Antenna Miniaturization Based on Supperscattering Effect

Transcription

1 512 JING-JING YANG, MING HUANG, FU-CHUN MAO, JING SUN, ANTENNA MINIATURIZATION BASED ON SUPPERSCATTERING Antenna Miniatuiation Based on Suppescatteing Effect Jing-jing YANG, Ming HUANG, Fu-chun MAO, Jing SUN School of Infomation Science and Engineeing, Yunnan Univesity, Kunming , PR China Abstact. Antennas ae essential components of all existing adio equipments. The miniatuiation of antenna is a key issue of antenna technology. Based on suppescatteing effect, we found that when a small hon antenna is located inside of a dielectic coe and coveed with a complementay laye, its fa field adiation patten will be equivalent to a lage hon antenna. The complementay laye with only axial paametes vaying with adius is obtained using coodinate tansfomation theoy. Besides, the influence of loss and petubations of paametes on suppescatteing effect is also investigated. Results show that the device is obust against the petubation in the axial mateial paametes when the efactive index is kept invaiant. Full-wave simulations based on finite element method ae pefomed to validate the design. Keywods Supescatteing effect, hon antenna, tansfomation optics. 1. Intoduction It is well known that the diective coefficient of an antenna is a diect popotion to apetue, but an invese popotion to the squae of wavelength. Fo a equied antenna gain, how to achieve it using a small apetue antenna instead of a lage one is a key issue in antenna design. In the past decade, a fascinating tem metamateials [1] has attacted a geat deal of attentions since it povides many possibilities to exploe unknown physical phenomena and fabicate novel devices such as pefect lens [2], antennas [3-5], and sensos [6], [7]. The idea of tansfomation optics genealied by Leonhadt and Pendy et al. [8], [9] built up a bidge between the function of metamateials and mateial paamete distibution, and povided geat convenience to the manipulation of electomagnetic field. Cloak is pehaps the most famous application. Since the fist cloak [10] was ealied at micowave band based on metamateial technology, geat attentions has been dawn to this aea [11-16]. Apat fom cloak of invisibility, some othe electomagnetic devices [17-24], such as concentato, tanspaent stuctue, field otato, beam expande and shinking device can also be ealied with this methodology. Recently, the concept of supescattee was poposed by Yang et al. [25]. It means that the object looks like a scattee lage than its geomety sie in electomagnetic wave diection. The effect of supescatteing plays an impotant ole in electomagnetic camouflage. Fo example, it is capable of concealing an entance [26] o building up an invisible tunnel between two waveguide [27]. Based on suppescatteing effect, we popose a novel diective antenna with small apetue but the same gain as a lage one in this pape. Constitutive mateial paametes with only axial components vaying with adius ae deived. Full wave simulation consideing the influence of metamateial loss and mateial paamete deviation ae caied out to validate the pefomance of the device. 2. Method and Simulation Model Fig. 1 shows the schematic diagam fo the constuction of a supescattee. The coe media with a adius a satisfies linea tansfomation of f( ) = c /a, and the mateial paametes can be easily obtained as 1, 2 1, ( c/ a). The complementay media laye coloed in black is obtained by folding the ai laye bounded between b and c in the vitual space ( ) into the egion bounded between a and b in the physical space ( ).We suppose the tansfomation function between the physical space and the vitual space is in the fom of f( ), whee f ( ) is a continuous function of, and it satisfies f(a) = c, f(b) = b. Accoding to the optical tansfomation theoy and the fom invaiance of the Maxwell s equations, elative pemittivity and pemeability of the complementay media can be witten as: f( ), (1a) df ( ) d df ( ) d, (1b) f( ) f ( ) df( ) d. (1c)

2 RADIOENGINEERING, VOL. 21, NO. 1, APRIL By compessing the domain ( < c) into the domain ( < a), we obtain a small hon antenna embedded in the dielectic coe, and coated by the complementay laye, as shown in Fig. 2(b). Geomety sie of the small hon antenna is minimied by a facto of c/a with elative to the lage one. In the next section, we make full wave simulation to demonstate supescatteeing effect. Fig. 1. (Colo online) Schematic demonstation fo the coodinate tansfomation of the suppescattee. We can notice that numeical values in (1a) and (1b) ae ecipocal, that is, if one is set as a constant, the othe can be fixed. Suppose that: df ( ) d m. (2) 0 f( ) Solution of this diffeential equation is given by f m m0 ( ) (3) (1 0 ) whee m0 log ( a/ b) ( c/ b), m b m. Then mateial paametes of the complementay media laye with only axial components vaying as a function of adius can be obtained as follows., (4a) 1/ m0, (4b) m 0 2( m0 1) m0 b. (4c) With this coodinate tansfomation, egions (a,b) and (b,c) ae complementay to each othe, and the whole physical space is optically equal to a cicle of ai with adius c, and is thus invisible to any incident wave. If we eplace the dielectic coe with a pefect electic conducto (PEC), the device with a adius b will have an equivalent scatteing coss section to that of a lage PEC with a adius c, and this is the supescatteing effect. Now we use this intiguing effect to design a small diective hon antenna with the same functionality as an equivalent lage one. Fig. 2(a) shows a lage hon antenna made of PEC mateial is placed in the egion of < c in the oiginal space. 