Nanotechnology Can be Helped by a New Technology for Electromagnetic Waves

On this paper we propose the use of a recently developed technology about the substitution of metamaterials with electromagnetic t ime reversal procedures for apply in some issues of nanotechnology. The general concept is to take advantage of two important facts: first we can localize the electromagnetic signals much better; secondly, in many cases we can use waves of minor frequency than that we would use in absence of this technology. To this end we give some examples of specific research where it is possible to apply the vector-matrix formalis m to nanotechnology.


Introduction
Nowadays we have an intense research about several new fields of application of nanotechnology; since development of materials with ext raordinary physical p roperties like the very strong carbon nanotubes, to the modeling o f artificial atoms that interact with single microwave photons that could be push the quantum computers near to reality. Many of those fields are close related to the emp loy of microwaves in a natural way because of possibility to an easy man ipulation of this range of the electromagnetic spectrum in addition to their propert ies to carry informat ion on co mmunicat ions. But one of the tools employed to magnify images and focus signals is the use of metamaterials. Metamaterials are also a new excit ing field of physics research and have his own essential or enclosure applications. Nevertheless, metamaterials are not the only possibility of access to the nanotechnology world. Thanks to many recent works we know that there are other possibilit ies like the use of time reversal methods to reproduce and even improve the results of metamaterials in a large class of nanotechnology problems. The question is then when we can use alternative time reversal methods?
The answer is in the manufacture of metamaterials, because usually it is a difficult and expensive task. So, it is justified in many cases to employ time reversal methods.
In this wo rk, we g ive in section 3 a blueprint o f a general method we call the vector-matrix formalis m that gives us an easy to apply way to overco me the diffract ion limit and focus a microwave signal. As a preface we before co mment in section 2 so me recent researches on nanotechnology and finally in section 4 we propose how we could improve the results obtained by using time reversal procedures.
The novelty of this work is in the tool itself, but also in the blueprint of its applications to nanotechnology, because we can now design (By building the kernel (3)) devices that will can focus laser or micro waves beams with a minor frequency that can be focused more precisely. To be more specific, we show with an example for electro magnetic pincers, how the magnetic mo ment of the target reacts with the electro magnetic field of the beams; or in the examp le of artificial ato ms how a better electro magnetic localizat ion of a micro wave beam could improve the performance of a new kind of Nano-devices.

A sight to Nanotechnology
In a very interesting paper of 2007 [1], the authors have find that microwaves shows his particle identity on a class of macroscopic systems they called artificial ato ms (see figure  1). So they observed the effects of quantum mechanics but in a scale near to a visib le one. These results marked a clear line of research about the manufacture of quantum co mputers and other related devices[2 and 3] that now seems to be near to reality.
The process they observed was the interaction of micro wave photons with the artificial ato ms which have a size very much larger than the traditional quantum domain.
Direct implications are between others, that communicat ion process on Nano-devices can be optimized by allow the long-range neighbor interactions without errors.
Because the microwave interaction also can reach atomic spins, molecules and even atoms, other nanotechnology fields can be grows, for example man ipulation of nanoparticles by using the interaction between particle spins and electromagnetic beams[4, 5, and 6] wh ich permits the building of electro magnetic pincers .
Maybe the more known field is the development of optical amp lifiers or lenses which provides well defined images of the Nano-scale world. The general mechanism is the recovery of the so named near field that consist in evanescent waves [7]. This is a field where the use of metamaterials is strongly used (see figure 2) and the wavelength is less restricted to micro waves, that is the images usually are in the visible spectrum. One of these simplest devices consists in a thin layer of a semiconductor with a silver layer as a top.
The manufacturing of Nano-engines is another very excit ing branch of nanotechnology with amazing results which includes not only engines but also Nano-structures that seems to be automobiles wh ich can move by its own resources and whose individual parts are made with single mo lecules. Even when there is not a necessary relat ion with this singular engines with microwaves it is clear that his composition are inclined to react with this range of wavelengths (see for examp le [8] ). Nano-medicine is also one of the more act ive branches of Nano-technology research with an obvious great importance whose real devices depend on microwave co mmunicat ions between the device and the medical observer.

