Due to the existence of the quantum effect, the characteristics of nanostructure is difficult to explain entirely based on classical mechanics method. With the development of the FDTD method, its application in the field of optics is becoming increasingly widespread. In this paper, based on finite difference time domain (FDTD) method to study the nonlocal optical properties of two-dimensional structures was applied directly. The existence conditions of local and nonlocal optical characteristics under different nanometer radius, the impact of structural shapes with their extinction cross section properties were also obtained. The numerical results clearly show that with the decrease of the nanometer structure size and the shape of the structure, the non-locality becomes more pronounced. Our theory and results can provide a reference for the practical design of new nanoscale devices.
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