Abstract

In this paper, we report the formation of sharp Fano resonance in planar metamaterial array with perturbed periodicity. Rigorous sheet impedance theory is given to analyze the electric-magnetic and magnetic-magnetic coupling effects. It is found that periodicity perturbation can provide a general approach for Fano resonance with ultra-strong local field enhancement.

© 2013 OSA

1. Introduction

Metamaterials, as an artificial engineered material based on the strong interaction between electromagnetic radiation and conduction electrons at metallic interfaces or in subwavelength metallic structures, have attracted much attention in the last decade due to their unique electromagnetic properties such as negative [13] and zero refractive index [4, 5]. One most important property of plasmonic metamaterial is that the transmission spectrum and working bandwidth can be controlled by the shape and size of the subwavelength structure. While broadband property have been intensively studied for applications such as invisibility cloak [6], perfect absorber [710], extremely narrow bandwidth and high Quality factor (Q-factor, defined as ff) was pursued in recent work concerning biological sensing [11], slow light [12], etc. Unfortunately, ultrahigh Q-factor is difficult to realize for two dimensional metamaterial due to the lack of large volume confinement of electromagnetic fields and strong coupling to free space [13].

Quite recently, it is found that sharp trapped mode with ultrahigh Q-factor can be obtained in planar metamaterial by introducing symmetry breaking in the shape of its structural elements [13]. The Q-factor of such trapped mode is reversely related to the asymmetry factor (defined as the relative difference between structural elements). Later, pronounced Fano resonance and extraordinary optical transmission (EOT) are observed in asymmetric structure and attributed to the coexistence and interference of super-radiant and sub-radiant modes [14, 15]. The asymmetric metamaterial is termed coherent since the electromagnetic response is a collective phenomenon and strong interactions between metamolecules exist [16, 17]. The combination of sharp trapped mode and coherence paves the way for lasing spaser, a coherent source supported by gain [18, 19]. In addition, asymmetric Fano resonance has been utilized recently for ultrasensitive spectroscopy and identification of molecular monolayers [20]. Theoretically, the physical explanation of Fano resonance in metamaterial can be given by using classical analogy [21] or ab initio theory based on Feshbach formalism [22]. The classical analogy is a general technique but not rigorous enough. The Feshbach formalism, however, is much more complicated and the relation between spectrum and structure is not so clear.

In this paper, a planar metamaterial with perturbed periodicity and sharp Fano resonance is proposed. Generalized impedance theory and equivalent circuit theory are used to investigate the Fano-type resonance. Electric-magnetic coupling and periodicity perturbation induced magnetic-magnetic coupling are demonstrated unambiguously. Full-wave simulations agree well with the theoretical results. We expect that the approach proposed here can also be used to analyze other asymmetric metamaterial structures.

2. Structure and simulation

As illustrated in Fig. 1(a) , the structure proposed here is a periodic metallic wire pair configuration, which has been widely used to create artificial magnetic response and negative refractive index [2325]. Here different widths of wire pairs (depicted by grey, orange, and red colors) are used to perturb the periodicity. In this case, three wire pairs actually act as a new unit cell. The center-to-center distances between adjacent wire pairs are kept as p = 5 mm and the thickness of the dielectric spacer is set as d = 0.75 mm. Metal is assumed as perfect conductor while the permittivity of dielectric material is chosen as 12 with loss tangent τ = 0 (the material loss will be considered later).

 

Fig. 1 (a) Schematic of the wire pairs with perturbed periodicity. The grey, orange, and red colors depict different widths. (b) Sketch map of the surface current distributions for the two subradiant modes.

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As is well known, metallic wire pairs have strong magnetic response which can be described by effective magnetic dipoles. Giant magnetic response can be obtained with anti-parallel surface currents when the electric field is perpendicular to the long axis of wire pairs. Different subradiant modes, which couples weakly with the external field, may exist at different resonance conditions (Fig. 1(b)). In numerical simulation, Comsol Multiphysics, a commercial finite element method (FEM) solver is used with periodic boundary condition in x direction and perfectly matched layer in ± z direction. The structure is assumed to be infinite long in y direction while the electric and magnetic fields are along x and y directions, respectively (i.e. normal incidence). The incident magnetic field is set as unit.

In order to investigate the influence of structure asymmetry, the transmission coefficients of both symmetric and asymmetric metamaterial at normal incidence are calculated and shown in Fig. 2 . For the symmetric structure (w1 = w2 = w3 = 4 mm), the transmission peak at 9.78 GHz is induced by the magnetic resonance. Similar with Fano resonance, the transmission profile is asymmetric and a transmission dip occurs at 11.1 GHz.

