EP3547450B1 - Radiating element with circular polarisation implementing a resonance in a fabry-perot cavity - Google Patents

Description

The invention relates to a radiating element with circular polarization, in particular for a planar antenna, and intended to be used in particular in space communications, on board satellites or in user terminals. The invention also relates to an array antenna comprising at least one such radiating element.

Different types of radiating elements have recently been developed, responding to the constraints and specificities of space communications.

The so-called "compact" radiating elements, such as for example the resonant cavity antennas from Fabry Perot, make it possible in particular to offer a good compromise between several specifications: good surface efficiency over the entire operating band, sufficient bandwidth for adaptation and in radiation, a small size and a low mass. Congestion is particularly critical in the low frequency bands L (1 to 2 GHz), S (2 to 4 GHz), C (from 3.4 to 4.2 GHz in reception and 5.725 and 7.075 GHz in transmission) penalized by significant wavelengths. Also, the search for compact and wideband elements is particularly active for multispot antennas, associating a reflector and a focal array made up of a large number of sources. Fabry Perot's cavity resonant antennas, currently used in space communications, are linearly polarized. Obtaining circular polarization on such antennas must be achieved without degrading the compactness of the radiating element by adding a device making it possible to obtain radiation in circular polarization.

Radiating elements having continuous linear radiating openings, such as quasi-optical beamformers, for example, make it possible to radiate several fronts. plane waves over a large angular sector. They are formed by a waveguide with parallel plates terminated by a longitudinal horn, which makes the transition between the waveguide with parallel plates and free space. A focusing / collimator device is inserted on the radiofrequency wave propagation path, between the two parallel metal plates, making it possible to convert cylindrical wave fronts from the sources into plane wave fronts. These continuous radiating linear apertures operate over a very wide band (for example at 20 and 30 GHz), due to the absence of resonant propagation modes. They are also capable of radiating over a very large angular sector. However, in their nominal operation, the polarization of the radiated wave is that of the wave which propagates in the waveguide with parallel plates, namely linear.

In order to obtain identical beam widths in the two planes, it is moreover known to widen the continuous radiating linear aperture by using a splitter with parallel plates. These linear aperture arrays also radiate in linear polarization, like each radiating linear aperture.

There is therefore a current need to find devices capable of converting a linear polarization into circular polarization, compatible with the existing radiating apertures, and capable moreover of acting as a radiating element with circular polarization.

A first known solution consists in covering the radiating element with a polarizing radome consisting of several frequency selective surfaces (FSS), the characteristics of which are optimized so as to generate a phase difference of 90 ° between the two orthogonal polarizations, without interfere with the operation of the antenna. Polarizing radomes cascading quarter-wave layers exhibit good bandwidth and oblique incidence performance, however with a thickness (thickness of the order of one wavelength in a vacuum) detrimental to the compactness of the antenna. Fine polarizers have been also developed, but their performances in bandwidth and in oblique incidence are limited.

A solution consisting in combining a polarizer and a Fabry Perot cavity can be found in the document “Self polarizing Fabry-Perot antennas based on polarization twisting element” (SA Muhammad, R. Sauleau, G. Valerio, LL Coq, and H. Legay, IEEE Trans. Antennas Propag., Vol. 61, no. 3, pp. 1032-1040, Mar. 2 ). The solution is illustrated by the figure 1 . The frequency-selective surface Fabry Perot cavity radiates similarly in two subspaces (upper and lower). It consists of two periodic partially reflecting surfaces (FSS1, FSS2) according to a linear polarization Ex, and is excited according to this polarization. Periodic surfaces are transparent to the Ey wave. A polarization reversal ground plane reflects the emitted wave in the lower plane, transforms its linear polarization (for example from Ex to Ey), and returns the wave in the upper direction. This ground plane PM is produced by means of COR corrugations of depth λ / 4, inclined at 45 ° with respect to the grids constituting the periodic partially reflecting surfaces (FSS1, FSS2). A distance of λ / 8 (where λ is the wavelength in the radiating element) between the polarization inverted PM ground plane and the Fabry Perot cavity with periodic partially reflecting surfaces achieves a phase delay of 90 ° on the component Ey, necessary to obtain the circular polarization. The cavity being transparent to the component Ey, the field is radiated in the upper sub-space. The frequency behavior of this solution is however relatively low band. Indeed, as illustrated by figure 4 of the cited document, the rate of ellipticity of the wave at the output of the polarizer is at 1 dB over a frequency band corresponding to approximately 2.5% of the central frequency. This weak band behavior is linked on the one hand to the corrugations of the ground plane PM, the height ( λ / 4) of which is a function of the wavelength. It is also linked to the spacing ( λ / 8) between the lower partially reflecting periodic surface FSS1 and the ground plane PM, which is a function of the wavelength.

Other radiating elements of the state of the art are disclosed in the article “Design method for circularly polarized Fabry-Perot cavity antennas” (Robert Orr et al.), and in the patent application WO 2011134666 A1 .

The invention therefore aims to obtain a radiating element with circular polarization from a linear excitation, both compact in height and very wide band.

• au moins une ouverture d'excitation d'une onde polarisée linéairement selon une première polarisation dite d'excitation ;
• une surface sélective en fréquence, partiellement réfléchissante pour la polarisation d'excitation et transparente pour une deuxième polarisation orthogonale à la polarisation d'excitation, dite polarisation orthogonale, et à la direction de propagation de l'onde, et disposée dans un plan défini par la polarisation d'excitation et par la polarisation orthogonale ;

• l'élément rayonnant comprenant en outre une métasurface, totalement réfléchissante, faisant face à la surface sélective en fréquence, et comprenant un réseau bidimensionnel et périodique d'éléments planaires conducteurs formant cellules à métasurface,
• l'ouverture d'excitation débouchant sur la métasurface,
• la surface sélective en fréquence et la métasurface formant une cavité résonante pour la polarisation d'excitation,
• les cellules à métasurface étant toutes orientées de façon identique vis-à-vis de la polarisation d'excitation et configurées pour :
  • o réfléchir une onde incidente selon la polarisation d'excitation pour former une onde réfléchie polarisée selon la polarisation d'excitation, et
  • o dépolariser et réfléchir l'onde incidente pour former une onde réfléchie polarisée selon la polarisation orthogonale avec une différence de phase sensiblement égale à ± 90° par rapport l'onde réfléchie polarisée selon la polarisation d'excitation, et avec une amplitude sensiblement égale à l'amplitude d'une onde rayonnée par la surface sélective en fréquence, issue de l'onde réfléchie polarisée selon la polarisation d'excitation.

