球形电磁波集中器内的光线跟踪研究

Ray Tracing on Spherical Electromagnetic Wave Concentrator

利用几何光学理论,引入了光线在超介质材料中的哈密顿量,通过求解光线运动方程,获得了光线在三维球形电磁波集中器内的传输轨迹,比较直观地解释了光线在超介质材料,尤其是负折射率材料中的传播过程.计算表明,只有在器件实际尺寸范围内的入射光线会受到影响.当包裹层内介电常数和磁导率为正时,只有在转换区域范围以内的入射光线进入被包裹核内;当包裹层为负折射率材料时,在器件实际尺寸范围内的入射光线都会进入被包裹核,并且随着压缩率的增加,核内的光线逐渐向中心轴线处靠近,实际光线占据的区域向中心轴缩小,核内其他区域由入射波的激发光线占据,并且在器件内部形成循环回路,此部分光线对器件外的光线传输无影响.给出了光线在超介质材料器件中传播轨迹的定量结果,对理解超介质材料中的电磁波传播行为有重要的参考意义.

Based on geometric ray optics in anisotropic media, we obtained the ray propagation behavior in three-dimensional spherical electromagnetic （EM） wave concentrator. By introducing proper Hamiltonian and solving the equations of ray motion in concentrator composed of meta-materials, a very intuitive physical image about light trajectories is given. It is shown that only the incident light rays in actual size range of an EM device would be affected. When the permittivity and permeability of the coated layer are positive, the incident light in range r ~ R3 would be transferred into the inner core. If they are all negative （NIM, meta-materials with negative refractive indexes）, all the incident light rays in the actual size range （included in r ~ Rz ） would entered into the inner core. With the increase of the compression ratio s, the light rays in inner core will approach gradually the center axis and the region occupied by the corresponding light is gradually compressed. The rest of space in inner core is occupied by the excited rays resulted from external incident wave excitation. The excited rays circulate in concentrator itself and have no effect on light propagation outside the device. Our work gave the light trajectories in meta-materials, especially in NIM, so it will provide important theoretical reference for researchers to understand the propagation behavior in recta-materials.