1. Double-Positive (DPS) Double-Negative (DNG) Epsilon-Negative (ENG)
Brief introduction to metamaterials (N. Tedeschi, Università di Roma La Sapienza)
How many different possibilities do exist for permittivity and permeability?
Double-Positive (DPS)
Double-Negative (DNG)
Epsilon-Negative (ENG)
Mu-Negative (MNG)

2. negative group velocity
Maxwell equations:
Looking for a plane wave solution exp (-jkr)
DPS materials
k, E, and H are RH
DNG materials
k, E, and H are LH
Poynting vector in the frequency domain:
DPS materials
S, E, and H are RH
DNG materials
S, E, and H are RH
In a DNG material the propagation vector and the Poynting vector are anti-parallel, i.e., they lie on the same line, but they point in opposite directions.
and
with
negative group velocity
backward-wave materials

3. Doppler effect
Cerenkov radiation

4. with evanescent waves exponentially decaying
What is there new to say other than to polish the lens more perfectly and to invent slightly better dielectrics?
Consider an infinitesimal dipole of frequency w in front of a lens. The electric component of the field will be given by some 2D Fourier expansion,
with
For large values of the transverse vector
evanescent waves exponentially decaying
Propagating waves limited to
maximum resolution

5. Negative phase! It is the phase reversal
Slab of material with n = -1
Transport of energy in the +z direction requires that
Overall the transmission coefficient of the medium is
kz’=kz
J. B. Pendry, PRL 2000
Negative phase! It is the phase reversal
that enables the medium to refocus light
By canceling the phase acquired by light as
It moves away from its source.
V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).

6. The NEW THING is: the medium cal also cancel the decay of evanescent waves (from Pendry on…). Such waves decay in amplitude not in phase, as they propagate away from the object plane. Therefore to focus them it is needed to amplify them rather than changing the phase. Pendry showed that the evanescent waves emerge from the far side of the medium enhanced in amplitude by the transmission process. This does not violate energy conservation because evanescent waves transport no energy.
Pendry showed
Transmitted field has the same magnitude of the incident one (R=0). A similar result holds for P-polarized evanescent waves
The conclusion is that the medium does amplify evanescent waves! With this new type of lens both propagating and evanescent waves contribute to the resolution of the image. There is no physical obstacle to perfect reconstruction of the image beyond practical limitations of apertures and perfection of the lens surface.

7. W. J. Padilla et al, Negative refractive index metamaterials, Materials Today 9, 28 (2006).

8. How to realize a metamaterial in practice??
There are nowadays several different schemes. One of the most spread out is to realize a unit cell made of the couple Wire Medium (ε<0) + Split Ring Resonator (SRR, <0)
Wire Medium (ε<0)
It is shown that
R is the resistance per unit length of the wire
L is the effective inductance per unit length of the wire

9. The effective permittivity can be designed, by varying the dimensions of the wire arrays (parameters a,r), i.e. the plasma frequency, so to obtain negative values of ε at a very low frequency. We can then design an artificial medium with configurable permittivity.

10. Split Ring Resonator (SRR, <0)
S is the effective surface looking at the SRR as an elemental current loop. R is the resistance due to conductive losses of the loop.
L is the inductance due to the ring shape.
C is the capacitance due to the slpit on the ring.
 is the effective volume of the SRR.
An expression similar to the permeability of the magnetized ferrite is found. With this medium a configurable value of the permeability is possible

11. How to realize a metamaterial in practice??

12. Ongoing applications!!

14. The design

15. The characterization

16. Results

17. Something similar going on in the yard nearby home..

19. The experiment