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Discretization of the Lippmann–Schwinger integral equation with complex conjugate gradient method and fast Fourier transform (CCGM-FFT) is solved, which can reduce the memory storage and the CPU time compared with the traditional method, MOM. Thus objects with large size and multiple scattering objects could be simulated with CCGM-FFT. The total intensity and the distribution of each field component of the dielectric and metallic objects under the excitation of the TE/TM-polarized wave are calculated with photon scanning tunnelling microscopy (PSTM) at the constant height. The simulating results are analysed and explained reasonably. The results show that the polarization plays an important role for imaging of PSTM.

Optical properties of plasmon resonance with Ag/SiO2/Ag multi-layer nanoparticles are studied by numerical simulation based on Green's function theory. The results show that compared with single-layer Ag nanoparticles, the multi-layer nanoparticles exhibit several distinctive optical properties, e.g. with increasing the numbers of the multi-layer nanoparticles, the scattering efficiency red shifts, and the intensity of scattering enhances accordingly. It is interesting to find out that slicing an Ag-layer into multi-layers leads to stronger scattering intensity and more "hot spots" or regions of stronger field enhancement. This property of plasmon resonance of surface Raman scattering has greatly broadened the application scope of Raman spectroscopy. The study of metal surface plasmon resonance characteristics is critical to the further understanding of surface enhanced Raman scattering as well as its applications.

Optical properties of silver nanoparticles such as extinction, absorption and scattering efficiencies are studied based on Green's function theory. The numerical simulation results show that optical properties of silver nanoparticles are mainly dependent on their sizes and geometries; the localized plasmon resonance peak is red shifted when the dielectric constant of the particle's surrounding medium increases or when a substrate is presented. The influences of wave polarizations, the incident angles of light, the composite silver and multiply-layers on the plasmon resonance are also reported. The numerical simulation of optical spectra is a very useful tool for nanoparticle growth and characterization.