FIELD OF THE INVENTION

The present invention relates to the field of antennae.

BACKGROUND PRIOR ART

In radar systems, there is a constant need for improvement in range and tracking capabilities. In the past, rotating antenna systems with reflectors have been used to direct the beam at a target. The introduction of more advanced electronic systems allowed for the individual control of antenna elements, and this allows for electronic beam steering in one or two dimensions. Electronic beam steering is much quicker than mechanic beam steering which allows for the tracking of multiple targets simultaneously. Besides advanced electronic beam steering technologies higher signal powers allows for a significant increase in range which is desirable when manufacturers are trying to meet more stringent demands of lower signatures of targets and higher velocities. Developments in Gallium Nitride (GaN) power amplifiers show a clear trend to more and more RF output power, by virtue of improved heat transfer in the radio frequency (RF) integrated circuit (1C) and in 1C packages to a cooling manifold. Obviously, the generated output power has to pass the antenna. Printed circuit board (PCB)-based antennas such as patch antennas use transmission lines that cannot tolerate higher power levels due to dielectric and conduction losses. Cooling the antenna is not always enough, especially when components are thermally isolated. At very high power levels, air filled waveguides have low losses. One downside of open-ended waveguides versus patch antennas is that large arrays of open-ended waveguides are much more difficult and thus expensive to fabricate. But due to recent developments of metal 3D printing technologies, these fabrication costs can be reduced significantly. When constructing phased array antennas, one ideally wants to maximize the element spacing to maximize the gain without introducing grating lobes. Flere grating lobes are extra unwanted directions of transmission. The antenna gain is directly proportional to the surface area of the antenna. This means that a larger antenna spacing directly allows one to increase the surface area and thus gain without increasing the cost due to additional electronics. The large size of some antenna geometries such as the open- ended waveguide antennas forces one to increase the antenna grid spacing correspondingly. At scan angles where grating lobes are present, one might also find blind spots. At these angles, propagation modes along a surface increase the mutual coupling which increases the active Sn parameter, that is, the coefficient of reflection indicating the ratio between the back scattered field and the incident field. The antenna spacing can also become electrically longer for antennas realized on printed circuit boards due to the fact that the higher dielectric constant of the printed circuit board slows down the electromagnetic wave. Blind spots can therefore be a problem for larger antenna grid spacings or antenna arrays in dielectric media in general.

Phased array antennas are arrays of antenna elements on a two-dimensional grid. The phase and amplitudes of each antenna can be controlled electronically or digitally which allows the operator to control the shape and direction of the beam at will.

Figure 1 shows a phased antenna array as known in the prior art.

Specifically, Figure 1 shows an illustration of a one-dimensional array with an implemented phase delay b between antenna elements 100 spaced at an equal distance d to realize a plane wave under an angle 0 _sca n·

If the array spacing d is too large, multiple directions will experience constructive interference and thus grating lobes will be formed. The transmitted energy can be calculated using a simple summation of plane waves with a phase shift determined by the displacement of the elements with respect to each other and a phase delay where k = 2pί/o ₀ , d the antenna spacing (assumed constant) and 0 _scan the scan direction. The transmitted energy as a function of the scan angle can be calculated as: where A(q) is the radiation pattern of the individual antenna.

The maximum scan angle can be defined to be the scan angle at which a grating lobe to appear in the visible range at Q = 90°. Then the maximum allowed spacing can be calculated using the formula: where q ₀ is the maximum scan angle. Applying the formula predicts a maximum spacing for a scan angle of 30° to be 2/3 l. Open-ended waveguide antennas require one dimension of the aperture to be at least half a wavelength of the transmitting signal in order for the propagation mode to be real and not evanescent (below cutoff). Preferably, that dominant direction should be bigger for better impedance matching with free space but smaller than the next propagation mode. In the other direction, the size of the waveguide does not influence the impedance, only the electric field strength given a signal energy. The wave impedance in a waveguide for TE modes is calculated as: where f _c is the cutoff frequency of the waveguide calculated as f _c = c ₀ /2a, c ₀ the speed of light and a the length of the long side of the waveguide. The open-ended waveguide can be oriented to have its short or its long side in the array direction. While in a one-dimensional array one would preferably choose the short side orientation in order to keep the distance smaller, in two-dimensional array one has to include both. Because of this, the widest antenna size dimension should fit in antenna spacing.

For one-dimensional arrays, the minimum spacing has to be the width of the aperture a _wg = 1/2l implying that the maximum scan angle is 90°. The issue for a linear array of waveguides arranged with the longest side next to each other is that the spacing has to be larger than a _wg since the waveguide has some physical thickness causing the maximum scan angle to drop below 90°.