 

Fig. 2 Transmission coefficients for the symmetric and asymmetric metamaterial slabs. Two regions are highlighted. Region I shows typical asymmetric line shape of Fano resonance. Region II demonstrates the ultra-sharp resonance peak induced by inter-element coupling.

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For the asymmetric structure, the widths of three wires can have three or two different values. Without loss of generality, we choose w1 = 4 mm, w2 = 3.6 mm and w3 = 3.56 mm as an example. Compared with the symmetry case, the line shape around 9.8 GHz becomes more asymmetric. Moreover, ultra sharp transmission dip at the center of a transmission peak is observed at frequencies around 10.8 GHz with Q-factor as large as 100. Interestingly, this is in contrary to the metamaterial analogy of electromagnetic induced transparency (EIT) [26], where a transmission sharp peak arises in a reflective frequency region.

3. Analysis and discussion

3.1 Generalized impedance theory

The above exotic transmission properties can be understood by using generalized surface impedance theory, which has been used to retrieve effective material parameter for thin sheets such as graphene and single-layer metamaterials [27].

As illustrated in Fig. 3 , thin metamaterial slab can be treated as a combination of electric impedance and magnetic impedance with the following boundary condition:

Ei+Er=Et+n^×jm,Hi+Hr=Ht+n^×je.
By definition, there are Er = rEi, Hr = rHi, Et = tEi and Ht = tHi, where Ei = Z0Hi is the incident electric field, Z0 = 1/Y0 = 377 Ω is the vacuum impedance, r and t are the reflection and transmission coefficients. The electric sheet current je and magnetic sheet current jm are related with the average electric and magnetic field through the corresponding electric admittance Ye and magnetic impedance Zm:
je=1ZeEaverage=YeEaverage=Ye(1+r+t)Ei/2,jm=ZmHaverage=Zm(1r+t)Hi/2.
Combining Eqs. (1) and (2), one can obtain that:
Ye=2Y01rt1+r+t,Zm=2Z01+rt1r+t,
r=12(2Y0Ye2Y0+Ye+Zm2Z0Zm+2Z0),t=12(2Y0Ye2Y0+YeZm2Z0Zm+2Z0),
and

 

Fig. 3 Schematic of sheet impedance description for thin metamaterial. The magnetic and electric responses are described by equivalent magnetic and electric sheet currents.

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je=2Y0Ye2Y0+YeEi,jm=2Z0ZmZm+2Z0Hi.

Equations (3)-(5) are the central results of the generalized sheet impedance theory. Using Eq. (3), the effective magnetic and electric impedances can be retrieved from simulated or measured S parameters (r and t). In the following, the generalized impedance theory is used to interpret the formation of Fano resonances in the planar metamaterial as shown in Fig. 2.

3.2 Fano resonance induced by the interference of magnetic and electric resonances

For the structure without asymmetry (w1 = w2 = w3 = 4 mm), the line shape shown in Fig. 2 is asymmetric. In order to understand the physical meaning behind it, the electric and magnetic sheet impedances are retrieved using Eq. (3). As depicted in Figs. 4(a) and 4(b), the electric admittance is nearly flat in the whole frequency range and magnetic impedance manifests itself as a sharp resonance. We noted that this phenomenon is similar with Fano resonance, which stems from the interference of a discrete state with a continuum.

 

Fig. 4 (a) The electric admittance and (b) magnetic impedance of the symmetric structure (w1 = w2 = w3 = 4 mm). (c) The transmission coefficients for the real structure and pure magnetic impedance. The fitted magnetic impedance using LC circuit model is also shown in (b).

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As given by Eq. (4), the transmission coefficient of any metasurface can be decomposed into two parts, one electric and the other magnetic. To analysis the influence of the electric admittance on the transmission spectrum, the electric admittance is set as ∞ (Ze = 0) artificially and the corresponding transmission coefficient is plotted in Fig. 4(c). Obviously, the asymmetric line shape will transform into symmetric one when the electric resonance is not taken into account. Thus, one can conclude that it is the interference of the broadband electric resonance and narrowband magnetic resonance leads to the asymmetric Fano resonance.

In addition, to describe the magnetic resonance quantificationally, the magnetic impedance can be described by a simple equivalent LC circuit model in the form of:

Zm=11/(iωL)+iωC=iωL1ω2LC,
where ω is the angular frequency, L and C are the effective inductance and capacitance. The values of L and C can be evaluated by fitting the results retrieved from r and t. For the case of Fig. 4, L and C are 0.708 nH and 0.369 pF, which agrees well with the retrieved results.

