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1032 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 61, NO. 3, MARCH 2013 Self-Polarizing Fabry–Perot Antennas Based on Polarization Twisting Element Shoaib Anwar Muhammad, Ronan Sauleau, Senior Member, IEEE, Guido Valerio, Member, IEEE, Laurent Le Coq, and Hervé Legay Abstract—A new conguration of a self-polarizing Fabry–Perot (FP) antenna is presented to generate circular polarization with high gain levels using a simple linearly polarized feed. It consists of an FP resonator combined with a polarization-twisting ground plane. An analytical model is proposed to facilitate the antenna de- sign, and the corresponding results are shown to be in very close agreement with full-wave simulations. The experimental prototype built in -band exhibits a combined bandwidth (3 dB axial ratio, 3 dB gain drop, and 10 dB impedance matching) of 3% with a maximum realized gain of 18.0 dB. The antenna is completely shielded with an aperture size of and a height of only . Such antennas are attractive candidates for high-power space applications at low frequencies ( -to -bands) where stan- dard horns are very bulky. Index Terms—Circular polarization (CP), Fabry–Perot (FP) resonators, horns, self-polarization. I. INTRODUCTION T HE ORIGINAL concept of Fabry–Perot (FP) antennas [1] has received a lot of attention over the last years. The main reason is that these antennas allow achieving high gain while keeping low-prole structures [2]–[4]. Most of the pre- vious studies focused on linearly polarized (LP) FP antennas (e.g., [5]–[8]). Recently, new congurations called self-polarizing FP cavity antennas have been proposed [9], [10]. The aim is to avoid using circular polarization (CP) feed networks that are usually bulky for high-power applications from - to -bands [11] and to re- place them by simple LP feeds exciting the FP antenna element. The particularity of this concept is that the antenna itself gener- ates the CP and provides high gain simultaneously. In [9], a three-layered frequency selective surface (FSS) structure is placed over a metallic ground plane to combine the FP and self-polarizing effects. The experimental results obtained for a antenna size have shown good results: combined bandwidth [3-dB axial ratio (AR) Manuscript received February 08, 2012; revised July 15, 2012; accepted Oc- tober 09, 2012. Date of publication November 16, 2012; date of current ver- sion February 27, 2013. This work was supported by Thales Alenia Space, France. This work was performed using HPC resources from GENCI-IDRIS under Grant 2012-050779. S. A. Muhammad, R. Sauleau, G. Valerio, and L. Le Coq are with the IETR, UMR CNRS 6164, University of Rennes 1, 35042 Rennes, France (e-mail: [email protected]; [email protected]; [email protected]; [email protected]). H. Legay is with Thales Alenia Space, France, 31037 Toulouse Cedex 1, France (e-mail: [email protected]). Color versions of one or more of the gures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identier 10.1109/TAP.2012.2227443 and 10-dB impedance matching] of 2.24%, and maximum measured gain of about 21 dB. The conguration introduced in [10] is very different. The authors proposed to combine a single-layered polarizing FSS and linear corrugations to control at the same time the polar- izing and FP effects. The corresponding antenna is very com- pact , but exhibits a much narrower combined bandwidth (around 1.4%) with a 13.3 dB maximum gain. A new self-polarizing antenna conguration is studied here. The idea consists in using a nonresonant FSS to produce the FP resonance and a polarizing twisting surface to generate the CP with an improved bandwidth in terms of AR and impedance matching. The outline of this paper is as follows. In Section II-A, the an- tenna concept is presented, along with its geometry and working principle. As there are many parameters to be optimized, an an- alytical model is proposed to facilitate the predesign of the an- tenna (Sections II-B and II-C). Full-wave simulation results and experimental data are compared in Section III. The conclusions are drawn in Section IV. II. ANTENNA CONCEPT AND MODELING A. Basic Idea and Antenna Geometry The main idea is to separate the FP resonance effect and the CP generation part. To this end, we can imagine a simple FP resonator (Fig. 1) composed of two partially reecting surfaces or FSSs (with their respective reection and transmission coef- cients); both FSSs are separated by a distance dictated by the classical resonance condition at [1], [5], [12] (1) where is the speed of light in vacuum, and is an integer . and are the reection coefcient phase values of the lower and upper FSS, respectively. When this resonator is excited by a source element (wave- guide, patch, etc.) placed between the two FSSs, the antenna resonates at and, depending on the FSS characteris- tics [1], [2], [12], a highly directive wave is radiated on both sides of the resonator (i.e., in and directions). If both FSSs have the same reectivity, the magnitude of energy is the same in both directions. Let us consider now that the resonator is excited in linear polarization (e.g., -polarization) and is made with two one-di- mensional (1-D) FSSs that are highly reective for only one polarization ( -polarization here) and nearly transparent for 0018-926X/$31.00 © 2012 IEEE
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Page 1: Self-Polarizing Fabry–Perot Antennas Based on Polarization Twisting Element

