手性介质中斜入射电磁波散射问题的积分方程法

The integral equation method for the scattering problem of obliquely incident electromagnetic waves in a chiral medium

考虑均匀手性介质中无限长阻抗柱体斜入射电磁散射问题。在某些假设下,该散射问题可以表示为电场和磁场z分量的具有广义斜导数边界条件的二阶椭圆方程组。通过场量分解部分解耦以及位势理论,将该散射问题转化为两个积分方程组。与电磁波垂直入射情形不同,该积分方程组不是通常的第二类Fredholm算子方程形式,因为该方程组中含有单层势的切向导数。说明了该算子是指标为0的Fredholm算子。利用Fredholm理论,证明了边界积分方程解的存在唯一性,并给出了一种求解该积分方程的数值方法。

The scattering of an obliquely incident electromagnetic wave by an infinite impedance cylinder which is embedded in a homogeneous chiral medium is considered.Under certain assumptions,the scattering problem can be formulated as a second order elliptic system with generalized oblique derivative boundary conditions for the z components of the electric and magnetic fields.By partly reducing the coupling via a decomposition method and potential theory,the oblique scattering problem is transformed to a system of two integral equations.It is not a usual Fredholm system of the second kind as that in the case of normal incidence,since the system involves the tangential derivatives of the single-layer potential.It is shown that this system of operators is of Fredholm type with index 0.By using the Fredholm theory,the uniqueness and the existence of solutions for the boundary integral equations are justified.A numerical scheme for solving the integral equations is also presented.