Title: Horn antennas for generating radio waves bearing orbital angular momentum by using spiral phase plate
Abstract: IET Microwaves, Antennas & PropagationVolume 10, Issue 13 p. 1420-1427 ArticleFree Access Horn antennas for generating radio waves bearing orbital angular momentum by using spiral phase plate Wenlong Wei, Wenlong Wei Institute of Electronics and Telecommunications of Rennes (IETR), UMR CNRS no. 6164, University of Rennes 1, Rennes, FranceSearch for more papers by this authorKourosh Mahdjoubi, Corresponding Author Kourosh Mahdjoubi [email protected] Institute of Electronics and Telecommunications of Rennes (IETR), UMR CNRS no. 6164, University of Rennes 1, Rennes, FranceSearch for more papers by this authorChristian Brousseau, Christian Brousseau Institute of Electronics and Telecommunications of Rennes (IETR), UMR CNRS no. 6164, University of Rennes 1, Rennes, FranceSearch for more papers by this authorOlivier Emile, Olivier Emile Laser Physics Laboratory (LPL), University of Rennes 1, Rennes, FranceSearch for more papers by this author Wenlong Wei, Wenlong Wei Institute of Electronics and Telecommunications of Rennes (IETR), UMR CNRS no. 6164, University of Rennes 1, Rennes, FranceSearch for more papers by this authorKourosh Mahdjoubi, Corresponding Author Kourosh Mahdjoubi [email protected] Institute of Electronics and Telecommunications of Rennes (IETR), UMR CNRS no. 6164, University of Rennes 1, Rennes, FranceSearch for more papers by this authorChristian Brousseau, Christian Brousseau Institute of Electronics and Telecommunications of Rennes (IETR), UMR CNRS no. 6164, University of Rennes 1, Rennes, FranceSearch for more papers by this authorOlivier Emile, Olivier Emile Laser Physics Laboratory (LPL), University of Rennes 1, Rennes, FranceSearch for more papers by this author First published: 01 October 2016 https://doi.org/10.1049/iet-map.2016.0064Citations: 22AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract The design of two new horn antennas for the generation of radio waves bearing orbital angular momentum (OAM) is presented. The OAM mode ℓ = 1 or −1 is generated by combining the guided modes of a circular waveguide with a spiral phase plate. The authors present here two structures to generate OAM wave based on TE11 and TM01 modes. The resulting magnitude and phase patterns of the electrical field and the radiation patterns evidence the presence of waves carrying OAM. 1 Introduction Orbital angular momentum (OAM) has been proposed to improve spectral efficiency [1-4] in radio communications, by creating multiple sub-channels of propagation corresponding to the twisting degree of the electromagnetic wave. Whereas the phase of a usual plane wave is constant on the wave front, the phase α of OAM waves undergoes a linear variation along the angular coordinate φ (roll angle): α = ℓφ, where ℓ is an integer number called the ‘topological charge’ or the order of the OAM mode. The application of OAM waves for communication purposes is still subject to intense debates [5]. However, they can be used for other applications [6-8]. The objective of this paper is to generate OAM waves which are not restricted to communications, but could also be used for any existing or future application. Up to now, in radio frequency bands, two main families of antennas have been proposed to generate OAM waves: ‘high gain’ and ‘low gain’ families. For the first one, we can mention the example of reflector antenna [2] working at 2.4 GHz and using an 80 cm twisted parabolic reflector dish to induce a linear phase distribution (along the φ angle). Later, spiral phase plates (SPP) [9-11] and flat drilled phase plates [12, 13] have been used in millimetre wave frequency band to create the linear phase variation. In the ‘low gain’ family, a single patch antenna [14] and some phased arrays of patch antennas [15, 16] are proposed to generate the OAM type phase variation. The purpose of this paper is to create a middle gain antenna using a horn structure as it is commonly done in microwave technology [17]. This antenna can be used as a primary source for a parabolic reflector. In this case, the reflector does not need to be a twisted one as proposed in [2], but a simple and conventional one. The horn antennas need to be fed through a waveguide part. Guided waves bearing OAM have already been studied in optics for dielectric (silicon) rectangular waveguides by combining the modes [18]. Here we will use a metallic circular waveguide working at radio frequencies. In a previous work, guided waves have been utilised in conjunction with a horn antenna to generate radio OAM waves [19]. The OAM mode of ℓ = 1 was generated by combining the guided TE11 mode with a single SPP or the TE21 mode with two half-turn SPPs. In these designs, the working frequency for TE11 mode needed to be much higher than the cut-off frequency. Here, we present two new designs based on TE11 and TM01 modes, where the working frequency is reduced to be near cut-off. 2 TE11 mode and a single SPP The technique of SPP is usually used to generate OAM waves in free space, it is rarely used in the waveguide except in [20]. In this paper, we present two original methods based on simulations to generate the OAM mode in waveguide by combining the classical modes of a circular waveguide with the SPP. The first one is based on TE11 mode and the second one, on TM01 mode. 2.1 SPP in waveguide The first structure to generate OAM wave is presented in Fig. 1. The SPP is made of Teflon (ɛr ≃ 2.1) and is placed inside the waveguide with the same diameter. In the first stage the TE11 mode is excited ideally by a waveport in HFSS software. The E-field is polarised along x-axis. The other end of the waveguide is covered by perfectly matched layers to make sure that the reflected wave is totally vanished. Fig. 1Open in figure viewerPowerPoint Geometry of the TE11 mode with a single SPP The field distribution of the TE11 mode is shown in Fig. 2a, and the corresponding magnitude and phase patterns of the Ex component in Figs. 2b and c. One can see that the magnitude of the electrical field of the TE11 mode is very strong at the centre, while it should be null or very weak for the OAM wave (due to the field vortex or singularity, created by the linear variation of the phase on the wavefront). Hence, the main difficulty to generate OAM wave from the TE11 mode is to shape the magnitude and phase diagrams of the electrical field. It can be seen from the simulations that in order to achieve this behaviour, we should increase the working frequency until the wavelength becomes quite small compared with the waveguide diameter. Fig. 2Open in figure viewerPowerPoint Field distribution of TE11 mode and the corresponding magnitude and phase patterns of Ex component a Field distribution b Normalised magnitude pattern c Phase pattern The phase of the Ex component of the TE11 mode is constant on the wavefront. Thus, to create an OAM mode |ℓ| = 1, the SPP should realise a phase shift of 2π in one turn (along φ angle) and the required step height h is given by [9] (1)However, in waveguide, k1 and k2 should be replaced by kg1 and kg2 which are the guided propagation constants for waveguide filled, respectively, with Teflon and air (2)where f is the working frequency, c is the speed of light in free space, ɛi is the dielectric permittivity of the material inside the waveguide (i = 1 for Teflon and i = 2 for air), r is the radius of the waveguide, and η is a constant which depends on the guided mode. For TE11 mode, η is equal to 1.841. Here, we set the diameter of the empty waveguide as 4.4 cm. The corresponding cut-off frequency of the TE11 mode is 4 GHz. Since the wavelength of the working frequency needs to be quite small compared with the waveguide diameter, we choose a working frequency of 40 GHz, and therefore, the height step of the SPP becomes: h = 1.7 cm. The magnitude and phase patterns of the Ex component for the wave passing through the SPP are plotted in Fig. 3. We can note that the magnitude at the centre is much smaller than the surroundings and the phase variation in one turn is equal to 2π. This shows indeed that both the amplitude and the phase correspond to a wave bearing an OAM mode with |ℓ| = 1. We can also observe that even at the frequency of 40 GHz, the magnitude and phase of the Ex field are not quite satisfactory. To improve the results, one solution