3.3 Fano resonance induced by coupled magnetic resonances

For the structure with perturbed periodicity, the adjacent magnetic resonators will couple with each other. As shown in Fig. 5 , the electric and magnetic impedances as well as the corresponding sheet currents are calculated using Eqs. (3) and (5). Similar with the symmetric structure, the electric admittance is still rather flat. The magnetic impedance, however, shows complex resonant characteristics. Since there are three resonant peaks, the magnetic impedance shown in Fig. 5(c) can be written as a combination of individual magnetic resonances, as described by equivalent LC circuit model:

Zm=n=13Zmn=n=13iωLn1ω2LnCn.
Here, L1, L2, L3, C1, C2 and C3 are the corresponding inductances and capacitances. The resonant frequencies areω1=(L1C1)1/2,ω2=(L2C2)1/2, andω2=(L3C3)1/2, respectively. By fitting Eq. (7) with the retrieved magnetic sheet impedance, the LC parameters can be obtained as L1 = 0.295 nH, L2 = 0.273 nH, L3 = 0.27 nH, C1 = 0.896 pF, C2 = 0.8 pF and C3 = 0.794 pF. The corresponding resonant frequencies are 9.79 GHz, 10.77 GHz and 10.87 GHz.

 

Fig. 5 (a) Electric admittance and (b) electric sheet current for the asymmetric structure. (c) The corresponding magnetic impedance and (d) magnetic sheet current.

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Similar with the magnetic sheet impedance, the magnetic sheet current is also a summation of all the individual sheet currents:

jm=n=13jmn,
where

jmn=2Z0ZmnZm+2Z0Hi,n=1,2,3.

Using Eqs. (7) and (9), the sheet currents for different resonators can be easily calculated. As shown in Fig. 6(a) , the current of the first resonator dominates at frequencies around 9.79 GHz. On the contrary, the second and third resonators dominate the frequency region around 10.8 GHz. From Fig. 6(b) one can find that the first resonator is out of phase with the other two resonators for 9.79 GHz < f <10.77GHz. Also, For 10.77 GHz < f <10.87 GHz, the third one is out of phase with the others.

 

Fig. 6 (a) Amplitudes and (b) phases of the effective magnetic sheet current calculated using Eq. (5). The fitted parameters of inductances and capacitors are used (see text). The three frequencies where the phase changes occur are highlighted. At theses frequencies, the corresponding amplitudes are zero.

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In fact, the π phase shift between these resonators is the key of resonant enhancement of sheet current. As an example, at frequencyω0=(L2+L3)1/2(L2L3(C2+C3))1/2=10.82GHz there are |Zm1||Zm2||Zm3| and|Zm1||Zm|. Thus, one can obtain that:

jm1Z0Hijm2=iL2L3(L2+L3)(C2+C3)L3C3L2C2Hi.jm3=jm2=iL2L3(L2+L3)(C2+C3)L2C2L3C3Hi

The second and third sheet currents in Eq. (10) are out of phase and reversely proportional withω32ω22=L3C3L2C2. As a result, higher enhancement factor and narrower bandwidth can be achieved by decreasing the difference between ω2 and ω3. Using previous fitted parameters, the sheet current at 10.82 GHz can be calculated as jm1 = 3.3iHi, jm2 = 2000i Hi, and jm3 = −2000i Hi, which agree well with that shown in Fig. 6(a).

In general, the magnetic field inside the planar metamaterial is proportional to the sheet current. Recalling Eq. (1) and the Maxwell equation:

Ei+ErEt=n^×jmLEdl=ddtsBdS
One can obtain that:
n^×jmL=ddt(BLΔ),
where L = p is the unit cell length and Δ is the effective thickness of the metamaterial layer. As a result, the magnetic field Hz can be calculated as:
|Hz|=|jm|iωμ0Δ.
It should be noted that Eq. (13) is only an approximation under the condition Δ<<λ, for which the electric field integration along the thickness direction can be neglected.

In order to further prove above discussion, the magnetic fields at the center of the three resonators for different frequencies are calculated using Comsol Multiphysics and illustrated in Fig. 7 , which are very similar with the magnetic sheet currents calculated from S parameters. At f1 = 8 GHz, all the three wire pairs are out of resonance and the maximum magnetic field is only 3.6 Hi. At f2 = 9.79 GHz, the first resonator is resonant and the maximum magnetic field increases to 69 Hi. At f3 = 10.77 GHz, and f5 = 10.87 GHz, the second and the third wire pairs are resonant, respectively. Since f3 and f5 are spectrally close, a new resonant mode takes place between them. At f4 = 10.8 GHz, the second and the third wire pairs are on resonance with opposite phase. The maximum magnetic field becomes as high as 140 Hi.