An object of the invention is therefore a radiating element with circular polarization, comprising:

• at least one excitation opening of a linearly polarized wave according to a first so-called excitation polarization;
• a frequency selective surface, partially reflecting for the excitation polarization and transparent for a second polarization orthogonal to the excitation polarization, called orthogonal polarization, and to the direction of propagation of the wave, and arranged in a plane defined by the excitation polarization and by the orthogonal polarization;

• the radiating element further comprising a fully reflecting metasurface facing the frequency selective surface and comprising a two-dimensional and periodic array of planar conductive elements forming metasurface cells,
• the excitation opening leading to the metasurface,
• the frequency selective surface and the metasurface forming a resonant cavity for the excitation polarization,
• the metasurface cells being all oriented identically with respect to the excitation polarization and configured for:
  • o reflect an incident wave according to the excitation polarization to form a reflected wave polarized according to the excitation polarization, and
  • o depolarize and reflect the incident wave to form a reflected wave polarized according to the orthogonal polarization with a phase difference substantially equal to ± 90 ° with respect to the reflected wave polarized according to the excitation polarization, and with an amplitude substantially equal to the amplitude of a wave radiated by the frequency selective surface, resulting from the wave reflected polarized according to the excitation polarization.

[S] étant la matrice de répartition de la métasurface, et [R] une matrice de rotation d'angle Ψ.Advantageously, the metasurface comprises a ground plane on which are arranged a substrate and the network of metasurface cells arranged in rows, the centers of each metasurface cell of the same row being aligned along an alignment axis, the axis alignment being oriented by an angle of rotation ( Ψ ) with respect to the excitation polarization, the angle of rotation ( Ψ ) being determined so as to obtain a matrix [ S ' ] of diagonal type, where: $$\left[S\text{'}\right]{=}^t\left[R\right]\left[S\right]\left[R\right],$$

[ S ] being the matrix of distribution of the metasurface, and [ R ] a matrix of rotation of angle Ψ .

Advantageously, the cells with metasurfaces of the same row are coupled by an interconnection line with a metasurface elongated along the alignment axis.

Advantageously, the rows are connected to one another by means of the metasurface cells, forming with the metasurface interconnection lines a grid pattern with a rectangular mesh.

As a variant, the metasurface cells of the same row are isolated from each other.

Advantageously, the metasurface cells of the same row are all spaced periodically.

Advantageously, all the metasurface cells of the metasurface have the same dimensions.

Advantageously, the frequency selective surface comprises an array of parallel metal wires, spaced periodically, and aligned with the excitation polarization.

Alternatively, the frequency selective surface comprises a two-dimensional array of metallic dipoles arranged periodically.

Advantageously, the excitation opening comprises at least one waveguide opening opening into the resonant cavity.

Advantageously, the excitation opening comprises a double power supply formed by two waveguides opening symmetrically into the resonant cavity, and connected to an impedance matching network.

Advantageously, the excitation opening is a horn with a radiating linear opening.

Advantageously, the radiating element comprises a plurality of excitation openings, the excitation openings being formed by an array of linear radiating openings.

Advantageously, the radiating element comprises at least one second cavity cascaded over the frequency selective surface.

Advantageously, the metasurface cells are rectangular in shape.

The invention also relates to an array antenna comprising at least one aforementioned radiating element.

• figure 1, un élément rayonnant à polarisation circulaire de l'état de l'art ;
• figure 2, une représentation schématique, dans le plan yz, de l'élément rayonnant selon l'invention, à partir de la théorie des rayons ;
• figure 3, une vue d'ensemble et une vue détaillée, dans le plan xy, de plusieurs rangées de cellules à métasurface constitutives de la métasurface et isolées l'une de l'autre;
• figure 4, une vue en perspective des cellules à métasurface isolées l'une de l'autre, illustrant plus particulièrement l'orientation entre l'axe d'alignement des cellules à métasurface par rapport à la polarisation d'excitation ;
• figure 5, une vue d'ensemble et une vue détaillée, dans le plan xy, de plusieurs rangées de cellules à métasurface constitutives de la métasurface et reliées par une ligne d'interconnexion;
• figure 6, une vue en perspective des cellules à métasurface couplées les unes aux autres par une ligne d'interconnexion ;
• figure 7, une vue en perspective des cellules à métasurface formant un grillage à maille rectangulaire ;
• figure 8, une application de l'élément rayonnant selon l'invention, où l'ouverture d'excitation est un cornet d'ouverture linéaire rayonnante ;
• figure 9, une application de l'élément rayonnant selon l'invention, où les d'ouvertures d'excitation sont des ouvertures linéaires rayonnante mises en réseau ;
• figures 10A, 10B et 10C, un mode de réalisation dans lequel l'ouverture d'excitation comprend une alimentation double ;
• figures 11A et 11B, des courbes illustrant la directivité et le taux d'ellipticité en fonction de la fréquence, pour plusieurs configurations d'éléments rayonnants.

