| Periodic structure (PS) has been used in many applications such as slow wave structure (SWS) and frequency selective surface. SWS is the key part of the RBWO and RTWT, whose characteristic could determine the speciality of RBWO and RTWT. The dispersive characteristic of SWS is a very important parameter of the RBWO and RTWT, other parameters such as the phase velocity, group velocity, coupling impedance can be derived from the linear dispersion relation. Recently, the Photonic crystal have attracted many attentions of the scientists, which has become a hot point of the research, it is also a PS. So it is important and necessary to analyze the dispersive characteristic of the PS quickly and accurately.In this paper, a method based on finite-difference time-domain(FDTD) arithmetic is used to analyze the dispersive characteristic of PS. With the application of the periodic boundary condition (PBC), the computing domain can be restricted to a single period, which greatly improve the computing efficiency and accuracy. This method can be used to analyze the dispersive characteristic of arbitrary mode SWS with arbitrary boundary in theory. Considering the photonic crystal is also a periodic structure, this method can be also extended to analyze the band structure of photonic crystal.In the first part of the paper, the explicit form of difference equation and periodic boundary condition is derived in Cartesian coordinate system. Secondly, the dispersive characteristic is analyzed in Cylinder coordinate system for many high power microwave devices use cylinder SWS. And then the method is extended to calculate the band structure of 2-D photonic crystal, a modified Yee's grid is introduced to calculate the dispersive characteristic in the case of triangular lattice, so that both square lattice and triangular lattice cases can be solved in Cartesian coordinate system. At last, a 31 GHz narrow band filter is designed as an application of the photonic crystal. |
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