Electric and magnetic resonances in broadside coupled split-ring resonators: An extended mode-expansion theory

Physical Review B - Condensed Matter and Materials Physics

Volumn 77, Issue 23, 2008, Pages

  Huang, Xueqin ^a   Zhang, Yi ^a   Chui, S T ^b   Zhou, L ^a  

^a FUDAN UNIVERSITY   (China)

^b UNIVERSITY OF DELAWARE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 44949157193     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.77.235105     Document Type: Article

References (36)

1. V. C. Veselago, Sov. Phys. Usp. SOPUAP 0038-5670 10.1070/ PU1968v010n04ABEH003699 10, 509 (1968).
2. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.4184 84, 4184 (2000).
3. R. A. Shelby, D. R. Smith, and S. Schultz, Science SCIEAS 0036-8075 10.1126/science.1058847 292, 77 (2001).
4. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. IETMAB 0018-9480 10.1109/22.798002 47, 2075 (1999).
5. J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.223902 95, 223902 (2005).
6. D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.65.195104 65, 195104 (2002).
7. N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.1695439 84, 2943 (2004).
8. P. Markos and C. M. Soukoulis, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.036622 65, 036622 (2002).
9. Bogdan-Ioan Popa and S. A. Cummer, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.72.165102 72, 165102 (2005).
10. T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science SCIEAS 0036-8075 10.1126/science.1094025 303, 1494 (2004).
11. S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, Science SCIEAS 0036-8075 10.1126/science.1105371 306, 1351 (2004).
12. V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, Opt. Express 11, 735 (2003). 1094-4087
13. G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, Opt. Lett. OPLEDP 0146-9592 10.1364/OL.30.003198 30, 3198 (2005).
14. S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.137404 95, 137404 (2005).
15. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, Science SCIEAS 0036-8075 10.1126/science.1126021 312, 892 (2006).
16. P. Gay-Balmaz and O. J. F. Martin, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.1496507 81, 939 (2002).
17. C. R. Simovski and S. He, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(03)00494-8 311, 254 (2003).
18. C. R. Simovski and B. Sauviac, Radio Sci. RASCAD 0048-6604 10.1029/2003RS002898 39, RS2014 (2004).
19. E. Verney, B. Sauviac, and C. R. Simovski, Phys. Lett. A PYLAAG 0375-9601 10.1016/j.physleta.2004.07.032 331, 244 (2004).
20. T. Koschny, L. Zhang, and C. M. Soukoulis, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.71.121103 71, 121103 (R) (2005).
21. J. D. Baena, L. Jelinek, R. Marqués, and J. Zehentner, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.2190442 88, 134108 (2006).
22. J. D. Baena, L. Jelinek, and R. Marqués, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.76.245115 76, 245115 (2007).
23. J. D. Baena, L. Jelinek, and R. Marqués, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.2806915 91, 191105 (2007).
24. M. Shamonin, E. Shamonina, V. Kalinin, and L. Solymar, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.1652251 95, 3778 (2004).
25. M. Shamonin, E. Shamonina, V. Kalinin, and L. Solymar, Microwave Opt. Technol. Lett. MOTLEO 0895-2477 10.1002/mop.20567 44, 133 (2005).
26. L. Zhou and S. T. Chui, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.74.035419 74, 035419 (2006).
27. L. Zhou and S. T. Chui, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.2431776 90, 041903 (2007).
28. B. Sauviac, C. R. Simovski, and S. A. Tretyakov, Electromagnetics ETRMDV 0272-6343 10.1080/02726340490457890 24, 317 (2004).
29. N. Lagarkov, V. N. Semenenko, V. A. Chistyaev, D. E. Ryabov, S. A. Tretyakov, and C. R. Simovski, Electromagnetics 17, 213 (1997). 0272-6343
30. R. Marques, F. Medina, and R. Rafii-El-Idrissi, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.65.144440 65, 144440 (2002).
31. R. Marques, F. Mesa, J. Martel, and F. Medina, IEEE Trans. Antennas Propag. IETPAK 0018-926X 10.1109/TAP.2003.817562 51, 2572 (2003).
32. J. Garcia-Garcia, F. Martin, J. D. Baena, R. Marques, and L. Jelinek, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.2006224 98, 033103 (2005).
33. K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/7/1/168 7, 168 (2005).
34. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999).
35. C. M. Butler, IEEE Trans. Antennas Propag. IETPAK 0018-926X 10.1109/TAP.1984.1143308 AP-32, 226 (1984).
36. We note that some previous analytical calculations (say, Ref.) predicted that the current distribution along a thin metallic strip should be a Maxwellian form in which the current density diverges on the edges of the metallic strip. For the case that we studied, as the wavelength we considered is much larger than the width of the ring, the current in a Maxwellian form is almost uniform in the strip except in the region very close to the edges (see Ref.), which is indeed the case found in our FDTD simulations. However, since our FDTD mesh is not dense enough, we failed to find the divergences near the edges (see Fig. 1). Nevertheless, we note that the uniform distribution that we took is still a valid (although quite rough) approximation of the true current distribution and yields good results of resonance frequencies as compared with FDTD simulations (see Fig. 2). The reason of such good agreement is also partly due to the fact that the resonance frequency is a variational quantity which does not depend much on the detailed forms of the current distribution.