Horn Antenna Generating Electromagnetic Field with Orbital Angular Momentum

Transcription

1 Progress In Eletromagnetis Researh M, Vol. 60, 57 65, 2017 Horn Antenna Generating Eletromagneti Field with Orbital Angular Momentum Min Huang *, Xianzheng Zong, and Zaiping Nie Abstrat A novel method for generating eletromagneti field with orbital angular momentum (OAM) and orrespondingly a pratial design based on onial horn antenna are proposed in this paper. The OAM modes of ±m for r/ϕ field omponents and ±(m 1) for x/y ones an be generated by superposing the two orthogonal polarization degenerate TE mn modes in irular waveguide through a mode-transformation setion, and then radiated from the horn in the far end. The effetiveness of the proposed method is analyzed from physial mehanisms and demonstrated by both simulation and experiment for the presented new-typed OAM horn antenna. 1. INTRODUCTION Vortex wave is a type of eletromagneti(em) wave arrying orbital angular momentum(oam) [1], and its phase wavefront is no longer a plane, but rotates around the diretion of propagation, with twisted struture [2]. The phase rotation fator e jlϕ [3] determines the spatial phase distribution struture of the vortex beam, in whih l represents the mode of the orbital angular momentum. Moreover, the OAM beams with different modes are mutually orthogonal and have different spatial strutures. Therefore, the OAM EM wave is onsidered to improve the spetral utilization by modulating the multipath signal to different orbital angular momentum modes [4]. In reent years, a lot of antenna designs have been proposed to generate OAM EM waves, whih an be divided into two ategories. The first one is asymmetri physial struture or feed struture, suh as the modified spiral paraboloid antenna [5], stepped refletor antenna [6], spiral phase plate [7], horn antenna with SPP [8], elliptial mirostrip antenna [9], spiral antenna [10]. Among them, antennas in [5 8] with spiral struture on azimuth ϕ whih result in the phase delay of the refleted wave or the transmitted wave, thus the orbital angular momentum is obtained. In the artile [9, 10], the asymmetri struture of antennas lead to the asymmetry of the radiation field. The seond is to reate phase differene using multi-point feeding, suh as the irular path antenna [11], irular antenna array [12 16], the half mode substrate integrated waveguide antenna [17], et. Antennas in [11, 17] fed with two same signals but with a π/2 phase shift to get phase fator e jlϕ. Antennas in n elements irular antenna array of [12 16] are fed with same amplitude and a progressive 2πl/n phase shift signals in order to get 2πl phase delay. However, antennas in the first type are restrited to a single OAM mode, and most of them only an generate the first-order OAM. The strutures of seond type are omplex, espeially the ompliated feed network of the irular antenna array. On the ontrary, this paper presents a rather simple method (has been briefly introdued in paper [18]) to generate orbital angular momentum eletromagneti wave using horn antenna. In order to demonstrate the feasibility of this method, a design based on TE 21 mode to generate an OAM with order ±m and ±(m 1) is presented. Reeived 8 Marh 2017, Aepted 10 May 2017, Sheduled 29 August 2017 * Corresponding author: Min Huang (huangmin@std.uest.edu.n). The authors are with Department of Mirowave Engineering, University of Eletroni Siene and Tehnology of China, Chengdu, Sihuan , China.

2 58 Huang, Zong, and Nie 2. THEORETICAL ANALYSIS The struture of a irular waveguide has a high degree of axial symmetry, and the expressions of eah field omponent of TE mn (m 0)modeinthewaveguideare E z =0 E r = ±j ωμm 2 r H 0J m ( r) sin(mϕ) os(mϕ) e jβz (1) E ϕ = j ωμ H 0 J m( r) os(mϕ) sin(mϕ) e jβz where r is the radius of the waveguide, the utoff wavenumber, J m the m-order Bessel funtion, J m the derived funtion of m-order Bessel funtion, ϕ the azimuth, and m the mode number of irular waveguide. From the expressions above, the x and y omponents an be expressed as: E x = E r os ϕ E ϕ sin ϕ = ± 1 (A B)sin(m+1)ϕ 2 os(m+1)ϕ ± (A + B)sin(m 1)ϕ os(m 1)ϕ (2) E y = E r sin ϕ + E ϕ os ϕ = 1 (A B)os(m+1)ϕ 2 sin(m+1)ϕ + 1 (A + B)os(m 1)ϕ 2 sin(m 1)ϕ (3) where A = j ωμm 2 r H 0J m ( r)e jβz B = j ωμ (4) H 0 J m( r)e jβz The ratio of (A + B)/(A B) is shown in Fig. 1, and it is obvious that (A + B) is signifiantly bigger than (A B) (the dominant position of (A + B) is also refleted in the phase diagram of Fig. 4), and Equations (2) and (3) an be written as: E x ± 1 2 H 0 E y 1 2 H 0 [ j ωμm 2 r J m( r)+j ωμ J m ( r) [ j ωμm 2 r J m( r)+j ωμ J m ( r) ] sin(m 1)ϕ e jβz os(m 1)ϕ ] os(m 1)ϕ sin(m 1)ϕ e jβz (5) Due to the symmetry of irular waveguide, there are two possible distributions of the field expressions along ϕ: sin(mϕ) and os(mϕ). The field strutures of two distributions are exatly the same, exept Figure 1. (A B). Ratio between the terms (A + B) and Figure 2. Eletri field distribution in irular waveguide.