1032 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 61, NO. 3, MARCH 2013

Self-Polarizing Fabry–Perot Antennas Based onPolarization Twisting Element

Shoaib Anwar Muhammad, Ronan Sauleau, Senior Member, IEEE, Guido Valerio, Member, IEEE,Laurent Le Coq, and Hervé Legay

Abstract—A new configuration of a self-polarizing Fabry–Perot(FP) antenna is presented to generate circular polarization withhigh gain levels using a simple linearly polarized feed. It consistsof an FP resonator combined with a polarization-twisting groundplane. An analytical model is proposed to facilitate the antenna de-sign, and the corresponding results are shown to be in very closeagreement with full-wave simulations. The experimental prototypebuilt in -band exhibits a combined bandwidth (3 dB axial ratio,3 dB gain drop, and 10 dB impedance matching) of 3% witha maximum realized gain of 18.0 dB. The antenna is completelyshielded with an aperture size of and a height ofonly . Such antennas are attractive candidates for high-powerspace applications at low frequencies ( -to -bands) where stan-dard horns are very bulky.

Index Terms—Circular polarization (CP), Fabry–Perot (FP)resonators, horns, self-polarization.

I. INTRODUCTION

T HEORIGINAL concept of Fabry–Perot (FP) antennas [1]has received a lot of attention over the last years. The

main reason is that these antennas allow achieving high gainwhile keeping low-profile structures [2]–[4]. Most of the pre-vious studies focused on linearly polarized (LP) FP antennas(e.g., [5]–[8]).Recently, new configurations called self-polarizing FP cavity

antennas have been proposed [9], [10]. The aim is to avoid usingcircular polarization (CP) feed networks that are usually bulkyfor high-power applications from - to -bands [11] and to re-place them by simple LP feeds exciting the FP antenna element.The particularity of this concept is that the antenna itself gener-ates the CP and provides high gain simultaneously.In [9], a three-layered frequency selective surface (FSS)

structure is placed over a metallic ground plane to combinethe FP and self-polarizing effects. The experimental resultsobtained for a antenna size have showngood results: combined bandwidth [3-dB axial ratio (AR)

Manuscript received February 08, 2012; revised July 15, 2012; accepted Oc-tober 09, 2012. Date of publication November 16, 2012; date of current ver-sion February 27, 2013. This work was supported by Thales Alenia Space,France. This work was performed using HPC resources from GENCI-IDRISunder Grant 2012-050779.S. A. Muhammad, R. Sauleau, G. Valerio, and L. Le Coq are with

the IETR, UMR CNRS 6164, University of Rennes 1, 35042 Rennes,France (e-mail: [email protected]; [email protected];[email protected]; [email protected]).H. Legay is with Thales Alenia Space, France, 31037 Toulouse Cedex 1,

France (e-mail: [email protected]).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TAP.2012.2227443

and 10-dB impedance matching] of 2.24%, and maximummeasured gain of about 21 dB.The configuration introduced in [10] is very different. The

authors proposed to combine a single-layered polarizing FSSand linear corrugations to control at the same time the polar-izing and FP effects. The corresponding antenna is very com-pact , but exhibits a much narrowercombined bandwidth (around 1.4%) with a 13.3 dB maximumgain.A new self-polarizing antenna configuration is studied here.

The idea consists in using a nonresonant FSS to produce theFP resonance and a polarizing twisting surface to generate theCP with an improved bandwidth in terms of AR and impedancematching.The outline of this paper is as follows. In Section II-A, the an-

tenna concept is presented, along with its geometry and workingprinciple. As there are many parameters to be optimized, an an-alytical model is proposed to facilitate the predesign of the an-tenna (Sections II-B and II-C). Full-wave simulation results andexperimental data are compared in Section III. The conclusionsare drawn in Section IV.

