Metamaterials are materials artificially synthesized with unusual dielectric and magnetic properties, generally attained by including metals or usual dielectrics inside a host material.
The metamaterials idea rises from the observation that the concept of homogeneity is absolutely relative, indeed, in a sense, every material is a composite, even if the individual ingredients consist of atoms and molecules. The original objective in defining a permittivity, ε, and permeability, μ, was to present an homogeneous view of the electromagnetic properties of a medium. Therefore it is only a small step to replace the atom of the original concept with structure on a larger scale .
If we consider a periodic structure defined by a unit cell of dimension a (Fig.1b), the content of the unit cell will determine the effective response of the system as a whole if the applied field frequency satisfies the condition:
Indeed, in this case, the external field is too myopic to detect internal structure, and, in this limit, the medium can be characterized by means of an effective permittivity and permeability defined as:
So, an accurate choice of the geometry, position and parameters of the materials which compose the medium unit cell, allows us to synthesise unusual value of eff ed eff , this can be achieved thanks to the nanotechnologies.
Double Negative Materials (DNG)
DNG is a new class of metamaterials, which have negative values of both the dielectric permittivity and the magnetic permeability, while a material which have only one of these parameters less than zero is referred as Single Negative
They were introduced in 1968, by Veselago  who predicted their unusual properties and named it Left-Handed Media (LHM), since the electric and magnetic fields form a left-handed system with the wave vector (backward wave ). So, in a DNG medium, the phase velocity (which is directed as the wave vector k) is antiparallel to the group velocity (which is directed as the poynting vector S).
The index of refraction of a DNG medium has been shown to be negative and the interaction of an electromagnetic (EM) field with such material allows to observe interesting phenomena such as: reversed refraction (Fig.2a), reversed Doppler effect, backward Cherenkov radiation, near-field focusing from homogeneus slabs (Fig.2b).
Since a DNG material doesn’t exist, the Veselago’s theoretical disquisitions were not enough to capture the attention of the scientific world, indeed at the time although they were able to synthesize a ENG material as array of thin wire on a dielectric substratum, they didn’t know a particle with strong magnetic properties such to realize an MNG medium.
They were brought to the attention of the scientific community only in 2000 by Smith  who synthesized a LH material as a medium composed of two structures separately having ε<0 and μ<0 for the microwave regime (Fig. 3).
In the last years numerous applications for these materials have been predicted or realized: phase-shifters , compact-cavity resonators , coupled-line couplers , leaky-wave antennas .
We have elected an FDTD approach for the analysis of the DNG medium behaviour.
The FDTD method proposed has two basic appealing features, making it amenable for the characterization of metamaterial device:
1_The possibility to introduce three different source in the FDTD lattice :
- Pointwise E ed H hard sources,
- Field radiated by an electric dipole
- Plane wave in a Total Field/Scattered Field formulation
Then we are able to evaluate the response of an object with any shape and dimension to a propagating wave, or to evanescent wave.
2 _Implementation of the ‘lossy Drude model’ to deal with the DNG dispersive behaviour (metamaterials are generally dispersive materials, i.e. their properties are frequency dependent).
The tool’s affidability is demonstrated by the results achieved, in agreement with those reported by authoritative studious that for a long time deal him with the matter.
Fig. 4 shows the propagation of an m-n-m pulse (a signal with a small bandwidth) in a matched to free space DNG medium; it is evident that the medium phase velocity is negative.
While, Fig. 5 shows the reflected field of a ENG, MNG e DNG slab (the input signal is a single pulse).
Now we are studying the propagation of a modulated signal in a DNG medium, Fig.5 shows the results achieved for a plane wave x-directed electric field z-polarized (carrier frequency equal to 10 GHz) amplitude modulated by a Gaussian pulse. It is evident the dispersive medium behaviour, indeed the signal experiences a strong distorsion as it propagate in the DNG medium.
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