scholarly journals Dyadic Green’s Function and the Application of Two-Layer Model

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1688
Author(s):  
Gendai Gu ◽  
Jieyu Shi ◽  
Jinghua Zhang ◽  
Meiling Zhao
Keyword(s):  
Green’S Function ◽  
Electric Fields ◽  
Green's Function ◽  
Dipole Source ◽  
Layer Model ◽  
Field Problem ◽  
Dyadic Green’S Function ◽  
Electromagnetic Problems ◽  
Dyadic Green's Function ◽  
Two Layer Model

Dyadic Green’s function (DGF) is a powerful and elegant way of solving electromagnetic problems in the multilayered media. In this paper, we introduce the electric and magnetic DGFs in free space, respectively. Furthermore, the symmetry of different kinds of DGFs is proved. This paper focuses on the application of DGF in a two-layer model. By introducing the universal form of the vector wave functions in space rectangular, cylindrical and spherical coordinates, the corresponding DGFs are obtained. We derive the concise and explicit formulas for the electric fields represented by a vertical electric dipole source. It is expected that the proposed DGF can be extended to some more electric field problem in the two-layer model.

scholarly journals Dyadic Green’s Function for Multilayered Planar, Cylindrical, and Spherical Structures with Impedance Boundary Condition

2021 ◽  
Author(s):  
Shiva Hayati Raad ◽  
Zahra Atlasbaf
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Biomedical Application ◽  
Spherical Geometry ◽  
Impedance Boundary Condition ◽  
Purcell Factor ◽  
Dyadic Green’S Function ◽  
Electromagnetic Problems ◽  
Anisotropic Surface ◽  
Dyadic Green's Function

The integral equation (IE) method is one of the efficient approaches for solving electromagnetic problems, where dyadic Green’s function (DGF) plays an important role as the Kernel of the integrals. In general, a layered medium with planar, cylindrical, or spherical geometry can be used to model different biomedical media such as human skin, body, or head. Therefore, in this chapter, different approaches for the derivation of Green’s function for these structures will be introduced. Due to the recent great interest in two-dimensional (2D) materials, the chapter will also discuss the generalization of the technique to the same structures with interfaces made of isotropic and anisotropic surface impedances. To this end, general formulas for the dyadic Green’s function of the aforementioned structures are extracted based on the scattering superposition method by considering field and source points in the arbitrary locations. Apparently, by setting the surface conductivity of the interfaces equal to zero, the formulations will turn into the associated problem with dielectric boundaries. This section will also aid in the design of various biomedical devices such as sensors, cloaks, and spectrometers, with improved functionality. Finally, the Purcell factor of a dipole emitter in the presence of the layered structures will be discussed as another biomedical application of the formulation.

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