II. ANTENNA CONCEPT AND MODELING

A. Basic Idea and Antenna Geometry

The main idea is to separate the FP resonance effect and theCP generation part. To this end, we can imagine a simple FPresonator (Fig. 1) composed of two partially reflecting surfacesor FSSs (with their respective reflection and transmission coef-ficients); both FSSs are separated by a distance dictatedby the classical resonance condition at [1], [5], [12]

(1)

where is the speed of light in vacuum, and is an integer. and are the reflection coefficient

phase values of the lower and upper FSS, respectively.When this resonator is excited by a source element (wave-

guide, patch, etc.) placed between the two FSSs, the antennaresonates at and, depending on the FSS characteris-tics [1], [2], [12], a highly directive wave is radiated on bothsides of the resonator (i.e., in and directions). If bothFSSs have the same reflectivity, the magnitude of energy is thesame in both directions.Let us consider now that the resonator is excited in linear

polarization (e.g., -polarization) and is made with two one-di-mensional (1-D) FSSs that are highly reflective for only onepolarization ( -polarization here) and nearly transparent for

0018-926X/$31.00 © 2012 IEEE

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MUHAMMAD et al.: SELF-POLARIZING FABRY–PEROT ANTENNAS BASED ON POLARIZATION TWISTING ELEMENT 1033

Fig. 1. Proposed antenna configuration. Both FSSs are 1-D inductive gridsalong -direction. The twisting surface is made of horizontal corrugations tiltedat 45 .

the orthogonal one ( -polarization), as shown in Fig. 1; thisassumption is validated in Appendix-B. If a polarizationtwisting element is placed on one side of the FP resonator (likecorrugations tilted at 45 as illustrated in Fig. 1), it will convertthe incident -polarized wave into a reflected -polarizedwave that travels back to the FP resonator. As the latter istransparent to -polarization (Appendix-B), the energy passesthrough the cavity without any disturbance. By controlling thedistance between the resonator and the polarization twister

, a 90 -phase difference between the two orthogonalpolarizations can be obtained. Consequently, both componentsand combine each other in the upper space to produce a

CP wave. A similar concept has been reported in literature forthe design of folded reflectarrays using a planar polarizationtwister, e.g., [13] and [14].

B. Analytical Model

The antenna architecture is defined by many parameters(FSS and twister dimensions, , , , etc.). An analyticalmodel is presented here to facilitate its predesign. This modelis based on the multiple-reflection approach (e.g., [1] and[12]) where an infinite FP interferometer is modeled using raytracing. This model provides good results for antenna aperturesin the order of few wavelengths or larger, e.g., [6].The analytical model implemented here is summarized in

Fig. 2. It consists of an infinite FP resonator with two 1-DFSS elements (as those shown in Fig. 1) characterized by theirrespective reflection and transmission coefficients

and separated by a distance . The polariza-tion twister (metallic corrugations at 45 , Fig. 1) is modeledby its reflection coefficient representing the polarizationconversion of an incident -polarized wave into a reflected-polarized wave. The excitation element is assumed to be awaveguide source radiating in the direction, placed at a dis-tance from the bottom FSS. Using the ray-tracing method,and assuming that the point source is linearly polarized withunit magnitude (i.e., ) and that there is no loss in theantenna and twister parts, the paths traced by the rays emittedby the source are represented in Fig. 2.

Fig. 2. Analytical model of the proposed antenna based on ray-tracing method.The rays for -polarization are represented as black dots, and the rays presentingthe -polarized ray by gray dots.

To calculate the axial ratio of this antenna, we first need to findthe transmission coefficients and in - and -polariza-tions. Each transmission coefficient is simply the summation ofall far-field components radiated by the antenna after an infinitenumber of multiple reflections between the two FSSs.Using the simple procedure outlined in Appendix-A along

with an infinite series summation formula, the transfer functionfor both polarizations can be expressed as follows:

(2)

(3)

It is important to mention here that only the broadside valuesof the transfer functions are retained as the antenna di-

rectivity is maximum at broadside. For configurations where themaximum directivity is required for other angles, the termcan be included in the model for optimization (Appendix-A).Next, the axial ratio can be easily computed from (2) and (3)

using the following expression:

(4)

where , , and.