One would ideally want the waveguide to be bigger so clearly, in one dimensional phased array antennas this shows that the occurrence of grating lobes cannot be avoided at lower scan angles. A solution is needed in order to make open ended waveguide apertures practical.

One option for a two-dimensional array layout is to put the elements on a square grid where the horizontal and vertical spacing is the same. The longest spatial period of antennas on this grid occurs in the X-direction (cp = 0° ) and the Y-direction (cp = 90° ). To decrease the spatial period in the X-direction, one can put the antennas in a equilateral triangular grid which cuts the grid spacing in the horizontal direction in half. However, this action does introduce a new diagonal periodicity which has to be taken into account. There are two variations of this array. The first variation is the type A array in which elements are offset along their shortest side. Alternatively, in a type B array elements are offset along their longest side.

Figure 2 shows a 2-dimensional array as known in the state of the art.

Figure 2 presents a type B array as described above. The cell is designed keep all antennas as close to each other. The horizontal spacing between elements is defined as d _x and d _y the vertical spacing. The maximum scan angle 0 _max now holds for the horizontal f= 0° scan plane and the f = 60° scan plane. When implementing this diagonal array with an open-ended waveguide antennas one must take into account the dimensions of the waveguide. The waveguide array width is a _wg and its smallest side is b _wg . The grid width is denoted by d _x and its depth in the y-direction is denoted by d _y . Because the waveguide aperture needs to have a width bigger than half a wavelength, its crucial to find the setup that makes it possible to fit in the waveguide aperture with some room to spare on each side. Because of the orientation of the waveguide aperture, it is known that w has to be significantly greater than d. Array type B offers an advantage in this way over the type A because it allows one to double the d _x value while halving the d _y value without the loss of grating lobe performance. Given this knowledge it is possible to calculate the array spacing given a 0 _max and wavelength l. The scan angle can be found for the B type array by rewriting the equation for the maximum grid spacing knowing that the distance 1/2d _x represents the longest distance. While at large distances the radiation pattern approaches that of a TEM-mode, it is possible to assign two propagation modes in the near field radiating in the XY direction to neighbouring apertures. As is visible from the fields sketched above, the electric field is always vertical (Z-direction) at the interface of the conducting plane. The side view illustrates a wave propagating in the Y-direction as a TM-wave because the E-field points in the YZ-plane. For propagation in the X-direction, the electric field is always perpendicular which represents a TE-wave along the surface. In rectangular arrays, it is difficult to position waveguide apertures without grating lobes at small scan angles. For triangular arrays this is different. The type B array allows for a one lambda spacing limit for grating lobes. Because a full 90 degree scan angle is often not required, it is possible to increase the allowed antenna spacing even further but it is important to realize that even small increases drastically lower the maximum scan angle at which a grating lobe exists.

Because radar signals have an operating bandwidth, it is often true that grating lobe designs are optimized for the centre of the bandwidth which means that at the higher frequency edge of the band blind-spots inside the scan range can be observed. The existence of blind spots due to mutual coupling between elements and the introduction of grating lobes due to the grid spacing are related to each other. Blind spots occur if the Floquet modes of the radiated field correspond to a propagating mode at the surface in a square lattice. This can be mathematically written as:

Where k|| is the magnitude of the propagation constant of the transmitted plane wave tangential to the array surface (XY-plane), m and n are the Floquet mode indices and the free space phase constant ko= 2 pί/c. This equation generalizes to different array designs with dielectric materials. This equation will be used for free space coupling between antenna elements so that k|| = k ₀ in one direction only so that d _y and f = 0. When substituting this in the equation yields: This last expression shows that given a scan angle at which a blind spot occurs, the array grid sizes include the maximum grid spacing for grating lobes. In conclusion, there is a direct relation between free space coupling between elements, blind spots and grating lobes in that blind spots will occur also when grating lobes occur in free space because in this scenario, the resultant horizontal propagation constant equals the lattice spacing and a resonance occurs.

While the preceding discussion focusses on a type B array, the skilled person will appreciate that equivalent considerations can be applied to other arrangements. Currently, several solutions have been presented to decrease the effects of mutual coupling between antenna array elements and thus grating lobes and blind spots. One approach in the literature involves the use of dielectric layers, aperture irises and a dielectric radar radome for mode matching as described in the articles by Shung-Wu Lee and W.Jones, entitled “On the suppression of radiation nulls and broadband impedance matching of rectangular waveguide phased arrays,” IEEE Transactions on Antennas and Propagation, vol. 19, no. 1 , pp. 41-51 , January 1971, and by H. van Schaik, entitled “The performance of an iris-loaded planar phased- array antenna of rectangular waveguides with an external dielectric sheet,” IEEE Transactions on Antennas and Propagation, vol. 26, no. 3, pp. 413-419, May 1978.. Other more novel solutions involve the manipulation of mutual coupling levels and phases due to "surface wave” modes that transports power between elements. Changing the surface impedance can help either to reduce the power of these surface modes or change the phase of the coupling so as to reduce the active Sn component. Changing the surface impedance changes the coupling. A high impedance surface will prevent propagation when it is capacitive or change the mutual coupling when it is very highly inductive (a perfect electric conductor has a very small inductive surface impedance).