Other characteristics, details and advantages of the invention will emerge on reading the description given with reference to the appended drawings given by way of example and which represent, respectively:

• figure 1 , a radiating element with circular polarization of the state of the art;
• figure 2 , a schematic representation, in the yz plane, of the radiating element according to the invention, from the theory of rays;
• figure 3 , an overview and a detailed view, in the xy plane, of several rows of metasurface cells constituting the metasurface and isolated from each other;
• figure 4 , a perspective view of the metasurface cells isolated from one another, more particularly illustrating the orientation between the alignment axis of the metasurface cells with respect to the excitation polarization;
• figure 5 , an overview and a detailed view, in the xy plane, of several rows of metasurface cells constituting the metasurface and connected by an interconnection line;
• figure 6 , a perspective view of the metasurface cells coupled to each other by an interconnect line;
• figure 7 , a perspective view of the metasurface cells forming a rectangular mesh screen;
• figure 8 , an application of the radiating element according to the invention, where the excitation opening is a radiating linear aperture horn;
• figure 9 , an application of the radiating element according to the invention, where the excitation openings are linear radiating openings networked;
• figures 10A , 10B and 10C , an embodiment in which the excitation opening comprises a dual feed;
• figures 11A and 11B , curves illustrating the directivity and the rate of ellipticity as a function of the frequency, for several configurations of radiating elements.

The figure 2 illustrates a schematic representation, in the yz plane, of the radiating element according to the invention, from the theory of rays. The radiating element comprises an excitation opening OE, which opens onto a metasurface S1. The S1 metasurface comprises an array of conductive planar elements forming metasurface cells (not shown on the figure 1 ), exhibiting a certain pattern repeated periodically in a two-dimensional fashion. Metasurface cells have dimensions less than the operating wavelength of the radiating element (so-called “sub-lambda” dimensions).

A wave linearly polarized according to a first excitation polarization is produced at the excitation opening OE. The excitation opening OE is represented by a rectangular waveguide penetrating into the S1 metasurface without protruding from the S1 metasurface, or by slightly protruding from the latter. The linearly polarized wave propagates in the cavity, delimited by the metasurface S1 and by a frequency selective surface S2, comprising an arrangement of metallic wires or of periodically distributed dipoles. The metasurface S1 and the frequency selective surface S2 are spaced from each other by a distance D1. The frequency selective surface S2 is partially reflecting for the excitation polarization Ex (also called polarization TE, for "Transverse Electric") and transparent for a second polarization Ey orthogonal to the excitation polarization Ex, called orthogonal polarization (also called orthogonal polarization. polarization TM, for "Transverse Magnetic"), and the direction of wave propagation. The frequency selective surface S2 is therefore characterized respectively by reflection and transmission coefficients r _{2 x} and t _{2 x} . The wave produced by the excitation opening is partly radiated (Etx), and partly reflected. This reflected part is called the incident wave Eix.

The S1 metasurface is fully reflective. It acts in a ground plane, facing the frequency selective surface S2. The metasurface S1 is characterized respectively by the reflection coefficients r _{1 xx} and r _{1 yx} , which translate the components of the reflected wave according to the polarizations Ex and Ey for the incident wave Eix.

A resonance is established between the two surfaces for the wave in Ex excitation polarization, typical of Fabry Perot resonators. The incident wave Eix, which propagates in the cavity, undergoes a series of reflections on the frequency selective surface S2 and on the metasurface S1. At each reflection on the frequency selective surface S2, part of the incident wave Eix is radiated. At each reflection on the metasurface S1, part of the incident wave Eix undergoes a polarization rotation, also called depolarization, producing the polarized wave Er1y according to the orthogonal polarization Ey. The amplitude of the polarized wave Er1y according to the orthogonal polarization Ey is determined by the reflection coefficient r _{1 yx} . Another one part of the incident wave Eix retains its polarization, producing the polarized wave Er1x according to the excitation polarization Ex. The amplitude of the polarized wave Er1x according to the excitation polarization Ex is determined by the reflection coefficient r _{1 xx} . The synthesis of a radiation in circular polarization is obtained when the wave radiated E'tx by the selective surface in frequency S2, and coming from the reflected wave Er1x polarized according to the excitation polarization Ex, corresponds in amplitude to l wave polarized Er1y according to the orthogonal polarization Ey, with a phase shift of ± 90 °. The amplitude of the wave radiated E'tx by the frequency selective surface S2 is determined by the transmission coefficient t _{2 x} . The frequency selective surface S2 being transparent to the orthogonal polarization Ey, the polarized wave Er1y according to the orthogonal polarization Ey is radiated without being attenuated. The wave polarized Er1y according to the orthogonal polarization Ey is denoted E'ty. A first radiation in circular polarization is therefore composed of E'tx and E'ty waves.

The reflected wave Er1x undergoes a new reflection on the frequency selective surface S2, with a reflection coefficient r _{2 x} , and, according to the same principle, a second radiation in circular polarization is composed of the waves E "tx and E" ty , then a third radiation in circular polarization, composed of the waves E '"tx and E'" ty.

A circularly polarized beam is thus obtained, which is attenuated more and more as one moves away from the excitation opening OE.

• la taille de cavité est infinie dans le plan xy ;
• la surface sélective en fréquence S2 est caractérisée respectivement par les coefficients de réflexion et de transmission r _2x et t _{2 x}. Elle est complètement transparente à l'onde polarisée Ey ;
• la distance entre la surface sélective en fréquence S2 et la métasurface S1 est égale à D1 ;
• la métasurface S1 est caractérisée respectivement par les coefficients de réflexion r _1xx et r _1yx traduisant les composantes de l'onde réfléchie selon les polarisations Ex et Ey pour une onde incidente Eix.