C. Analytical Optimization

The analytical model presented above is implemented hereto optimize the antenna parameters. The following procedure isemployed.For a given FSS configuration and twister

characteristics , the antenna height parametersare varied in order to obtain the broadest 1-dB AR bandwidthwith the maximum of the transfer function centered around .The FSS characteristics can be obtained ei-ther analytically for 1-D inductive grids with zero thickness(e.g., [15]–[17]) or numerically using full-wave simulations andperiodic boundary conditions for more complex FSS shapes.The latter method has been chosen here because rigid and thick

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1034 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 61, NO. 3, MARCH 2013

metallic FSS screens without any dielectric support are requiredhere for high-power space applications.The parameter is calculated in the same way, using peri-

odic boundary simulations (HFSS) around a unit cell of linearcorrugation (tilted by 45 ), and by illuminating it with a planewave polarized along and observing the reflection coefficientin -direction. The reference curves for the most interestingcases are detailed in Appendix-B.It should also be noted here that this model can be used also

for planar self-polarizing antennas by including a dielectric sub-strate with an FSS etched on both sides and a planar twister el-ement (as the one reported in [18]).To keep a simple antenna structure, thick 1-D inductive grids

and rectangular corrugations are used. Their typical frequencyresponses are given in Appendix-B. This database is employedto predefine the antenna geometry and select the best set of pa-rameters providing the largest AR bandwidth and the highestdirectivity at broadside , which is indicated by the mag-nitude of the transfer function calculated from (2) and (3). Foroptimization runs, the values of and are varied over awide range of values around a central starting value. The startingpoint for is calculated using (1), while the starting point for

is chosen to be around a quarter wavelength . Then,a range of values around these starting values is selected (first awide range with large steps, then a finer range with smaller stepsfor fine-tuning) to calculate the transfer functions and the axialratio over a given frequency band and a given FSS reflectivitypair for the two FSS layers.For this study, both FSSs are identical in order to radiate the

same energy in both directions, and the losses are assumed to benegligible. Some representative results are represented in Fig. 3.In Fig. 3(a), the antenna transfer function ratios [from (2)

and (3)] are shown for different FSS reflectivity values, where and . It can be ob-

served that as is decreased, the magnitude of the -polarizedwave becomesmore important than the -polarized one. In otherwords, the ratio between the two transfer func-tions is increased. This is an expected result due to waveguidetype of excitation source used to model this antenna. As the FSSreflectivity is decreased, there is less energy going toward thetwister. Hence, the antenna does not produce good-quality cir-cularly polarized wave for lower FSS reflectivity values. Con-sequently, the AR curves [Fig. 3(b)] degrade for lower values of. Using a source that radiates equally toward both and

directions (for example a dipole) would remedy this problem;but in this study, the waveguide source is retained as requestedby Thales Alenia Space, France.Fig. 3(c) shows that, for a fixed value of , the use of a smaller

twister periodicity leads to an enlargement of the AR band-width. The value of is adjusted to ensure that the twister oper-ates around the center frequency of 3.9 GHz. The transfer func-tion ratio for a fixed reflectivity and a variable twister periodicity(not shown here) does not change.From the above results, we can infer that we must use highly

reflective FSS in order to ensure a good-quality circularly po-larized wave. On the other hand, the twister configuration hasa direct impact on the AR bandwidth, but does not modify theantenna radiation characteristics.

Fig. 3. Analytical results. Impact of the FSS reflectivity (for a fixed twisterconfiguration, mm, mm) on (a) the ratio of the transferfunctions , and (b) the axial ratio. (c) Impact of the twister con-figuration ( and , in millimeters) on the axial-ratio bandwidth (with a fixedFSS reflectivity ).

To further improve the proposed configuration, we studiedthe analytical model with different FSS reflectivity values tocompensate for the difference between the - and -polarizedtransfer function magnitudes. The case with ,mm, and mm was selected as it provides the best

axial-ratio bandwidth. The reflectivity of the lower FSS (in Fig. 1) was lowered to allow for more energy to go towardthe twister. The best results (observed forand ) are shown in Fig. 4 and comparedto the case with equal FSS reflectivity values. We observe thatwe obtain equal magnitude for both transfer functions [Fig. 4(a)]and better axial-ratio minima [Fig. 4(b)] as compared to the casewhere both FSSs have the same reflectivity values. However, the3-dB axial-ratio bandwidth does not change.

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MUHAMMAD et al.: SELF-POLARIZING FABRY–PEROT ANTENNAS BASED ON POLARIZATION TWISTING ELEMENT 1035

Fig. 4. Comparison between the analytical results using sameand different ( , and ) FSS reflectivity values

for the upper and lower FSS (for a fixed twister configuration, mm,mm). (a) Ratio of the magnitude of the transfer functions

and and (b) the axial ratio.

