Applications Of Green Function-Complex Conjugate Gradient Method-Fast Fourier Transform In Near-field Optics Images

Photon Scanning Tunneling Microscope (PSTM) is one kind of Scanning ProbeMicroscope (SPM), which obtains nanometer scale super-resolution images , exceeds thediffraction limits of conventional optical microscope, by using a optical-fiber tip probingultra-high frequency optical information consist in evanescent wave. There are many factorsinfluencing the images so it is necessary to study the rules of near-field imaging based onnear-field optical theory. In this paper, we use Green function to study the near-field imaging,which describes availably the interactions between light field and objects. We can obtain theelectrical field distribution by dispersing the Lippmann-Schwinger integral equation, avoiddealing with boundary conditions compared with differential equations, because boundaryconditions are contained in integral equation, so it diminishes the error with the unperfectboundary conditions. But the traditional numerical method uses mainly matrix inverse thusMethod of Moment (MOM), which is not apt to solve the big size and multiple scatteringsbecause of the matrices storage and the product between the matrices and vectors are～ N~2, ～ N~3 respectively. We apply Complex-Conjugate Gradient Method (CCGM) and FastFourier Transform (FFT) to solve the Lippmann-Schwinger integral equation, CCGM reducesmemory storage and FFT reduces CPU computing to accelerate matrix multiply vector ineach iterative procedure. So the matrices storage and the product between the matrices andvectors reduce from ～ N~2 and ～N~3 to ～ N and ～ N log N, thus we can calculate bigsize and multiple scattering.In this paper, we apply CCGM-FFT to study some samples imaging in near-field, including dielectric and metal, explain the meaning of imaging, we conclude that the imaging is a intricate near-field intervene, we also find out that the metallic imaging exhibit the electrical field enhancement and the distribution of electrical field attenuate quickly with the distance increasing between sample and detection position because of the roles of electrical field is along the Z axis- evanescent wave, which accords with the surface plasmon polaritons exists several nanometer bound in sample surface.