A pre-dimensioning of this radiating element can be carried out on the basis of the theory of rays, traditionally used for this category of radiating element. We suppose that :

• the cavity size is infinite in the xy plane;
• the frequency selective surface S2 is characterized respectively by the reflection and transmission coefficients r _{2 x} and t _{2 x} . It is completely transparent to the Ey polarized wave;
• the distance between the frequency selective surface S2 and the metasurface S1 is equal to D1;
• the metasurface S1 is characterized respectively by the reflection coefficients r _{1 xx} and r _{1 yx} reflecting the components of the reflected wave according to the polarizations Ex and Ey for an incident wave Eix.

$$\begin{array}{l}{T}_y=\frac{E_{\mathit{trans}}\left(y\right)}{E_{\mathit{inc}}}=\left[{E^{\prime }}_{\mathit{ty}}+{E^{″}}_{\mathit{ty}}+\cdots \right]\\ \mathrm{Où}{E}_{\mathit{inc}}=1\end{array}$$

Où E _inc = 1From the above, the transfer functions T _x and T _y for the polarized transmitted waves E _trans (x) and E _trans (y) can be written as the sum of all the fields transmitted in the far field: $$T_x=\frac{E_{\mathit{trans}}\left(x\right)}{E_{\mathit{inc}}}=\left[E_{\mathit{tx}}+{E^{\prime }}_{\mathit{tx}}+{E^{″}}_{\mathit{tx}}+\cdots \right]$$

$$\begin{array}{l}{T}_y=\frac{E_{\mathit{trans}}\left(y\right)}{E_{\mathit{inc}}}=\left[{E^{\prime }}_{\mathit{ty}}+{E^{″}}_{\mathit{ty}}+\cdots \right]\\ \mathrm{Or}{E}_{\mathit{inc}}=1\end{array}$$

Where E _inc = 1

From (1) the transfer function T _x can be determined: $$\begin{array}{l}{T}_x=\\ t_{2x}+t_{2\mathrm{<figure-callout\; id="1"\; label="x\; r"\; filenames="imgf0001.png,imgf0008.png"\; state="\{\{state\}\}">x</figure-callout>}}{r}_{}{}_{1\mathit{xx}}{r}_{2x}{e}^{-{\mathit{<figure-callout\; id="0"\; label="jk"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">jk</figure-callout>}}_0\left(2{\mathrm{<figure-callout\; id="1"\; label="D"\; filenames="imgf0001.png,imgf0008.png"\; state="\{\{state\}\}">D</figure-callout>}}_1\right)\cos \left(\theta \right)}+t_{2\mathrm{<figure-callout\; id="1"\; label="x\; r"\; filenames="imgf0001.png,imgf0008.png"\; state="\{\{state\}\}">x</figure-callout>}}{r_{}}^{}{{}_{1\mathit{xx}}}^2{r_{2x}}^2{e}^{-{\mathit{<figure-callout\; id="0"\; label="jk"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">jk</figure-callout>}}_0\left(4{\mathrm{<figure-callout\; id="1"\; label="D"\; filenames="imgf0001.png,imgf0008.png"\; state="\{\{state\}\}">D</figure-callout>}}_1\right)\cos \left(\theta \right)}+\cdots \end{array}$$

$$T_x=\frac{t_{2x}}{1-r_{1\mathit{xx}}{r}_{2x}{e}^{-{\mathit{jk}}_0\left(2D_1\right)\cos \left(\theta \right)}}$$

Where k ₀ is the wave number in free space, namely 2π / λ ₀ , and θ is the angle of incidence of the excitation wave. $$T_x=t_{2x}{\displaystyle {\sum }_{\mathrm{not}=0}^{\infty }{\left({\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="imgf0001.png,imgf0008.png"\; state="\{\{state\}\}">r</figure-callout>}}_{1\mathit{xx}}{r}_{2x}\right)}^{\mathrm{not}}{e}^{-{\mathit{<figure-callout\; id="0"\; label="jk"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">jk</figure-callout>}}_0\left(2{\mathit{<figure-callout\; id="1"\; label="nD"\; filenames="imgf0001.png,imgf0008.png"\; state="\{\{state\}\}">nD</figure-callout>}}_1\right)\cos \left(\theta \right)}}$$

$$T_x=\frac{t_{2x}}{1-{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="imgf0001.png,imgf0008.png"\; state="\{\{state\}\}">r</figure-callout>}}_{1\mathit{xx}}{r}_{2x}{e}^{-{\mathit{<figure-callout\; id="0"\; label="jk"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">jk</figure-callout>}}_0\left(2{\mathrm{<figure-callout\; id="1"\; label="D"\; filenames="imgf0001.png,imgf0008.png"\; state="\{\{state\}\}">D</figure-callout>}}_1\right)\cos \left(\theta \right)}}$$

$$T_y=r_{1\mathit{yx}}{r}_{2x}{e}^{-{\mathit{jk}}_0\left(2D_1\right)\cos \left(\theta \right)}{\displaystyle {\sum }_{n=0}^{\infty }{\left(r_{1\mathit{xx}}{r}_{2x}\right)}^n{e}^{-{\mathit{jk}}_0\left(2{\mathit{nD}}_1\right)\cos \left(\theta \right)}}$$

$$T_y=\frac{r_{1\mathit{yx}}{r}_{2x}{e}^{-{\mathit{jk}}_0\left(2D_1\right)\cos \left(\theta \right)}}{1-r_{1\mathit{xx}}{r}_{2x}{e}^{-{\mathit{jk}}_0\left(2D_1\right)\cos \left(\theta \right)}}$$