The best case selected from this optimization study is the onewith mm mm , and

mm mm and a twister configurationwith mm, mm (largest AR bandwidth). Inthis case, a 3-dB AR bandwidth of about 6.7% is obtained for

mm and mm. The other dimensions(FSS and twister) can be found in Appendix-B.

III. SIMULATION AND EXPERIMENTAL RESULTS

A. Full-Wave Optimization

Once the concept has been validated analytically, the nextstep is to simulate a finite antenna using a full-wave simula-tion tool. For this, HFSS has been used to simulate an antennawith a square aperture and shielding cavity walls for better in-tegration into an array configuration and to minimize couplingbetween neighboring sources [8], [10]. The simulation setup andthe dimensions are defined in Fig. 5. The antenna aperture size(defined by Thales Alenia Space, France) is about so as toproduce a pencil beam with a directivity of about 20 dBic in-band GHz .The antenna is fed by a standard rectangular

waveguide (WR229) with interior dimensions of58.17 29.08 mm mm . This waveguidepenetrates through the twister part into the FP cavity (asschematized in Fig. 1). The impedance matching is optimized

Fig. 5. Simulation setup. (a) 3-D cross-section view (half antenna). (b) Cross-section view.

by varying the waveguide penetration inside the cavityand the iris width placed at the bottom FSS as illustratedin Fig. 5(b). Previous studies have confirmed the relevance ofthis impedance-matching system [8], [10].A parametric study has been carried out with HFSS in order

to take into account the finite-size effects and the presence ofshielding walls that were not modeled in Section II-B. Thisstudy consists in three steps: 1) the FSS parameters and cavityheight are varied to obtain the maximum directivity;2) the corrugation parameters and the distance are thenadjusted to obtain the maximum 1-dB AR bandwidth; 3) fi-nally, the impedance-matching level is improved by adjustingthe waveguide penetration and iris width .The final dimensions are given in Table I. We can observe

that they are rather close to those derived from the analyticaloptimization (Section II-C). The width of the top FSS islarger than the bottom one as predicted by the analyticalmodel. This allows for more energy flowing toward the twisteras compared to the energy leaving the FP cavity toward thedirection. In other words, the reflectivity value of the bottomFSS layer is slightly lower as suggested by the analytical model.In the optimized design, the reflectivity of and at3.9 GHz equal 88% and 95%, respectively. This difference withthe analytical results is due to the combined effect of the finitesize of the antenna, the close proximity of shielding walls, andthe size of the waveguide source, which were not taken intoaccount in the analytical model.The cavity wall thickness equals 8 mm. The total antenna

height is only 73mm without the excitation wave-guide source.

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1036 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 61, NO. 3, MARCH 2013

Fig. 6. Simulation results. (a) Black: directivity. Gray: reflection coefficient.(b) Axial ratio. (c) Radiation patterns in left-hand CP (LHCP) and right-handCP (RHCP) at 3.90 GHz.

TABLE IFINAL DIMENSIONS FOR THE SELF-POLARIZING FP ANTENNA (AS A REMINDER,THE DIMENSIONS OPTIMIZED ANALYTICALLY ARE GIVEN INTO BRACKETS)

B. Optimization Results

The simulation results of the optimized configuration aresummarized in Fig. 6. A maximum directivity of about 20 dBic

Fig. 7. Fabricated prototype for operation in -band. (a) 3-D view with thesupporting structure. (b) Zoomed view.

is achieved at 3.93 GHz with a reflection coefficient below17.5 dB [Fig. 6(a)]. The 3-dB AR bandwidth equals 5.1%

[3.82–4.02 GHz, Fig. 6(b)]. This value is slightly lower thanthe one predicted analytically (6.7%). The main reason for thisdifference is the presence of the surrounding cavity walls, thefinite size of the antenna, and the presence of the waveguide.The left- and right-hand CP radiation patterns are shownin Fig. 6(c) at 3.90 GHz (frequency point where the AR isminimum). Very clean patterns with sidelobe level lower than13.5 dB and cross-polarization level below 17.5 dB are

obtained for all observation planes.

