Design And Fabrication Of Non-resonant Metamaterial Luneburg Lens

Luneburg lens exhibit unique gradient permittivity distribution,which is suitable to be used as multi-beam antenna and beam-scanning antenna.Luneburg lens can be compressed by means of transformation optics,so that its volume and weight can be reduced and its spherical focusing surface can be changed into planar surface,which is easier to be integrated with feeding systems.Constructing the lens with metamaterial unti cells is likely to solve the difficulty of conventional manufacture.The gradient-size microstructure based on metamaterial is suitable to be fabricated by 3D print.The passage did the research of the design and 3D print fabrication of new-type Luneburg lens based on transformation optics and metamaterial.Luneburg lens was compressed by quasi-conformal mapping and the non-resonant cross-rod was used as unit cell.The lens antenna performance was simulated by CST software and the entity was fabricated by fused deposition modeling.The printable BaTiO₃/PLA composites with high permittivity were also prepared and researched.Approaches to transform the lens,which is based on quasi-conformal mapping,was explored.By use of MATLAB and its Partial Differential Toolbox,Luneburg lens's one-side compression was achieved.With the help of self-made calculating program,permittivity distribution under different transformed angle were obtained.When the angle get larger,the lens become flatter,the permittivity get higher,and the isotropy become worse.The non-resonant 4mm length cross-rod was used as metamaterial unit cell.On the basis of quasi-conformal lens's permittivity distribution under 120 degree transformed angle,cross-rod transformed lens was designed.On the basis of Luneburg lens's permittivity distribution,cross-rod Luneburg lens was designed.Both lenses work in X-band.The far field patterns and near electric fields were simulated by CST,so that the two designed metamaterial lens could be compared with conventional layered Luneburg lens.The results show that the cross-rod Luneburg lens almost have the same radiating properties as the layered Luneburg lens,but the cross-rod transformed lens's directivity become smaller.When the feed was placed out of center,the cross-rod transformed lens deflected the beam with larger angle than the other two lenses,demonstrating excellent planar beam-scanning properties with the largest scanning angle as 48 degree at 10GHz.PLA's permittivity was 2.3,and it was used to print the lens.Half cross-rod Luneburg lens was fabricated by fused deposition modeling.However,the cross-rod transformed lens could not be fabricated without a kind of high permittivity printable material.By means of melt blending,BaTiO₃ powders which own high permittivity were added to PLA substrate.10wt%?20wt%and 30wt%BaTiO₃/PLA composites were prepared,permittivity of which reached 2.35?2.79 and 3.02 respectively.But composites with high concentration met problem of nozzle clogging.SEM?XRD?TG?DSC?flowing properties and melt flowing rate of the BaTiO₃/PLA composites were tested.The results showed that the submicron BaTiO₃ particles were dispersed evenly in PLA,aggregation of powders were not found.The bonding between BaTiO₃ and substrate was weak,and glass-transition temperature and melting point did not change.With testing condition of 2.16Kg weights,BaTiO₃/PLA composites had higher melt flowing rate than PLA,which agreed with lower viscosity of BaTiO₃/PLA composites in low shearing rate.According to theoretical calculation based on Maxwell-Garnett formula,the key point to raise composites'permittivity further is to raise the additives'volume fraction and the substrates'permittivity.Raising the additives'permittivity will not make a big difference.