From (2), the transfer function T _y can be determined: $$\begin{array}{l}{T}_y=r_{2\mathrm{<figure-callout\; id="1"\; label="x\; r"\; filenames="imgf0001.png,imgf0008.png"\; state="\{\{state\}\}">x</figure-callout>}}{r}_{}{}_{1\mathit{yx}}{e}^{-{\mathit{<figure-callout\; id="0"\; label="jk"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">jk</figure-callout>}}_0\left(2{\mathrm{<figure-callout\; id="1"\; label="D"\; filenames="imgf0001.png,imgf0008.png"\; state="\{\{state\}\}">D</figure-callout>}}_1\right)\cos \left(\theta \right)}+{r_{2x}}^2{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="imgf0001.png,imgf0008.png"\; state="\{\{state\}\}">r</figure-callout>}}_{1\mathit{<figure-callout\; id="1"\; label="xx\; r"\; filenames="imgf0001.png,imgf0008.png"\; state="\{\{state\}\}">xx</figure-callout>}}{r}_{}{}_{1\mathit{yx}}{e}^{-{\mathit{<figure-callout\; id="0"\; label="jk"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">jk</figure-callout>}}_0\left(4{\mathrm{<figure-callout\; id="1"\; label="D"\; filenames="imgf0001.png,imgf0008.png"\; state="\{\{state\}\}">D</figure-callout>}}_1\right)\cos \left(\theta \right)}+\\ {r_{2x}}^3{{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="imgf0001.png,imgf0008.png"\; state="\{\{state\}\}">r</figure-callout>}}_{1\mathit{xx}}}^2{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="imgf0001.png,imgf0008.png"\; state="\{\{state\}\}">r</figure-callout>}}_{1\mathit{yx}}{e}^{-{\mathit{<figure-callout\; id="0"\; label="jk"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">jk</figure-callout>}}_0\left(6{\mathrm{<figure-callout\; id="1"\; label="D"\; filenames="imgf0001.png,imgf0008.png"\; state="\{\{state\}\}">D</figure-callout>}}_1\right)\cos \left(\theta \right)}+\cdots \end{array}$$

$$T_y={\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="imgf0001.png,imgf0008.png"\; state="\{\{state\}\}">r</figure-callout>}}_{1\mathit{yx}}{r}_{2x}{e}^{-{\mathit{<figure-callout\; id="0"\; label="jk"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">jk</figure-callout>}}_0\left(2{\mathrm{<figure-callout\; id="1"\; label="D"\; filenames="imgf0001.png,imgf0008.png"\; state="\{\{state\}\}">D</figure-callout>}}_1\right)\cos \left(\theta \right)}{\displaystyle {\sum }_{\mathrm{not}=0}^{\infty }{\left({\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="imgf0001.png,imgf0008.png"\; state="\{\{state\}\}">r</figure-callout>}}_{1\mathit{xx}}{r}_{2x}\right)}^{\mathrm{not}}{e}^{-{\mathit{<figure-callout\; id="0"\; label="jk"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">jk</figure-callout>}}_0\left(2{\mathit{<figure-callout\; id="1"\; label="nD"\; filenames="imgf0001.png,imgf0008.png"\; state="\{\{state\}\}">nD</figure-callout>}}_1\right)\cos \left(\theta \right)}}$$

$$T_y=\frac{{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="imgf0001.png,imgf0008.png"\; state="\{\{state\}\}">r</figure-callout>}}_{1\mathit{yx}}{r}_{2x}{e}^{-{\mathit{<figure-callout\; id="0"\; label="jk"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">jk</figure-callout>}}_0\left(2{\mathrm{<figure-callout\; id="1"\; label="D"\; filenames="imgf0001.png,imgf0008.png"\; state="\{\{state\}\}">D</figure-callout>}}_1\right)\cos \left(\theta \right)}}{1-{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="imgf0001.png,imgf0008.png"\; state="\{\{state\}\}">r</figure-callout>}}_{1\mathit{xx}}{r}_{2x}{e}^{-{\mathit{<figure-callout\; id="0"\; label="jk"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">jk</figure-callout>}}_0\left(2{\mathrm{<figure-callout\; id="1"\; label="D"\; filenames="imgf0001.png,imgf0008.png"\; state="\{\{state\}\}">D</figure-callout>}}_1\right)\cos \left(\theta \right)}}$$

The resonance condition is achieved when: $$\angle {\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="imgf0001.png,imgf0008.png"\; state="\{\{state\}\}">r</figure-callout>}}_{1\mathit{xx}}+\angle r_{2x}+2\mathit{N\pi }=2k_0{\mathrm{<figure-callout\; id="1"\; label="D"\; filenames="imgf0001.png,imgf0008.png"\; state="\{\{state\}\}">D</figure-callout>}}_1\cos \left(\theta \right)$$

Where ∠ r _{1 xx} represents the in-phase component of the reflection coefficient r _{1 xx} , ∠r _{2 x} represents the in-phase component of the reflection coefficient r _{2 x} , and N any integer.

Où : $$G={\rho }_L+\frac{1}{{\rho }_L}$$

$$\phi =\angle T_x-\angle T_y$$

$${\rho }_L=\frac{\left|T_x\right|}{\left|T_y\right|}$$

Using the transfer functions calculated in (5) and (8) for the two polarizations, it is possible to calculate the ellipticity ratio (AR Axial Ratio) for the entire antenna, using the following relation: $$\mathit{AR}=\frac{\sqrt{G+\sqrt{G^2-4{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="imgf0008.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\left(\phi \right)}}}{\sqrt{G-\sqrt{G^2-4{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="imgf0008.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\left(\phi \right)}}}$$

Or : $$G={\rho }_{\mathrm{THE}}+\frac{1}{{\rho }_{\mathrm{THE}}}$$

$$\phi =\angle T_x-\angle T_y$$

$${\rho }_{\mathrm{THE}}=\frac{\left|T_x\right|}{\left|T_y\right|}$$

$$\angle t_{2x}=\angle r_{1\mathit{yx}}+\angle r_{2x}-2k_0{D}_1\cos \left(\theta \right)+\frac{\pi }{2}+2\mathit{N\pi }$$

Starting from relations (12) and (13), and using the transfer functions calculated in (5) and (8), it is therefore possible to write the condition to produce a pure circular polarization with the following relations: $$\left|t_{2x}\right|=\left|{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="imgf0001.png,imgf0008.png"\; state="\{\{state\}\}">r</figure-callout>}}_{1\mathit{yx}}{r}_{2x}\right|$$

$$\angle t_{2x}=\angle {\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="imgf0001.png,imgf0008.png"\; state="\{\{state\}\}">r</figure-callout>}}_{1\mathit{yx}}+\angle r_{2x}-2k_0{\mathrm{<figure-callout\; id="1"\; label="D"\; filenames="imgf0001.png,imgf0008.png"\; state="\{\{state\}\}">D</figure-callout>}}_1\cos \left(\theta \right)+\frac{\mathrm{<figure-callout\; id="2"\; label="\pi "\; filenames="imgf0008.png"\; state="\{\{state\}\}">\pi </figure-callout>}}{2}+2\mathit{N\pi }$$