3. Results and Discussions In this section, electomagnetic chaacteistics of the miniatue hon antenna ae simulated based on the commecial softwae COMSOL Multiphysics. We conside the case of tansvese-electic (TE) polaiation, and only ε, μ, μ φ components of the mateial paametes ae equied. Fig. 3(a) shows the electic field distibution in the vicinity of a lage hon antenna, of which the apetue width is w 1 = mm, the tape length is L 1 = 76.1 mm, the length and width of the feeding waveguide is w 2 = 60 mm and L 2 = 177 mm, espectively. It is excited by a cuent line souce located at the vetex of the tape. The fa field intensity is plotted in Fig. 3(c) (the solid line). The halfpowe beamwidth (HPBW) is about 6.9 o. It indicates that this hon antenna possesses a good diectional adiation chaacteistic. Fig. 3(b) displays the electic field distibution in the computational domain of a small hon antenna coated with the tansfomation media, of which the inne and oute boundaies ae a = 0.05 m, b = 0.1 m, and c = 0.15 m. We can clealy obseve that outside the egion of = c, the functionalities of both the two antennas ae almost the same. Fig. 2. (Colo online) (a) The lage hon antenna in the oiginal space. (b) The small hon antenna embedded in the dielectic coe of the tansfomation media. Fig. 3. (Colo online) Electic field distibution of a lage hon antenna (a) and a small hon antenna coated with the tansfomation media (b). (c) Fa field intensity. The fa field intensity pofile is shown in Fig. 3(c) (dashed line). The HPBW is about 7.6 o. As can be seen,

3 514 JING-JING YANG, MING HUANG, FU-CHUN MAO, JING SUN, ANTENNA MINIATURIZATION BASED ON SUPPERSCATTERING the diectional popety of the small hon antenna coated with the tansfomation media coincide well with that of the lage one. Compaed with dielectic lens antenna, of which the diective emission lies on the shape of the lens, the diectivity of a hon antenna is mainly detemined by the hon apetue sie. Besides, since the sie of a lens antenna possesses a lage electic length, it usually opeates at millimete wave band. The above simulation esults indicate that the effective sie of a small hon antenna can be amplified based on the supescatteing effect, and then the same diectivity as a lage one can be achieved. That means the effective sie of a desied hon antenna can be miniatuied based on the supescatteing effect, which is quite impotant in moden antenna design. angle. Cuves in Fig. 5 show the scatteing width of the supescattee with electic and magnetic loss tangents (tgδ) of 0, 0.001, 0.01, and 0.1, espectively. We can obseve that when loss tangent is 0.001, it has little influence on the pefomance of the supescattee. Futhe incease the loss tangent of metamateials will esult in a decease in scatteing width. When loss tangent is equal to 0.01 and 0.1, the deviation of scatteing width with espect to the pefect value will be 0.9 db and 3.5 db, espectively. Since metamateials ae always lossy, in what follows, we investigate the influence of loss tangent on the supescatteing effect, and mateial paamete deviation is also consideed. Fig. 4(a) shows the scatteing patten of a PEC cylinde with adius of = 0.15 m. The TE plane wave with fequency of 3 GH and unit amplitude popagates fom left to ight. Such a lage scattee can be eplaced by a smalle suppescattee, as shown in Fig. 4(b). Geomety sie of the supescattee is two-thids that of the PEC cylinde. Fig. 5. Scatteing width of the supescattee with loss tangents of 0, 0.001, 0.01 and 0.1 espectively. To investigate the influence of mateial paamete deviation on supescatteing effect, we simulated the electic field distibution in the computational domain of the supescattee when the axial component ε is multiplied by a coefficient of η. This epesents the axial mateial paamete is slightly deviated fom the pefect value. Both the negative (η = 0.9) and positive (η = 1.1) deviation is consideed. Simulation esults ae shown in Fig. 6. We can obseve that negative deviation in axial paamete has a weak impact on the pefomance of the supescattee. But a positive deviation will deteioate supescatteing effect especially in the fowad scatteing egion. When the axial paamete is deviated by a facto of η = 1.1, the following two cases ae consideed: (i) the impedance ( Z / and / ) is kept Fig. 4. (Colo online) Electic field distibution in the computational domain. (a) PEC cylinde. (b) Ideal supescattee. (c) tg (d) tg 0.1. Compaing Fig. 4(a) with 4(b), it is clea that field pattens in the egion of 0.1 m ae almost identical. It indicates that the supescattee effectively acts as a special device with lage scatteing coss section than its eal sie. But when loss tangent (tgδ) is intoduced into the complementay laye, it will affect the field patten both in the fowad and backwad scatteing egion, as shown in Fig. 4(c) and 4(d). To give a quantitative illustation of the influence of loss on supescatteing effect, scatteing width defined as σ(φ) = 2π R Esc(φ, R)/Einc 2 is calculated. Hee, R is the distance fom the object whee the fa-field scatteed field Esc is evaluated, Einc is the incident field, φ is the incident invaiant; (ii) the efactive index ( n and ) is kept invaiant. Fig. 6. (Colo online) Electic field distibutions in the vicinity of the supescattee when axial paamete ε is deviated fom pefect value. (a) η = 0.9. (b) η = 1.1.

