A Regularized Analytic Extension on the Upper Half Plane

• Main Authors: Luo, Yen Po, 羅彥博
• Other Authors: Wang, Wei Cheng
• Format: Others
• Language: en_US
• Published: 2016
• Online Access: http://ndltd.ncl.edu.tw/handle/52150744941839789853

碩士 === 國立清華大學 === 數學系 === 104 === In electromagnetism, the electric displacement field D represents how an electric field E affects in a given medium. The actual permittivity ε is calculated by =ε_r ε_0=(1+χ)ε_0 , where χ is the electric susceptibility of given material. The electric susceptibility χ satisfies the Kramers-Krönig relation. From the wave equation, electric susceptibility χ , the refractive index n and attenuation coefficient q have the relation χ=〖(n+iq)〗^2. However we can only measure n and q within a finite bandwidth. In this paper, we will find out a subset of the kernel of the Kramer-Krönig relation, and then use a minimization with a regularized extension to recover χ outside the measured bandwidth. We will recover the data of silicon and silver. For silver, we observe the singularity of its data χ_s and apply the KK-relation on χ-χ_(s ). For the singularity of conductors, we put the detail in the section 1.3.