Wave propagation, scattering and focusing effect of Luneberg lens

• Main Authors: Hao-Hsien Lin, 林浩賢
• Other Authors: 陳瑞琳
• Format: Others
• Language: zh-TW
• Published: 2006
• Online Access: http://ndltd.ncl.edu.tw/handle/22554174513656683807

碩士 === 國立臺灣大學 === 應用力學研究所 === 94 === Luneberg lens is a spherical lens which its permittivity varies with normalized radial coordinates. It is fabricated by using different homogeneous dielectric centrically layered media. The lens can focus a parallel beam of rays from any direction exactly at a point on the surface. If it is made by adding a reflecting surface “metallic cap”, it is called Luneberg lens reflector. It can reflect incident wave into plane wave in incoming direction. It is usually applied in antenna, radar reflector, satellite-based, and mobile-communucation. The main points of this thesis are about wave propagation, scattering and focusing effect of Luneberg lens. First we use spherical harmonics, the Mie theory, to express the electric and magnetic field in spherical polar coordinate system. We expand a plane wave in vector spherical harmonics. This problem can not be solved by the same boundary condition, because there are two different materials, dielectric and metallic, on the surface. So we use point-matching method (PMM) to solve this mixed boundary value problem. The method consists of satisfying the boundary conditions in the contact plane only at a finite point. Then we use the boundary condition of each layer, we can find the coefficient of each layer. Finally we can find the all field of the incident wave into a Lungberg lens. In the discussion, we use different layers of lens to approach the ideal Lungberg lens. We take the balance in different layers and the focusing effect. What is the influence of the different wave length and what is the difference between Lungberg lens and Lungberg lens reflector in scattering patterns. We also provide a picture of wave propagation through Lungberg lens to see if the points are exactly on the surface, the incoming wave reflected by the metallic cap is a perfect plane wave or not. Finally, we provide the poynting vector on the special surface. The purpose is to see if the energy focuses to a point on the surface.