# Non linear properties of Metamaterials

1. Aug 21, 2010

### Sana5643

im having diificulty in solving Equations in this research paper
how ohms law has been witten in Eq (1)
how can we write microscopic form of ohms law for non linear meta materials?

#### Attached Files:

• ###### Nonlinear Properties of Left-Handed Metamaterials.pdf
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2. Aug 22, 2010

### Dr Lots-o'watts

Reactance X is proportional to frequency, cross-section and inductance : X = omegaSL. Impedance is Imp = R + iX.
Ohm's law is j = E/Imp.

Agree?

3. Aug 23, 2010

### Sana5643

j = E / ( R + iωSL)
& by substituting
R = d /ơS
we get
j = EơS / ( d + iωơS2L)
but this is not the required relation ??vj = E / ( R + iωSL)
& by substituting
R = d /ơS
we get
j = EơS / ( d + iωơSSL)
but this is not the required relation ??

4. Aug 23, 2010

### Dr Lots-o'watts

j=E/impeditivity

j=E/(rho + i X)

j=(sigma/sigma)E/(rho + iX)

j=E/(1 + i(sigma)X)

j=E/(1 + i(sigma)(wSL))

5. Aug 23, 2010

### Dr Lots-o'watts

... I mean:

j=E/impeditivity

j=E/(rho + iX)

j=(sigma/sigma)E/(rho + iX)

j=sigmaE/(1 + i(sigma)(wSL)

6. Aug 25, 2010

### Sana5643

i was using relation Z= R +i X with resistance 'R'
it means we can use Z= ρ + i X with resistivity 'ρ' as well

7. Aug 25, 2010

### Dr Lots-o'watts

Impedance = resistance + i reactance.

multiplying by (cross-section/length) gives:

Impeditivity = resistivity + i reactivity.

(the units are different, so the symbols should also be, but except rho, I'm not sure what they are)

8. Aug 28, 2010

### Sana5643

Thanks for helping me to understand form of Ohms law given in this paper