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• W2092381718 abstract "Subwavelength focusing (SF) is a very useful tool that can be carried out with the use of left hand materials for optics that involve the range of the microwaves. Many recent works have described a successful alternative procedure using time reversal methods. The advantage is that we do not need devices which require the complicated manufacture of left-hand materials; nevertheless, the theoretical mathematical bases are far from complete because before now we lacked an adequate easy-to-apply frame. In this work we give, for a broad class of discrete systems, a solid support for the theory of electromagnetic SF that can be applied to communications and nanotechnology. The very central procedure is the development of vector-matrix formalism (VMF) based on exploiting both the inhomogeneous and homogeneous Fredholm's integral equations in cases where the last two kinds of integral equations are applied to some selected discrete systems. To this end, we first establish a generalized Newmann series for the Fourier transform of the Green's function in the inhomogeneous Fredholm's equation of the problem. Then we go from an integral operator equation to a vector-matrix algebraic one. In this way we explore the inhomogeneous case and later on also the very interesting one about the homogeneous equation. Thus, on the one hand we can relate in a simple manner the arriving electromagnetic signals with those at their sources and we can use them to perform a SF. On the other hand, we analyze the homogeneous version of the equations, finding resonant solutions that have analogous properties to their counterparts in quantum mechanical scattering, that can be used in a proposed very powerful way in communications. Also we recover quantum mechanical operator relations that are identical for classical electromagnetics. Finally, we prove two theorems that formalize the relation between the theory of Fredholm's integral equations and the VMF we present here." @default.
• W2092381718 created "2016-06-24" @default.
• W2092381718 creator A5011950794 @default.
• W2092381718 date "2012-10-01" @default.
• W2092381718 modified "2023-10-14" @default.
• W2092381718 title "Fredholm's equations for subwavelength focusing" @default.
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• W2092381718 doi "https://doi.org/10.1063/1.4759502" @default.
• W2092381718 hasPublicationYear "2012" @default.
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