would be to increase again the frequency. In the next section we propose a more practical solution. Fig. 3Open in figure viewerPowerPoint Normalised magnitude (left-hand side) and phase (right-hand side) patterns of Ex component for the structure with a single SPP at the frequency 40 GHz 2.2 Horn antenna design Our purpose is to create a directive OAM antenna. Thus, we design a conical horn antenna based on the circular waveguide. In addition, according to the above analysis, when the SPP is placed inside the waveguide, the wavelength at the working frequency should be much smaller than the diameter of the waveguide (∼1/10). This will enable the high-order modes of the circular waveguide to exist at the same time, which makes it difficult to obtain a pure TE11 mode in practice. To solve this problem, we place the SPP inside the horn instead of inside the waveguide, as shown in Fig. 4. In this way, the working frequency can be reduced to be quite near to the cut-off frequency of the TE11 mode. Fig. 4Open in figure viewerPowerPoint Geometry of the OAM horn antenna with a single SPP a 3D view of the antenna structure b 2D view for showing the probe parameters and horn dimensions In this new design, the empty waveguide has a diameter of 1 cm and the corresponding cut-off frequency of the TE11 mode is 17.6 GHz. The horn aperture has a diameter of 10 cm. The heights of the waveguide and the horn are, respectively, 1 and 10 cm. We choose a working frequency of 20 GHz. The bottom surface of the waveguide is set as a metallic plate. A coaxial line exciting the monopole probe is placed along the radial direction of the circular waveguide, d = 0.7 cm above the metallic plate, for creating the TE11 mode. The coaxial line with ɛr = 2.1 (Teflon) has an inner diameter of 1.3 mm and an outer diameter of 4.4 mm, and these parameters correspond to a characteristic impedance of 50 Ω. The probe length is optimised at g = 0.3 cm to realise a good impendence matching. Because the SPP here is placed inside the horn, we can no more use the above equations to calculate the height step of the SPP. According to the simulations, the optimised height step of the SPP becomes: h = 3.7 cm. As depicted in Fig. 5a, the horn antenna is well matched around 20 GHz and has a very large frequency bandwidth for the input impedance. Figs. 5b–d present the 3D radiation pattern and the 2D radiation and phase patterns at 20 GHz. The 3D radiation pattern has a null at the centre that is a signature of OAM waves. The 2D radiation patterns correspond to the xOz and yOz cuts of the 3D plot. It can be seen that the maximum directivity is obtained at an angle of 14°. Compared with the OAM antenna using a circular phased array of four patches [16], where the maximum directivity is at 30°, the new antenna is therefore much more directive. We present the phase patterns (Fig. 5d) for three values of the spherical angle (aperture) θ: 10°, 15° and 20°. The spiral form of the phase variation versus roll angle φ is due to the polar representation of the linear phase variation. We can observe that the quality of the phase pattern is good at small values of θ angle, but degrades as θ increases. Fig. 5Open in figure viewerPowerPoint Reflection coefficient and radiation and phase patterns of the OAM horn antenna with a single SPP a S11 b 3D radiation pattern c 2D radiation patterns in E and H planes d Normalised phase patterns (in radians) at different θ angles The magnitude and phase patterns of the propagated wave, observed on a plane perpendicular to the direction of propagation, are plotted in Fig. 6. The observation window is a circular area with a radius of 5 cm, lying 2 cm above the horn aperture. It can be seen that the magnitude is minimum at the centre and the phase rotates around the centre with a 2π phase shift in one turn. This confirms the generation of an OAM bearing wave with |ℓ| = 1. Besides, we can observe that compared with the results in Fig. 3, the quality of the phase of Ex field is improved, while the magnitude is still not very satisfactory. To improve this, in the next part we design another horn antenna based on the TM01 mode. Fig. 6Open in figure viewerPowerPoint Normalised magnitude (left-hand side) and phase (right-hand side) patterns of Ex component for the OAM horn antenna with a single SPP at the frequency of 20 GHz To show the purity of the generated OAM waves, we give the mode expansion at 20 GHz in Fig. 7. The mode decomposition is obtained by Fourier transform of the phase distribution on a circle corresponding to the magnitude maximum [21], as shown in Fig. 6. It can be seen that the OAM mode ℓ = −1 is clearly predominate with a proportion of about 53%. Since this value is almost 7 times of the secondary mode, we can consider that the result is quite good. Fig. 7Open in figure viewerPowerPoint Mode decomposition for the OAM horn antenna with a single SPP at the frequency of 20 GHz 3 TM01 mode and two half-turn SPPs 3.1 SPP in waveguide The geometry of the second structure is presented in Fig. 8. It is similar to the previous one in the sense that again a SPP is used to create the phase shift. The main difference is that it contains two half-turn SPPs which have the same geometry. The two SPPs are placed inside the waveguide at the same height with a 180° rotation along Z-axis from each other. Fig. 8Open in figure viewerPowerPoint Geometry of the TM01 mode with two half-turn SPPs Fig. 9 shows the field distribution of the TM01 mode and the corresponding magnitude and phase patterns of the Ex component. The magnitude of the electrical field of the TM01 mode is minimal at the centre and in this respect; it is close to the OAM wave (there is in fact a field vortex or singularity, created by the linear variation of the phase on the wavefront). Therefore, it should be easier to transform the TM01 mode into an OAM wave. The phase of the Ex component of the TM01 mode (Fig. 9c) can be divided into two parts. For each part, the phase is constant on a plane perpendicular to the direction of propagation, and the phase difference between the two parts equals π. Thus, for creating the OAM mode of |ℓ| = 1, two half-turn SPPs are needed. The step height of each SPP should realise a phase shift equal to π. In this way, the total phase shift in one turn will meet the requirement of 2π. We use again (1) and (2) to calculate the step height of each half-turn SPP, but we should replace 2π by π in (1). For TM01 mode, the η parameter is equal to 2.405 in (2). Fig. 9Open in figure viewerPowerPoint Field distribution of TM01 mode and the corresponding magnitude and phase patterns of Ex component a Field distribution b Normalised magnitude pattern c Phase pattern The waveguide has a diameter of 4.4 cm, and the cut-off frequency of the TM01 mode is 5.3 GHz. The working frequency can be chosen to be much lower than that of the first structure; in fact, it just needs to be higher than the cut-off frequency of the TM01 mode. We choose a working frequency of 7.4 GHz, and therefore, the height step of each half-turn SPP becomes: h = 3.6 cm. The magnitude and phase patterns of the Ex component for the wave at the end of the SPPs are given in Fig. 10. We can observe that the magnitude pattern has a null at the centre and the phase pattern has a linear variation along the roll angle φ with a 2π phase shift in one turn. This shows indeed that an OAM bearing wave with |ℓ| = 1 is generated. We can also note that the results are better than those of the first structure. Fig. 10Open in figure viewerPowerPoint Normalised magnitude (left-hand side) and phase (right-hand side) patterns of Ex component for the structure with two half-turn SPPs at the frequency of 7.4 GHz 3.2 Horn antenna design We also design a conical horn antenna based on TM01 mode to make the OAM waves more directive, as shown in Fig. 11. As discussed above, for TM01 mode, the working frequency can be quite near to the cut-off frequency, hence no high-order modes will exist. Besides, the SPPs can be kept inside the waveguide. The diameters of the waveguide and the horn aperture are, respectively, 4.4 and 12 cm, and the heights are both 10 cm. The working frequency is kept at 7.4 GHz, and the height step of each half-turn SPP at 3.6 cm. The bottom surface of the waveguide is also set as a metallic plate. A coaxial line exciting the monopole probe placed along the direction of propagation is