Previously electromagnetic bandgap materials have been used to improve isolation between antenna elements such as wire structures and Sievenpiper mushroom structures as described in the articles by D. Sievenpiper, Lijun Zhang, R. F. J. Broas, N. G. Alexopolous, and E. Yablonovitch, entitled “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Transactions on Microwave Theory and Techniques, vol. 47, no. 11 , pp. 2059-2074, Nov 1999 and by J.S. Sandora, entitled “Isolation improvement with electromagnetic bandgap surfaces,” 2012. While these structures show a lot of potential, they generally require several electromagnetic bandgap (EBG) cells to achieve good isolation. While these EBG elements are small (typically around 1/4l to 1/6l, one requires more elements for good isolation than can fit in between array elements. Besides that, many of the articles proposing EBG materials as a solution do not report insertion loss characteristics. If crosstalk improvements are at the cost of drastically lower return losses, no real gain is made.

It is accordingly desired to develop new radar structures better addressing the foregoing considerations. SUMMARY OF THE INVENTION

In accordance with the present invention in a first aspect there is provided an antenna comprising a plurality of radiating elements arranged in a two dimensional array in a first plane, where each radiating element comprises a radiating structure in the plane of the two dimensional array, and a plurality of conductive pin elements arranged in one or more rows parallel to an edge of the radiating structure or element, or to an axis defined by the plurality of radiating elements, each pin intersecting the plane of the two dimensional array.

In accordance with a development of the first aspect, the plurality of conductive pin elements is arranged in two or more rows parallel to the edge of the radiating structure or element.

In accordance with a development of the first aspect, the antenna is an open-ended waveguide antenna, and the radiating elements are waveguide elements, and wherein the radiating structures are apertures in the plane of the two-dimensional array.

In accordance with a development of the first aspect, the distance between each adjacent pair of pins in a given row is a predetermined distance.

In accordance with a development of the first aspect, the diameter of each pin is less than the predetermined distance.

In accordance with a development of the first aspect, the pins of a first row are offset with respect to a second, adjacent the row parallel to the first row, along the axis of the first row, by an amount between 0.5 times the distance between adjacent pins in the same row and zero.

In accordance with a development of the first aspect, each pin is formed contiguously with the respective radiating element.

In accordance with a development of the first aspect, each pin is formed monolithically with the respective radiating element structure.

In accordance with a development of the first aspect, a proximal extremity of each pin in at least one row coincides with the plane of the two-dimensional array.

In accordance with a development of the first aspect, the radiating structure is circular or rectangular.

In accordance with a development of the first aspect, each radiating element is of identical dimensions in the plane, and wherein the two dimensional array comprises a first plurality of the radiating elements arranged in a first row, and a second plurality of the radiating elements arranged in a second row parallel to the first row, wherein the pins of radiating elements of the first row are offset with respect to the second row by an amount between 0.5 times the length of each open ended waveguide element and zero.

In accordance with a development of the first aspect, each radiating element is of identical dimensions in the plane, and wherein the two dimensional array comprises a first plurality of the radiating elements arranged in a first row, and a second plurality of the radiating elements arranged in a second row parallel to the first row, and wherein the edges of the radiating structures or elements comprising the pins are adjacent to each other, and wherein at least one edge of the adjacent edges comprises two or more rows of pins.

In accordance with a development of the first aspect, the adjacent edges comprise a different or same number of rows of pins.

In accordance with a development of the first aspect, the plurality of conductive pin elements is arranged in one or more rows parallel to the first row of radiating elements and the second row of radiating elements, and between the first row of radiating elements and the second row of radiating elements.

In accordance with a development of the first aspect, no pins are provided between radiating structures of adjacent radiating elements of the first row, or between radiating structures of adjacent radiating elements of the second row, respectively.

In accordance with a development of the first aspect, the length of the pins is longer than the speed of light in the medium in which the pins are embedded, divided by four times the lower frequency limit (f1) of the waveguide and shorter than the speed of light in the medium in which the pins are embedded, divided by two times the lower frequency limit (f1 ).

