Typically the reflection and transmission properties of a medium, illuminated by a plane wave at normal incidence, is used to characterize its effective medium properties. Suppose we have a slab of wire medium embedded in a dielectric--which could even be air--and, for E-field parallel to the wires, we find that the medium is ENG. This implies the the stored electrical energy (reactive) is negative for this medium and we can use it to compensate for the positive reactance of a small antenna. But, if we compute the fields inside the physical slab containing the wires, we will find that
(epsilon*E-magnitude square) is positive, in contradiction with the effective medium prediction.
Does anyone have an explanation that reconciles this contadiction?
rmarques
- meaning of effective parameters
|Author
|2008-06-20 12:37:19
I think we can agree in that any effective parameter that we can extract from any experiment shoud be more predictive than the simple statement of the result of the experiment. Otherwise it has no physical meaning.
Starting from this general consideration, I am everyday amazed by the increasing number of scientific papers which extracts some effective parametars (usually inspired on continuous media theory, such as epsilon or mu) from the measurement of the trasnmission and reflection coefficient of a plane TEM wave impinging on a two-dimensional metalo-dielectric structure. What are the new predictions (aparte from the experimental results itself) that we can infere from these effective parameters, if any?
The question of effective parameters of metamaterials is interesting for me too. I propose to start from a bit simpler structures.
Let us consider usual 2D photonic crystal consits of high-index dielectic and air. The particular questions are:
1. Are there any confirmed calculated (or measured) curves dielectric constant(DC) vs. frequency for the most popular materials (silicon, alumina...)?
2. In the long-wavelength limit the meaning of effective DC is more or less clear. What about the range where the wavelength is of the same order or higher than the period of a PhC? Can we really use the "effective DC"? If yes what is the definition?
3. If we increase the filling fraction of high-index material OR somehow increase the DC of one of the materials the band gaps as well as the band structure (and transmission spectrum) will be shifted to the lower frequencies. I would say this happens just because of increasing "effective DC" but I'm not sure how to define this "effective DC"
alexeivinogradov
|Author
|2008-08-20 10:30:24
Concerning energy. Negative permittivity does not mean negative energy because of frequency dispersion inevitably existing at negative permittivity. Thus, the energy will be positive.
Wire medium. It seems very doubtful that wire medium can be described by effective permittivity-permeability even at normal incidence (at oblique incidence the effects of spatial dispersion are strong enough see Belov-Simovsky-Tretyakov at al). The reason is that (I have no rigorous proof) there is no static solution to the problem of diffraction on a single wire. We always have a scale that is much greater than wavelength that is the infinite length of the wire. Computer simulation shows that is senseless to take into account terms of the order of kD, where D is the maximal size of the inhomogeneity (period of PC, distance between inclusions and so on). Other way we obtain unphysical solution and strong dependence on system size. This concerns S-parameter procedure: exact values may be unphysical, because effective parameters are approximation and they can describe experiment with accuracy kD only.
PC. There is no effective parameters of 1D PC even the period is much smaller than wavelength. Our computer simulation shows strong dependence on system thickness even D/lamda=10(-6) but system thickness L=lambda. Moreover PCV at BG may frequencies support both TE and TM surface waves. Thus it may be considered simultaneously as SEN amd SMN medium.
Homogenization. There is no mathematically strong background for homogenization of operators which are not positively determined. Thus homogenization of metamaterials is a phenomenological activity.