4 RADIOENGINEERING, VOL. 21, NO. 1, APRIL Simulation esults of scatteing width ae plotted in Fig. 7. It is obvious that scatteing width of the non-ideal supescattee agees well with the pefect one when efactive index is kept invaiant. That means keeping the efactive index invaiant is the best choice to educe the influence of mateial paamete deviation on the pefomance of the supescattee. Fig. 7. Scatteing width of the supescattee with positive deviation in axial mateial paametes. Case I: the impedance is kept invaiant; Case II: the efactive index is kept invaiant. The solid line denotes the scatteing width of the ideal supescattee. 4. Conclusion In conclusion, a miniatue diective antenna is poposed based on supescatteing effect. Using full wave simulation, we demonstate that when a small hon antenna is located in the a dielectic medium and coated with a complementay laye, its adiation popeties will be equivalent to a lage one, which shows some advantages in opening up an avenue fo minimiing the sie of antennas and may have potential applications in adio engineeing. Acknowledgements This wok was suppoted by the National Natual Science Foundation of China (Gant Nos , ), the Scientific Reseach Foundation of Yunnan Univesity (Gant No. 2010YB025), and NSFC-YN (Gant No. U ). Refeences [1] SHELBY, R. A., SMITH, D. R., SCHULTZ, S. Expeimental veification of a negative index of efaction. Science, 2001, vol. 292, no. 5514, p [2] PENDRY, J. B. Negative efaction makes a pefect lens. Phys. Rev. Lett., 2000, vol. 85, no. 18, p [3] CHEN, P. Y., ALÙ, A. Sub-wavelength elliptical patch antenna loaded with μ-megative metamateials. IEEE Tansactions on Antennas and Popagation, 2010, vol. 58, no. 9, p [4] YANG, J. J., HUANG, M., PENG, J. H., XIAO, Z. Design of multi-beam antennas based on Epsilon-Nea-Zeometamateials. Intenational Jounal of Electonics and Communications (AEü), 2011, vol. 65, no. 6, p [5] YANG, J., HUANG, M., PENG, J. H. Diective emission obtained by mu and epsilon-nea-eo metamateials. Radioengineeing, 2009, vol. 18, no. 2, p [6] YANG, J. J., HUANG, M., YU, J., LAN, Y. Z. Suface whispeing-galley mode. Euophysics Lett., 2011, vol. 96, no. 5, p [7] HUANG, M., YANG, J., SUN, J, SHI, J. H., PENG, J. H. Modelling and analysis of Ω-shaped double negative mateial-assisted micowave senso. J. Infaed Milli Teah Waves, 2009, vol. 30, no. 11, p [8] PENDRY, J. B., SCHURIG, D., SMITH, D. R. Contolling electomagnetic fields. Science, 2006, vol. 312, no. 5781, p to [9] LEONHARDT, U. Optical confomal mapping. Science, 2006, vol. 312, no. 5781, p [10] SCHURIG, D., MOCK, J. J., JUSTICE, B. J., CUMMER, S. A., PENDRY, J. B., STARR, A. F., SMITH, D. R. Metamateial electomagnetic cloak at micowave fequencies. Science, 2006, vol. 314, no. 5801, p [11] LIU, R., JI, C., MOCK, J. J., CHIN, J. Y. CUI, T. J., SMITH, D. R. Boadband gound-plane cloak. Science, 2009, vol. 323, no. 5912, p [12] LIU, X., LI, C., YAO, K., MENG, X., FENG, W., WU, B., LI, F. Expeimental veification of boadband invisibility using a cloak based on inducto-capacito netwoks. Appl. Phys. Lett., 2009, vol. 95, no. 19, p [13] ALITALO, P., TRETYAKOV, S. Electomagnetic cloaking with metamateials. Mateials Today, 2009, vol. 12, no. 3, p [14] LAI, Y., CHEN, H. Y., ZHANG, Z. Q., CHAN, C. T. Complementay media invisibility cloak that cloaks objects at a distance outside the cloaking shell. Phys. Rev. Lett., 2009, vol. 102, no.9, p [15] YANG, C. F., YANG, J. J., HUANG, M., XIAO, Z., PENG, J. H. An extenal cloak with abitay coss section based on complementay medium and coodinate tansfomation. Optics Expess, 2011, vol. 