A Differential Form of the Kramers-Kronig Relation for Determining a Lorentz-Type of Refractive Index

Published

July 22, 2015

Author(s)

Sung Kim, David R. Novotny, Joshua A. Gordon, Jeffrey R. Guerrieri

Abstract

The integral forms of the Kramers-Kronig (KK) relations that relate the real and imaginary parts, n' and n", of a refractive index require the integral to be conducted over the full spectrum. In this paper, we derive a differential form of the KK relation that removes a need of knowing n" at all frequencies (omega) to calculate n', which is more practically beneficial in measurements. Moreover, we show that, in a finite frequency range, our differential form of the KK relation can generate a resonant effective n' for an artificial medium composed of a periodic structure more accurately than do the integral forms of the KK relations, making use of n" obtained from a full-wave simulation.

Conference Dates

July 19-25, 2015

Conference Location

Vancouver

Conference Title

Proceedings of 2015 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting

Pub Type

Conferences

Keywords

artificial medium, Kramers-Kronig, Lorentz model, materials characterization, refractive index

Citation

Kim, S. , Novotny, D. , Gordon, J. and Guerrieri, J. (2015), A Differential Form of the Kramers-Kronig Relation for Determining a Lorentz-Type of Refractive Index, Proceedings of 2015 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting, Vancouver, -1 (Accessed October 10, 2025)