Study On Transmission Characteristics Of Tunable Graphene Hyperbolic Metamaterial And The Design Of Super-sensitive Tunable Planar Lens

Metamaterials are artificial media structured with electromagnetic?EM?characteristics which are not found in natural materials.By designing a variety of metamaterial structures,we can control EM wave and discover many interesting phenomena,such as slow light,negative refraction,and super-collimation.As a branch of metamaterials,hyperbolic metamaterials?HMMs?exhibit unusual EM properties,such as high anisotropy and supporting for transmission of large wave vectors,so they have attracted widespread attention.We can utilize HMMs to construct lots of optical devices,such as the optical modulator,the optical waveguide,and the superlens.Graphene is the two-dimensional carbon nanomaterial with a hexagonal honeycomb lattice formed by sp2hybrid orbitals and its conductivity is very sensitive to external electric field,magnetic field,chemical potential,optical pump,so that combining graphene with HMMs can design a variety of tunable optical devices.Here,we adopt research methods of theoretical analysis and numerical simulation.More specifically,the research methods include effective medium theory,equi-frequency contour?EFC?analysis,and Finite-Difference Time-Domain.By combining the tunability of graphene with the high anisotropy of HMMs,we investigate dispersion properties of graphene HMM and transmission characteristics of EM wave.Then we explore the related application,for example,super-sensitive tunable planar lens.We finally analyze some optical properties of the lens.The specific research contents are as follows:1.We investigate transmission characteristics of graphene HMM which is consisting of alternative graphene sheets and dielectric layers and we also realize the function of tunable concave or convex lens.We find that the effective relative permittivity tensor of graphene HMM includes parallel??_|?and vertical??_??components to the graphene sheets.?_?is determined by the permittivity of dielectric layers,which is a positive number.However,?_| is a positive or negative number which can be tuned by changing the chemical potential of graphene??_c?.When we choose the working frequency to be 30 THz,there is the critical value of?_c=0.6 e V where?_|=0.Therefore,by tuning?_c,the dispersion relation of graphene HMM is topologically switchable between ellipse??_c<0.6 e V?and hyperbola??_c>0.6 e V? where positive and negative refractions occur respectively.Utilizing the above transmission characteristics of EM wave,we further realize the function of tunable concave or convex lens.More specifically,when?_c<0.6 e V,the Gaussian beam undergoes two times of positive refractions at interfaces between graphene HMM and the air,and finally diverges to propagate in air region.At the moment,graphene HMM plays the role of a concave lens. However,when?_c>0.6 e V,the Gaussian beam undergoes two times of negative refractions at the same interfaces,and finally focuses at a far-field point in air region.At this time, graphene HMM acts as a convex lens.Hence,we can change?_c to make the lens act as a concave or convex one.2.According to the above research,we design super-sensitive tunable planar lens and explore some of its optical parameters.In the case of?_c>0.6 e V,we find that EFCs of graphene HMM are hyperbolas with different opening sizes when we choose different values of?_c. Though the incident angle?₁ keeps the same,the position of the focal point in air region varies sensitively as?_c increases,so that a lens with tunable focal point is designed.For the sensitivity of the focal length,we find that with increasing?_c,the focal length decreases dramatically at first?when?_c<0.75 e V?and then slowly?when?_c>0.75 e V?.In other words, the sensitivity of the focal length in the case of?_c closer to 0.6 e V is higher than that in the case of?_c far away from 0.6 e V.In terms of the transmittance,for 0.2??_c?0.54e V or 0.64??_c?1 e V,the lens can act as a concave or convex lens,and the transmittance maintains high?>92%?and stable,meaning that the lens can work well within a wide chemical potential range.Finally,we investigate the resolution of the lens by the full width half maximum?FWHM?of the curve at the focal point.We find that the higher?_c is the smaller the FWHM is,which means that higher?_c is beneficial for enhancing the resolution of the lens.