Abstract:
A metamaterial is proposed which is composed of base elements having six ports with two ports, respectively. The base element further comprises four nodes connected with a central point via inductors, to which nodes the ports are connected via capacitors.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
   The present application is a continuation of pending International patent application PCT/DE2006/002227 filed on Dec. 13, 2006 which designates the United States and claims priority from German patent application 10 2005 059 392.5 filed on Dec. 13, 2005, the content of which is incorporated herein by reference. 

   FIELD OF THE INVENTION 
   The invention relates to a base unit for the transmission of electro-magnetic fields with six ports having two poles, respectively. 
   Furthermore, the invention relates to a device for the transmission of electromagnetic fields. 
   BACKGROUND OF THE INVENTION 
   Such a device is known from GRBIC, A.; ELEFTHERIADES, G. V.: An isotropic three-dimensional negative-refractive-index transmission-line metamaterial. In: Journal of Applied Physics, VOL. 98, 043106 (2005). The known device comprises a base unit with a plurality of ports having two poles, respectively. Metamaterials having a negative refractive index can be provided using the base unit. 
   Metamaterials are artificial structures exhibiting both negative dielectricity coefficients as well as negative permeability coefficients in certain frequency ranges. An extensive survey on metamaterials is given, for example, in the publication by LAI, A.; ITOH, T.: Complete Right/Left-Handed Transmission Line Metamaterials. In: IEEE Microwave Magazine, September 2004, pp. 34-50. Metamaterials are composed of base units set up next to each other. 
   Lenses whose resolution is lower than the resolution limits of λ/2 can be constructed, in principle, using metamaterials. Furthermore, antennas which have a higher sensitivity than conventional antennas are conceivable. Finally, the development of materials is also conceivable, which guide radiation incident on a body around the body free of reflection, so that the body cannot be detected by the reflected or scattered portions of the incident electromagnetic radiation. 
   In particular, it could thus be possible to develop materials that cannot be detected by radar. 
   Based on this prior art, the invention is therefore based on the object of providing base units and devices for the transmission of electromagnetic fields that are suitable for metamaterials. 
   SUMMARY OF THE INVENTION 
   This object is achieved by a base unit and a device having the features of the independent claims. Preferred embodiments and developments are specified in the claims dependent thereon. 
   The base unit for the transmission of electromagnetic fields has six ports having two poles, respectively. In addition, there are four nodal points connected with a central point via inductors, wherein the ports can be grouped into three pairs whose poles are respectively connectable to different nodal points via capacitors. 
   It was possible to show that devices with a plurality of such base units have negative refractive indices in broad frequency ranges. 
   Preferably, the base unit is formed as a three-dimensional cell, so that the devices composed of the base units are suitable for spatial applications. 
   Furthermore, the base unit preferably has a cuboid structure, which facilitates setting up the base units next to each other. 
   Devices for the transmission of electromagnetic fields based on the base unit preferably comprise two complementary types of base unit, which are hereinafter referred to as A cell and B cell. The A cells and B cells can be set up next to each other in series, with A cells respectively connected to B cells and B cells respectively connected with A cells. This structure suggests itself if the A cells and B cells must be realized separately. 
