In a simple forced damped oscillator... the real component describes the phase lag between the driving and response frequency (slowing down of light in a material, described by the refractive index) and the imaginary component is the damping factor (loss of energy or absorption of light, described by the absorption co-efficient in the Lambert Beer law, although in a real material the absorption is of course quantised)

I wish to ask about the significance of refractive index ( real part ) less than unity.

Thank you, Behnam Farid, for that excellent, fundamental view.  In some devices and applications, we wish to know the same kinds of answers for the case of finite (strong) externally-applied electric field.  Also, we wish to know other things, such as the electron densities in the field-distorted condition.  This is computationally difficult.  Progress has been made.  Here is  a good review to start with:

R. Resta and D. Vanderbilt, "Theory of Polarization: A Modern Approach", in K. Rabe, C. H. Ahn, J.-M. Triscone (eds.): Physics of Ferroelectrics: A Modern Perspective, Topics Appl. Physics 105, pp. 31–68 (Springer-Verlag, 2007, Berlin).

Shamjid,

Regarding your question:  "If we know real and imaginary part of dielectric constant a material, can we predict the material property from it?",

I think the answer is "no".  Loss mechanisms aside (the imaginary part), the dielectric constant is a scalar, bulk, average number, which is a composite of many influences or contributors.  For example, it is customary to invoke the Born approximation (separability of electronic and heavy-atom motions) and speak of a lattice dielectric tensor (heavy or 'nuclear' part) and a high-frequency dielectric constant (electronic part).  For example, for the high-k dielectric material HfO2, the average lattice k might be around 17 and the high frequency part around 5, to give approx k = 22 we think of as charateristic for that material. 

In any case, for both k and the losses, this is a scalar that is the summation or composite of many, many atomic and structural details.  Can you calculate basic mechanical properties (hardness and Young's modulus) from k?  No.  Can you calculate resistivity from k?  No.  Etc.  There might be correlations with k, for some properties, within a narrow family of materials.  But no deterministic relationship.

Dear Behnam,

I have it, the Marzari et al. paper, though I have not 'mastered' it, being an experimentalist.

I did come accross a very recent paper, maybe not even published yet.  You might be able to review it for us in regard to the questions at hand:

Starke & Schober, Microscopic Theory of the Refractive Index, in

arXiv:1510.03404v3 [cond-mat.mtrl-sci] 17 Jun 2016.

Dear Behnam,

Very nice dsitinction.  I probably would have missed that proviso, at least initially, then been confused.  Thank you.

While I have your attention, may I ask you to comment on an (apparently) old concept of ponderable media?  This comes up in the titles of two articles, which on first glance may seem to bear on Shamjid Palappra's original question about determining material properties from k.  But, in fact, the author is referring more to energy and momentum conservation of light while passing through a medium than referring to the medium, I think.  Here are the two papers:

Mansuripur, Electromagnetic Stress Tensor in Ponderable Media, Optics Express, Vol. 16, No. 8, pp5193-5198 (2008).

https://arxiv.org/ftp/arxiv/papers/1402/1402.7261.pdf

Mansuripur, Electromagnetic force and torque in ponderable media, Optics Express, Vol. 16, No. 19, pp14821-35 (2008).

https://arxiv.org/ftp/arxiv/papers/1402/1402.7262.pdf

Mansuripur seems to define a ponderable medium as one in which "polarization density P and magnetization density M describe the electromagnetic properties of the material (and where the macroscopic version of Maxwell’s equations, incorporating P and M, are applicable)".

So I guess this model is a sort of classical model in which the medium is something like 'dielectric jellium', a continuum?  Could you comment on distinctions between such a model (as you properly define it) and your discrete lattice model and Starke's "uniform system"?  And when each 'picture' is appropriate to use?

Many thanks,  Dave

dear Shamjid Palappra

the slow group velocity (slow light[1]) maybe of interest for you.

1. Dirac-graphene in slow-light [http://arxiv.org/pdf/1607.04476v1],     Light-field driven currents in graphene [http://arxiv.org/pdf/1607.04198v1]

Behnam,

Yes, RE "ponderable", I did see an early writing of Einstein using it as I was poking around on the internet trying to gain insight.  Apparently, one usage of "ponderable" object/material.medium was to distinguish from the equally archaic "ether" (or aether), which we would call a vacuum nowadays.  I was just curious about your classification of "ponderable" media in mathematical terms applicable to modern electrostatics and electrodnamics.  I.e., uniform, homogeous, or whatever.  I think it is still true (correct?) that classical, macroscopic descriptions of electromagnetics are still useful at some scales and for some applications.

