The Analytical Solution Of Electromagnetic Scattering By A Buried Isotropic Medium Sphere

The study of buried target electromagnetic scattering problems has important implications for tunnels,pipelines,mine burial,soil stratification,subsurface monuments,geophysical exploration and skin tumor detection.A simple and efficient analytical solution for solving the electromagnetic scattering characteristics of subsurface isotropic sphere is obtained in this paper.The three-dimensional vector wave function addition theorem is mainly used to derive the scattering expression of the subsurface target,and the recursive algorithm is used to solve the coordinate transformation coefficient in the addition theorem.Firstly,according to the propagation characteristics of uniform plane wave in unbounded space and the vertical incidence of uniform plane wave on the interface of conductive medium,the reflected wave and transmitted wave of the medium plane are obtained.The boundary condition of the medium boundary plane is used to solve the reflection and transmission coefficient of the medium plane;The transmitted wave of the medium plane acts as the incident wave of the isotropic medium sphere,and the transmitted wave of the medium plane is developed according to the analytic formula of the product of the eigenvector and the plane wave factor,and then the boundary wave condition of the medium sphere is used to solve coefficient matrix of the transmission and reflection wave of the medium sphere;The reflected wave of the medium sphere will be incident perpendicularly as the incident wave of the medium plane.Since the original charge is the medium sphere,the reflected wave and the transmitted wave of the medium plane are solved by he image method and the additive theorem,and the recursive algorithm is used to solve coordinate system transform coefficient of the additive theorem;The reflected wave of the medium plane will again act as the incident wave of the dielectric sphere,and the cycle repeats until it converges.Numerical results between this paper and the software Feko are given and they are agreement very well as we expected.It has great advantages in calculation time.Some numerical results with the permittivity,wave frequency,the radius of the buried sphere and the depth of the buried are given in the end of this paper.