 

Fig. 7 (a) Normalized magnetic fields (Hz) at the center of these resonators. The inset shows the unit cell and the points where the magnetic fields are extracted. (b)(c)(d)(e)(f) Magnetic field distributions at frequencies of f1 = 8 GHz, f2 = 9.79 GHz, f3 = 10.77GHz, f4 = 10.82 GHz and f5 = 10.87 GHz.

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In order to further understand the influence of the periodicity perturbation on the Fano resonance, the effect of wire width is investigated. Here, two wires have the same width of 4 mm while the third wire width is changed from 3.8 mm, 3.96mm to 4mm. As illustrated in Fig. 8 , as the asymmetry decrease, two isolated resonances become very close and a third sharp resonance occurs. When the three wire pairs all have the same widths, the transmission spectrum will degenerate to a single magnetic resonance.

 

Fig. 8 Transmission spectrum of the metamaterial slab for different asymmetry. Here the geometrical parameters are w1 = w2 = 4 mm, while w3 is variable.

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Finally, it should be noted that the Fano resonance proposed here is a coherent process thus practical performance is highly dependent on the unit cell numbers of finite arrays [18]. In addition, the fabrication error may also limit the achievable bandwidth, especially if the structure is scaled to higher frequencies, where the intrinsic loss in metal is another restriction of high Q-factor resonance.

3.4 Influence of loss

In the above discussion, the material loss is neglected since the dielectric material is lossless and metal is set as perfect electric conductor. In general, the loss of material has great influence on the performance. In order to take it into account, a typical loss tangent of 0.003 is added in the dielectric material and metal is used as copper with conductivity of 5.7e7 S/m. As shown in Fig. 9(a) , obvious absorption is observed at the resonant frequencies 9.8 GHz and 10.8 GHz. Nevertheless, the magnetic field enhancement factor only decreases a little, as shown in Fig. 9(b).

 

Fig. 9 (a) Reflection (r), transmission (t) and absorbance (1-r2-t2) of the lossy metamaterial slab. (b) Normalized magnetic fields extracted from Comsol Multiphysics.

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In fact, the loss mechanism in the asymmetric structure can be utilized to realize wideband wide-angle absorber, which has been intensively studied in recent years [8, 9]. Typical structure is shown in the inset of Fig. 10 , where a metallic ground plane is added in the center of wire pair structure. Here, the geometric parameters are optimized as p = 5 mm, d = 0.75 mm, w1 = 4 mm, w2 = 4.12 mm and w3 = 3.9 mm. The permittivity is set as 12 with a higher loss tangent of τ = 0.015. The achieved bandwidth for 90% absorption is about 0.5 GHz, which is larger than that of metamaterial absorber without asymmetry (0.2 GHz) at the same thickness (p = 5 mm, w = 4 mm, τ = 0.025).

 

Fig. 10 Absorption of the wideband absorber for different angles of incidence. The absorption for the symmetric structure is also shown for comparison. Inset is schematic of the absorber which is composed of asymmetric wires and a metallic ground plane.

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4. Conclusion

In conclusion, we demonstrated analytically and numerically that Fano-type resonance can be excited in planar metamaterial with perturbed periodicity. Generalized impedance surface theory is given to interpret these exotic phenomena unambiguously, which agrees well with the numerical results calculated using finite element method. It is found that the electric-magnetic and magnetic-magnetic coupling effects in planar metamaterial cannot only generate pronounced Fano resonance but also sustain giant field enhancement which has potential applications in slow light, nonlinear optics and biological sensing etc.

Acknowledgment

This work was supported by 973 Program of China (No. 2011CB301800) and National Natural Science Funds for Distinguished Young Scholar (No. 60825405).

References and Links

1. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001). [CrossRef]   [PubMed]  

2. R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(5), 056625 (2001). [CrossRef]   [PubMed]  

3. N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005). [CrossRef]   [PubMed]  

4. R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046608 (2004). [CrossRef]   [PubMed]  

5. M. Silveirinha and N. Engheta, “Design of matched zero-index metamaterials using nonmagnetic inclusions in epsilon-near-zero media,” Phys. Rev. B 75(7), 075119 (2007). [CrossRef]  

6. R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009). [CrossRef]   [PubMed]  

7. Q. Feng, M. Pu, C. Hu, and X. Luo, “Engineering the dispersion of metamaterial surface for broadband infrared absorption,” Opt. Lett. 37(11), 2133–2135 (2012). [CrossRef]   [PubMed]  

8. C. Wu and G. Shvets, “Design of metamaterial surfaces with broadband absorbance,” Opt. Lett. 37(3), 308–310 (2012). [CrossRef]   [PubMed]  