Hmmm... the vector potential A.  Yes, I remember that from an undergraduate physics course in the 1970s.  I have not used it since.  I might pull out that old text book (if I still have it) and refresh my understanding.

Would you please send me a PDF of your paper: Solid State Commun, 104, 227 (1997).?  My off-line E-mail is [email protected]

Thanks,  Dave

Behnam,

Thank you for your perspective and the resources to which you point. 

For a variety of reasons which I could discuss later, I am very interested in "local fields".  I believe "local" may include field variations over distances the size of atoms.  For ex., within a unit cell of a crystal of a dielectric material (a small, simple unit cell but larger than one atom and containing at least two different kinds of atoms), one may expect various strengths and directions of electric fields, correct?  And these would qualify as local fields?  Many of these would exist even when there is no externally-applied electric field. Or, if an extra electron (or hole) was located and stationary somewhere in a dielectric, we certainly expect some local field, albeit the extra charge would be 'screened' by adjustment in electron density of neighboring atoms or orbitals. 

Getting back closer to the topic of the OP (original post), can we not expect to find finite local variations in k value?  What is that called, or how is it expressed/described?  (If this is well-established, e.g., in Quinn and Yi, I will look it up.)

Adding to above comments, from the practical point of view:

The dielectric constant epslionr = epsilon/ epsilon0 is the ratio of the permitivity of the material to the permitivity of free space. It is a dielectric material property where it is defined by the ratio of the dielectric flux density D to the applied electric field E.

Accordingly D= epsilon0 epsilonr E,

Applying an electric field on a dielectric material is reacts with an electric flux density. It is an indication how the material is easy to polarize.

Epsilonr = Epsiloner real + j epsilonr imajinary.

One of the straight forward consequence when you know epsilonr you determine D. This is in solving electric field problems.

One of the major applications of the dielectric material is using them to increase the value of the capacitance and thereby reducing their size.

By filling the capacitor with dielectric its capacitance increases by epsilonr such that:

C= epsilonr Cvac,

For parallel plat capacitor

Cvac= epsilon0 A/d, with A the area of the parallel plates of the capacitors and d is the spacing.

The last comment is the imaginary part of dielectric constant represents the polarization losses of the material in alternating electric field.

Best wishes

The diectric costant is the efficiency of dielectric material to store the electrical energy and the dielectric loss indicates to loss of electrical enenergy as heat energy.

One part represent the energy gain and other represent the energy loss of material in term of electric field

For time varying fields: ε(ω)=ε’(ω)-ε”(ω); where ε(ω) is the complex permittivity, ε’(ω) is the lossless permittivity (due to L and C) and ε”(ω) is the lossy permittivity (due to R and G). The lossless permittivity represents the energy stored in the electric (C) and magnetic fields (L) and the lossy permittivity represents the energy lost as heat (R) and dielectric leakage (G).

I agreed answer of Libi Mol V.A

if the material has the high dielectric constant and low dielectric loss that's refer to this material has good insulator and good efficiency as dielectric material.

when a dielectric is subjected an alternating electric field the permittivity of the dielectric material is complex ,because in a lossless dielectric the energy loss due the propagation of electric field is zero,but in lossy dielectric when there is propagation of sinusoidal electric field through the medium some of energy corresponding to this electric field get converted to heat or some loss energy,so the real part of permittivity corresponds to the efficiency of a dielectric material to store the field energy and imaginary part accounts for the losses of energy due the variation of ac electric field in the dielectric material.

Please, one answer must be insert references.

Dear colleagues,

welcome,

The physical significance and the definition of the real dielectric constant and the imaginary part of the dielectric constant are explained in full details in the course about the properties of the dielectric materials by Abdelhalim Zekry given in the link: Book properties of dielectric materials BY abdelhalim zekry

Best wishes

https://arxiv.org/pdf/1002.1545

Agreed with

@ Khalid Mujasam Batoo

Dielectric constant mainly improved the charge density of the materials.

The real part represents the ability of the material to store the electric energy and related to the polarization while the imaginary part is responsible for the damping of the wave and dissipation of energy.

** In THz frequency domain: Negative values in ε can be achieved twice:

• close to the resonance frequency of a harmonic oscillator

• for free electrons.

This can be seen from the classical Drude – Lorentz – Sommerfeld equation for the dielectric function: {please see the "(https://www.wiley.com/en-us/Optical+Properties+of+Nanoparticle+Systems%3A+Mie+and+Beyond-p-9783527410439)" - Chapter 5}

** In GHz frequency domain: The ε is negative = This indicates that there is no feasibility of propagating the electric field of the electromagnetic wave inside the material.

{please see the : Article Measurement of Electric and Magnetic Properties of ZnO Nanop...