Layered Media Theory Of Metasurfaces

Metamaterial is a kind of artificial material which is composed of sub wavelength cell structure arranged periodically in three-dimensional space.Unlike natural electromagnetic materials,they have positive permittivity and permeability.Metamaterials rely on artificial design,processing and manufacturing.After coupling with electromagnetic wave,they show many abnormal electromagnetic characteristics including negative refraction and artificial magnetism.Because of these characteristics,the potential of artificial electromagnetic materials in various fields is huge,such as electromagnetic sensor,microwave antenna,optical imaging,etc.But the metamaterials also have the disadvantages of large volume,high loss and strong dispersivity.Metasurface is another kind of material with abnormal electromagnetic characteristics.It is composed of sub wavelength cell structure arranged periodically on two-dimensional surface.The phase jump of electromagnetic wave occurs on its surface,so it can control electromagnetic wave.At the same time,metasurface is small in volume,low in loss and easy to integrate.In recent years,metasurface has become a hot topic in the field of materials.Among the many research directions of metasurface,the calculation of metasurface is one of the topics.According to the distribution of the unit structure,metasurface is usually divided into three types: plane,cylinder and spherical surface.At present,people mainly rely on commercial software to simulate and calculate various shapes of metasurfaces.They use full wave numerical methods based on mesh segmentation and periodic boundary conditions,but the characteristics of multi-layer cascade of metasurfaces are not used.Based on the consideration of the cascade characteristics of metasurface,the paper uses the surface impedance to characterize the properties of metasurface.Combining Floquet theorem and the classic layered media theory,an analytical theory is developed for the calculation of layered metasurface.Its advantages are flexible calculation method,when some certain layer of metasurface changes,It is not necessary to recalculate all interfaces,but only the scattering matrix of this layer is needed.The specific work of this paper includes:1.we first established a single layer metasurface model,and then,according to Maxwell equations and Floquet theorem,we found the specific form of z component of scattering wave on periodic surface,and found that it exists in the form of Floquet mode.We give the amplitude of the z component of the incident wave to be 1,so the amplitude of the scattering wave is the scattering coefficient to be solved.All expressions in the calculation are represented by three-dimensional coordinates.Then we derive the relation between the tangent field and the longitudinal field of a single plane wave and obtain the tangential field of periodic surface by using it.We use the impedance boundary conditions to the field on both sides of the interface,and finally calculate the amplitude of each scattering wave,including the scattering wave with the same polarization and the rotational polarization.Then we use the electromagnetic software CST to simulate the single layer metasurface,and obtain the S parameters of the main mode.Then we convert the calculation results of the formula into S parameters,and compare with the results of CST.2.we establish a model of the layered metasurface,and on the basis of the classical layered media theory,the formula suitable for metasurface is derived.Taking two layers of metasurface as an example,we first use the formula of single layer metasurface to calculate the scattering of incident wave in different directions,and then combine them to form the scattering coefficient matrix of the whole single layer interface.Then we substitute the results into the formula of layered metasurface,and then calculate the generalized scattering coefficient matrix.Finally,we use CST to model and calculate the layered metasurface,and then convert the formula results to s parameters.3.because we use the method of solving the disbanded wave by given incident wave to calculate the single-layer metasurface,and then calculate the scattering in different incident directions to form the scattering matrix of the whole single layer metasurface,this method is inefficient.Therefore,we propose an optimization algorithm for scattering matrix by using transfer matrix transformation.It does not need to give the size of incident wave,but only needs to calculate from the relationship between fields by matrix,which greatly shortens the calculation time.Finally,we calculate the results of the single layer and two layer metasurface by using the new algorithm,and convert them into S parameters,and compare with the results of CST.