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be better understood and its various features and advantages will emerge from the following description of a number of exemplary embodiments provided for illustration purposes only and its appended figures in which: Figure 1 shows a phased antenna array as known in the prior art;

Figure 2 shows a 2-dimensional array as known in the state of the art;

Figure 3 shows an open-ended waveguide antenna in accordance with an embodiment;

Figure 4 shows an orthographic projection of a single waveguide element of the array of figure 3;

Figure 5a shows a first example of an intersection of the plane of the two- dimensional array;

Figure 5b shows a second example of an intersection of the plane of the two- dimensional array;

Figure 5c shows a third example of an intersection of the plane of the two- dimensional array;

Figure 6a presents a schematic representation of a meta material embedded in a well in accordance with a first variant; and

Figure 6b presents a schematic representation of a meta material embedded in a cavity in accordance with a second variant;

Figure 7 presents a further pin distribution variant in accordance with embodiments; and

Figure 8 illustrates a number of examples of different radiating structures in accordance with embodiments.

DETAILED DESCRIPTION OF THE INVENTION

Mutual coupling in phased array antennas is the cause of blind spots due to coherent addition in the coupling terms. It is also influenced by the near field radiation of an open-ended waveguide.

For array antennas the propagation mode is mostly free space and hence the addition of surface media will introduce new physical effects and potential coupling mechanisms that where not previously there.

In the following discussion a number of embodiments will be presented with reference to an open-ended waveguide antenna. Although for the sake of simplicity the detailed embodiments are presented consistently in this context, the principles presented herein are equally applicable to other antenna array types, including for example patch antenna arrays, and other antenna types as may readily occur to the skilled person. In particular, any reference to an open-ended waveguide antenna will be understood to apply equally to array antennas in general, any reference to waveguide elements will be understood to apply equally to radiating elements in general, and any reference to a waveguide aperture will be understood to apply equally to radiating structures in general insofar as the they correspond to the other structural and functional characteristics of the invention.

Figure 3 shows an open-ended waveguide antenna in accordance with an embodiment. As shown, an open-ended waveguide antenna comprises a plurality of open-ended waveguide elements 310, 320, 330 arranged in a two-dimensional array in a first plane 301. As shown, each waveguide element 310, 320, 330 comprises a respective aperture 311 , 321 , 331 in the plane 301 of the two-dimensional array. As shown, the individual waveguide elements are rectangular and arranged in rows with their shorter edges aligned, and with adjacent rows offset by half of the length of their longer sides. The skilled person will appreciate that the principles set out below may be applied to any other waveguide array configuration. Each waveguide element 310, 320, 330 further comprises a respective plurality of conductive pin elements 312, 322, 332, arranged in one or more rows parallel to an edge of said aperture 311 , 321 , 331 , and parallel to an edge of said waveguide element 310, 320, 330, each pin intersecting said plane of said two-dimensional array. The pins are not necessarily in air, but can be located in a dielectric medium (not shown).

The open-ended waveguide elements 310, 320, 330, or radiating elements of other antenna array types, may alternatively be referred to as “array cells”.

The radiating elements may either be separate elements that together form said array antenna, but it is also possible that the radiating elements form one integral part. In the latter case no physically separate elements are provided, but in the array antenna a pattern of radiating elements can be recognised, wherein the apertures or other radiating structures are aligned in rows. In such case the conductive pin elements 312, 322, 332, are arranged in one or more rows parallel to the rows of apertures or other radiating structures.

The radiating elements are shown to be rectangular, but may have any suitable shape, in particular any shape that allows said radiating elements to form said array. For example, the shape may alternatively be square, hexagonal, or any other suitable, polygonal shape.

Specifically, as shown each waveguide element 310, 320, 330 comprises conductive pin elements arranged two rows parallel to each edge of the respective aperture, each pin intersecting said plane of said two-dimensional array at their respective proximal ends.

In different embodiments, the radiating structure may define different numbers of edges. For example, a circular radiating structure may define a single edge, a triangular radiating structure may define three edges, a rectangular radiating structure as shown in figure 3 will define 4 edges, and so on. Where the radiating structure defines two or more edges, all edges may be provided with rows of pins as described herein, or one edge, or any intervening number of edges depending on the geometry of the radiating structure. Each edge may be provided with a different or same number of parallel rows of pins. While at least one edge is provided with at least two rows of parallel pins, other edges may be provided with no rows, one row, two rows, or a number of rows greater than two, respectively.

As shown, each open-ended waveguide antenna is a rectangular waveguide, however other embodiments may comprise open ended waveguide antennae of any form, for example oval, circular or ridged. Open ended waveguide antennae of different forms may be incorporated in the same array.

As shown, each open-ended waveguide element is of identical dimensions in the plane 301 , and the two-dimensional array comprises a first plurality of open ended waveguide elements 310, 220 arranged in a first row, and a second plurality (330 and other elements not shown) of open ended waveguide elements arranged in a second row parallel to said first row. A plurality of radiating elements may define an axis. For example, in the example of figure 3, this may be seen as parallel to the first row etc. i.e. parallel to the x axis as shown, or at right angles thereto (i.e. parallel to the y axis as shown), or otherwise depending on the geometric characteristics of the arrangement. Where such an axis is defined, the plurality of conductive pin elements may be arranged in one or more rows parallel to an axis defined by said plurality of radiating elements, as well as or instead of an edge of said radiating structure or element.

For rectangular waveguides, the lowest TE mode may be used, for which, the polarization is defined, that is to say, there is a vertical electric field (along the b- direction of the waveguide). For an array with this type of waveguide elements the horizontal rows of pins are needed.

In different shapes of waveguide elements, for instance circular waveguides, the polarization of the electric field at the output is not defined by the geometry, the polarization can be in any direction. In that case the pins may be placed for example in rings around the waveguide elements. Rows of pins may be provided substantially as described above, disposed in concentric rings (at least two rings per radiator).

As shown, a plurality of conductive pin elements is arranged in four rows parallel to the first row of open-ended waveguide elements 310, 320 and a second row 330 of open ended waveguide elements, and between the first row 310, 320 of open ended waveguide elements the said second row 330 of open ended waveguide elements.

There may be provided one, two, three or any other number of parallel rows.

As shown, additional rows are provided at right angles to the rows of pins parallel to the rows of waveguide elements, on the narrow side of each aperture, so that each aperture is entirely surrounded by pins. In other embodiments, these additional rows may be omitted, may have the same number of pins as rows of pins parallel to the rows of waveguide elements, or some other number of pins. In particular, in certain embodiments no pins may be provided between apertures of adjacent open ended waveguide elements of the first row, or between apertures of adjacent the open ended waveguide elements of the second row, respectively.

While the array of figure 3 comprises only two rows, and a total of three waveguide elements, it will be appreciated that the described arrangements may be scaled to any number of rows, and any number of waveguide elements.

Figure 4 shows an orthographic projection of a single waveguide element of the array of figure 3.

As shown in figure 4, the waveguide element 400 comprises conductive pin elements arranged two rows parallel to each edge of the respective aperture. The distance between each adjacent pair of pins in a given said row is a predetermined distance as described in more detail below. As discussed below, for optimal operation the plasma frequency f _p is preferably higher than the operating band of the antenna. In the definition as presented in equation 11 below both a and a/r play a role in the value of f _p . For proper operation f _p »f _0p eratin _g (=Co/A) with a/r > 4. In preferred embodiments having more than 2 rows of pins between two rows of waveguide elements, this implies that a < 0.25A.

The spaced conductive pin elements are grounded, for example by connection to a conducting surface. The wire lattice acts as a low frequency anisotropic metal. Metals reflect electromagnetic waves below a certain frequency called the plasma frequency. The mobility of the electrons in a metal enables them to oppose incoming waves and reflect them.

Because of the limited mobility of the electrons, electromagnetic waves with a frequency higher than the plasma frequency can partially pass through the metal. The properties of these materials can be modelled via a frequency dependent dielectric permittivity model called Drude’s model for metals.

Above the plasma frequency, the dielectric constant 0 < e _G < 1 and waves can pass through. For metals, the plasma frequency is typically above the visible spectrum. For a lattice constant smaller than the wavelength, the wire medium can be thought of as an anisotropic metal as it behaves as a metal for incoming waves that have the electric field polarized parallel to the wires. The plasma frequency however can be tuned at will by means of the lattice spacing and wire radius. For waves with the electric field polarized perpendicular to the wire direction, the wire medium is transparent and a normal TEM mode is allowed to exist.

The plasma frequency of this material in air can be approximated via a simple formula if the assumption is made that the ratio of the lattice spacing a to the wire radius r is at least 10 or larger (a/r > 10), bearing in mind that the formula is only exact for infinitely thin wires but sufficiently accurate as long as a/r > 10.

If the wire radius is made smaller compared to the lattice spacing the plasma frequency will decrease and when the radius is made larger, the plasma frequency will approach c ₀ /a.

Accordingly, the diameter of each pin is preferably less than the predetermined distance between elements.

While as shown the open-ended waveguide antenna of figure 4 comprises conducting pin elements arranged in two parallel rows around each waveguide element, other arrangements may be considered. In particular, it is desirable to provide as many rows as possible as far as consistent with the pin diameter and spacing considerations presented herein, as dictated by the available space between waveguide apertures.

In this regard, simulation data indicate for a typical configuration that the introduction of more rows yields more attenuation due to the exponential decay in the propagation direction inside the medium. Two rows of pins show an approximate attenuation of the S21 parameter of roughly 10dB depending on the frequency. Four rows medium adds another 5dB to this attenuation in the lower frequency region. Going from 4 to 6 rows only adds another 2.5dB suggestion an approximate attenuation gain of the S21 parameter of roughly 5dB per doubling of the number of layers.

