The purpose of this paper is threefold. The first aim is to discuss the superlensing effect in left-handed material presented originally by Veselago [Sov. Phys. Usp. 10, 509 (1968) ] and Pendry [Phys. Rev. Lett. 85, 3966 (2000) ] for . Our discussion is based on an integral expression for the electromagnetic fields (i.e., the Extinction Theorem), and it allows us to demonstrate that such superlensing effect does not exist. The second aim is to discuss some basic questions about structured metamaterials formed by periodic resonator arrays. We will show that a set of antennas can never emulate a negative refractive index material. The third, concurrent, aim is to discuss the experimental evidence for negative refraction in structured periodic materials. We present another possible explanation of the experimental results concerning negative refraction that is based on the coherent interference of wavelets originated in the subwavelength structures.
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