Dear Abuzar Baquir,

the anomalous dispersion through  very narrow metal prisms has been studied by Kundt (Über die Brechungsexponenten der Metalle – 1888), by Hagen and Rubens, by Quincke and by others around 1900. Anomalous dispersion means that, differently from transparent dielectrics, in the visible range the refractive index n doesn't increase with decreasing wavelength. Rather, it decreases. Handling metals like transparent dielectrics, one finds that for silver – say – in the visible n is positive, but much less than 1. Handling light as an electromagnetic radiation, one puts n=√(εμ), where ε is the relative permittivity, and μ=1, and finds that metallic permittivity is very small, too.

However, measuring optical parameters of metals is no easy matter. Drude explained optical properties assuming the Wiedemann-Franz law. I would suggest to have a look at: “Verifying the Drude response” by Dressel and Scheffler, if you can. According to that theory, the refractive index is a complex quantity, i.e. n=n*+ik, where k is the attenuation. And a metal shows both, dispersion ε1= n*2-k2 and absorption ε2=2n*k. Around plasma frequencies the contribution due to k becomes important , and there ε1 becomes negative.

As dr. Shahverdiev neatly points out, ferroelectrics can show the same behavior ("Experimental Observation of Negative Capacitance in Ferroelectrics at Room Temperature" by Appleby et al.)

The relevance of negative permittivity and permeability was first theoretically disclosed by Veselago in 1968, handling n2=εμ somewhat like congeneric surd equations. His paper is short and clear.

http://www3.nd.edu/~djena/ee358/veselago_original_paper.pdf.

According to Wikipedia, natural materials with negative ε and μ have yet to be discovered

https://en.wikipedia.org/wiki/Metamaterial.

As I know natural materials can not have negative permittivity or permeability.

Therefore, metamaterials has made huge impact on engineering world.

However, you can obtain negative permitttivity by making engineering design with metals.

Dear Abuzar Baquir,

the anomalous dispersion through  very narrow metal prisms has been studied by Kundt (Über die Brechungsexponenten der Metalle – 1888), by Hagen and Rubens, by Quincke and by others around 1900. Anomalous dispersion means that, differently from transparent dielectrics, in the visible range the refractive index n doesn't increase with decreasing wavelength. Rather, it decreases. Handling metals like transparent dielectrics, one finds that for silver – say – in the visible n is positive, but much less than 1. Handling light as an electromagnetic radiation, one puts n=√(εμ), where ε is the relative permittivity, and μ=1, and finds that metallic permittivity is very small, too.

However, measuring optical parameters of metals is no easy matter. Drude explained optical properties assuming the Wiedemann-Franz law. I would suggest to have a look at: “Verifying the Drude response” by Dressel and Scheffler, if you can. According to that theory, the refractive index is a complex quantity, i.e. n=n*+ik, where k is the attenuation. And a metal shows both, dispersion ε1= n*2-k2 and absorption ε2=2n*k. Around plasma frequencies the contribution due to k becomes important , and there ε1 becomes negative.

As dr. Shahverdiev neatly points out, ferroelectrics can show the same behavior ("Experimental Observation of Negative Capacitance in Ferroelectrics at Room Temperature" by Appleby et al.)

The relevance of negative permittivity and permeability was first theoretically disclosed by Veselago in 1968, handling n2=εμ somewhat like congeneric surd equations. His paper is short and clear.

http://www3.nd.edu/~djena/ee358/veselago_original_paper.pdf.

According to Wikipedia, natural materials with negative ε and μ have yet to be discovered

https://en.wikipedia.org/wiki/Metamaterial.

i think , this ref have very good answer for your question:

ELECTROMAGNETIC METAMATERIALS: TRANSMISSION LINE THEORY AND MICROWAVE APPLICATIONS

The Engineering Approach

CHRISTOPHE CALOZ

University of California at Los Angeles

Dear Abuzar Baquir,

There are natural materiels that exhibit negative permittivity or permeability at 

certain frequency ranges  and they are used in used in practice.

Examples are as follows.

1) Superconductors at microwave frequencies (very large negative permittivity)

IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 23,

pp.1501011 - 1501011,  2013

2) Metals Au, Ag at optical frequencies (well known phenomena associated

with plasmons)

3) Ferrimagnetics at microwave frequencies (Nature Sc. Rep. 6, 34739 , 2016)

Some natural materials, such as superconductors (e.g. YBCO) , exhibit negative permittivity at microwave frequencies. For more details see the paper

Complex Conductivity of YBCO Films in Normal and Superconducting States Probed by

Microwave Measurements

ieeexplore.ieee.org/iel5/77/6419836/06450123.pdf

Thank you Prof. Jerzy Antoni

Than you Sara Liyuba Vesely and Ahmed Fawazy

I would like to discuss the meaning of the negative permitivity from the principle point of view. At first let us define the permitivity of the material can be expressed by epsilon= D/E, if epsilon is positive which is the case for the conventional dielectric materials then D will be in the direction of E that the electric flux and the applied electric field will be in the same direction. If epsilon is negative , this will dictate that the electric flux density will be in the reverse direction of the electric field. This means that the material will be polarized at the reverse direction of the electric field. To understand this more let us build a capacitor with such material and see how it reacts at the charging and discharging process.

For the capacitor we have i =C dV/dt, if the permitivity is negative then C will be negative and we have,

i= -C dV/dt,

What is the meaning of this equation? It means that when the capacitor voltage increases it sources out a current which is the opposite of the normal capacitor and when the the capacitor voltage decreases it sink current rather than sourcing current as the normal capacitor. This means that the capacitor becomes an active source of charge.

Best wishes

Negative Permitivity is exhibited by conductors, superconductors and meta-materials over certain frequency ranges. In conductors and superconductors the negative permitivity is very high and the electric field can be assumed to be excluded from the material. In this case the boundary conditions can be approximated as zero transverse electric field on the boundaries as with PEC materials. In electromagnetic meta-materials negative permitivity is finite over narrow frequency bands resulting in negative refractive index.

Spencer Terry-Wood,

Pls read the question carefully.