The Time-domain Methods For Numerical Electromagnetic Calculations Of Near-field Optics

As a new type of optical instrument, the scanning near-field optical microscope (SNOM)employs an optical-fiber tip to collect the evanescent wave existing in immediate proximity tothe surface of the observed sample, and obtains the image with the sub-wavelength spatialresolution far beyond the diffraction limit. SNOM that is used to observe appearance orinvestigate immanent essence of sub-wavelength objects, has played an important role invarious ranges, such as physics, chemistry, biology, medical science, geology and so on.Since firstly presented by K. S. Yee in 1966, the Finite Difference Time Domain (FDTD)method, characterized by simplification and directness, has been applied extensively invarious electromagnetic space. Now FDTD is the main method of the numerical simulation innear-field optics. In 1996, Krumpholz and Katechi first introduced the multi resolution timedomain scheme (MRTD). Compared with FDTD, MRTD has great potential and can savecomputer resources.This article has studied the theory of FDTD and MRTD, improvement of the algorithm,and the application in the numericalelectromagnetic calculations of near-field optics. In theFDTD algorithm, the performance of the absorbing boundary condition is critical to theaccuracy of numerical simulations. In this article, several commonly used ABCs, such asMur's ABC, Liao's ABC, PML, are discussed, and several improvements of the boundarycondition at the interface have been made.MRTD is a new time domain method of numerical electromagnetic calculations. In thisarticle the MRTD method is applied to the computation of near-field optics. Compared withthe FDTD result and the experimental data, MRTD is approved to be an effective method.MRTD will be a new method for the numerical electromagnetic calculations of near-fieldoptics.