Unexpectedly, the reflection coefficient in this setup is also significantly lowered, this is something not seen in simulations of infinite arrays. Generally, in other experiment, the reflection coefficient worsens. The reflection coefficient is not dependent on the number of rows suggesting that the primary effect might be due to the presence of the first row.

In some cases, the number of rows of pins along the long sides of each waveguide element may be smaller than or greater than the number of rows of pins along the short sides of each waveguide element. The plurality of conductive pin elements may be arranged in three or more rows parallel to an edge of said aperture.

The spacing between adjacent pins a in the same row, and between adjacent rows may be constant, or may be varied across the array. Generally, it is advantageous for a strong coupling reduction that the amount of rows of pins is maximized. This implies that a is small compared to lambda.

The pins of one row may be offset with respect to an adjacent parallel row, by an amount between 0.5 times the distance between adjacent pins in the same row and zero.

When the operating frequency is sufficiently far below the materials plasma frequency, a grounded slab of this medium can be shown to allow Plane Trapped Surface Wave (PTSW) modes at periodic intervals depending on the height of the medium. This is a very desirable property because now its frequency dependent behaviour is no longer a function of its geometry in the direction of propagation but rather orthogonal to it.

Grounding conducting pins into arrangements as described above yields a certain set of PTSW modes. An approximate model for the horizontal propagation constant k|| of a grounded wire medium in air can be made which assumes an infinite plasma frequency:

Where k ₀ = w/c and k _p the plasma wave number k _p = 2pί _r /qo and L the length of the wires.

The solution for the horizontal propagation constant emerges as the plasma frequency approaches infinity:

Here yo is the damping factor of the wave above the wire medium in the vertical Z direction.

It may be borne in mind that the model of equation 12 calculates the solutions in the passband only as it also predicts solutions in the stop band that are incorrect. Equation 13 meanwhile specifies this same relation but without the inclusion of solutions in the stop band.

Mathematically the cutoff regions of the wire medium can be written as:

Bearing in mind that while n = 0, ±1 , ±2 etc is the entire set of solutions mathematically, in practice only the set of solutions for n=1 ,2,3,4 and onwards is important because negative frequencies are not physically interesting but rather more mathematical. From this it is possible to write the first stopband for n = 0 as:

The end of the stop band is always two times the start of the stop band (for the first one), i.e. Co/4fi < L < co/2fi _, where fi is the beginning of the stopband. This assumes no dielectric material. In that case the length is decreased by factor of the dielectric material. More simply one can write v/4fi < L < v/2fi where v is the group velocity of TEM electromagnetic waves in that dielectric medium, or v = Co/n where n is the refractive index of the material. As described above, each waveguide element 310, 320, 330 comprises a plurality of conductive pin elements 312, 322, 332, arranged in one or more rows parallel to an edge of said aperture 311 , 321 , 331, each pin intersecting plane 301 of the two-dimensional array. The pins are not necessarily in air, but can be located in a dielectric medium. Encapsulating the pins in a dielectric medium may facilitate the manufacturing process and improve the robustness of the device.

The intersection of the plane of the two-dimensional array may occur at different points along the length of the pins.

Figure 5a shows a first example of an intersection of the plane of the two- dimensional array.

As shown in figure 5a, the plane 301 is intersected by the pins 512 at the lower, proximal extremity of each pin. The PTSW modes can be excited by electric fields due to apertures adjacent to the wire medium. It is therefore expected that the wire medium supports propagation of PTSW modes below its cutoff frequency. Above the first cut off frequency, there are no PTSW modes. One would predict that coupling below cutoff due to the presence of a strongly bound PTSW mode can aid in coupling over larger distances. This mode becomes more and more confined closer to the surface because yo gets larger and thus a stronger exponential decay. Besides the Transverse Magnetic (TM) modes in the pass band regions, there are also Transverse Electromagnetic (TEM) and Transverse Electric (TE) solutions if both the electric is polarized perpendicular to the wire medium. Certain implementations of the embedded wire medium may support TE modes. If the pins are placed inside a well, a TE mode can propagate through the channel, although this mode of operation may be less effective than implementations where the pins are situated above the plane of the waveguide as described above. A covered medium realization of the meta material may act in a manner similar to a line of trees besides a highway reducing noise pollution. The medium seen as a homogenized medium supports an evanescent mode through it above the cutoff frequency of the wire medium.