3 Progress In Eletromagnetis Researh M, Vol. 60, the diretion of polarization with a 90 -phase differene, whih is the speial polarization degenerate harateristi in the irular waveguide, as shown in Fig. 2. Therefore, the required phase fator an be obtained by ombining two orthogonal polarization degenerate TE mn modes (Here m is equivalent to l, whih refers to orbital angular momentum orders, and is a non-zero integer). TE mn ± jte mn : E r (r, ϕ, z) =±j ωμm 2 H 0 J m ( r)e ±jmϕ e jβz (6) E ϕ (r, ϕ, z) =j ωμ H 0 J m( r)e ±jmϕ e jβz E x ± 1 [ 2 H 0 j ωμm 2 J m ( r)+j ωμ ] J m( r) e ±j(m 1)ϕ e jβz E y 1 [ 2 H 0 j ωμm 2 J m ( r)+j ωμ ] (7) J m( r) e ±j(m 1)ϕ e jβz It is obvious from Expressions (6) and (7) that the field omponents of r and ϕ ontain the phase rotation fator e ±jmϕ, and omponents of x and y have the phase rotation fator e ±j(m 1)ϕ.Inorderto verify the analysis above, TE 11, TE 21 and TE 31 modes of irular waveguide are simulated in HFSS to observe the phase distribution of different field omponents. As shown in Fig. 3 and Fig. 4, the phase (a) (b) () Figure 3. Phase patterns of r omponents of eletri field. (a) Two orthogonal TE 11 modes; (b)two orthogonal TE 21 modes; () two orthogonal TE 31 modes.

4 60 Huang, Zong, and Nie (a) (b) () Figure 4. Phase patterns of x (left) and y (right) omponents of the eletri field. (a) Two orthogonal TE 11 modes; (b) two orthogonal TE 21 modes; () two orthogonal TE 31 modes. hanges of r and ϕ omponents are 2mπ, and on the ontrary, the phase hanges of x and y omponents are 2(m 1)π. 3. ANTENNA DESIGN AND SIMULATION In the previous setion, the theory of the orbital angular momentum generated by the irular waveguide is desribed. In order to verify the theory, an antenna worked at 9.2 GHz is presented. The detailed dimensions of the antenna are marked in Fig. 5. The antenna is omposed of three setions. The first setion is the main mode exitation setion of irular waveguide, the radius of whih satisfies the transmission ondition of the main mode: λ T M01 <λ<λ T E11 λ = 2πr μ mn (8) λ = /f 9.56 mm <r<12.49 mm In Formula (8), λ is the utoff wavelength and μ mn the root of Bessel funtion. The seond setion is the transition setion, and the radius of the one gradually varies from the single mode transmission ondition to TE 21 mode transmission ondition, whih satisfies the transmission ondition of the TE 21

5 Progress In Eletromagnetis Researh M, Vol. 60, Figure 5. Shemati diagram of antenna. Figure 6. Antenna simulation model. mode: λ T M01 <λ<λ T E21 (9) mm <r<19.88 mm The third setion is the mode transition setion where the main mode will be onverted to TE21 mode by diaphragm perturbation. Therefore, in the first setion, r 1 = 10 mm, only the main mode of the waveguide an be exited and spread. In the seond setion, r 2 = 12 mm, so that the main mode an be adequately spread. In the third setion, r 3 = 17 mm, the TE 21 mode an be formed by the perturbation of the three piees of metal. The length of eah setion and dimension of the metal diaphragm are seleted to make sure that antenna is well mathed at 9.2 GHz. An example of a horn antenna in HFSS, whih an generate orbital angular momentum beam of order 2 or 2, and 1 or 1, is shown in Fig. 6. The irular waveguide setion at the bottom of the antenna has two exitation ports, and these two ports are arranged with a 90-degree angle on the irumferene and fed by oaxial ables. The output frequenies and amplitudes of these two soures are the same, exept the 90-degree phase differene, whih is used to exite two orthogonal polarization modes. The 90 or 90 of the feed phase differene determines the positive or negative of the OAM order, that is, the phase pattern rotation is lokwise or antilokwise. As shown in Fig. 7, the three diaphragms have the same size and are spaed 120 degrees, whih are used to disturb the eletri field Figure 7. Distribution metal diaphragms.

