Vector Singular Beams’Properties Of Propagation,Tightly Focusing And Its Applications

In this thesis, we focus on investigating the properties of propagation, tightly focusing of vector singular beams and their applications in some fields. Through the rigorous analysis of vector Electromagnetic theory and by the support of numerical simulation with high accuracy, we demonstrate systemically the properties of vector singular beams’amplitude and polarization, certify that vector singular beams with high-order polarization topological charge are one of vector beam solutions of Helmholtz equation. In addition, we investigate the feasibility of their applications in Micro-Nano optics.We obtain some achievements as follows:1. We proved, for the first time, that vector singular beams with high-order polarization topological charge are one of vector beam solutions of Helmholtz equation. By the rigorous analysis of vector theory, we find that, the vector singular beams with high-order polarization topological charge have a amplitude with Bessel-Gaussian distribution. In addition, the well-known radially and azimuthally polarized beams are the vector Bessel-Gaussian beams with1-order topological charge. This result provides the theoretical fundament for their applications in surface plasmatic optics and micro-nano optics. The Bessel-Gaussian beams with vector singular enrich the vector-beam family.2. We suggest that the Fresnel diffraction can be used to describe the polarization and intensity profiles of the vector beams when they propagate in a medium with an obstruction. The Fresnel diffraction is the easiest way to describe the vector paraxial beams’ propagation, especially for the obstruction with irregular pattern. This method gives the reliable proof for the lab assistants who investigate the vector singular beams experimentally.3. We find the quantitative parameter Ro that determinates the focusing properties of radially polarized beam, for the first time. With the help of the parameter, we simplify and improve the design of diffraction optical elements (DOE) with multi-belt phase for the purpose of realizing the strong longitudinally polarized "Needle" in the focal region. We correct some mistakes that are made by others in design this kind of DOE. In addition, in order to realize the longitudinally polarized field, we also suggest a new DOE with continuous transmission of complex amplitude.4. We introduce the azimuthally polarized beam with helical phase (APH) into the solid immersion lens (SIL)-based optical systems, for the first time. In the APH illumination, we solve the problems of the discrete intensity distribution at the interface of two media and the enlargement of focused spot with the increment of refractive index of measured sample. In contrast with other vector beams, the APH beam has the smaller focused spot in free space or in a stratified focal region, which opens a new door to improve the performance of the optical device by introducing a source with novel polarization and phase.5. In some applications of DOE, for an optical system with Fourier lens whosite targeted plane is located in out-of-focus plane, we suggest an equivalent system without the lens for simplify the original system. We utilize this optical system to realize the spectral splitting and shaping in the concentrator for solar system and investigate the feasibility of our idea.