C.A. Vargas

Communication theory and resonances on electromagnetic systems

We have shown that some electromagnetic systems allow specific frequencies to satisfy special equivalent conditions to make use of a left hand material. We called these frequencies resonances because of their properties, similar to those solutions of the homogeneous Fredholms equation for nuclear physics. But the process of information transmission requires not only the envoy of a limited number of frequencies but a very broad set of them. To answer the question of how we can use the knowledge of the resonances on a real system, we make use of the communication theory and the other properties, like the super-oscillating addition of functions and the mathematical deformation of the contour of the spectral representation of signals in order to create a set of frequency packs labeled with the final effect to optimize the information broadcast. In this paper we also suggest how we can preserve the convenience of this resonant point of view even when we cannot guaranty that the resonant conditions can be sustained permanently.

The confinement of electromagnetic waves and Fredholm's alternative

Nowadays, the question about the recovery of lost information due to the presence of the so called electromagnetic evanescent waves, seems to be explained enough. But in fact we know that travelling and evanescent waves both originate from very different stems of integral or differential equations and whose behavior is classified as mutually discriminating; that is, we cannot have simultaneous validity of both kinds of equations for the same physical circumstances. Nevertheless, if our system can be described by a Fredholms equation we can at least build a bridge between these two sets of rules, based to the Fredholms eigenvalue. When the Fredholms eigenvalue falls into certain range then Fredholms equation describes a normal travelling spectrum; otherwise, we are in the presence of another type of equation with abnormal or special behavior. In this work, we analyze the so-named Fredholms alternative, which enables us to describe the change of positive refraction index-like conditions of broadcasting media to negative refraction index-like conditions. We also sketch the frequency dependence of Fredholms eigenvalue in order to establish general rules for the breaking of the waves confinement.

Resonances on discrete electromagnetic time reversal applications

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 Greens function carry the most complete information to recreate the source signals. In this work, we find that solutions of the corresponding homogeneous vector-matrix 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.

Resonance regime on a plasma sandwich simulates a left-hand material broadcasting condition

The very fast variations on the real propagation conditions for electromagnetic waves can be simulated by a plasma sandwich model consistent in three iterated plasma layers: unmagnetized-magnetized-unmagnetized, in which we can establish resonant conditions (left-hand material conditions) by tuning the magnetization and electric potential intensity. In this paper we show how to prevent drastically changes on the broadcasting conditions to maintain high definition and few waste of information for a continuous process. To this end we recall some recent results we have obtained about the role of the Fredholms alternative on the resonant regime broadcasting conditions. Then we use the plasma sandwich model to predict the sudden real media changes. So we suggest incorporating a double system that oscillates between both to avoid the loss of the signal as occurs nowadays. In other words we do not try to avoid waves confinement but we take it into account.

Electromagnetic scalar and vector potentials on the problem of left-hand materials conditions

We review the electromagnetic scalar and vector potentials from the point of view of the Generalized Fredholm Integral Equations. Then we revise two sensitive concepts as the retarded and advanced Green functions. Provided we have developed the appropriate desired equations; we go to the problem of left-hand materials conditions for optimized broadcasting. We give also an academic but simple example.

Fredholm and Maxwell equations in the confinement of electromagnetic field

We recall some results about the confinement of electromagnetic field from the Fredholms equations properties perspective. Then we review some relations between the Maxwell equations and the generalized Fredholms equations and show the equivalence between these two points of view when we analyze the change in the broadcasting conditions from confined electromagnetic field to travelling waves, underlying limiting range situations. We propose some general suggestions in order to diminish the waste of power and information when it is necessary some kind of electromagnetic packaging.

Resonant Technology and Electromagnetic Packaging

Under the concept of the so called Resonant Technology, recently we had proposed a device that can transport a lot of different signals, all of them of similar frequencies although different recording time, packed around the resonant frequencies. With the aim to implement physically the device, we had developed an algorithm, which is inserted in a FPGA to build information packs and send it. Also, we analyze the Gap Waveguide Electromagnetic Packaging Technology, taking into account the signal integrity and the Electromagnetic Broadband Packaging Model.