19, no. 2, p [16] MA, H., QU, S., XU, Z., WANG, J. The open cloak. Applied Physics Lettes, 2009, vol. 94, no.10, p [17] RAHM, M., SCHURIG, D., ROBERTS, D. A., CUMMER, S. A., SMITH, D. R., PENDRY, J. B. Design of electomagnetic cloaks and concentatos using fom-invaiant coodinate tansfomations of Maxwell s equations, Photonics and Nanostuctues- Fundamentals and Applications, 2008, vol. 6, no.1, p [18] YANG, J. J., HUANG, M., YANG, C. F., XIAO, Z., PENG, J. H. Metamateial electomagnetic concentatos with abitay geometies. Optics Expess, 2009, vol. 17, no. 22, p [19] YANG, C. F., YANG, J. J., HUANG, M., SHI, J. H., PENG, J. H. Electomagnetic cylindical tanspaent devices with iegula coss section. Radioengineeing, 2009, vol. 19, no. 1, p [20] RAHM, M., ROBERTS, D. A., PENDRY, J. B., SMITH, D. R. Tansfomation-optical design of adaptive beam bends and beam expandes. Optics Expess, 2008, vol. 16, no.15, p [21] JIANG, W. X., CUI, T. J., YANG, X. M., MA, H.F., CHENG, Q. Shinking an abitay object as one desies using metamateials. Appl. Phys. Lett., 2011, vol. 98, no. 20, p

5 516 JING-JING YANG, MING HUANG, FU-CHUN MAO, JING SUN, ANTENNA MINIATURIZATION BASED ON SUPPERSCATTERING [22] CHEN, H., CHAN, C. T. Tansfomation media that otate electomagnetic fields. Appl. Phys. Letts., 2007, vol. 90, no. 24, p [23] CUI, T. J., LIU, R., SMITH, D. Metamateials: Theoy, Design, and Applications. Boston, MA: Spinge-Velag US, [24] CHEN, H., CHAN, C. T., SHENG, P. Tansfomation optics and metamateials. Natue Mateials, 2010, vol. 9, no. 5, p [25] YANG, T., CHEN, H., LUO, X., MA, H. Supescattee: Enhancement of scatteing with complementay media. Optics Expess, 2008, vol. 16, no. 22, p [26] LUO, X., YANG, T., GU, Y., CHEN, H., MA, H. Conceal an entance by means of supescattee. Appl. Phys. Lett., 2009, vol. 94, no. 22, p [27] ZHANG, J., LUO, Y., CHEN, H., HUANGFU, J., WU, B. I., RAN, L., KONG, J. A. Guiding waves though an invisible tunnel. Optics Expess, 2009, vol. 17, no. 8, p About Authos... Jing-jing YANG was bon in Hekou, Yunnan, China. She eceived the B.S. and M.S. degees in Electic Engineeing fom Yunnan Univesity, China, in 2005 and 2007, espectively, and eceived the Ph.D degee in 2010 fom Kunming Univesity of Science and Technology, China. He main eseach inteests include wieless communication, computational electomagnetism and electomagnetic theoy. Ming HUANG was bon in Wenshan, Yunnan, China. He eceived the B.S. and M.S. degees in Electic Engineeing fom Yunnan Univesity, Kunming, China, and the Ph. D degee in Micowave Engineeing fom Kunming Univesity of Science and Technology, China, in 1984, 1987, and 2006, espectively. He is cuently a pofesso at School of Infomation Science and Engineeing, Yunnan Univesity. His main eseach inteests include wieless communication, micowave powe application, and metamateials. In his eseach aea, he has (co-) authoed 5 books, ove 90 efeeed jounal papes and intenational confeence papes. One of his eseach papes was highlighted by Natue China in June, Fu-chun MAO was bon in Dali, Yunnan, China. He eceived the B.S. degee fom Yunnan Univesity, in Now he is a gaduate student at School of Infomation Science and Engineeing, Yunnan Univesity. His eseach inteests ae in the fields of electomagnetic computation and eseach of metamateials. Jing SUN was bon in Xu Zhou, Jiangsu Povince, China. She eceived the B.S. degee in Electic Engineeing fom Yunnan Univesity, Kunming, China, in She is cuently an associate pofesso at School of Infomation Science and Engineeing, Yunnan Univesity. He main eseach inteests include electonic and wieless communication.