Why Time Reversal and Not
Meta-materials?
On section 2 we have underline the close relation between Nanotechnology and the microwaves used at different levels, not only as a direct reactive agent but also as a source of power and a carrier of information. Also, we co mmented that the use of metamaterials is very frequently in order to localize electro magnetic signals. But in many cases, the sole procedure to build metamaterials is difficu lt and expensive. A relat ively recent tool has been developed that allow to make an extremely efficient signal localization ( ) 30 λ  for micro waves about 2.5 GHz [4 ] and it is a fact that is superior to the more nearest results with the use of This tool is known as Time Reversal (TR) and consists in sending a signal but in time reversal order. This procedure was developed first to localize acoustic signals, but then the researchers export the techniques to electromagnetic waves. But how a TR can recover the evanescent waves like a metamaterial? In 2009 [9] we discussed that the Green's function needed for TR (for acoustic signals) have similar properties than the explicit expressions of complex index of refraction in a metamaterial (for electro magnetic waves), then it was a natural feeling to hope that must exist a formalism that can reproduce the effects of a metamaterial under the electro magnetic field but without his physical existence (of the metamaterials). But experiments support this hope as we have mentioned above, so we write a vector-matrix formalis m [10] that contains all the information about an specific d iscrete electro magnetic system and that can be applied to imp rove the process of sending a signal and localize them with the minor loss of informat ion. Then we present the formalism as the final vector-matrix equation and his possible applications. Before this we recognize some physical limits. First, only discrete systems can be considered; secondly we suppose that the position of the emitters-receptors is chosen in a non-periodic array and third, some of the sink terms (at least one) must be located in the near zone. The three conditions guarantee to avoid that the negative effects of interference destroy information and that we preserve a mathematical base to represent the complete electro magnetic process. The vector-matrix equation for a TR is: For ro w vectors Where the kernel is defined as 22 32 23 33 (13) We can see that the previous equations are the co mponents of equation (1) (after mu lt iplication) when we choose the case of three emitters and three receptors. So that the three relations can be written as  (14) By substituting the expressions for the "matrix" c then     1  1  1  11,2  21,2  31,2   1  1  1  12,2  22,2  32,2   1  1  1  13,2  23,2  33,2   1  1  1  11,3  21,3  31,3  1  1  1  12,3  22,3  32,3  1  1  1  13,3  23,3  33,3   2  2  2  11,2  21,2  31,2  2  2  2  12,2  22,2  32,2 13,    2  2  2  11,3  21,3  31,3  2  2  2  12,3  22,3  32,3  2  2  2  2  2  2  2  23,2  33,2  13,3  23,3  33,3   3  3  3  3  3  3  11,2  21,2  31,2  11,3  21,3  31,3  3  3  3  12,2  22,2  32,2  3  3  3  13,2 23,2 33,2 3  3  3  12,3  22,3  32,3  3  3  3  13,3 23,3 33,3 Equations (1), (2), and (3), resume the effo rts to make a better envoy of information in a discrete electro magnetic system (for examp le the broadcast by an antenna arrangement in MIM O technology [11, 12,

Suggested Nanotech Applications
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. The possibility to manipulate microwaves could make an easiest procedure this extremely difficu lt issue. Due to the fact that micro waves can interact d irectly with so me mo lecules and even atoms, maybe we can operate over elaborated Nano-engines and other important Nano-structures. In figure (3) we present the results of a real experiment realized by K. Volke et al. [4] in which they compare the effect of two distinct in shape laser beams over a silica sphere immersed in water and it is possible to move it. This is an example of electro magnetic pincers based on laser beams but that shows the way to the employ of general electro magnetic waves including microwaves not necessary in the form of a "maser" beam (that is the precursor of the laser). Then one of our strongest proposals is to manipulate Nano-structures with the aid of microwaves controlled by the TR tools including the vector-matrix formalis m.

Conclusions
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).
If we want to apply our results to design a specific device involving magnetic mo ment interactions we must built the kernel (3) wh ich defines how the target (for examp le silica spheres) reacts with the electromagnetic beam, but now we can also focus it in a subwavelength manner. In the other hand, we can reach targets with a very minor size (thirty times minor) with this new technology.