C. Prototyping and Experimental Results

The optimized antenna (dimensions given in Table I) has beenmanufactured in separated parts. The FSSs have been fabri-cated usingwater-jet cutting technology, the twister surface witha CNC milling machine, while the waveguide, the impedancematching system, and the cavity walls were produced using amanual milling machine. The assembled antenna is shown inFig. 7 with its supporting structure for measurement purposes.The measurement results are shown in Fig. 8. A maximum di-

rectivity level of about 18.5 dBic is measured at 3.9 GHz, with

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MUHAMMAD et al.: SELF-POLARIZING FABRY–PEROT ANTENNAS BASED ON POLARIZATION TWISTING ELEMENT 1037

Fig. 8. Comparison between simulation and measured results. (a) Directivityand realized gain. (b) Axial ratio. (c) Reflection coefficient. (d) Measured radi-ation patterns in LHCP and RHCP at 3.90 GHz.

a reflection coefficient below 18 dB [Fig. 8(a)]. A max-imum realized gain of 18 dB is measured. The 0.5-dB differ-ence between the measured directivity and realized gain is verylikely due to the cumulative effects of fabrication, assemblyand alignment errors. The measured is lower than 18 dBover the entire 3-dB gain drop bandwidth. The measured 3-dBaxial-ratio bandwidth is about 4.6% [3.81–3.99 GHz, Fig. 8(b)].Again, the frequency shift ( MHz, i.e., 0.6%), observed be-

Fig. 9. Angular variation of axial ratio at 3.90 GHz. (a) Simulation and(b) measurements.

tweenmeasurements and simulations, is attributed to fabricationuncertainties.As a summary, a combined bandwidth of 3% (3 dB axial-ratio

bandwidth, 3 dB gain drop bandwidth, and 10 dB impedancematching) has been obtained experimentally (3.84–3.96 GHz).This value is significantly better than the self-polarizing solu-tions proposed in [9] (much compact) and [10] (more efficient).Finally, he measured CP patterns at 3.90 GHz [Fig. 8(c)] showsimilar behavior as in simulations. The 3-dB gain drop band-width could be improved further by using tapered reflectivityfor the FSS [19].The axial-ratio variation with respect to at 3.9 GHz is shown

in Fig. 9 in simulations and measurement. Both results are inexcellent agreement. From simulations, we have a 3-dB axial-ratio beamwidth of about 24 around the axial direction, whilethe measurements show a beamwidth of 20 .

IV. CONCLUSION

A new concept of self-polarizing FP antennas simultane-ously combining the principles of FP resonators and polarizingtwisting elements has been studied analytically, numerically,and experimentally. The antenna predesign is defined usingan analytical model based on ray tracing. Then, full-waveoptimization results for a finite antenna have been presentedand successfully validated around 3.9 GHz. This concept isquite general and could be extended to planar antennas forlow-power applications.

APPENDIX

A. Analytical Calculations

Using the definitions of Fig. 2, the transfer function for the- and -polarized waves can be written as a sum of all fields

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1038 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 61, NO. 3, MARCH 2013

transmitted in the far-field region (assuming the source positionas the reference plane)

(A-1)

(A-2)

where , , , , etc., are the far-field rays gen-erated by multiple reflections of the incident wave between thetwo FSS layers; and , , , etc., are the far-field raysgenerated by the corrugations at 45 (twister surface). It is as-sumed here that there is no -component reflected from the cor-rugations (i.e., ) and the FSS layers are completelytransparent to the -polarized wave coming from the corruga-tions (i.e., , and ). These as-sumptions hold true over the small frequency band around thecentral design frequency (see Appendix-B) and consequentlysimplify a great deal the analytical model.Now, by replacing these rays by the corresponding reflec-

tion and transmission coefficients of the FSS and the twister,we obtain [1], [5], [12]

(A-3)

(A-4)

where is the incidence angle of the excitation wave, and isthe wavenumber in free space.The above equations can be transformed easily using infinite

series summation, which gives

(A-5)

(A-6)

In our calculations, we assume as we are interestedonly in the antenna characteristics at broadside. Finally, we have

(A-7)

(A-8)

B. Reference Curves Used for the Analytical Study

Inductive FSS: The analytical results of Section II-B havebeen generated using a set of reference curves for the FSS re-flection and transmission coefficients, and

Fig. 10. HFSS simulation results for FSS with reflectivity values ranging be-tween 45% and 90%. Reflection coefficient in (a) magnitude and (b) phase.Transmission coefficient in (c) magnitude and (d) phase. Both FSSs are assumedidentical.

Fig. 11. -parameters for the - and -polarized incident plane waves on a1-D FSS infinite surface (HFSS simulations) with 90% reflectivity.