By combining equation (9), describing the resonance condition, and equation (15), describing the circular polarization condition, the following relationship can be obtained: $$\angle t_{2x}=\angle {\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="imgf0001.png,imgf0008.png"\; state="\{\{state\}\}">r</figure-callout>}}_{1\mathit{yx}}-<figure-callout\; id="1"\; label="\angle \; r"\; filenames="imgf0001.png,imgf0008.png"\; state="\{\{state\}\}">\angle </figure-callout>r_{}{}_{1\mathit{xx}}+\frac{\mathrm{<figure-callout\; id="2"\; label="\pi "\; filenames="imgf0008.png"\; state="\{\{state\}\}">\pi </figure-callout>}}{2}+2{\mathrm{NOT}}^{\prime }\pi$$

Where N 'is any integer.

Equation (16) does not depend on the first order of the frequency (the wave number k ₀ is not found in the equation), but relates only the components of the reflection and transmission matrices of the selective surface in frequency S2 and metasurface S1. The band pass-through is no longer limited by the mechanism for generating the circular polarization, but by the operating mechanism of the Fabry Pérot cavity. The bandwidth widening techniques for the latter can then be used, without effects on the circular polarization. In particular, the cascading of a second cavity, above the frequency selective surface S2, makes it possible to widen the pass band, without this degrading the quality of the circular polarization.

The phase component of the transmission coefficient t _{2 x} of the frequency selective surface S2 determines the directivity of the radiating element; it is therefore predetermined and known, as a function of the desired directivity. Thus, according to equation (16), in order to produce pure circular polarization, the in-phase components of the reflection coefficients r _{1 yx} and r _{1 xx} should be appropriately selected.

The distribution matrix [S] (or “scattering matrix” in Anglo-Saxon terminology) of the metasurface S1 can be written in a conventional way in the form: $$\left[S\right]=\left[\begin{array}{cc}{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="imgf0001.png,imgf0008.png"\; state="\{\{state\}\}">r</figure-callout>}}_{1\mathit{<figure-callout\; id="1"\; label="xx\; r"\; filenames="imgf0001.png,imgf0008.png"\; state="\{\{state\}\}">xx</figure-callout>}}& r_{}{}_{1\mathit{xy}}\\ {\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="imgf0001.png,imgf0008.png"\; state="\{\{state\}\}">r</figure-callout>}}_{1\mathit{<figure-callout\; id="1"\; label="yx\; r"\; filenames="imgf0001.png,imgf0008.png"\; state="\{\{state\}\}">yx</figure-callout>}}& r_{}{}_{1\mathit{yy}}\end{array}\right]$$

However, the metasurface S1 does not receive in incidence any wave in orthogonal polarization Ey, insofar as the frequency selective surface S2 is transparent to the orthogonal polarization. The reflection coefficients r _{1 xy} and r _{1 yy} , which respectively translate the reflection coefficient in excitation polarization Ex and in orthogonal polarization Ey for an incident wave in orthogonal polarization Ey, are therefore irrelevant for the dimensioning of the metasurface S1. Only the reflection coefficients r _{1 xx} and r _{1 yx} must be taken into account for the dimensioning of the metasurface S1, and determined by relation (16).

An Ox'y'z coordinate system is defined as being the result of the rotation of an angle Ψ around the Oz axis of the Oxyz coordinate system (the Ox axis is defined by the excitation polarization Ex, and the Oy axis by the orthogonal polarization Ey).

One thus seeks to obtain, starting from the matrix of distribution [S] in the Oxyz coordinate system, a distribution matrix [S '] of diagonal type in the Ox'y'z coordinate system, being able to be written in the form: $$\left[S^{\prime }\right]=\left[\begin{array}{cc}{e}^{{\mathit{j\phi }}_1}& 0\\ 0& {\mathrm{<figure-callout\; id="2"\; label="e\; j\phi "\; filenames="imgf0008.png"\; state="\{\{state\}\}">e</figure-callout>}}^{{\mathit{j\phi }}_{}}\end{array}\right]$$

Where the diagonal reflection coefficients e ^{jϕ 1} and e ^{jϕ 2} respectively represent the phase components of the waves reflected respectively in excitation polarization and in orthogonal polarization, in the frame Ox'y'z. The amplitude components of the waves reflected in excitation polarization and in orthogonal polarization are equal to 1, reflecting the lossless character of the S1 metasurface.

Under normal incidence condition (θ = 0 °), there is thus a congruence relation between the distribution matrix [S] in the Oxy plane, and the distribution matrix [S '] in the Ox'y' plane, which can therefore be written in the form: $$\left[S\text{'}\right]{=}^t\left[R\right]\left[S\right]\left[R\right]$$

Where [ R ] is a rotation matrix of angle Ψ : $$\left[R\right]=\left[\begin{array}{cc}\cos \left(\mathrm{\Psi }\right)& \mathit{sin}\left(\mathrm{\Psi }\right)\\ -\mathit{sin}\left(\mathrm{\Psi }\right)& \mathit{cos}\left(\mathrm{\Psi }\right)\end{array}\right]$$

It is therefore necessary to identify the angle Ψ which makes it possible to transform the required distribution matrix [S] into a diagonal matrix. For this calculation, which is not detailed here, only the reflection coefficients r _{1 xx} and r _{1 yx} are specified for the operation of the antenna, the reflection coefficients r _{1 xy} and r _{1 yy} being only adjustment variables. Thus, once the angle Ψ has been identified to obtain a diagonal matrix, the diagonal reflection coefficients e ^{jϕ 1} and e ^{jϕ 2} are determined from relations (17) and (18).

