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In this paper, we realize the electrically coupled resonances between two metamaterial resonators based on two metal split-ring resonators gap-to-gap placed. The theoretical analysis and numerical calculation of the microwave equivalent circuit of the electrically coupled metamaterial resonators are performed. The results show that there are two resonance frequencies produced by the two coupled metamaterial resonators. For the two resonance frequencies, one gradually shifts towards the lower frequency with the coupling strength increasing, while the other is fixed at the resonance frequency of the single metamaterial resonator. The measured and simulated results of the microwave transmission spectra show that the two resonance peaks move respectively towards the lower and higher frequency with the coupling strength increasing. The analysis shows that the lower resonance frequency is mainly determined by the electrical coupling strength between the two metamaterial resonators, and the difference between the higher resonance frequency and the resonance frequency of the single resonator is mainly caused by the inevitable magnetic coupling between the two resonators. Moreover, the smaller the coupling space, the greater the influence of magnetic coupling is. The proposed dual resonance property and its tunability based on the electromagnetic coupling between the two metamaterial resonators greatly enhance the scopes of the design and application for metamaterials.
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Keywords:
- metamaterial resonators /
- coupling resonance /
- microwave equivalent circuit /
- electromagnetic wave
[1] Kurs A, Karalis A, Moffatt R, Joannopoulos J D, Fisher P, Soljacic M 2007 Science 317 83
[2] Florijn B, Coulais C, van Hecke M 2014 Phys. Rev. Lett. 113 175503
[3] Silva A, Monticone F, Castaldi G, Galdi V, Alu A, Engheta N 2014 Science 343 160
[4] Moitra P, Yang Y M, Anderson Z, Kravchenko I I, Briggs D P, Valentine J 2013 Nat. Photon. 7 791
[5] Smith D R, Pendry J B, Wiltshire M C K 2004 Science 305 788
[6] Shalaev V M 2007 Nat. Photon. 1 41
[7] Huang H Y, Ding S, Wang B Z, Zang R 2014 Chin. Phys. B 23 064101
[8] Li T H, Huang M, Yang J J, Yuan G, Cai G H 2014 Chin. Phys. B 23 054102
[9] Al-Naib I A I, Jansen C, Koch M 2008 Appl. Phys. Lett. 93 083507
[10] Schneider A, Shuvaev A, Engelbrecht S, Demokritov S O, Pimenov A 2009 Phys. Rev. Lett. 103 103907
[11] Burckel D B, Wendt J R, Ten Eyck G A, Ellis A R, Brener I, Sinclair M B 2010 Adv. Mater. 22 3171
[12] Gabbay A, Reno J, Wendt J R, Gin A, Wanke M C, Sinclair M B, Shaner E, Brener I 2011 Appl. Phys. Lett. 98 203103
[13] Guclu C, Luk T S, Wang G T, Capolino F 2014 Appl. Phys. Lett. 105 123101
[14] Li T Q, Liu H, Li T, Wang S M, Wang F M, Wu R X, Chen P, Zhu S N, Zhang X 2008 Appl. Phys. Lett. 92 131111
[15] Liu H, Genov D A, Wu D M, Liu Y M, Liu Z W, Sun C, Zhu S N, Zhang X 2007 Phys. Rev. B 76 073101
[16] Liu N, Liu H, Zhu S N, Giessen H 2009 Nat. Photon. 3 157
[17] Cheng Y Z, Gong R Z, Cheng Z Z, Nie Y 2014 Appl. Opt. 53 5763
[18] Cheng Y Z, Nie Y, Cheng Z Z, Gong R Z 2014 Prog. Electromagn. Res. 145 263
[19] Cheng Y Z, Cheng Z Z 2011 Microw. Opt. Technol. Lett. 53 615
[20] Zhou J F, Economon E N, Koschny T, Soukoulis C M 2006 Opt. Lett. 31 3620
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[1] Kurs A, Karalis A, Moffatt R, Joannopoulos J D, Fisher P, Soljacic M 2007 Science 317 83
[2] Florijn B, Coulais C, van Hecke M 2014 Phys. Rev. Lett. 113 175503
[3] Silva A, Monticone F, Castaldi G, Galdi V, Alu A, Engheta N 2014 Science 343 160
[4] Moitra P, Yang Y M, Anderson Z, Kravchenko I I, Briggs D P, Valentine J 2013 Nat. Photon. 7 791
[5] Smith D R, Pendry J B, Wiltshire M C K 2004 Science 305 788
[6] Shalaev V M 2007 Nat. Photon. 1 41
[7] Huang H Y, Ding S, Wang B Z, Zang R 2014 Chin. Phys. B 23 064101
[8] Li T H, Huang M, Yang J J, Yuan G, Cai G H 2014 Chin. Phys. B 23 054102
[9] Al-Naib I A I, Jansen C, Koch M 2008 Appl. Phys. Lett. 93 083507
[10] Schneider A, Shuvaev A, Engelbrecht S, Demokritov S O, Pimenov A 2009 Phys. Rev. Lett. 103 103907
[11] Burckel D B, Wendt J R, Ten Eyck G A, Ellis A R, Brener I, Sinclair M B 2010 Adv. Mater. 22 3171
[12] Gabbay A, Reno J, Wendt J R, Gin A, Wanke M C, Sinclair M B, Shaner E, Brener I 2011 Appl. Phys. Lett. 98 203103
[13] Guclu C, Luk T S, Wang G T, Capolino F 2014 Appl. Phys. Lett. 105 123101
[14] Li T Q, Liu H, Li T, Wang S M, Wang F M, Wu R X, Chen P, Zhu S N, Zhang X 2008 Appl. Phys. Lett. 92 131111
[15] Liu H, Genov D A, Wu D M, Liu Y M, Liu Z W, Sun C, Zhu S N, Zhang X 2007 Phys. Rev. B 76 073101
[16] Liu N, Liu H, Zhu S N, Giessen H 2009 Nat. Photon. 3 157
[17] Cheng Y Z, Gong R Z, Cheng Z Z, Nie Y 2014 Appl. Opt. 53 5763
[18] Cheng Y Z, Nie Y, Cheng Z Z, Gong R Z 2014 Prog. Electromagn. Res. 145 263
[19] Cheng Y Z, Cheng Z Z 2011 Microw. Opt. Technol. Lett. 53 615
[20] Zhou J F, Economon E N, Koschny T, Soukoulis C M 2006 Opt. Lett. 31 3620
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