TABLE IIFSS DIMENSIONS FOR DIFFERENT REFLECTIVITY VALUES

for the corrugated twister . These curves have been com-puted with HFSS (as explained in Section II-C) as a functionof frequency around the central frequency (3.9 GHz here) andpresented in Fig. 10.The FSS periodicity considered in this paper (Fig. 1) is given

in Table II. The FSS thickness and widthare constant for all cases (5 mm).To validate the assumption made in Appendix-A and stating

that the FSS is completely transparent to the -polarized wavecoming from the corrugations below, the -parameters for the90% reflectivity case are shown in Fig. 11 for - and -polarizedplane-wave excitation. It can be seen that the transmission co-efficient is nearly equal to 1 and a very low level of -polarized

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MUHAMMAD et al.: SELF-POLARIZING FABRY–PEROT ANTENNAS BASED ON POLARIZATION TWISTING ELEMENT 1039

Fig. 12. HFSS simulation results for an infinite flat corrugated surface tiltedat 45 and illuminated by an -polarized plane wave under normal incidence.Reflection coefficient in (a) magnitude and (b) phase for three values ofand .

Fig. 13. Reflection coefficient in the -polarized and -polarized wave fromthe corrugations with an incident -polarized plane wave for mm,

mm and mm.

energy is reflected by the FSS. Hence, the assumptions in theprevious calculations ( , and )are valid.

Corrugated Twister: We assume that the width of thecorrugations equals 3 mm in all cases. Only their periodicityand depth are varied to make the twister operating around

GHz.Three relevant and representative twister configurations

are selected here (Fig. 12). Their reflection coefficients in-direction (for a normally incident plane wave polarizedalong -direction) are plotted in amplitude and phase for threevalues of and in Fig. 12(a) and (b). We can see fromFig. 12(a) that, for mm and mm, we obtainthe largest bandwidth over which the energy is converted from- to -polarization, while from Fig. 12(b) we can see thatthe phase is nearly constant around 180 for the same case

mm mm . This explains why we obtainthe widest AR bandwidth using this twister configuration.The magnitude of the - and -polarized components re-

flected from the corrugations is shown in Fig. 13. We can seethat the -polarized field is negligible, and hence the assump-tions for the calculations in the previous sections are valid (i.e.,

).

ACKNOWLEDGMENT

This work has been carried out at the “Institut d’Electroniqueet de Télécommunications de Rennes,” IETR, Rennes, France.

REFERENCES

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[2] D. R. Jackson and A. A. Oliner, “A leaky-wave analysis of the high-gain printed antenna configuration,” IEEE Trans. Antennas Propag.,vol. 36, no. 7, pp. 905–910, Jul. 1988.

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Shoaib Anwar Muhammad received the Bachelorof Electrical Engineering degree from the NationalUniversity of Sciences and Technology, Islamabad,Pakistan, in 2005, the Master’s degree in telecom-munications from the Université de Nice, SophiaAntipolis, France, in 2007, and the Ph.D. degree intelecommunications and signal processing from theUniversité de Rennes1, Rennes, France, in 2010.He has worked with the Institut Mines Telecom—

Telecom Bretagne, Brest, France, in 2012 as aResearch Engineer on millimeter-wave antennas.

Currently, he is working with the Microwavevision group, SATIMO, Brest,France, as an R&D Engineer. His research interests include electromagneticband-gap antennas, Fabry–Perot cavity antennas, frequency selective surfaces,leaky-wave antennas for space applications, and millimeter-wave antennaapplications.

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1040 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 61, NO. 3, MARCH 2013

Ronan Sauleau (M’04–SM’06) graduated inelectrical engineering and radio communicationsfrom the Institut National des Sciences Appliquées,Rennes, France, in 1995. He received the Agrégationdegree from the Ecole Normale Supérieure deCachan, Cachan, France, in 1996, and the Doctoraldegree in signal processing and telecommunicationsand the “Habilitation à Diriger des Recherches”degree from the University of Rennes 1, Rennes,France, in 1999 and 2005, respectively.He was an Assistant Professor and Associate Pro-

