基于变换光学的波导弯接头设计

Waveguide bends design based on transformation optics

变换光学是一种通过设计改变传输介质的电磁特性实现调控电磁波任意传输的理论.根据麦克斯韦方程组在空间变换下的协变性,可以通过坐标变换设计出具有特定电磁参数的材料,从而设计新型电磁器件满足对电磁波传输的特定需求.基于变换光学的方法,人们陆续提出了隐身斗篷,隐身地毯以及波束集中器等新型电磁功能器件.基于上述背景,应用变换光学的理论方法,本文提出并设计了一种可实现无反射传输的90°波导弯接头.对波导弯接头材料的电磁参数进行了重新设计,实现了对于入射波的传输方向的操控,满足无反射传输要求.然而,经过变换光学得到的波导接头材料电磁参数通常是各向异性的,因此在实际制备中很难实现.本文根据等效介质理论使用两种各向同性材料在特定方向上层叠等效实现了波导弯接头处各向异性材料的电磁特性.基于有限元方法,对设计的波导接头进行了数值仿真,结果表明:在填充了特定材料的弯曲波导接头处,电磁波可以实现无反射传播从而大幅提高了传输效率.

Transformation optics is a newly proposed theory which involves into a powerful tool set for the design of various novel electromagnetic devices that are difficult to conceive using regular methods.By taking advantage of the invariance of Maxwell Equations upon coordinate transformation,transformation optics yields a precise prescription of spatially-varying and anisotropic optical constant to guide wave propagation at our wills.It is well known that traditional waveguide bends inherently suffer from reflections and mode distortions since a wave has to travel along paths of various lengths counting on the radial or cornered location inside the bends.To eliminate such vast reduction of transmission,we utilize the method of transformation optics to design a metamaterial placed in a 90 degree waveguide bend which can completely suppress the reflections and modes perturbations to support perfect transmission.The constitutive parameters of the associated metamaterial in the waveguide bend are analytically obtained,and are validated available using numerical simulations based on the finite element method.We further propose a stacked bilayer structure to substitute unprocurable anisotropic material inside the waveguide bend on the basis of Effective Medium Theory.The bilayer structure is composed of both isotropic materials which are more prone to prepare in laboratory fabrication.The numerical simulated results completely validate the correctness of our theoretical analysis and feasibility of practical application.