6 62 Huang, Zong, and Nie distribution of the main mode, thus forming the TE 21 mode. The phase patterns of the proposed struture have been simulated by FEO. The phase patterns of r and ϕ omponents of the radiated eletri field are shown in Fig.8, and x and y omponents are shown in Fig. 9. The phase patterns are alulated at a 20λ distane from the horn aperture. It is apparent that the phase patterns of r and ϕ omponents have a lokwise or antilokwise rotation with a4π phase hange, whih orresponds to the phase fator of e ±j2ϕ, and the phase patterns of x and y omponents have the same rotation diretion but with a 2π phase hange, whih orresponds to the phase fator of e ±jϕ. (a) (b) Figure 8. Phase patterns at 9.2 GHz. (a) ϕ omponent of the eletri field; (b) r omponent of the eletri field. (a) (b) Figure 9. Phase patterns at 9.2 GHz. (a) x omponent of the eletri field; (b) y omponent of the eletri field.

7 Progress In Eletromagnetis Researh M, Vol. 60, MEASUREMENTS The proposed horn antenna with the speifi struture shown in Fig. 6 is fabriated. Two SMA onnetors are used to feed the horn, as shown in Fig. 10. The phase patterns are measured in a mirowave anehoi hamber. The phase pattern results of x omponent measured at 20λ distane from the horn aperture are shown in Fig. 11. Obvious spiral phase distribution orresponding to OAM of order 1 an be observed in the figure, whih is well onsistent with the simulation result in Fig. 9. The measured amplitude distribution is shown in Fig. 12, and the minimum amplitude orresponds to the vortex enter, whih is the harateristi of the vortex beam. Figure 10. Photograph of onial horn antenna. Figure 11. Measured x omponent radiation phase pattern. Figure 12. Measured x omponent radiation amplitude distribution.

8 64 Huang, Zong, and Nie 5. CONCLUSION A novel method and a simple antenna design for generating radio OAM waves are proposed in this paper. Both the theoretial analysis and experiment results are presented. Based on TE 21 mode of the irular waveguide, the OAM with mode of l =2orl = 2 is generated for E r and E ϕ omponents, l =1orl = 1 fore x and E y omponents, respetively. The measured phase patterns of eletrial field omponents are onsistent with the simulation results. In onlusion, with a proper design, irular waveguide an generate OAM eletromagneti field of order ±m and ±(m 1). In addition, ompared with other forms of OAM antenna already published, the antenna designed in this paper is simpler, easier to proess and an realize two modes simultaneously. ACNOWLEDGMENT This work is supported by the National Natural Siene Foundation of China (NSFC) under Projet Nos and REFERENCES 1. Cohen-Tannoudji, C., J Dupont-Ro, and G. Grynberg, Chapter 5. Introdution to the Covariant Formulation of Quantum Eletrodynamis. Photons and Atoms: Introdution to Quantum Eletrodynamis, , Wiley-VCH Verlag GmbH, Poynting, J. H., The wave motion of a revolving shaft, and a suggestion as to the angular momentum in a beam of irularly polarised light, Proeedings of the Royal Soiety A, Vol. 82, No. 557, , Thidé, B., H. Then, J. Sjöholm, et al., Utilization of photon orbital angular momentum in the low-frequeny radio domain, Physial Review Letters, Vol. 99, No. 8, Gibson, G., J. Courtial, M. Padgett, et al., Free-spae information transfer using light beams arrying orbital angular momentum, Optis Express, Vol. 12, No. 22, , Tamburini, F., E. Mari, A. Sponselli, et al., Enoding many hannels in the same frequeny through radio vortiity: First experimental test, New J. Phys., Vol. 14, No. 3, , Tamburini, F., E. Mari, B. Thide, et al., Experimental verifiation of photon angular momentum and vortiity with radio tehniques, Applied Physis Letters, Vol. 99, No. 20, 321, Bennis, A., R. Niemie, C. Brousseau, et al., Flat plate for OAM generation in the millimeter band, European Conferene on Antennas and Propagation, , Wei, W.,. Mahdjoubi, C. Brousseau, et al., Horn antennas for generating radio waves bearing orbital angular momentum by using spiral phase plate, Iet Mirowaves Antennas & Propagation, 10, Barbuto, M., A. Tosano, and F. Bilotti, Single path antenna generating eletromagneti field with orbital angular momentum, IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Siene Meeting, , IEEE, Al-Bassam, A., M. A. Salem, and C. Caloz, Vortex beam generation using irular leaky-wave antenna, Antennas and Propagation Soiety International Symposium, , IEEE, Barbuto, M., F. Trotta, F. Bilotti, and A. Tosano, Cirular polarized path antenna generating orbital angular momentum Progress In Eletromagnetis Researh, Vol. 148, 23 30, Thidé, B., H. Then, J. Sjöholm, et al., Utilization of photon orbital angular momentum in the low-frequeny radio domain, Physial Review Letters, Vol. 99, No. 8, , Mohammadi, S. M., L.. S. Daldorff, and J. E. S. Bergman, Orbital angular momentum in radio A system study, IEEE Transations on Antennas & Propagation, Vol. 58, No. 2, , Wu, H., Y. Yuan, and Z. Zhang, UCA-based orbital angular momentum radio beam generation and reeption under different array onfigurations, Sixth International Conferene on Wireless Communiations and Signal Proessing, 1 6, IEEE, 2014.

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