ar X iv : c on d - m at / 0 20 20 78 v 2 1 0 M ay 2 00 2 Diffraction in left - handed materials and theory of Veselago lens
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چکیده
A theory of diffraction in the system consisting of the left-handed and the right-handed materials is proposed. The theory is based upon the Huygens's principle and the Kirchhoff's integral and it is valid if the wavelength is smaller than any relevant length of the system. The theory is applied to the calculation of the smearing of the foci of the Veselago lens due to the finite wavelength. We show that the Veselago lens is a unique optical instrument for the 3D imaging, but it is not a " superlens " as it has been claimed recently. In his seminal work Veselago [1] has introduced the concept of the left-handed materials (LHM's). In a simplest case the LHM's are materials with simultaneously negative electric permittivity ǫ and magnetic permeability µ in some frequency range. It is easy to show that in the LHM the vectors k, E, H form a left-handed set, while in the usual materials (ǫ > 0, µ > 0) they form a right-handed set. If imaginary parts of ǫ and µ are small, the electromagnetic waves (EMW's) propagate in the LHM but they have some unusual properties. All these properties originate from the fact that in the isotropic LHM the Poynting vector S = E × H is anti-parallel to the wave vector k. Consider a propagation of the EMW from a point source located at the point z = −a through an infinite slab of the LHM with the thickness d and a usual right-handed material (RHM) at z < 0 and z > d (Fig.1). It is obvious that S z > 0 everywhere at z > −a because the energy propagates from its source. The directions of vector k for different rays are shown by arrows. They should be chosen in such a way that at both interfaces tangential components of vector k for incident, reflected and refracted waves are the same. Another
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