In this thesis, the RO and EM models have been investigated systematically. Calculating optical forces in the miro-/nano-scale has been detailed. The researches on theoretical methods are the foundations of understanding the particle's behaviors in an optical trap and designing our experiments. In our experiments, the nanoparticles have been manipulated in three dimensions, and this process can be observed in wide field. The calibrating stiffness of ACF was analyzed in detail. Those researches will extend the applications of optical tweezers in nanotechnology field.
引文
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