Theoretical Model Of Optical Tweezers And Manipulation Of Nanoparticles

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.