A High-accuracy Metasurface Simulation Algorithm Based On Generalized Sheet Transition Conditions

Metasurfaces are subwavelength artificial thin layer metamaterials,which have 2D functional planar structures composed of many nano-scattering particle arrays.Compared with other metamaterials,metasurfaces have the advantages of low dissipation,light weight,ease of manufacture,and the ability to arbitrarily adjust the phase,amplitude,and polarization of light waves.It can perform such complex and practical transformations due to its characteristic of simultaneously stimulating the discontinuity in the electric fields and magnetic fields when the propagating electromagnetic wave passing through it.This discontinuity is different from the single physical quantity discontinuity(only the electric or only the magnetic discontinuity),which is usually represented by the traditional transition conditions(TCs).So the TCs is unsuitable for numerical simulations of metasurfaces now.Fortunately,the generalized sheet transition conditions(GSTCs),involving the discontinuity of electric and magnetic fields,can compatibly describe the characteristics of metasurfaces.However,directly modeling and computing the subwavelength-thickness metasurface would cause the multiscale structures of the electrically small thickness and the electrically large scale of computational domain,resulting in a huge amount of calculation,which challenges to the computer’s memory and CPU time.An effective method,combining spectral element method(SEM)and GSTCs,is hence proposed in our study to replace the metasurface by a thin sheet with zero thickness,which avoids the huge mesh numbers generated by discretizing the metasurface directly,thus saving computer resources.In our method,the SEM is employed to solve the vectorial Helmholtz equation.In this process,the transversal and the longitudinal field is expanded by the mixed-order vector basis functions and completely continuous scalar basis functions constructed by the Gauss-LobattoLegendre(GLL)polynomials,respectively.The quadrilateral meshes are used to divide computational domain,which are as flexible as the triangular meshes used in finite element method(FEM).Specially,the SEM is easier to achieve high-order basis functions discretization in sparser meshes,which will further improve calculation speed.We first introduce a simple case to verify the feasibility of SEM-GSTCs.Then,a fully absorbed metasurface that could replace the perfectly matched layer(PML)is designed.After that,we extend the SEM-GSTCs to the full vector form to simulate the metasurface with complex susceptibility parameters.Finally,two kinds of metasurfaces,i.e.polarization transformer and polarization beam splitter(PBS),are designed for the extended method.The results show that the full vectorial SEM-GSTCs algorithm has the capability of numerically simulating bianisotropic metasurfaces and birefringent metasurfaces.