9. Y. Cui, J. Xu, K. Hung Fung, Y. Jin, A. Kumar, S. He, and N. X. Fang, “A thin film broadband absorber based on multi-sized nanoantennas,” Appl. Phys. Lett. 99(25), 253101 (2011). [CrossRef]  

10. M. Pu, Q. Feng, M. Wang, C. Hu, C. Huang, X. Ma, Z. Zhao, C. Wang, and X. Luo, “Ultrathin broadband nearly perfect absorber with symmetrical coherent illumination,” Opt. Express 20(3), 2246–2254 (2012). [CrossRef]   [PubMed]  

11. N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010). [CrossRef]   [PubMed]  

12. C. Wu, A. B. Khanikaev, and G. Shvets, “Broadband slow light metamaterial based on a double-continuum fano resonance,” Phys. Rev. Lett. 106(10), 107403 (2011). [CrossRef]   [PubMed]  

13. V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett. 99(14), 147401 (2007). [CrossRef]   [PubMed]  

14. F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett. 8(11), 3983–3988 (2008). [CrossRef]   [PubMed]  

15. A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, “Symmetry breaking in a plasmonic metamaterial at optical wavelength,” Nano Lett. 8(8), 2171–2175 (2008). [CrossRef]   [PubMed]  

16. V. A. Fedotov, N. Papasimakis, E. Plum, A. Bitzer, M. Walther, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Spectral collapse in ensembles of metamolecules,” Phys. Rev. Lett. 104(22), 223901 (2010). [CrossRef]   [PubMed]  

17. N. Papasimakis, V. A. Fedotov, Y. H. Fu, D. P. Tsai, and N. I. Zheludev, “Coherent and incoherent metamaterials and order-disorder transitions,” Phys. Rev. B 80(4), 041102 (2009). [CrossRef]  

18. N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2(6), 351–354 (2008). [CrossRef]  

19. E. Plum, V. A. Fedotov, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Towards the lasing spaser: controlling metamaterial optical response with semiconductor quantum dots,” Opt. Express 17(10), 8548–8551 (2009). [CrossRef]   [PubMed]  

20. C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater. 11(1), 69–75 (2011). [CrossRef]   [PubMed]  

21. Y. S. Joe, A. M. Satanin, and C. S. Kim, “Classical analogy of Fano resonances,” Phys. Scr. 74(2), 259–266 (2006). [CrossRef]  

22. B. Gallinet and O. J. F. Martin, “Ab initio theory of Fano resonances in plasmonic nanostructures and metamaterials,” Phys. Rev. B 83(23), 235427 (2011). [CrossRef]  

23. G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett. 30(23), 3198–3200 (2005). [CrossRef]   [PubMed]  

24. V. D. Lam, J. B. Kim, S. J. Lee, Y. P. Lee, and J. Y. Rhee, “Dependence of the magnetic-resonance frequency on the cut-wire width ofcut-wire pair medium,” Opt. Express 15(25), 16651–16656 (2007). [CrossRef]   [PubMed]  

25. N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater. (Deerfield Beach Fla.) 19(21), 3628–3632 (2007). [CrossRef]  

26. S.-Y. Chiam, R. Singh, C. Rockstuhl, F. Lederer, W. Zhang, and A. A. Bettiol, “Analogue of electromagnetically induced transparency in a terahertz metamaterial,” Phys. Rev. B 80(15), 153103 (2009). [CrossRef]  

27. P. Tassin, T. Koschny, and C. M. Soukoulis, “Effective material parameter retrieval for thin sheets: Theory and application to graphene, thin silver films, and single-layer metamaterials,” Physica B 407(20), 4062–4065 (2012). [CrossRef]  