Due to the misalignment of the metasurface S1 with respect to the excitation polarization Ex, each incident wave in linear polarization is reflected with an excitation polarization component Ex and an orthogonal polarization component Ey. In the case of an S1 metasurface made up of an arrangement of planar conductive elements rectangular (also called “patches” according to Anglo-Saxon terminology), the phase responses according to the Ex or Ey polarization are controlled in the first order by the dimensions of the conducting planar element.

The S1 metasurface may include an array of MS metasurface cells, as shown in figure 3 . The dimensions of MS metasurface cells can be obtained relatively independently as a function of the in-phase components of the diagonal reflection coefficients. Thus, the dimensions of each cell with a metasurface MS (length ly and width wy) are adjusted as a function of the in-phase components of the diagonal reflection coefficients e ^{jϕ 1} and e ^{jϕ 2} previously determined.

The metasurface cells can advantageously be rectangular. The S1 metasurface can therefore be made up of several rows RA of cells with an MS metasurface.

As illustrated by figure 4 , the MS metasurface cells of the same row RA are isolated from one another, and placed on a substrate SUB1. These elements are arranged between the ground plane crossed by the excitation opening, and the frequency selective surface S2. Each cell with an MS metasurface therefore forms a dipole, having a mainly capacitive behavior for the excitation polarization Ex and for the orthogonal polarization Ey. All CE centers of MS metasurface cells are aligned along an AX alignment axis. The alignment axis AX is therefore oriented by the angle Ψ with respect to the excitation polarization Ex.

MS metasurface cells can all have the same length (ly dimension on the figure 3 ), and there can be the same spacing between two MS metasurface cells (px dimension on the figure 3 ).

According to a variant, illustrated by figure 5 , the S1 metasurface can include LG metasurface interconnection lines. LG metasurface interconnection lines interconnect all MS metasurface cells of the same row RA. They advantageously allow to evacuate the electrostatic charges present in the MS metasurface cells, and thus improve the overall behavior of the radiating element. MS metasurface cells have remarkably stable properties in incidence, since particularly small patterns can be used, in order to obtain broadband or even dual-band characteristics. The cells with a metasurface MS in the same row RA are coupled at their center CE, orthogonally, to an interconnection line with a metasurface LG.

As illustrated by figure 6 , the interconnection line with metasurface LG is oriented by the angle Ψ with respect to the excitation polarization Ex. For each row RA, the assembly formed by the interconnection line LG and by the cells with metasurface MS constitutes therefore a grid with stubs (or with adaptation elements). The stub gate has a mainly inductive behavior for the Ex excitation polarization, and capacitive for the orthogonal Ey polarization.

The frequency selective surface S2, partially reflecting, consists of an array of metallic wires FI spaced periodically, and oriented according to the excitation polarization Ex. As a variant, the frequency selective surface S2 can consist of dipoles, of slot types or "patches" (or "plaques" in French). The slits can be made in a metal plate, and the patches placed on an electrically transparent substrate.

The network of cells with a metasurface MS is placed on a substrate SUB1, itself placed on a ground plane PM. The ground plane PM is crossed by the excitation opening OE. The substrate SUB1 may for example be composed of two layers of Astroquartz ™, between which there is a layer of nidaquartz.

According to a variant, illustrated by figure 7 , the rows RA are connected to one another via the cells with a metasurface MS. Together with the LG metasurface interconnection lines, they thus form a pattern rectangular mesh netting. The metasurface S1 thus has an inductive behavior for the excitation polarization Ex and for the orthogonal polarization Ey.

The figure 8 illustrates the case where the excitation opening OE is a CRN horn with a radiating linear opening. The radiating linear opening, crossing the metasurface S1 and opening into the cavity, can constitute the radiative part of a quasi-optical beam former, characterized in particular by a large lateral opening. This solution therefore makes it possible to maintain a wide spectral opening, while radiating the circular polarization. The larger the size of the radiating linear aperture, the smaller the adaptation or radiation passband. However, this has no influence on the quality of the circular polarization, as indicated in relation (16).

The figure 9 illustrates the case where there is a plurality of excitation openings OE. The excitation openings OE are formed by an array RES of linear radiating openings, resulting for example from a divider with parallel plates. The use of a divider with parallel plates makes it possible in particular to better distribute the field on the excitation openings OE. In order to limit the couplings between the linear radiating openings, it is advisable to strongly limit the coupling between the ports, for example to -15 dB.

The figures 10A , 10B and 10C illustrate an embodiment of the invention, in which the excitation opening OE is doubled. It comprises a double power supply formed by two waveguide openings (WG1, WG2) opening symmetrically into the resonant cavity, and connected to an impedance matching network RAD. The RAD impedance matching network comprises at least one IR iris, in order to widen the matching band. This embodiment makes it possible to cancel a possible parasitic TEM mode present in the radiating element. This TEM mode, which generates cross-polarized lobes, is independent of the OE excitation aperture type. The figure 10C illustrates such an opening excitation, integrated in a radiating element according to the invention. In the figure 10C , each MS metasurface cell forms a dipole, with no interconnection line. The splitting of the excitation opening can be achieved in the same way when the MS metasurface cells are connected by an interconnection line, or when they form a rectangular mesh grid.

