### Abstract

All materials, by nature, possess a frequency-dependent permittivity. This dispersion can be expressed in the form of the Kramers-Krönig relations by invoking the analytic consequences of causality in the upper half of the complex frequency plane. However, the Hubert transform pair character of these relations makes them useful only when half of the answer is already known. In order to derive a more general form useful for both synthesis and analysis of arbitrary materials, it is necessary to analytically continue the permittivity function into the lower half plane. Requiring that the dielectric polarization be expressible in terms of equations of motion, in addition to obeying causality, conservation of energy and the second law of thermodynamics is sufficient to obtain the desired expression as a sum of special complex functions. In the appropriate limits, this sum reduces to the Debye relaxation and Lorentz resonance models of dielectrics, but it also contains phenomena not expressible in terms of those classical models. In particular, the classic problem of the existence of optical transparency in water is resolved.

Original language | English (US) |
---|---|

Pages (from-to) | 1602-1610 |

Number of pages | 9 |

Journal | IEEE Transactions on Antennas and Propagation |

Volume | 45 |

Issue number | 11 |

DOIs | |

State | Published - Dec 1 1997 |

Externally published | Yes |

### Fingerprint

### Keywords

- Dispersive media

### ASJC Scopus subject areas

- Condensed Matter Physics
- Electrical and Electronic Engineering

### Cite this

*IEEE Transactions on Antennas and Propagation*,

*45*(11), 1602-1610. https://doi.org/10.1109/8.650071

**An analytic continuation method for the analysis and design of dispersive materials.** / Diaz, Rodolfo; Alexopoulos, Nicolaos G.

Research output: Contribution to journal › Article

*IEEE Transactions on Antennas and Propagation*, vol. 45, no. 11, pp. 1602-1610. https://doi.org/10.1109/8.650071

}

TY - JOUR

T1 - An analytic continuation method for the analysis and design of dispersive materials

AU - Diaz, Rodolfo

AU - Alexopoulos, Nicolaos G.

PY - 1997/12/1

Y1 - 1997/12/1

N2 - All materials, by nature, possess a frequency-dependent permittivity. This dispersion can be expressed in the form of the Kramers-Krönig relations by invoking the analytic consequences of causality in the upper half of the complex frequency plane. However, the Hubert transform pair character of these relations makes them useful only when half of the answer is already known. In order to derive a more general form useful for both synthesis and analysis of arbitrary materials, it is necessary to analytically continue the permittivity function into the lower half plane. Requiring that the dielectric polarization be expressible in terms of equations of motion, in addition to obeying causality, conservation of energy and the second law of thermodynamics is sufficient to obtain the desired expression as a sum of special complex functions. In the appropriate limits, this sum reduces to the Debye relaxation and Lorentz resonance models of dielectrics, but it also contains phenomena not expressible in terms of those classical models. In particular, the classic problem of the existence of optical transparency in water is resolved.

AB - All materials, by nature, possess a frequency-dependent permittivity. This dispersion can be expressed in the form of the Kramers-Krönig relations by invoking the analytic consequences of causality in the upper half of the complex frequency plane. However, the Hubert transform pair character of these relations makes them useful only when half of the answer is already known. In order to derive a more general form useful for both synthesis and analysis of arbitrary materials, it is necessary to analytically continue the permittivity function into the lower half plane. Requiring that the dielectric polarization be expressible in terms of equations of motion, in addition to obeying causality, conservation of energy and the second law of thermodynamics is sufficient to obtain the desired expression as a sum of special complex functions. In the appropriate limits, this sum reduces to the Debye relaxation and Lorentz resonance models of dielectrics, but it also contains phenomena not expressible in terms of those classical models. In particular, the classic problem of the existence of optical transparency in water is resolved.

KW - Dispersive media

UR - http://www.scopus.com/inward/record.url?scp=0031274468&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031274468&partnerID=8YFLogxK

U2 - 10.1109/8.650071

DO - 10.1109/8.650071

M3 - Article

VL - 45

SP - 1602

EP - 1610

JO - IEEE Transactions on Antennas and Propagation

JF - IEEE Transactions on Antennas and Propagation

SN - 0018-926X

IS - 11

ER -