Kramers-Kronig关系的研究与发展

阎春生

doi:10.3788/CO.20191202.0179

Volume 12 Issue 2

Apr. 2019

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Chinese Optics > 2019 > 12(2): 179-198.

YAN Chun-sheng. Research and development on Kramers-Kronig relationship[J]. Chinese Optics, 2019, 12(2): 179-198. doi: 10.3788/CO.20191202.0179

Citation:

YAN Chun-sheng. Research and development on Kramers-Kronig relationship[J]. Chinese Optics, 2019, 12(2): 179-198. doi: 10.3788/CO.20191202.0179

YAN Chun-sheng. Research and development on Kramers-Kronig relationship[J]. Chinese Optics, 2019, 12(2): 179-198. doi: 10.3788/CO.20191202.0179

Citation:

YAN Chun-sheng. Research and development on Kramers-Kronig relationship[J]. Chinese Optics, 2019, 12(2): 179-198. doi: 10.3788/CO.20191202.0179

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Research and development on Kramers-Kronig relationship

doi: 10.3788/CO.20191202.0179

YAN Chun-sheng^{1, 2
,
,}

1.
Library of Zhejiang University, Hangzhou 310058, China
2.
College of Optical Science and Engineering, Zhejiang University, Hangzhou 310058, China

Funds:

National Natural Science Foundation of China 11621101

National Natural Science Foundation of China 91233208

Fundamental Research Funds for the Central Universities from the Science and Technology Department of Zhejiang Province 2017FZA5001

More Information

Corresponding author: YAN Chun-sheng: E-mail:yancs@zju.edu.cn
Received Date: 11 Jun 2018
Rev Recd Date: 13 Jul 2018
Publish Date: 01 Apr 2019

Abstract

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.
- Kramers-Kronig relationship,
- Hilbert transformation,
- causality,
- space KK stealth medium,
- KK optical transceiver

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References(82)

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