   The A cell is a six-port unit cell for transmission of electromagnetic fields wherein the A cell has a 3-dimensional cell structure. The 3-dimensional structure of the A cell is depicted with respect to an orthogonal right-handed coordinate system. The A cell comprises 6 ports, each port having two nodes. The direction of an electrical field between the nodes of each port can be shown aligned in various directions. The B cell is a six-port unit cell for transmission of electromagnetic field that is complementary to the A cell. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Other properties and advantages of the invention become apparent from the following description in which exemplary embodiments of the invention are explained in detail with reference to the accompanying drawing. In the figures: 
       FIG. 1  shows the structure and the circuit of a first unit cell; 
       FIG. 2  shows the structure and the circuit of a second unit cell; 
       FIG. 3  shows a simplified representation of the first unit cell from  FIG. 1 ; 
       FIG. 4  shows a simplified representation of the second unit cell from  FIG. 2 ; 
       FIG. 5  shows an arrangement comprising two first and two second unit cells; 
       FIG. 6  shows an arrangement comprising four first and four second unit cells; 
       FIG. 7  shows the representation of a merged unit cell; 
       FIG. 8  shows the enlarged representation of the ports of the unit cell from  FIG. 7 ; 
       FIG. 9  shows a representation of the circuit of a unit cell projected onto a plane; 
       FIG. 10  shows the representation in perspective of a realized first unit cell; 
       FIG. 11  shows the representation in perspective of a realized second unit cell; 
       FIG. 12  shows the representation in perspective of a realized combination of the first and the second unit cell; 
       FIG. 13  shows a photograph of a unit cell used for measurements; 
       FIG. 14  shows a calculated dispersion diagram; and 
       FIG. 15  shows another dispersion diagram combined with a representation of the wave impedance. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
     FIGS. 1 and 2  show the schematic representations of the geometry and circuitry of a first unit cell  100  and a second unit cell  200 . Each of the two unit cells  100  and  200  is a six-port. The first unit cell  100  will hereinafter be referred to as A cell and the unit cell  200  as B cell. The A cell of  FIG. 1  comprises six ports denoted  1  to  6 . From these ports, conductors run to the nodes  21 ,  22 ,  23  and  24 . A capacitor C is inserted into each of the twelve conductors from the ports  1  to  6  to the nodes  21  to  24 . Each of the four nodes  21  to  24  is connected with a central node  25  via an inductor L. The drawing not only schematically represents the circuit diagram, but also the geometrical arrangement of the lines. The arrows drawn into the ports represent the reference arrows for the port voltages and also indicate the direction of the electrical field between the two nodes of the respective port. The electrical field between the nodes of port  1  is oriented in the [0, 1,−1] direction, the electrical field between the nodes of port  2  is oriented in the [0,1,1] direction. The electrical field between the nodes of port  3  is oriented in the [−1,0, 1] direction and the electrical field between the nodes of port  4  is oriented in the [1,0,1] direction. The electrical field between the nodes of port  5  is oriented in the [1,−1,0] direction and the electrical field between the nodes of port  6  is oriented in the [1,1,0] direction. 
   It should be noted that the indication of the direction is given in relative coordinates. If the [0, 1,−1] direction is attributed to the direction of the electrical field between the nodes of port  1 , the direction of the electrical field between the nodes of port  2  must be oriented in the [0,1,1] direction and so on. 
   The B cell  200  shown in  FIG. 2  has a geometrically complementary arrangement with regard to the A cell. The unit cell  200  has ports  7  to  12  which are connected to internal nodes  31  to  34  via capacitors C. The circuit configuration of the B cell with capacitors C and inductors L corresponds to the circuit configuration of the unit cell  100 . However, the polarizations at the ports  7  to  12  are rotated by 90° compared with the A cell. For example, the polarization of the electrical field in port  7  is oriented in the [0,−1, 1] direction. 
   In the following, the schematic representation of the A cells and B cells according to  FIG. 3  and  FIG. 4  is used, with the capacitors and inductors not drawn in for the purpose of simplifying the representation. In all cases, however, the capacitors C and inductors L are included in the branches, corresponding to  FIGS. 1 and 2 . 
   The A cell is a six-port unit cell for transmission of electromagnetic fields wherein the A cell has a 3-dimensional cell structure as shown in  FIGS. 1 and 3 . In  FIGS. 1 and 3 , the 3-dimensional structure of the A cell is depicted with respect to an orthogonal right-handed coordinate system. As shown in  FIG. 1 , the A cell comprises 6 ports, each port having two nodes. The direction of an electrical field between the nodes of each port is shown aligned in various directions according to the arrows shown in  FIG. 1 . 