used to create the TM01 mode and it has the same parameters (material, inner and outer diameters) as the previous one. The SPPs are 2 cm above the probe. To satisfy the impedance matching, the probe length is optimised at 1.7 cm. Fig. 11Open in figure viewerPowerPoint Geometry of the horn antenna with two half-turn SPPs a 3D view of the antenna structure b 2D view for showing the probe parameters and horn dimensions We can see from Fig. 12a that the horn antenna with two half-turn SPPs is well matched around 7.4 GHz and the bandwidth is quite large (∼13%). The 3D radiation pattern and the 2D radiation and phase patterns at 7.4 GHz are shown in Figs. 12b–d. We can again observe a central hole in the 3D radiation pattern that is characteristic of an OAM wave. Moreover, compared with the previous antenna, the main lobe is more smooth and symmetric and the side lobes are lower. The 2D radiation patterns also correspond to the xOz and yOz cuts of the 3D plot. We can see that the maximum directivity is obtained at the angle of 15°. The phase patterns are plotted again for three values of the spherical angle (aperture) θ: 10°, 20° and 30°. We can also observe that the quality of the phase pattern degrades as θ increases. Fig. 12Open in figure viewerPowerPoint Reflection coefficient and radiation and phase patterns of the OAM horn antenna with two half-turn SPPs a S11 b 3D radiation pattern c 2D radiation patterns in E and H planes d Normalised phase patterns(in radians) at different θ angles The magnitude and phase patterns of the propagated wave, plotted on a circular area with a radius of 7 cm, lying 1 cm above the horn aperture, are presented in Fig. 13. We can observe that the magnitude at the centre is much smaller than the surroundings and the phase rotates around the centre with a 2π phase shift in one turn. This shows indeed that both the amplitude and the phase correspond to a wave carrying an OAM mode with |ℓ| = 1. Besides, compared with the first horn antenna, the magnitude of Ex field is improved. Fig. 13Open in figure viewerPowerPoint Normalised magnitude (left-hand side) and phase (right-hand side) patterns of Ex component for the OAM horn antenna with two half-turn SPPs at the frequency of 7.4 GHz As in Fig. 7 we make a mode expansion at 7.4 GHz to evaluate the mode purity of the generated OAM waves. This is shown in Fig. 14. The mode decomposition is obtained in the same manner as for the first structure. It can be seen that the OAM mode ℓ = 1 gives about 80% contribution. Compared with the first horn antenna (53%), the mode purity is considerably improved. Fig. 14Open in figure viewerPowerPoint Mode decomposition for the OAM horn antenna with two half-turn SPPs at the frequency of 7.4 GHz 4 Conclusion In this paper, we have proposed two new horn antennas for the generation of radio OAM waves. Both the ideal model and the practical design are presented and analysed. The OAM mode of ℓ = −1 or 1 is generated for the Ex component, based on TE11 mode with a single SPP, or TM01 mode with two half-turn SPPs. The resulting magnitude and phase patterns of the electrical field, and the radiation and phase patterns all confirm the generation of an OAM bearing wave. There are some differences between the two horn antennas: (i) to enable the working frequency to be near cut-off, for TE11 mode, the SPP should be placed inside the horn, while for TM01 mode, it can be maintained inside the waveguide; (ii) the magnitude pattern of Ex field of the second antenna is better than that of the first antenna; (iii) the second antenna has also a more smooth and regular radiation pattern with lower side lobes; (iv) the OAM modes generated by the second antenna are purer. In near future we will realise the second antenna (based on TM01 mode) for validation of the simulation results. 5 Acknowledgments The authors thank China Scholarship Council (CSC) (grant no. 201306090101) for scholarship support. 