The Analytical Solution Of Electromagnetic Scattering By A Buried Conducting Sphere

In recent years,with the application of electromagnetic theory in-depth study of all aspects of social life,the study of electromagnetic scattering from objects buried under a complex half-space medium has been a complex and practical subject,such as the buried target detection,pipeline and mine detection,mineral exploration,geophysical exploration,remote sensing,the discovery of skin tumors are of great significance.The analytical solution of electromagnetic scattering from a buried conducting sphere is obtained in this paper.First of all,there are reflected wave and transmitted wave on the boundary of the ground from the incident of homogeneous plane wave is perpendicular to the ground and the reflection coefficient and the transmission coefficient are calculated according to the interface conditions;Using the analysis of product of eigenvectors and plane wave factor,the electric and magnetic field expressions of transmitted waves can expand into the isotropic spherical vector wave function as the incident wave of conducting sphere;The scattering wave of conducting sphere is obtained by the boundary conditions on the surface of the conducting sphere;The scattering wave of conducting sphere can be as the incident wave to reflect and transmit at the interface and then the reflecting wave can be as the incident wave of the conducting sphere and so on.In this cycle process,deriving the specific expression of the electromagnetic scattering from the three-dimensional conducting sphere which of using a series of electromagnetic field theory including the relationship between spherical coordinate system and Cartesian coordinate system,the boundary condition of electromagnetic field,the expression of special function such as spheric Bessel function and associated Legendre function,the expression of spherical vector wave function and the addition theorem.The addition theorem of spherical vector wave function is used,in which the Guant coefficient is related to the addition theorem of spherical wave function,namely Bessel functions,Lengendre functions and trigonometric functions.A recursive method is used to compute the vector addition theorem coefficient of wave function.The calculation which of the electromagnetic scattering characteristics of buried conducting sphere under different frequencies,different buried depths and different conducting sphere radius and the numerical results are analyzed and discussed.