The pin medium may be selected such that the plasma frequency is sufficiently far above the operating region of interest. The PTSW modes that are improper inside the stop band are solutions assuming that the medium operates below the plasma frequency. The plasma frequency is controlled via the wire spacing a and the wire radius r. The plasma phase constant k _p = 2pί/o ₀ is always a fraction of the lattice vector k _a = 2Tr/a. This fraction decreases as the radius of the wire decreases for a given lattice spacing. For a ratio of r = 0.1a the plasma phase constant k _p is approximately 0.4k _a .

The choice of wires in practice depends on fabrication limits and when performing simulations on the mesh size. Very small wires are difficult to manufacturer robustly. Regarding simulations, designs with a small wire radius and lattice spacing will increase the complexity of the simulation model which makes them computationally expensive to solve. The precise method at which the PTSW bandgap interferes with the coupling is difficult to determine as not only the geometries are complex and the wires need to be simulated with a significant size in order to limit the computational complexity which means that the homogenization model is less accurate. Depending on desired system characteristics and operating conditions, suitable wire radius values may be found to fall for example between 0.1 mm and 5mm.

Figure 5b shows a second example of an intersection of the plane of the two- dimensional array.

As shown in figure 5b, the plane 301 is intersected by the pins 512 at an intermediate point along the length of each pin, such that the pins are partially submerged with respect to the plane 301 in a well 510 disposed in the upper surface of the waveguide element around the aperture 511.

Figure 5c shows a third example of an intersection of the plane of the two- dimensional array.

As shown in figure 5c, the plane 301 is intersected by the pins 512 at the upper, distal extremity of each pin, such that the pins are fully submerged with respect to the plane 301 in a well 510 disposed in the upper surface of the waveguide element around the aperture 511.

Figures 6a and 6b present certain variants of the arrangements of figure 5b and 5c.

Figure 6a presents a schematic representation of a meta material embedded in a well in accordance with a first variant.

As shown, the well 610a extends to infinity in the X direction with a wave propagating in the X direction and the electric field polarized in the Y direction.

Because only TM-modes can be blocked by the pins, it makes sense to orient the meta material as a flat horizontal line in between the aperture layers. The pin lattice is transparent for TE-modes and TEM modes. If the pin medium is disregarded for these modes, there is only a long trench left in the X-direction with a depth equal to the wire length L. This trench can be thought of as a quarter lambda resonator in the Z-direction.

At this angle, the incident field and the field inside the well are in phase which can induce blind spots. As a remedy to this mode, vertical walls can be introduced in the YZ-plane inside the well separated by a distance larger than 1/2l in order to make sure that the TE-mode in the pin medium does not end up far below cutoff. This automatically creates the cavity setup described in the following section.

Figure 6b presents a schematic representation of a meta material embedded in a cavity in accordance with a second variant.

As shown, the cavity 610b extends a finite distance in the X and Y-directions with the electric field polarized in the Y-direction.

When the medium oriented in the Z-direction is placed in a rectangular cavity as shown in figure 6b, which means that there are conducting boundaries in both the XZ and YZ plane, a typical waveguide TE mode exists inside the medium.). This geometry is equivalent to a shorted rectangular waveguide.

When considering the meta material embedded in a rectangular cavity, there is only the existence of a TE-mode. The solution of a resonator similar to the well can be used but now with an included width W. Due to the introduction of extra boundary conditions of the conducting walls inside the cavity, TM surface wave modes are excluded and TE modes are left over. Therefore, the prediction is that embedding the pin medium inside the conductor renders the wire medium ineffective as the PTSW modes are no longer solutions and the TE modes that can exist do not experience the wire medium.

As discussed above, a variety of different pin configurations may be envisaged.

Figure 7 presents a further pin distribution variant in accordance with embodiments. As shown in figure 7, a plurality of radiating elements 710, 720, 730 are provided, substantially as described above. Meanwhile, in embodiments for example as shown, pins may be arranged in a non-symmetrical fashion. Specifically, as shown, on each of the long sides of the radiating elements a different number of rows of pins are provided. In particular, on the top side, two rows 711 , 721 , 731 are provided, whilst on the bottom side, only one row is provided 712, 722, 732, meaning that between vertically adjacent radiating structures, three rows of pins are provided (e.g. 712 and 721 in combination).

As discussed above, variants may involve different antenna types.

Figure 8 illustrates a number of examples of different radiating structures in accordance with embodiments.

In a first variant 810, there is provided a radiating element 810 comprising a radiating structure 811 in the form of a rectangular waveguide outlet, substantially as shown in figures 3 or 4 for example. It may be noted that the pins may be distanced from the edge of the waveguide outlet. As shown, the pins are distanced from the upper and lower edges. In other embodiments, the pins may additionally or alternatively be distanced from the sides.

In a second variant 820, there is provided a radiating element 820 comprising a radiating structure 821 in the form of an “H” shaped waveguide outlet. The detailed dimensions may vary as will readily occur to the skilled person.