6 References 1Mohammadi, S.M., Daldorff, L., Bergman, J., et al.: ‘Orbital angular momentum in radio – a system study’, IEEE Trans. Antennas Propag., 2010, 58, (2), pp. 565– 572 (doi: 10.1109/TAP.2009.2037701) 2Tamburini, F., Mari, E., Sponselli, A., et al.: ‘Encoding many channels on the same frequency through radio vorticity: first experimental test’, New. J. Phys., 2012, 14, (3), p. 033001 (doi: 10.1088/1367-2630/14/3/033001) 3Wang, J., Yang, J.Y., Ahmed, N., et al.: ‘Terabit free-space data transmission employing orbital angular momentum multiplexing’, Nat. Photon., 2012, 6, (7), pp. 488– 496 (doi: 10.1038/nphoton.2012.138) 4Yan, Y., Xie, G.D., Ahmed, N., et al.: ‘High-capacity millimetre-wave communications with orbital angular momentum multiplexing’, Nat. Commun., 2014, 5, p. 4876 (doi: 10.1038/ncomms5876) 5Edfors, O., Johansson, A.J.: ‘Is orbital angular momentum (OAM) based radio communication an unexploited area?’, IEEE Trans. Antennas Propag., 2012, 60, (2), pp. 1126– 1131 (doi: 10.1109/TAP.2011.2173142) 6Emile, O., Brousseau, C., Emile, J., et al.: ‘Electromagnetically induced torque on a large ring in the microwave range’, Phys. Rev. Lett., 2014, 112, p. 053902 (doi: 10.1103/PhysRevLett.112.053902) 7Liu, K., Chen, Y.Q., Yang, Z.C., et al.: ‘Orbital-angular-momentum-based electromagnetic vortex imaging’, IEEE Ant. Wirel. Propag. Lett., 2015, 14, pp. 711– 714 (doi: 10.1109/LAWP.2014.2376970) 8Lin, M., Gao, Y., Liu, P., et al.: ‘Improved OAM-based radar targets detection using uniform concentric circular arrays’, Int. J. Antennas Propag., 2016, 2016, p. 1852659 (doi: 10.1155/2016/1852659) 9Turnbull, G.A., Robertson, D.A., Smith, G.M., et al.: ‘The generation of free-space Laguerre-Gaussian modes at millimeter-wave frequencies by use of a spiral phaseplate’, Opt. Commun., 1996, 127, (4-6), pp. 183– 188 (doi: 10.1016/0030-4018(96)00070-3) 10Schemmel, P., Pisano, G., Maffei, B.: ‘A modular spiral phase plate design for orbital angular momentum generation at millimetre wavelengths’, Opt. Express, 2014, 22, (12), pp. 14712– 14726 (doi: 10.1364/OE.22.014712) 11Hui, X., Zheng, S., Hu, Y., et al.: ‘Ultralow reflectivity spiral phase plate for generation of millimeter-wave OAM beam’, IEEE Ant. Wirel. Propag. Lett., 2015, 14, pp. 966– 969 (doi: 10.1109/LAWP.2014.2387431) 12Niemiec, R., Brousseau, C., Mahdjoubi, K., et al.: ‘Characterization of an OAM flat plate antenna in the millimeter frequency band’, IEEE Ant. Wirel. Propag. Lett., 2014, 13, pp. 1011– 1014 (doi: 10.1109/LAWP.2014.2326525) 13Cheng, L., Hong, W., Hao, Z.C.: ‘Generation of electromagnetic waves with arbitrary Orbital Angular Momentum modes’, Sci. Rep., 2014, 4, p. 4814 14Barbuto, M., Trotta, F., Bilotti, F., et al.: ‘Circular polarized patch antenna generating Orbital Angular Momentum’, Prog. Electromagn. Res., 2014, 148, pp. 23– 30 (doi: 10.2528/PIER14050204) 15Bai, Q., Tennant, A., Allen, B.: ‘Experimental circular phased array for generating OAM radio beams’, IET Electron. Lett., 2014, 50, (20), pp. 1414– 1415 (doi: 10.1049/el.2014.2860) 16Wei, W.L., Mahdjoubi, K., Brousseau, C., et al.: ‘Generation of OAM waves with circular phase shifter and array of patch antennas’, IET Electron. Lett., 2015, 51, (6), pp. 442– 443 (doi: 10.1049/el.2014.4425) 17Balanis, C.A.: ‘ Antenna theory: analysis and design’ ( John Wiley and Sons, 1997, 2nd edn.) 18Zhang, D., Feng, X., Cui, K., et al.: ‘Generating in-plane optical orbital angular momentum beams with silicon waveguides’, IEEE Photon. J., 2013, 5, (2), p. 2201206 (doi: 10.1109/JPHOT.2013.2256888) 19Wei, W.L., Mahdjoubi, K., Brousseau, C., et al.: ‘Horn antenna for generating Orbital Angular Momentum (OAM) waves’. Loughborough Antennas and Propagation Conf. (LAPC), November 2015, pp. 1– 3 20Kristensen, M., Beijersbergen, M.W., Woerdman, J.P.: ‘Angular momentum and spin-orbit coupling for microwave photons’, Opt. Commun., 1994, 104, (4–6), pp. 229– 233 (doi: 10.1016/0030-4018(94)90547-9) 21Yao, E., Arnold, S.F., Courtial, J., et al.: ‘Fourier relationship between angular position and optical orbital angular momentum’, Opt. Express, 2006, 14, (20), pp. 9071– 9076 (doi: 10.1364/OE.14.009071) Citing Literature Volume10, Issue13Special Issue: Selected Papers from the Loughborough Antennas & Propagation Conference (LAPC 2015)October 2016Pages 1420-1427 FiguresReferencesRelatedInformation
Publication Year: 2016
Publication Date: 2016-07-12
Language: en
Type: article
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