fessor with the University of Rennes 1 between 2000 and 2005, and between2005 and 2009, respectively. He has been appointed as a Full Professor withthe same university since 2009. His current research fields are numerical mod-eling (mainly FDTD), millimeter-wave printed and reconfigurable (MEMS) an-tennas, substrate integrated waveguide antennas, lens-based focusing devices,periodic and nonperiodic structures (electromagnetic band-gap materials, meta-materials, reflectarrays, and transmit arrays), and biological effects of millimeterwaves. He has been involved in more than 30 research projects at the nationaland European levels and has co-supervised 14 post-doctoral fellows, 18 Ph.D.students; and 40 master students. He has received eight patents and is the au-thor or coauthor of 135 journal papers and more than 280 publications in in-ternational conferences and workshops. He has shared the responsibility of theresearch activities on antennas at IETR in 2010 and 2011. He is now co-respon-sible for the research Department “Antenna and Microwave Devices” at IETRand is Deputy Director of IETR.Prof. Sauleau received the 2004 ISAP Conference Young Researcher Scien-

tist Fellowship, Japan, and the first Young Researcher Prize in Brittany, France,in 2001 for his research work on gain-enhanced Fabry–Perot antennas. In 2007,he was elevated to Junior member of the “Institut Universitaire de France”.His is currently a Guest Editor for the IEEE TRANSACTIONS ON ANTENNASPROPAGATION Special Issue on “Antennas and Propagation at mm and sub mmwaves.” He was awarded the Bronze medal by CNRS in 2008. He was the co-re-cipient of several international conference awards (Int. Sch. of BioEM 2005,BEMS 2006,MRRS 2008, E-MRS 2011, BEMS 2011, IMS 2012, Antem 2012).

Guido Valerio (S’06–M’10) received the Master’sdegree (cum laude and honorable mention) in elec-tronic engineering and Ph.D. degree in applied elec-tromagnetics from the Sapienza University of Rome,Rome, Italy, in 2005 and 2009, respectively.In 2008, he was a Visiting Scholar with the Uni-

versity of Houston, Houston, TX, USA. In 2011, hejoined the Institute d’Electronique et de Telecommu-nications de Rennes (IETR), Rennes, France, wherehe is currently a CNRS Researcher. His scientific in-terests involve numerical methods for wave propa-

gation and scattering in complex structures, such as periodic and multilayeredmedia. Among other topics, he studies efficient computation and interpolationschemes for Green’s functions in different kinds of periodic structures, the rig-orous modeling of the interaction of nonperiodic sources with periodic media,and modal properties of both conventional and metamaterial multilayered struc-tures. He is involved in the GPR characterization of Martian soil through bothexperimental and numerical approaches and in the design of UWB antennas,harmonic-tunable active antennas, leaky-wave antennas, and multifunction an-tenna arrays for weather and aircraft surveillance.Dr. Valerio was the recipient of the “Leopold B. Felsen Award for Excel-

lence in Electrodynamics” in 2008. In 2009, he was a finalist for the “YoungEngineering Prize” at the European Microwave Conference. In 2010, he wasthe recipient of the “Barzilai Prize” for the best paper at the National ItalianCongress of Electromagnetism (XVIII RiNEm).

Laurent Le Coq received the electronic engineering and radio communicationsdegree and the French DEA degree (M.Sc.) in electronics and the Ph.D. degreefrom the National Institute of Applied Science (INSA), Rennes, France, in 1995and 1999, respectively.In 1999, he joined the Institute of Electronics and Telecommunications of

Rennes (IETR), University of Rennes 1, Rennes, France, as a Research LabEngineer, where he is responsible for measurement technical facilities up to110 GHz. His activities in antenna measurements and development of relatedprocedures involved him in more than 30 research contracts of national or Euro-pean interest. He is the author and coauthor of 30 journal papers and 35 papersin conference proceedings.

Hervé Legay was born in 1965. He receivedthe Electrical Engineering Degree and the Ph.D.degree from the National Institute of Applied Sci-ences (INSA), Rennes, France, in 1988 and 1991,respectively.For two years, he was a Postdoctoral Fellow

with the University of Manitoba, Winnipeg, MB,Canada, where he developed innovating planar an-tennas. He joined Alcatel Space, Toulouse, France,in 1994, which is now Thales Alenia Space. Heinitially conducted studies in the areas of military

telecommunication advanced antennas and antenna processing. He designedthe architecture and the antijamming process of the Syracuse 3 antenna. Heis the author of 23 patents. He currently leads research projects in integratedfront ends and reflectarray antennas and coordinates the collaborations withacademic and research partners in the area of antennas.Dr. Legay is a co-prize-winner of the 2007 Schelkunoff prize paper award.

He received the Gold Thales Awards in 2008, rewarding the best innovations inthe group Thales.


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