| The engineering application of frequency selective surfaces (FSS) is broad. Up to now, most of the researches on the FSS still assumed that the FSS is planar and infinite-period array. But in practical applications, FSS arrays are usually finite structures, and sometimes are curved, even with dielectrics loaded. So the electromagnetic analysis on FSS with finite size and dielectric is valuable.In the background of mentioned Engineering applications, this article present a hybrid volume-surface integral-equation(VSIE) combined with moment method (MOM) to analyze the transmission and reflection characteristics of curved and finite FSS structures which have dielectric substrate. The hybrid integral equations approach has two advantages. One is the capability of modeling arbitrarily shaped FSS structures in detail, the other one allows us to easily apply the multilevel fast multipole algorithm (MLFMA) to analyze electrically large structures and speed up the solution speed.Firstly, this article also analysis the basic principles of VSIE and gives its formula. We use the method of VSIE to analysis the scattering of complex structure mixed with dielectrics and metal, including the curved and finite FSS structures, which FSS has dielectric substrate. This article also describes how to analysis the transmission and reflection characteristics of finite FSS, and gives the formula of transmission and reflection coefficient. The method of VSIE combined with MLFMA is used to analysis the curved and finite FSS structures loaded with dielectric substrate, these FSS are the arrays of Square-loop and Cross, then the transmission characteristics can be got from them. In the analysis, the normal incidence and oblique incidence of plane-wave are also considered in it. Then we analysis the transmission and reflection coefficient and compare them with some results got from simulating infinite-period array in a software, it can be seen that the results show a good characteristics of frequency-selective. |
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