Exploratory Mathematics

[Hakasays]

A meta-material must indeed appear as a homogeneous medium at the wavelength scale, i.e. the dimension of the resonant elements must be small compared to the wavelength, and in order to be able to speak of a "medium", they must be very numerous because they must occupy a large volume compared to the wavelength.

It's not a "hypothesis", it's the obvious conditions for it to work, known by everyone in the field.

What sources did you use to conclude that a metamaterial must be of a high volume?   (inversely relative to frequency)

The data I've been exploring seem to have no problem with single-layer metamaterials exhibiting negative refractive indices (and by extension, negative impedance)

Multilayer flexible metamaterials based on circular shape with negative refractive index at microwave spectrum
https://www.sciencedirect.com/science/article/abs/pii/S0924424721006713

Single-Layer Metamaterial Absorber for Radar Application
http://hig.diva-portal.org/smash/get/diva2:1049480/FULLTEXT01.pdf

Recent advances in metamaterial split-ring-resonator circuits as biosensors and therapeutic agents
https://sci-hub.se/https://www.sciencedirect.com/science/article/abs/pii/S0956566316306492?fr=RR-2&ref=pdf_download&rr=75145ec71d08ec5c

As long as the physics are the same, there should be no substantial difference between a sun-nanometer split-ring resonator and one that is the size of a Lakhovsy MWO.
Only the frequencies would change.

[F6FLT]

What sources did you use to conclude that a metamaterial must be of a high volume?   (inversely relative to frequency)
...

See the basics about a medium of propagation of a wave.
How do you measure a wavelength in a medium if the wave propagates also outside because the medium is smaller than the wavelength?
"sources" . Do you also want the sources if I tell you U=RI?

[Hakasays]

How do you measure a wavelength in a medium if the wave propagates also outside because the medium is smaller than the wavelength?

I'm not sure, but we can clearly see a significant portion of negative-index metamaterials in development are 2-dimensional structures.
I find it confusing because it would seem to contradict your earlier insight.

Single-layer metamaterials with large surface area but little volume seem to be quite common, in fact.  Maybe your conclusion is based on research done before the more recent breakthroughs?

[F6FLT]

I'm not sure, but we can clearly see a significant portion of negative-index metamaterials in development are 2-dimensional structures.
I find it confusing because it would seem to contradict your earlier insight.

Single-layer metamaterials with large surface area but little volume seem to be quite common, in fact.  Maybe your conclusion is based on research done before the more recent breakthroughs?

Again, these are obvious things that I shouldn't have to say. Everyone should make an effort to understand before responding.
If the wave is a surface wave, it is the surface dimensions that must be > lambda.
If it is in a volume, it is the dimensions of the volume.
If the wave straddles two media, both must be taken into account for its propagation, but this is not the subject here, nor is it of any interest in the debate, since it could not change the enormous order of magnitude of the volume required, for example at 10 MHz, unless one were to accept that for the propagation of the wave, only 0.1% of the volume of the medium of interest is required, while 99.9% of the wave would propagate elsewhere!

[Hakasays]

https://www.youtube.com/watch?v=hB0yluXJ--0

Wave propagation through negative-index media

[Hakasays]

Doing some more research through older OUR threads, focusing on 'polarization current' as a second distinct component to displacement current.

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

While Displacement current is a result of a time-varying electric field, Polarization Current seems to be the equivalent current generated from a change in relative permittivity.

In a direct mechanical analogy, displacement current is a changing strain on a spring, while polarization current is a changing K (spring constant) of the spring.   Or at least this would appear to be the case.


Relevant questions / thought experiments since this is 'exploratory mathematics' thread:
* How much energy is required to physically or electrically change the permittivity of a transmission line with total line capacitance of 1000pF from 3 to 2  (either transverse or longitudinal)?
* How much energy is required to change the value of an air variable capacitor from 1000pF to 10pF?


And one more paper related to above.

Frequency dependence of the permittivity
http://www.physics.usu.edu/Wheeler/EM/Notes/EMNotes11FreqDepPermittivity.pdf

[Grumpy]

Doing some more research through older OUR threads, focusing on 'polarization current' as a second distinct component to displacement current.

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

While Displacement current is a result of a time-varying electric field, Polarization Current seems to be the equivalent current generated from a change in relative permittivity.

In a direct mechanical analogy, displacement current is a changing strain on a spring, while polarization current is a changing K (spring constant) of the spring.   Or at least this would appear to be the case.


Relevant questions / thought experiments since this is 'exploratory mathematics' thread:
* How much energy is required to physically or electrically change the permittivity of a transmission line with total line capacitance of 1000pF from 3 to 2  (either transverse or longitudinal)?
* How much energy is required to change the value of an air variable capacitor from 1000pF to 10pF?


And one more paper related to above.

We are not told or even encouraged to discover that "space" can be manipulated.

Space as a dielectric can be imparted with a high charge., especially when rotating, and more so when biased magnetically or electrically.  Gravity can also bias but is very weak and requires a high velocity of rotation.

[Hakasays]

We are not told or even encouraged to discover that "space" can be manipulated.

Space as a dielectric can be imparted with a high charge., especially when rotating, and more so when biased magnetically or electrically.  Gravity can also bias but is very weak and requires a high velocity of rotation.

It would seem permeability might also be treated as a dynamic manipulable variable.  This can be observed by plotting the permeability of a ferromagnetic wire at various points as a high-frequency signal passes through it.
(Of course in real life this would depend on the frequency and BH curves and bias current and several other factors)

But while a dynamic change in permittivity results in polarization current, does a dynamic change in permeability also lead to an equivalent current?
Or would it perhaps result in something we might call 'polarization voltage' since it acts in the magnetic domain?  Or perhaps nothing at all if magnetism is a second-order effect?