References

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  1. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science292(5514), 77–79 (2001).
    [CrossRef] [PubMed]
  2. R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.64(5), 056625 (2001).
    [CrossRef] [PubMed]
  3. N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science308(5721), 534–537 (2005).
    [CrossRef] [PubMed]
  4. R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.70(4), 046608 (2004).
    [CrossRef] [PubMed]
  5. M. Silveirinha and N. Engheta, “Design of matched zero-index metamaterials using nonmagnetic inclusions in epsilon-near-zero media,” Phys. Rev. B75(7), 075119 (2007).
    [CrossRef]
  6. R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science323(5912), 366–369 (2009).
    [CrossRef] [PubMed]
  7. Q. Feng, M. Pu, C. Hu, and X. Luo, “Engineering the dispersion of metamaterial surface for broadband infrared absorption,” Opt. Lett.37(11), 2133–2135 (2012).
    [CrossRef] [PubMed]
  8. C. Wu and G. Shvets, “Design of metamaterial surfaces with broadband absorbance,” Opt. Lett.37(3), 308–310 (2012).
    [CrossRef] [PubMed]
  9. Y. Cui, J. Xu, K. Hung Fung, Y. Jin, A. Kumar, S. He, and N. X. Fang, “A thin film broadband absorber based on multi-sized nanoantennas,” Appl. Phys. Lett.99(25), 253101 (2011).
    [CrossRef]
  10. M. Pu, Q. Feng, M. Wang, C. Hu, C. Huang, X. Ma, Z. Zhao, C. Wang, and X. Luo, “Ultrathin broadband nearly perfect absorber with symmetrical coherent illumination,” Opt. Express20(3), 2246–2254 (2012).
    [CrossRef] [PubMed]
  11. N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett.10(7), 2342–2348 (2010).
    [CrossRef] [PubMed]
  12. C. Wu, A. B. Khanikaev, and G. Shvets, “Broadband slow light metamaterial based on a double-continuum fano resonance,” Phys. Rev. Lett.106(10), 107403 (2011).
    [CrossRef] [PubMed]
  13. V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett.99(14), 147401 (2007).
    [CrossRef] [PubMed]
  14. F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett.8(11), 3983–3988 (2008).
    [CrossRef] [PubMed]
  15. A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, “Symmetry breaking in a plasmonic metamaterial at optical wavelength,” Nano Lett.8(8), 2171–2175 (2008).
    [CrossRef] [PubMed]
  16. V. A. Fedotov, N. Papasimakis, E. Plum, A. Bitzer, M. Walther, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Spectral collapse in ensembles of metamolecules,” Phys. Rev. Lett.104(22), 223901 (2010).
    [CrossRef] [PubMed]
  17. N. Papasimakis, V. A. Fedotov, Y. H. Fu, D. P. Tsai, and N. I. Zheludev, “Coherent and incoherent metamaterials and order-disorder transitions,” Phys. Rev. B80(4), 041102 (2009).
    [CrossRef]
  18. N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics2(6), 351–354 (2008).
    [CrossRef]
  19. E. Plum, V. A. Fedotov, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Towards the lasing spaser: controlling metamaterial optical response with semiconductor quantum dots,” Opt. Express17(10), 8548–8551 (2009).
    [CrossRef] [PubMed]
  20. C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater.11(1), 69–75 (2011).
    [CrossRef] [PubMed]
  21. Y. S. Joe, A. M. Satanin, and C. S. Kim, “Classical analogy of Fano resonances,” Phys. Scr.74(2), 259–266 (2006).
    [CrossRef]
  22. B. Gallinet and O. J. F. Martin, “Ab initio theory of Fano resonances in plasmonic nanostructures and metamaterials,” Phys. Rev. B83(23), 235427 (2011).
    [CrossRef]
  23. G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett.30(23), 3198–3200 (2005).
    [CrossRef] [PubMed]
  24. V. D. Lam, J. B. Kim, S. J. Lee, Y. P. Lee, and J. Y. Rhee, “Dependence of the magnetic-resonance frequency on the cut-wire width ofcut-wire pair medium,” Opt. Express15(25), 16651–16656 (2007).
    [CrossRef] [PubMed]
  25. N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater. (Deerfield Beach Fla.)19(21), 3628–3632 (2007).
    [CrossRef]
  26. S.-Y. Chiam, R. Singh, C. Rockstuhl, F. Lederer, W. Zhang, and A. A. Bettiol, “Analogue of electromagnetically induced transparency in a terahertz metamaterial,” Phys. Rev. B80(15), 153103 (2009).
    [CrossRef]
  27. P. Tassin, T. Koschny, and C. M. Soukoulis, “Effective material parameter retrieval for thin sheets: Theory and application to graphene, thin silver films, and single-layer metamaterials,” Physica B407(20), 4062–4065 (2012).
    [CrossRef]

2012 (4)

2011 (4)

C. Wu, A. B. Khanikaev, and G. Shvets, “Broadband slow light metamaterial based on a double-continuum fano resonance,” Phys. Rev. Lett.106(10), 107403 (2011).
[CrossRef] [PubMed]

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater.11(1), 69–75 (2011).
[CrossRef] [PubMed]

B. Gallinet and O. J. F. Martin, “Ab initio theory of Fano resonances in plasmonic nanostructures and metamaterials,” Phys. Rev. B83(23), 235427 (2011).
[CrossRef]

Y. Cui, J. Xu, K. Hung Fung, Y. Jin, A. Kumar, S. He, and N. X. Fang, “A thin film broadband absorber based on multi-sized nanoantennas,” Appl. Phys. Lett.99(25), 253101 (2011).
[CrossRef]

2010 (2)

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett.10(7), 2342–2348 (2010).
[CrossRef] [PubMed]

