| The optical properties of metallic nanoparticles and their application in surface enhanced Raman scattering (SERS) have been a hot topic in nanoscience and nanotechnology. The main focus of this thesis is to surpass the limitation of Mie theory, whose application is rigorously limited to spherical particles, in order to theoretically study the quantitative dependence of the linear optical properties and electromagnetic (EM) enhancement mechanism of SERS on the size, shape, surrounding medium of metal nanoparticles with arbitrary shape.The thesis is divided into four chapters. In the first chapter, the aims and main tasks of this work was presented after reviewing theoretical methods for studying optical properties of metal nanoparticles, and main advantages, characteristics and recent progress of SERS. In chapter two, after a brief introduction to Mie and Gans theory, particular attention is devoted to the numerical method of discrete dipole approximation (DDA) that is capable of dealing with the interaction of light with nanoparticles with any arbitrary shape. Then, we simulated quantitatively the extinction spectra of gold and silver nanoparticles with various sizes, shapes, and environment media based on DDA calculations, which were compared with the experimental results. In chapter three, the EM mechanism of SERS was studied qualitatively and semi-quantitatively based on some simple physical models with the focus on the theoretical explanation of the EM mechanism for transition metal systems in the visible to UV light region. In chapter four, more detailed calculation of the EM field enhancement were made for a variety of complex systems based on the three dimensional finite difference time domain (3D-FDTD) method, with consideration of the size, shape, medium environment and interparticle-coupling effect. The"hot spot"with huge SERS activity of nanoparticles that is of increasing interest in single molecular SERS is also discussed.The main progresses of this work are listed as follows: (1) More quantitative and accurate calculation on optical properties of gold and silver nanoparticles were performed. The DDA calculation results show a better agreement with the experimental results in comparison with traditional Mie or Gans method. The empirical formula for the size, aspect ratio and the environment medium dependence of extinction spectra of gold and silver nanoparticles with various size and shape were obtained and discussed. (2) The electromagnetic enhancement mechanisms of SERS for transition metal systems are analyzed systematically for the first time through analytical solution of Maxwell equations based on the electromagnetic theory. The importance of surface roughness in SERS-active transition-metal substrates was theoretically demonstrated. The influence of surface plasmon resonance (SPR) and lightning rod effect on SERS of different metal systems were studied in detail. On the basis of the calculation result, it was pointed out for the first time that the lightning rod effect may play a key role in the transition-metal systems. A preliminary theoretical explanation was given to the SERS mechanism of Rh in the ultraviolet light region. (3) 3D-FDTD method was developed to simulate the near field distribution and calculate the electromagnetic enhancement of transition-metal nanoparticles (e.g., rhodium, nickel, and platinum) with various shapes and aggregate forms under laser illumination for the first time. Through taking the interparticles coupling effect into consideration, special attention has paid to the enhancement factor in the SERS"hot spot"of silver and gold nanoparticles. It has been shown that 3D-FDTD method is a very powerful tool to investigate the SERS mechanism of transition-metal systems. It will be beneficial to further understand the complex mechanism of SERS, as well as to guide the optimization of the SERS experimental setup to achieve the strongest SERS activity for the coinage and transition metals.
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