On computing the trace of the kernel of the homogeneous Fredholm’s equation

2013

AIP Advances

Self Cite

The recovery of information from the so called electromagnetic evanescent waves seems to be a very well explained item. Nevertheless, the travelling waves that becomes from the evanescent waves emerge from integral or differential equations that are very different to those describing the conventional ones. Indeed, we can say that the two kinds of solutions, the travelling and evanescent waves represent a mutually discriminating problem in which we cannot have simultaneous validity of both kinds of equations even they represents the physical evolution of a the same system. But if we can describe our system with a Fredholm's equation we can relate both situations through the properties of the Fredholm's eigenvalue. When the Fredholm's eigenvalue has its values into certain range then Fredholm's 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 Fredholm's 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 some general conditions for the Fredholm's eigenvalue in order to establish general rules for the breaking of the waves’ confinement.

Section: Introductionmentioning

confidence: 99%

Fredholm's alternative breaks the confinement of electromagnetic waves

2013

AIP Advances

Self Cite

“…For normalization conditions (the auxiliary and original equations must have the same solutions) the structure of must be the same of a phase factor, that is: (10) And when the resonant conditions are imposed, h must satisfy that ( ) q q q ih e (11) for the resonant frequency q , where in general That is, the resonant solutions vanish at the point sources.…”

Section: General Behavior Ofmentioning

confidence: 99%

“…978-1-4673-5707-4/13/$31.00 ©2013 IEEE But if we want to take advantage of the resonant solutions of the homogeneous vector Fredholm's equation we can follow the recipe for quantum Gamow (resonant) states [2,4,10,11]. That is we deform the path of integration over the real axis of equation (1) ; ;…”

Section: Introductionmentioning

confidence: 99%

The confinement of electromagnetic waves and Fredholm's alternative

2013 International Conference on Electromagnetics in Advanced Applications (ICEAA)

Granados-Samaniego

Vargas

2013

Self Cite

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 Fredholm's equation we can at least build a bridge between these two sets of rules, based to the Fredholm's eigenvalue. When the Fredholm's eigenvalue falls into certain range then Fredholm's 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 Fredholm's 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 Fredholm's eigenvalue in order to establish general rules for the breaking of the waves' confinement.

“…To this end, we assume that the theory of homogeneous Fredholm's equations [3,4,5] is applied and written explicitly the kernel ) (…”

Section: The Orthogonality Relation For Resonancesmentioning

confidence: 99%

Resonances on discrete electromagnetic time reversal applications

2011 International Conference on Electromagnetics in Advanced Applications

Vargas

Fernandez-Chapou

et al. 2011

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.