V. A. Fedotov, N. Papasimakis, E. Plum, A. Bitzer, M. Walther, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Spectral collapse in ensembles of metamolecules,” Phys. Rev. Lett.104(22), 223901 (2010).
[CrossRef] [PubMed]

2009 (4)

N. Papasimakis, V. A. Fedotov, Y. H. Fu, D. P. Tsai, and N. I. Zheludev, “Coherent and incoherent metamaterials and order-disorder transitions,” Phys. Rev. B80(4), 041102 (2009).
[CrossRef]

E. Plum, V. A. Fedotov, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Towards the lasing spaser: controlling metamaterial optical response with semiconductor quantum dots,” Opt. Express17(10), 8548–8551 (2009).
[CrossRef] [PubMed]

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science323(5912), 366–369 (2009).
[CrossRef] [PubMed]

S.-Y. Chiam, R. Singh, C. Rockstuhl, F. Lederer, W. Zhang, and A. A. Bettiol, “Analogue of electromagnetically induced transparency in a terahertz metamaterial,” Phys. Rev. B80(15), 153103 (2009).
[CrossRef]

2008 (3)

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics2(6), 351–354 (2008).
[CrossRef]

F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett.8(11), 3983–3988 (2008).
[CrossRef] [PubMed]

A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, “Symmetry breaking in a plasmonic metamaterial at optical wavelength,” Nano Lett.8(8), 2171–2175 (2008).
[CrossRef] [PubMed]

2007 (4)

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett.99(14), 147401 (2007).
[CrossRef] [PubMed]

M. Silveirinha and N. Engheta, “Design of matched zero-index metamaterials using nonmagnetic inclusions in epsilon-near-zero media,” Phys. Rev. B75(7), 075119 (2007).
[CrossRef]

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater. (Deerfield Beach Fla.)19(21), 3628–3632 (2007).
[CrossRef]

V. D. Lam, J. B. Kim, S. J. Lee, Y. P. Lee, and J. Y. Rhee, “Dependence of the magnetic-resonance frequency on the cut-wire width ofcut-wire pair medium,” Opt. Express15(25), 16651–16656 (2007).
[CrossRef] [PubMed]

2006 (1)

Y. S. Joe, A. M. Satanin, and C. S. Kim, “Classical analogy of Fano resonances,” Phys. Scr.74(2), 259–266 (2006).
[CrossRef]

2005 (2)

2004 (1)

R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.70(4), 046608 (2004).
[CrossRef] [PubMed]

2001 (2)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science292(5514), 77–79 (2001).
[CrossRef] [PubMed]

R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.64(5), 056625 (2001).
[CrossRef] [PubMed]

Adato, R.

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater.11(1), 69–75 (2011).
[CrossRef] [PubMed]

Altug, H.

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater.11(1), 69–75 (2011).
[CrossRef] [PubMed]

Arju, N.

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater.11(1), 69–75 (2011).
[CrossRef] [PubMed]

Bettiol, A. A.

S.-Y. Chiam, R. Singh, C. Rockstuhl, F. Lederer, W. Zhang, and A. A. Bettiol, “Analogue of electromagnetically induced transparency in a terahertz metamaterial,” Phys. Rev. B80(15), 153103 (2009).
[CrossRef]

Bitzer, A.

V. A. Fedotov, N. Papasimakis, E. Plum, A. Bitzer, M. Walther, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Spectral collapse in ensembles of metamolecules,” Phys. Rev. Lett.104(22), 223901 (2010).
[CrossRef] [PubMed]

Chiam, S.-Y.

S.-Y. Chiam, R. Singh, C. Rockstuhl, F. Lederer, W. Zhang, and A. A. Bettiol, “Analogue of electromagnetically induced transparency in a terahertz metamaterial,” Phys. Rev. B80(15), 153103 (2009).
[CrossRef]

Chin, J. Y.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science323(5912), 366–369 (2009).
[CrossRef] [PubMed]

Christ, A.

A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, “Symmetry breaking in a plasmonic metamaterial at optical wavelength,” Nano Lett.8(8), 2171–2175 (2008).
[CrossRef] [PubMed]

Cui, T. J.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science323(5912), 366–369 (2009).
[CrossRef] [PubMed]

Cui, Y.

Y. Cui, J. Xu, K. Hung Fung, Y. Jin, A. Kumar, S. He, and N. X. Fang, “A thin film broadband absorber based on multi-sized nanoantennas,” Appl. Phys. Lett.99(25), 253101 (2011).
[CrossRef]

Dolling, G.

Dorpe, P. V.

F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett.8(11), 3983–3988 (2008).
[CrossRef] [PubMed]

Ekinci, Y.