   The B cell is a six-port unit cell for transmission of electromagnetic field that is complementary to the A cell. The 3-dimensional cell structure of a B cell is shown in  FIGS. 2 and 4 . 
     FIG. 8  shows a simplified representation of the combined unit cell  500 . It can be seen from  FIG. 8  that the electromagnetic radiation incident on the basic cell  500  from any direction in space can be transmitted by it. Furthermore the relative orientation of the electrical fields between the nodes of the ports  1  to  6  and  7  to  12  with respect to an orthogonal reference system can be recognized. 
   Finally, a circuit of the unit cell  100  projected onto a plane is shown in  FIG. 9 . It can be seen from  FIG. 9  that the ports  1  to  6  each have two poles  40 . In addition, the circuit arrangement becomes clear in detail. 
   Simulation calculations were performed and experiments carried out for proving suitability for metamaterial. The setup of the experiment shall be explained with reference to  FIGS. 10 to 13 . 
     FIG. 10  shows a view in perspective of the unit cell  100  in a concrete realization. In the unit cell  100  shown in  FIG. 10 , lines  41 , starting from the central node  25 , lead to the internal nodes  21  to  24 , which are located at the corners of the cube. The lines  41  assume the function of the inductors L. Furthermore, plate capacitors  42  are disposed in the corners of the cube, which are connected in the corners to the allocated nodes  21  to  24 . The outer surfaces of the plate capacitors  42 , which on the side surfaces of the cube are disposed diagonally opposite, each form the poles of one of the ports  1  to  6 . 
   It should be noted that the edges of the plate capacitors do not touch each other. Only in the nodes  21  to  24  is there a connection between the internal electrodes of the plate capacitors  42 . 
     FIG. 11  shows the structure of the unit cell  200  complementary to the unit cell  100 . What was said with regard to  FIG. 10  applies here correspondingly. 
   It can be seen from  FIG. 12  that the unit cell  100  and the unit cell  200  can be composed to form the basic cell  500 . 
   Finally,  FIG. 13  is a representation of a concrete experimental setup for investigating the unit cell  100  or  200 , in which two ports have been equipped with terminals for cables, whereas the remaining four terminals have been terminated with Ohmic resistors. 
     FIG. 14  shows a dispersion diagram showing the results of simulation calculations for determining the dispersion relation.  FIG. 14  shows, in particular, the frequency ω plotted in arbitrary units against the wave vector k. It can be seen in  FIG. 14  that two left-handed modes  50  and two right-handed modes  51  form, respectively. The mode located at higher frequencies here forms a particularly broad frequency band. 
   The left-handed modes are those modes having a negative group velocity. For example, the left-handed mode  50  has a negative slope in the area between k=(0,0, 0) to k=(π,0,0), which results in a negative group velocity. A negative group velocity, however, is typical for metamaterials with a negative refractive index. 
   The dashed and the solid curves in  FIG. 14  were each calculated using different parameter values, with parasitic quantities such as, for example, parasitic capacitors connected in parallel to the inductors L or parasitic inductors connected in series with the capacitors C also having been taken into account. 
     FIG. 15  in the top diagram again shows the dispersion relation from  FIG. 14 , the abscissa being the frequency axis and the coordinate representing the phase shift χ. For the phase shift, χ=k x ·a applies, with a being the size of the unit cell. The dashed curves  60  are the results of the simulation already shown in  FIG. 14 , whereas the solid curves  61  are the result of measurements. 
   In the lower diagram, the wave impedance is plotted against the frequency. A dashed curve  62  is the result of simulation calculations, whereas a solid curve  63  results from measurements. It becomes clear in  FIG. 15  that, in the phase range between 0° and 90°, which corresponds to the frequency range between 1 and 1.4 GHz, a wave impedance of between 100 and 150 Ohms is to be expected, which makes an adjustment to the wave impedance of the vacuum appear possible.