The figures 11A and 11B illustrate the frequency behavior of the directivity and the rate of ellipticity ("axial ratio" in English terminology), for several antennas integrating the radiating elements in accordance with the invention, and comprising a double feed formed by two guide openings waves, in accordance with the embodiment described above. The radiating elements are distinguished by different values of the width (a) and of the length (b) of the excitation opening, and for different values of the reflectivity coefficient r _{2 x} . The values of the reflectivity coefficient r _{2 x} are noted "+", "++" or "+++" to indicate their relative value. a (mm) b (mm) S2 frequency selective surface reflectivity Radiant element 1 5 15 +++ Radiant element 2 5 15 ++ Radiant element 3 10 15 ++ Radiant element 4 10 15 +

The figure 11A illustrates the frequency behavior of the directivity of the radiating elements, for an angle θ = 0 °. The more directional the radiating element (and therefore the greater the reflectivity of the frequency selective surface S2), the less broadband the frequency behavior, which is typical of Fabry Perot cavity antennas. For radiating elements 2, 3 and 4, the bandwidth at -3 dB is of the order of 10% of the center frequency. The figure 11B illustrates the frequency behavior of the ellipticity rate of the radiating elements, for an angle θ = 0 °. The bandwidth at ―3 dB is greater than 10% for the four antennas, and remains of the order of 10% at -1 dB, which is clearly superior to the performance of the radiating elements of the state of the art. As demonstrated in Relation (16), the circular polarization generation technique operates over a wide bandwidth, and does not limit the operation of the radiating element.

The broadband behavior can be further improved by cascading a second cavity on the frequency selective surface S2. To achieve this cascading, at least one second resonant cavity is placed on the cavity which is the subject of the invention. The second resonant cavity has as its lower surface the frequency selective surface of the lower cavity, and as its upper surface a partially reflecting surface. The cross section of the upper cavity may be larger than that of the first lower cavity, as described in the document FR2959611 , or, alternatively, have a cross section substantially identical to that of the lower cavity. The so-called “two-cavity” embodiment makes it possible to lower the reflectivity of the frequency-selective surface of the lower cavity, which favors the broadband behavior of the radiating element, and without however having any influence. on the quality of circular polarization.

Claims (16)

1. A circularly polarized radiating element comprising:

   - at least one excitation aperture (OE) for a wave that is linearly polarized according to a first so-called excitation polarization (Ex);

   - a frequency selective surface (S2) that partially reflects the excitation polarization (Ex) and that is transparent to a second polarization (Ey), referred to as the orthogonal polarization, that is orthogonal to the excitation polarization (Ex) and to the direction of propagation of the wave, and that is placed in a plane defined by the excitation polarization (Ex) and by the orthogonal polarization (Ey);

   and further comprising a completely reflective metasurface (S1) facing the frequency selective surface (S2), and comprising a two-dimensional and periodic array of conductive planar elements forming metasurface cells (MS), the excitation aperture (OE) leading onto the metasurface (S1),

   the frequency selective surface (S2) and the metasurface (S1) forming a resonant cavity for the excitation polarization (Ex),

   the metasurface cells (MS) all being oriented identically with respect to the excitation polarization (Ex) and configured to:

   o reflect an incident wave (Eix) according to the excitation polarization (Ex) to form a reflected wave (Er1x) polarized according to the excitation polarization (Ex), and

   o depolarize and reflect the incident wave (Eix) to form a reflected wave (Erly) polarized according to the orthogonal polarization (Ey), having a phase difference substantially equal to ± 90° with respect to the reflected wave (Er1x) polarized according to the excitation polarization (Ex), and having an amplitude substantially equal to the amplitude of a wave (E'tx) radiated by the frequency selective surface (S2), generated from the reflected wave (Er1x) polarized according to the excitation polarization (Ex).
2. The radiating element according to claim 1, the metasurface (S1) comprising a ground plane (PM) on which are placed a substrate (SUB1) and the array of metasurface cells (MS), which cells are arranged in rows (RA), the centres (CE) of each metasurface cell (MS) of a given row (RA) being aligned along an alignment axis (AX), the alignment axis (AX) being oriented by a rotation angle (Ψ) with respect to the excitation polarization (Ex), the rotation angle (Ψ) being determined so as to obtain a diagonal type matrix [S'], where: $$\left[S^{\prime }\right]{=}^t\left[R\right]\left[S\right]\left[R\right],$$

   

   [S] being the scattering matrix of the metasurface (S1), and [R] a rotation matrix of angle Ψ.
3. The radiating element according to claim 2, the metasurface cells (MS) of a given row (RA) being coupled by a metasurface interconnect line (LG) that is elongated along the alignment axis (AX).
4. The radiating element according to claim 3, the rows (RA) being connected to one another by way of metasurface cells (MS), forming with the metasurface interconnect lines (LG) a rectangular-meshed grid pattern.
5. The radiating element according to claim 2, the metasurface cells (MS) of a given row (RA) being isolated from one another.
6. The radiating element according to one of claims 2 to 5, the metasurface cells (MS) of a given row (RA) all being periodically spaced.
7. The radiating element according to one of claims 2 to 6, all the metasurface cells (MS) of the metasurface (S1) having the same dimensions.
8. The radiating element according to one of the preceding claims, the frequency selective surface (S2) comprising an array of parallel metal wires (FI) that are periodically spaced and aligned with the excitation polarization (Ex).
9. The radiating element according to one of claims 1 to 7, the frequency selective surface (S2) comprising a two-dimensional array of metal dipoles that are arranged periodically.
10. The radiating element according to one of the preceding claims, the excitation aperture (OE) comprising at least one waveguide aperture leading into the resonant cavity.
11. The radiating element according to claim 10, the excitation aperture (OE) comprising a dual feed formed by two waveguides (WG1, WG2) that lead symmetrically into the resonant cavity, and that are connected to an impedance matching network (RAD).
12. The radiating element according to one of claims 1 to 9, the excitation aperture (OE) being a horn (CRN) of a linear radiating aperture.
13. The radiating element according to one of claims 1 to 9, comprising a plurality of excitation apertures, the excitation apertures being formed by an array (RES) of linear radiating apertures.
14. The radiating element according to one of the preceding claims, comprising at least a second cavity cascaded on the frequency selective surface (S2).
15. The radiating element according to one of the preceding claims, the metasurface cells (MS) being of rectangular shape.
16. An array antenna comprising at least one radiating element according to one of the preceding claims.

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