Here i want to discuss about relation between permittivity,refractive index and conductivity for plasmonic elements like gold,silver and graphene.

I quote definition **permittivity** from this link.

In electromagnetism,

permittivityorabsolute permittivity, usually denoted by the Greek letter ε (epsilon), is the measure of resistance that is encountered when forming an electric field in a particular medium. More specifically, permittivity describes the amount of charge needed to generate one unit of electric flux in a particular medium.

[latex]\epsilon=\epsilon_{r}\epsilon_{0}=\left(1+\chi\right)\epsilon_{0}[/latex]

I quote definition **conductivity** from this link.

Electrical resistivity(also known asresistivity,specific electrical resistance, orvolume resistivity) is an intrinsic property that quantifies how strongly a given material opposes the flow of electric current. A low resistivity indicates a material that readily allows the flow of electric current. Resistivity is commonly represented by the Greek letter ρ (rho). The SIunit of electrical resistivity is the ohm–metre (Ω⋅m).^{[1]}^{[2]}^{[3]}As an example, if a 1 m × 1 m × 1 m solid cube of material has sheet contacts on two opposite faces, and the resistance between these contacts is 1 Ω, then the resistivity of the material is 1 Ω⋅m.

Electrical conductivityorspecific conductanceis the reciprocal of electrical resistivity, and measures a material’s ability to conduct an electric current. It is commonly represented by the Greek letter σ (sigma), but κ (kappa) (especially in electrical engineering) or γ (gamma) are also occasionally used. Its SI unit is siemens per metre (S/m) and CGSE unit is reciprocal second (s^{−1}).

[latex]\sigma(conductivity)=\frac{1}{\rho(Resistace)}=\frac{J}{E}[/latex]

I quote definition **refractive index** from this link.

In optics, the

refractive indexorindex of refractionnof a material is a dimensionless number that describes how light propagates through that medium. It is defined as

[latex]n=\frac{c}{v}[/latex]

I quote definition** effective** **refractive index** from this link.

For plane waves in homogeneous transparent media, the refractive index

ncan be used to quantify the increase in the wavenumber (phase change per unit length) caused by the medium: the wavenumber isntimes higher than it would be in vacuum. Theeffective refractive indexn_{eff}has the analogous meaning for light propagation in a waveguide with restricted transverse extension: the β value (phase constant) of the waveguide (for some wavelength) is the effective index times the vacuum wavenumber:

[latex]\beta={n_{eff}}k_{0}[/latex]

**Relation between permittivity and refractive index:**

you can see proof from this link.

[latex]\epsilon_{r}=n^{2}[/latex]

**The relation between permittivity and conductivity**

see this link.

[latex]\epsilon(w)=\epsilon^{‘}(w)+\epsilon^{”}(w)=\epsilon_{r}(w)\epsilon_{0}+j\frac{\sigma(w)}{w}[/latex]

**Complex conductivity:**

see this link.

[latex]\sigma_{c}=jw\epsilon_{c}=\sigma+jw\epsilon[/latex]

** Graphene conductiviy kubbo formula:**

TagsAmateur Radio , Computer Science , conductivity , Electronic Design , permittivity , plasmonic , refractive index , Relation , stackdesign , StackDesign Blog , stackproramer

From above some we can easily stabilize the relation between Refractive index and Conductivity but is there any application if we take inorganic solution as sample. Please do reply as soon as possible….

Hi, the relation between Refractive index and Conductivity is very important for us(Optical electronics) in plasmonics and optical devices, we usually in designing optical -devices,we use graphene and silicon, Though we use Aluminium ,gold and silver elements in plasmonics. for solution is rarely used…