In a third variant 830, there is provided a radiating element 830 comprising a radiating structure 831 in the form of a circular patch antenna. It may be noted that the pins are still disposed in a rectangular pattern about the radiating structure. In alternative embodiments (whether for a patch antenna or otherwise) the pins may be arranged in the same pattern as the shape of the radiating structure. The detailed dimensions may vary as will readily occur to the skilled person.

In a third variant 840, there is provided a radiating element 830 comprising a radiating structure 831 in the form of a rectangular patch antenna. It may be noted that the pins are still disposed in a rectangular pattern about the radiating structure. It may be noted that the pins may be distanced from the edge of the waveguide outlet. As shown, the pins are distanced from the left and right edges. In other embodiments, the pins may additionally or alternatively be distanced from the upper and/or lower edges.

In any embodiment, the conductive pins may be formed with respect to the waveguide elements in a variety of manners. For example, each pin may be formed contiguously with the respective said waveguide, that is to say, that while each pin is formed separately from the waveguide, it is placed in electrical contact therewith. Alternatively, each pin may be formed monolithically with the respective said waveguide, that is to say, that each pin is formed of the same material and in a single piece with the waveguide element. Still further, pins may be physically and/or separated from the waveguide element, and connected to ground by a separate conductive matrix. The pins may by physically discrete elements which are inserted into corresponding sockets in the waveguide elements. Alternatively, the pins might also be separated by the waveguide by an isolating sheet such that they are electrically connected at RF frequencies, but not at DC.

Accordingly, in certain embodiments cross talk between elements of a waveguide antenna array is reduced by providing matrices of conductive pins, which are electrically coupled at RF frequencies to the waveguide bodies. The diameter and length of each pin is defined as a function of the operating frequencies of the antenna. The conductive pins are arranged in successive rows, where each pin is spaced apart from its neighbours in the same row by a distance defined as a function of the operating frequencies of the antenna. As many rows of pins as possible are included between adjacent array elements. a. Accordingly, there is provided in certain embodiments an open ended waveguide antenna comprising a plurality of open ended waveguide elements arranged in a two dimensional array in a first plane, where each said waveguide element comprises an aperture in the plane of said two dimensional array, and a plurality of conductive pin elements arranged in one or more rows parallel to an edge of said aperture, each said pin intersecting said plane of said two dimensional array. b. In certain variants of embodiments according to clause a, the distance between each adjacent pair of pins may be a given said row is a predetermined distance. c. In certain variants of embodiments according to clause a, the diameter of each said pin may be less than said predetermined distance. d. In certain variants of embodiments according to clause a,b or c. said plurality of conductive pin elements may be arranged in three or more rows parallel to an edge of said aperture. e. In certain variants of embodiments according to clause c, wherein the pins of a first said row may be offset with respect to a second, adjacent said row parallel to said first row, along the axis of said first row, by an amount between 0.5 times the distance between adjacent pins in the same row and zero. f. In certain variants of embodiments according to clause a to e each said pin may be formed contiguously with the respective said waveguide. g. In certain variants of embodiments according to clause a to e each said pin may be formed monolithically with the respective said waveguide. h. In certain variants of embodiments according to clause a to e each a proximal extremity of each said pin in at least one said row coincides with said plane of said two dimensional array. i. In certain variants of embodiments according to clause a to h each said waveguide may be a rectangular waveguide. j. In certain variants of embodiments according to clause i each said open ended waveguide element may be of identical dimensions in said plane, and wherein said two dimensional array comprises a first plurality of said open ended waveguide elements arranged in a first row, and a second plurality of said open ended waveguide elements arranged in a second row parallel to said first row, wherein the pins of open ended waveguide elements said first row are offset with respect to said second row by an amount between 0.5 times the length of each said open ended waveguide element and zero. k. In certain variants of embodiments according to clause j said plurality of conductive pin elements may be arranged in one or more rows parallel to said first row of open ended waveguide elements and said second row of open ended waveguide elements, and between said first row of open ended waveguide elements and said second row of open ended waveguide elements.

L. In certain variants of embodiments according to clause j no said pins may be provided between apertures of adjacent said open ended waveguide elements of said first row, or between apertures of adjacent said open ended waveguide elements of said second row, respectively. m. In certain variants of embodiments according to clause a to I each waveguide may be a circular waveguide. n. In certain variants of embodiments according to clause a to m the length of the pins may be longer than the speed of light in a vacuum divided by four times the lower frequency limit (f1) of the waveguide and shorter than the speed of light in a vacuum divided by two times the lower frequency limit (f1). The examples described above are given as non-limitative illustrations of embodiments of the invention. They do not in any way limit the scope of the invention which is defined by the following claims.