Materials with negative index of refraction and their properties
Victor G. Veselago ( v-DOT-veselago-AT-relcom-DOT-ru.gif )
Moscow Institute of Physics and Technology, Institute of General Physics, Vernadskogo 11-222/ Moscow 199311, Russia.

In materials with negative index of refractions vectors E, H and k formed left handed set, and it is a reason to give for this media a name "left-handed materials - LHM", in contradiction with common type "Right-handed materials - RHM". One of the possible examples of LHM are the materials with simultaneously negative electric $\varepsilon$ and magnetic $\mu$ permeabilities. For LHM all the optics and electrodynamics laws are valid, if we will use the negative sign of refraction index except positive. So from common form of Snellius law $n = sin \varphi / sin \psi$ one can see that on RHM-LHM interface refracted beam directed on the angle $-\psi$, symmetrically with the refracted beam in the case RHM-RHM. This principal difference was first observed experimentally by San Diego group [1], confirms in such a way predictions of the work [2]. The real meaning of work [1] is not only direct experimental verification of case $n < 0$, but, at first order, this work open us a possibility construct composite materials with regulated values $\varepsilon$, $\mu$, and not only with regulated value $n$, but also with regulated impedance $Z=(\mu/\varepsilon)^{1/2}$.

From the fact of possibility of negative refraction index follows some remarkable corrections not only in Snell law, but in Doppler effect, Cherenkov effect, properties of lens [1], and Fermate principle [3].

The last one now can not be formulated as a "light propagates on the way with shortest time of propagations". The right expression is only "the light propagates on the way with extremal optical length". The value "optical length" is $L = \int n dl$ where $n$ is refractive index, and integral is taken along the real path of light. Value of $n$ is negative for LHM, of course. Very interesting is LHM in the form of flat slab with parallel boundaries [2,4]. It is a sort of lens with some unique properties. For example, in this lens can be realized the zero value length of optical path between source and receiver of light.

References
  1. R.A.Shelby, D.R.Smith, S.Shultz, Science 292, 77 (2001)
  2. V.G.Veselago, Sov.Phys.Uspekhi 10, 509 (1968)
  3. Veselago V.G.(2002) About the wording of Fermat`s principle for light propagation in media with negative refraction index, http://xxx.lanl.gov/ftp/cond-mat/papers/0203/0203451.pdf
  4. A.L.Pokrovsky, A.L.Efros,.(2002) Diffraction in left-handed materials and theory of Veselago lens, http://xxx.lanl.gov/PS_cache/cond-mat/pdf/0202/0202078.pdf