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*1. Focusing of electrons in graphene, the right side is due to the applied confining potential has a negative refractive index. Red asterisk denotes an emitter, a blue — reservoir. *

Scientists from Russia and France have analytical solutions for focusing light in the half with a negative index of refraction. The results indicate that in the case of such media must radically change the formulation of the problem of the well-known in optics ideal lens.

In 1967, the Soviet physicist, then a staff member of FIAN, Victor Veselago hypothesized the existence of materials with negative refractive **index** — the so-called metamaterials. For this, the magnetic permeability and dielectric material must be both negative and the phase and group velocity of electromagnetic waves, as a result, have opposite directions. If the manufacture of a material parallel plate, it will focus light like a convex glass **lens**. Later, in 2000, the English physicist, Professor John Pendry gave arguments in favor of the fact that the ideal Veselago lens has no diffraction limitations on the resolution and will have such a high degree of focus, which will consider the matter at the nanoscale. An employee of the Physical Institute. PN Lebedev Physical Institute (LPI) Vasiliy Klimov and colleagues at the University of Paris 13 (France) Jacques Duclos Martial Bodoni and decided to thoroughly test this hypothesis, and found that taking into account absorption, albeit small, in real materials, the expected accuracy of the focus will not be .

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*2. Focus plate photons with negative refractive index (in the middle), comprising a radiation receiver. Two emitter located outside. *

"The **problem** is — the main researcher of the Physics Institute, Doctor of Physical and Mathematical Sciences Vasily Klimov — that the path of **light** is the region of space where the stationary solutions of Maxwell's equations, as such, does not exist. This is precisely the case when both the permeability and permittivity, and magnetic — negative, and the loss in the material is equal to zero. But the potential of a **negative** index of refraction is very large, it can not simply be discounted, so you need to think about a different formulation of the problem. "

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*3. Path of the perfect lens Victor Veselago, according to previously accepted point of view. *

One of the proposed formulations of the problem is to use not only the lights, but the receivers. One of the simplest options — put the light inside the receiver plate, and sources — from the outside (at the points of intersection of the rays in Fig. 3). In this **case**, the beam path will be almost the same as in the original problem, but a region of space where there is no solution of the problem, will not be. By the way, this idea is advantageous to use and to implement the process of excitation of atoms in a quantum computer. For quantum computers and quantum communications, which are now being actively developed, single-photon light sources are necessary to drive the nanowaveguides and other nanodevices and work at the quantum level. Now for the emission of a single photon at a given time (single-photon source) is required from 1 to 10 million photons, ie system turns extremely inefficient. But if we consider the plate with a **negative** refractive index and place it inside the unexcited atom, and the outside — two excited, then the probability that the photon will scatter to the sides and do not excite an atom inside, equal to one quarter, and the probability of its excitation — 0.75 . You can build a system contrary, and use one of the excited particles in the plate and two unexcited outside. Then, wherever I flew photon, it is sure to excite one of the two atoms on the **outside**, because the rays intersect at very small sizes. And since it is not clear in advance which of the atoms become excited, the result is a confusing state of the two excited atoms, which can be used in quantum cryptography.

Such calculations researchers conducted not only for the case of focusing the photons, but also for ultra-massless Dirac particles, such as electrons in graphene (Fig. 1). In this case the zone of negative refraction begins to border regions with a negative index of refraction (it right). A receiving side electrode the focal spot is more complicated than in the case of photons spatial structure. The resulting solution has a close analogy with the Klein paradox — the phenomenon of relativistic particle tunneling through a high potential barrier which is explained in the birth of particle-antiparticle pairs.