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 Green´s 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.