中国光学, 2019, 12 (2): 179, 网络出版: 2020-02-11
Kramers-Kronig关系的研究与发展
Research and development on Kramers-Kronig relationship
Kramers-Kronig关系 希尔伯特变换 因果关系 空间KK隐身介质 KK光通信收发机 Kramers-Kronig relationship Hilbert transformation causality space KK stealth medium KK optical transceiver
摘要
Kramers-Kronig关系(简称KK关系)是希尔伯特变换的一个特例, 描述了具有因果性的平方可积函数实部与虚部之间的数学联系, 具有普适的物理背景。本文介绍了KK关系的历史及数学物理本质, 详细阐述了其在电学、磁学、声学、光学、人工介质以及光通信中的具体形式、涵义及应用, 包括反射和透射响应函数、电极化率、介电常数、折射率、电导率、电阻抗、磁导率、原子散射因子、绝热压缩系数、声折射率、单边带时域信号、空间隐身介质还有各种非线性介质等。分析了截断误差在实际应用中对KK积分计算结果的影响, 总结了各种积分限外推方法以及各种基于锚点的减法KK关系, 包括单减KK关系、多减KK关系及差分多减KK关系等。
Abstract
The Kramers-Kronig(KK for short) relationship is a special case of Hilbert transformation, which describes the mathematical connection of square integrable function with causality between its real and imaginary parts. In this paper, the history, mathematics and physics essence of KK relationship are introduced. Its concrete form, meaning and application in electricity, magnetics, acoustics, optics, artificial medium and optical communication are presented, including its reflection and transmission functions, electric susceptibility, dielectric constant, refractive index, electrical conductivity, electrical impedance, magnetic permeability, atomic scattering factor, adiabatic compression coefficient, acoustic refractive index, single band time domain signal, space stealth medium and various nonlinear media and so on. The influence of truncation error on the calculation results of KK integral in practical applications is analyzed. Various integral limit extrapolation methods and various subtractive KK relationships based on anchor point are summarized, including single, multiple subtractive and differential multiple subtractive KK relationships.
阎春生. Kramers-Kronig关系的研究与发展[J]. 中国光学, 2019, 12(2): 179. YAN Chun-sheng. Research and development on Kramers-Kronig relationship[J]. Chinese Optics, 2019, 12(2): 179.