Non linear properties of Metamaterials

In summary, the conversation discusses the application of Ohm's law in solving equations and its microscopic form for non-linear meta materials. The equation for reactance in terms of frequency, cross-section, and inductance is given, as well as the equation for impedance. The conversation also includes a substitution of variables and a discussion on the use of impedance and impeditivity in representing Ohm's law.
  • #1
Sana5643
10
0
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?
 

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  • Nonlinear Properties of Left-Handed Metamaterials.pdf
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  • #2
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
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
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
... I mean:

j=E/impeditivity

j=E/(rho + iX)

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

j=sigmaE/(1 + i(sigma)(wSL)
 
  • #6
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
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
Thanks for helping me to understand form of Ohms law given in this paper
 

1. What are metamaterials and how do they differ from traditional materials?

Metamaterials are artificially engineered materials with unique properties not found in nature. They are created by arranging small subunits in a precise pattern to achieve desired properties. Unlike traditional materials, which have linear responses to external stimuli, metamaterials have nonlinear properties that can be manipulated to achieve specific functions.

2. What are some examples of nonlinear properties in metamaterials?

Some examples of nonlinear properties in metamaterials include negative refractive index, superlensing, and cloaking capabilities. These properties allow for the manipulation of light and electromagnetic waves in ways that are not possible with traditional materials.

3. How are metamaterials used in technology and engineering?

Metamaterials have a wide range of applications in technology and engineering, including in areas such as telecommunications, medical imaging, and energy harvesting. They can be used to create more efficient and compact devices, as well as to enhance the performance of existing technologies.

4. What challenges are faced in studying and utilizing nonlinear properties of metamaterials?

One of the main challenges in studying and utilizing nonlinear properties of metamaterials is the complexity involved in designing and fabricating these materials. The nonlinear behavior can also be highly sensitive to external factors, making it difficult to control and predict. Additionally, there is still much to be discovered and understood about the fundamental principles behind these properties.

5. What potential future developments can we expect in the field of nonlinear properties of metamaterials?

The potential for further advancements in the field of nonlinear properties of metamaterials is vast. Researchers are currently exploring new applications, such as in quantum computing and nanotechnology. There is also ongoing research to improve the design and fabrication techniques for metamaterials, as well as to better understand the underlying physics behind their nonlinear behavior.

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