Resonances on discrete electromagnetic time reversal applications

Abstract

Electromagnetic Time Reversal Vector formalism [1, 2] can be employed not only to the purpose of achieve subwavelength focusing. We can go far away of this initial goal and take the formalism as the starting point for analyzing the behavior of discrete electromagnetic systems in a regime that represents special but interesting physical usefully situations. The advantage over other possible approximations is that we can guaranteeing the minimum loss of information because the discrete formalism was built by thinking that time reversal increase the scattering section and then the Green's function carry the most complete information to recreate the source signals. In this work, we find that solutions of the corresponding homogeneous vectormatrix equation in Time Reversal formalism, have a strong similarity with the so called resonant states for nuclear reactions [3, 4] so they inherit some of their properties. The physical systems that we can model are reverberating or short living electromagnetic fields that can be localized inside real or imaginary cavities. Our ultimate purpose is the possible applications on communications related for example with MIMO microwave technology operating on imaginary cavities, that is, on some special regions of space.

Fredholm's alternative breaks the confinement of electromagnetic waves

“…5,15,17 That is we deform the path of integration over the real axis of equation (1) to include the resonances on the fourth complex quadrant in the spectral representation. Then we have the new spectral representation of the Green's function as follows 2,5,10,14,15 …”

“…Before we make of the Fredholm's alternative (FA) the center of our attention we recall that only recently we can talk about the connection between evanescent waves [6][7][8][9][10][11][12] and resonant solutions of the homogeneous Fredholm's equation. [13][14][15][16][17][18] But then we have a physical interpretation of the solutions we want to classify, that is if the integral equation is inhomogeneous we have a positive refraction index-like conditions but if the equation that describes the physical situation is homogeneous we then have negative refraction index-like conditions and the solutions can be called resonances. the two different kinds of physical conditions there are travelling waves that allow communications, their frequencies are basically different because in the positive refraction index-like conditions, the corresponding frequency values to the resonant ones are really hidden or in a practical sense are confined to the so called near zone without the possibility to bring any information because of their exponentially decaying amplitudes.…”

Nanotechnology Can be Helped by a New Technology for Electromagnetic Waves

“…Even we cannot show yet an application to nanotechnology this paper can shows theoretical results that are orig inal and that can be the mathematical base to real experiments on communications [15], also in this place we show how we can display the fo rmalis m in the case of three emitters and three receptors, so we can see that the introduced notation is very compact an appropriate for easy use in many branches including Nano-technology. The proposal has been supported by the reference of real man ipulation of Nano-structures with electro magnetic beams (laser beams).…”

“…On reference [15] we showed how we can improve the so called MIM O technology (Multiple Input-Multiple Output) ; this technology for communications could be scaled to reach Nano-devices in med ical applicat ions. But we guess that we can use localized microwave beams to play the role of electro magnetic pincers in the same way as the current optical pincers described in some experiments [4] in which the beam interacts with the spin of the Nano-particles.…”

Fourier Transforms for Generalized Fredholm Equations

“…Many of the problems we want to consider are those related with vector fields like the electromagnetic. For this situation we dedicate the present chapter first to the integral equation formulation of the electromagnetic traveling waves, and then, by the application of the Fourier transform, we obtain finally a matrix-vector formulation [9,10,12,14,18]. To this end we go from the conventional Fredholm equations to new vectorintegral equations we name generalized Fredholm equations proving that really they have the same properties of the conventional scalar Fredholm equations.…”