Metamaterial Antennas and Finlines Using Full Wave Analysis

Transcription

1 th WSEAS Intenational Confeence on COMMUNICATIONS, Heaklion, Geece, July 3-5, 8 Metamateial Antennas and Finlines Using Full Wave Analysis Humbeto Césa Chaves Fenandes Depatment of Electical Engineeing, Fedeal Univesity of Rio Gande do Note DEE-CT-UFRN, P.O.Box 583 CEP , Natal-RN BRAZIL Abstact Metamateials ae defined as atificial effectively non-homogeneous electomagnetic stuctues with desied anisotopic dielectic and magnetic chaacteistics. In this pa the bilateal fin line and plana antennas with EBG Electomagnetic Band Gap metamateial substate ae analyzed using the full wave TTL - Tansvese Tansmission Line, method. In ode to analyze these stuctues the effective dielectic constant, the attenuation constant and the patten fields ae detemined. The esults obtained fo these applications and the conclusions ae pesented. Key-Wods: -Metamateial, Antenna, Finline, TTL Method, Full Wave Analysis. Metamateial Stuctue A metamateial (MTM) is defined as atificial non-homogeneous electomagnetic stuctue not eadily available in natue []-[4]. One chaacteistic of this mateial shown in Fig., is the negative mittivity, ε, and meability, μ. p: iod) is the electic plasma fequency. ζ ε ω πσ, is the dumping facto due ( / ) / p a to metal loss. Analyzing the equation (), Re( ε ) < ω < ω ζ (), fo If conside ζ, esult: u Fig. Thin-wies (TW), with negative-ε/positive-μ if E y uu Split-ing esonato (SRR) positive-ε/negative-μ, if H z. If the excitation electic field u E is paallel to the y axis in the MTM thin-wie shown in fig. so to induces a cuent along them, and geneates equivalent electic dipole moment, this MTM can be chaacteized by plasmonic-ty mittivity fequency function of the fom [], ω ζω ε ( ω) + j ω + ζ ωω ( + ζ ) ω () π c (c: light sed, a: adius of the wies, p p ln( ) a ε < ω < ω (3) uu If the excitation magnetic field H is ndicula to the z axis in the MTM split-ing esonato shown in Fig. so to induce a cuent in the loop of the ing, and geneates equivalent magnetic dipole moment, this MTM can be chaacteized by plasmonic-ty meability fequency function of the fom [], Fω ( ω ω m) Fωζ μ ( ω) + j (4) ( ) ( ) ( ) ( ) ω ω + ωζ ω ω + ωζ F π a p ( / ), ω 3p c (w: width of π ln( wa / δ ) 3 the ings, δ : adial spacing between the ings) is a magnetic esonance fequency. The equation (4) analyze, eveals the ange of fequency whee the meability is negative: μ <, fo ISSN: ISBN:

2 th WSEAS Intenational Confeence on COMMUNICATIONS, Heaklion, Geece, July 3-5, 8 ω ω < ω < ωpm F ; ω is the magnetic plasma pm fequency. The stuctue descibed in the fig. is a LH bidimensional, so u E has to be diected along the axis of the wies, and two diections ae possible fo uu H, then we have the following conditions: ε ( ω < ω ) < ε ε > ; μ < fo ω < ω < ω and μ, μ >. pm The pa discusses the effect of the metamateial double anisotopy by utilizing the tenso poties, which ae expessed as []-[3]: μ μ μ μ μ ε ε ε ε ε (5) (6) Finlines and Antennas Applications Fin lines ae widely used as a millimete wave components, due to its vaious advantages such as educing size, weight, cost and because it intefaces easily with othe millimete wave devices. The metamateial bilateal fin line is shown in Fig.. In this analysis the concise full wave TTL method, making possible a significant algebaic simplification of the equations and educing the computational time []. The geneal equations of the fields in the TTL method ae obtained afte using the Maxwell s equations. The chaacteistic equation fo detemining the complex popagation constant Γ, is obtained by setting the deteminant of the system matix equal to zeo. The effective dielectic constant is detemined afte numeical solutions of the matix deteminant by the elation between the phase constant and the fee space wave numbe, ε ef (β/ko). This micostip antenna is composed of a ectangula patch, metamateial substate and a gound plane. The MTM imdes the popagation of electomagnetic waves in some fequency, which can be used to made devices most efficient, and eliminate unwanted fequencies. The analysis is made using the TTL method, with efficient bases function in both x and z diection, as is shown in the Fig. []. In ode to analyze this stuctue the esonant fequency and patten fields ae obtained [4]-[8]. The metamateial substate shown in egion of Fig. is modeled by using bi anisotopic tenso poties equations (5) and (6), togethe with wave equations which ae expessed as [4]-[5]: Ey % γ Ey % Hy % γ Hy % (7) Afte using the Maxwell s equations in the sctal domain, the geneal equations of the electic and magnetic fields to the metamateial esonato ae obtained as: xi jα n + ωμμxiβkh + ωμμzi βkh% γi + kεi Fig. a) Tansvesal cut of a bilateal fin line stuctue with metamateial substate. b) Micostip esonato antenna with metamateial. zi jβk E ωμμxiαn H ωμμziαn H γ + kεi H xi jαn H ωεε xiβk E ωεε ziβk E γ + kεi y ISSN: ISBN:

3 th WSEAS Intenational Confeence on COMMUNICATIONS, Heaklion, Geece, July 3-5, 8 H% zi jβ k H ωεε xiαne ωεεα zi n γ kε + + E + i (8) Whee: i, epesent the dielectic egions of i k the stuctue; γ α + β k is the popagation constant in y diection; αn is the sctal vaiable in x diection and β k is the n sctal vaiable in z diection; k is the wave numbe of the i dielectic σ i egion; ε i ε i j is the elative dielectic ωε constant of the metamateial with losses; k ω μμ εε i i ω με k ε i. ω ω + jω i is the complex angula fequency; ε ε is the dielectic i i constant of the metamateial. The equations above ae applied to Helmohltz equations (7) in the sctal domain, [4]-[5] to detemine the field s equations to the stuctue. The solutions of these equations to the egions and ae: A cosh( γ y) y e H% A sinh( γ y) y h y H% A y e h e γ A y e γ y (9) Substituting these solutions in the equations (8), as functions of the unknown constants A e, A h, A e and A h, and applng the bounday conditions in the inteface y g, elating the cuent densities in the sheets ( J % xt and J % zt ) and the magnetic fields, the imdance matix will be obtained. ε th zx Fo example, j wm g g. xz ~ E E ~ xg zg ~ J ~ J zg xg () ì gcot gh( gg )[ bk g wan em ( ex ez)( mx m)] ü z + ( g k )( mx mz) + + í ý g ( - bk g + wan me ) ( g k ) m î + þ () The matix invesion is used to obtain the imdance matix, and the cuent densities in the inteface ae expanded using base functions [4]-[5]. The Galekin method is applied to (.), to eliminate the electic fields and then, the complex esonant fequency is obtained numeically. 3 Numeical Results To calculate the numeical esults computational pogams in Fotan PoweStation and Matlab languages wee develod, accoding to the pevious theoetical analyses. As illustated in the pevious section the metamateial pesent negative meability e mittivity constants. Fig.3 shows the metamateial wavefoms. The fin line uses a WR-8 millimete wave guide, and at 7. GHz (esonance fequency) occus the theshold conditions to both cuves. The new esults fo the bilateal fin line with metamateial substate, in a WR-8 millimete wave guide, accoding to Fig., with g.5 mm, f mm, w w.5 mm and ε ε 3, ε and μ, given by Fig.3 and, ae shown in Fig.4 and. H % x - H % x % Jzt H % z - H % z - % Jxt () Substituting the equations (8), into the equations (), the admittance matix is obtained: ISSN: ISBN:

4 th WSEAS Intenational Confeence on COMMUNICATIONS, Heaklion, Geece, July 3-5, 8 The fig.5 and shows the wavefoms meability and mittivity constants, to the stuctue TW-SRR, used in the antenna esults. At.34 GHz (esonance fequency) occus the theshold conditions to both cuves. These chaacteistics ae vey impotant because a ange of values available to devices poject is inceased aound the esonance fequency point. It s also shown the fa fields compotment to oate in two diffeent anges (negative μ - ε and positive μ -ε ). Hee can be seen that the adiation pattens chaacteistic can change just vang the oation fequency. Fig.3 Pemeability fo the SRR stuctue, Pemittivity fo the TW configuation 3 m 3 c m 4 s m Fig.4 Effective dielectic constant vs. fequency, attenuation constant vs. fequency, fo a bilateal fin line, in a WR-8 millimete wave guide, with metamateial substate. (c) Fig.5 Pemeability fo the SRR stuctue, Pemittivity fo the TW configuation, and (c), E-Plane Radiation Patten. ISSN: ISBN:

5 th WSEAS Intenational Confeence on COMMUNICATIONS, Heaklion, Geece, July 3-5, 8 4 Conclusion Theoetical and numeical esults have been pesented fo the bilateal fin line and ectangula antenna esonato with metamateial substate, using the TTL method. The field s equations wee shown to a wide ange of meability and mittivity values, by vang the stuctue paametes. These chaacteistics ae vey impotant to impove the design of the antenna devices. It was obseved a consideable eduction in the algebaic development using the TTL method and a fomance impovement using the metamateial substate. New esults wee shown fo meability and mittivity paametes in the GHz ange, fo the attenuation and effective dielectic constants fo the fin line stuctue, as well as the fa fields and esonance fequency of metamateial antenna. The autho acknowledges the suppot of CNPQ, Bazilian Agency. REFERENCES: [] Fenandes, H. C. C. and Alves, G. D. F., Meta-Mateial Multilaye Substate Plana Resonatos with Suconductive Patch, PIERS7- Pogess In Electomagnetics Reseach Symposium, Paha, Czech Republic, pp. 38, ago 7. [] Smith, D. R., Rye, P., Vie, D. C., Sta, A. F., Mock, J. J. and Peam, T., Design and Measuement of Anisotopic Metamateial that Exhibit Negative Refaction, IEICE Tans. ELECTRON., vol. E87-C, Nº 3, 3 ma 4. [3] C. Caloz and T. Itoh, Electomagnetic Metamateials: Tansmission line Theoy and Micowave Applications, John Wiley & Sons, 6. [4] Fenandes, H. C. C, Aquino, M. B. L. and Bito D. B. Rectangula Slot Resonato with Fou Dielectics Layes, PIERS7- Pogess In Electomagnetics Reseach Symposium, Beijing, China, pp.-6, Ma 7. [5] Fenandes, H. C. C, and Bito, D. B., Unilateal fin line diectional couple, Intenational Jounal of Infaed and Millimete Waves, Vol. 8, Nº8 pp.65-66, USA, Ago. 7. ISSN [6] Fenandes, H.C.C. Medeios J.L.G. Aaujo, I. M. J. and Bito D. B., Photonic cystal at millimete waves applications, PIERS7- Pogess in Electomagnetics Reseach Symposium, Beijing, China, pp.3-36, Ma 7. [7] Bhat, B. and Koul, S. K. Analysis, Design and Applications of Fin Lines, Atech House, Inc., pp , Nowood, MA, USA, 987. [8] Wiesma, D. S. Batolini, P. Lagendijk, Ad and Righini, R. Localization of light in a dimensional medium, Lettes to Natue - Vol.39 8/5, Dec ISSN: ISBN: