| As the extensive applications of the laser beam, laser technology has been developed rapidly for its superior performance, and plays a much more crucial role in the current scientific and technological research. To take full advantage of laser technology, the key is to manipulate the optical field. The vector fields with manipulated state of polarization (SoP) are attracting more and more interests in investigating various optical-diffraction-related problems and exploring new effects of full vector optical fields which can benefit different applications. The space-variant SoP of vector field makes a great impact on the spatio-temporal evolution as well as the interaction of light with matter, which may lead to many novel phenomena and effects. These special effects make the vector fields be very potentially applicable to a variety of fields, such as biomedical science, high resolution imaging, laser acceleration, micro-fabrication, and optical manipulation. This thesis focuses on studies of vector beams and their applications to optical tweezers. First I reviewed the background of vector beams and their application. Then, I discussed the methods of generation of vector beams and present a proposal for realizing the radial split of spin angular momentum flux density in the focus of vector beams. Finally, I proposed a new vector non-diffraction beam that has character of abruptly autofocusing.Different methods to generate vector beams with spatially structured polarization and phase distribution have been theoretically proposed and experimentally demonstrated, especially including the liquid crystal spatial light modulators which allows to flexibly design the arbitrary spatial (phase or amplitude or both) modulation patterns to generate the desired optical modes. We proposed a convenient approach for generating space-variant vector beam with structured polarization and phase distribution in a 4f system with a spatial light modulator. By replacing one-dimensional holographic gratings with two-dimensional ones, we could realize the multiple-degree-of-freedom modulation of vector beam. By tailoring the modulation depth of holographic gratings, we obtained the arbitrary vector beams with space-variant shapes of amplitude, phase and polarization, all of which are modulated independently and simultaneously.The optical manipulation technology attracts more and more widespread attention. The optical tweezers provides an ideal tool for optical manipulation, and the capability of optical tweezers depends on the focus shaping. Because the vectorial property of optical field plays a key role in the focusing, vector beams are promising for optical manipulation. Our studies showed that the vector vortex beam could yield radial split of spin angular momentums under the condition of tight focusing. We experimentally demonstrated the rotation of liquid crystal particles trapped with vector vortex beam, which is in agreement with the theoretical prediction.Non-diffraction beams, a special type of light beams, share the property that their cross-sectional intensity distributions remain unchanged when they propagate in the free space. Combining the principle of generating Airy beam through a 3/2 radial phase-only pattern and the scheme of generating vector beam in a 4f system, we create a new type of abruptly autofocusing vector vortex beams, which have the characteristic of radial split of the spin angular momentum flux density during autofocusing as well. |