Boundary Element Method And Multiple Scattering Method For Electromagnetic Properties Of Finite And Periodic Structures

The scattering property of ununiform materials is always one of mostly important problems.Studying property of the ununiform materials which have the dimension near the wavelength and designing the structure of special functions is a hot topic,with the concept of photonic crystal(PC)being advanced and the applications of PC being studied.In this paper,we will use boundary element method(BEM)to study the scattering property of electromagnetic.We choose H_z,E_z,((?)H_z¹)/((?)n),((?)H_z²)/((?)n),((?)E_z¹)/((?)n),((?)E_z²)/((?)n)as the variables, then we found an arithmetic within the boundary integral equation and the boundary condition.We use this arithmetic and KKR method to study the scattering property of finite/infinite structures.The scattering property of finite structure:We calculate the scattering matrixes of cylinder and hexagonal pole.The result shows that the error is less than one percent when the step is less thanλ/(10)k/((k²-k_z²)^1/2for cylinder andλ/(80)k/((k²-k_z²)^1/2for the step near the corner of hexagonal pole when boundary of the hexagonal pole is firstly dispersed byλ/(10)k/((k²-k_z²)^1/2.The scattering property of infinite structure:We study the influence of the parameter truncated.We get approximately formulas that H≈(70ρ)/λ,ρ-the radius of cylinder,H=2N+1 and S≥(5α)/λ,α-the period of photonic crystal when we truncate Bessel function ranks as[-N,N]and plane wave numbers as[-S,S].We get energy bandgaps of dielectric and metal 2D square lattices.They agree with the references very well.The results show that BEM is more convergent and available for studying the property of finite and infinite structures.