A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, “Symmetry breaking in a plasmonic metamaterial at optical wavelength,” Nano Lett.8(8), 2171–2175 (2008).
[CrossRef] [PubMed]

Engheta, N.

M. Silveirinha and N. Engheta, “Design of matched zero-index metamaterials using nonmagnetic inclusions in epsilon-near-zero media,” Phys. Rev. B75(7), 075119 (2007).
[CrossRef]

Enkrich, C.

Fang, N.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science308(5721), 534–537 (2005).
[CrossRef] [PubMed]

Fang, N. X.

Y. Cui, J. Xu, K. Hung Fung, Y. Jin, A. Kumar, S. He, and N. X. Fang, “A thin film broadband absorber based on multi-sized nanoantennas,” Appl. Phys. Lett.99(25), 253101 (2011).
[CrossRef]

Fedotov, V. A.

V. A. Fedotov, N. Papasimakis, E. Plum, A. Bitzer, M. Walther, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Spectral collapse in ensembles of metamolecules,” Phys. Rev. Lett.104(22), 223901 (2010).
[CrossRef] [PubMed]

N. Papasimakis, V. A. Fedotov, Y. H. Fu, D. P. Tsai, and N. I. Zheludev, “Coherent and incoherent metamaterials and order-disorder transitions,” Phys. Rev. B80(4), 041102 (2009).
[CrossRef]

E. Plum, V. A. Fedotov, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Towards the lasing spaser: controlling metamaterial optical response with semiconductor quantum dots,” Opt. Express17(10), 8548–8551 (2009).
[CrossRef] [PubMed]

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics2(6), 351–354 (2008).
[CrossRef]

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett.99(14), 147401 (2007).
[CrossRef] [PubMed]

Feng, Q.

Fu, L.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater. (Deerfield Beach Fla.)19(21), 3628–3632 (2007).
[CrossRef]

Fu, Y. H.

N. Papasimakis, V. A. Fedotov, Y. H. Fu, D. P. Tsai, and N. I. Zheludev, “Coherent and incoherent metamaterials and order-disorder transitions,” Phys. Rev. B80(4), 041102 (2009).
[CrossRef]

Gallinet, B.

B. Gallinet and O. J. F. Martin, “Ab initio theory of Fano resonances in plasmonic nanostructures and metamaterials,” Phys. Rev. B83(23), 235427 (2011).
[CrossRef]

Giessen, H.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett.10(7), 2342–2348 (2010).
[CrossRef] [PubMed]

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater. (Deerfield Beach Fla.)19(21), 3628–3632 (2007).
[CrossRef]

Gippius, N. A.

A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, “Symmetry breaking in a plasmonic metamaterial at optical wavelength,” Nano Lett.8(8), 2171–2175 (2008).
[CrossRef] [PubMed]

Guo, H.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater. (Deerfield Beach Fla.)19(21), 3628–3632 (2007).
[CrossRef]

Halas, N. J.

F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett.8(11), 3983–3988 (2008).
[CrossRef] [PubMed]

Hao, F.

F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett.8(11), 3983–3988 (2008).
[CrossRef] [PubMed]

He, S.

Y. Cui, J. Xu, K. Hung Fung, Y. Jin, A. Kumar, S. He, and N. X. Fang, “A thin film broadband absorber based on multi-sized nanoantennas,” Appl. Phys. Lett.99(25), 253101 (2011).
[CrossRef]

Hentschel, M.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett.10(7), 2342–2348 (2010).
[CrossRef] [PubMed]

Heyman, E.

R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.64(5), 056625 (2001).
[CrossRef] [PubMed]

Hu, C.

Huang, C.

Hung Fung, K.

Y. Cui, J. Xu, K. Hung Fung, Y. Jin, A. Kumar, S. He, and N. X. Fang, “A thin film broadband absorber based on multi-sized nanoantennas,” Appl. Phys. Lett.99(25), 253101 (2011).
[CrossRef]

Ji, C.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science323(5912), 366–369 (2009).
[CrossRef] [PubMed]

Jin, Y.

Y. Cui, J. Xu, K. Hung Fung, Y. Jin, A. Kumar, S. He, and N. X. Fang, “A thin film broadband absorber based on multi-sized nanoantennas,” Appl. Phys. Lett.99(25), 253101 (2011).
[CrossRef]

Joe, Y. S.

Y. S. Joe, A. M. Satanin, and C. S. Kim, “Classical analogy of Fano resonances,” Phys. Scr.74(2), 259–266 (2006).
[CrossRef]

Kaiser, S.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater. (Deerfield Beach Fla.)19(21), 3628–3632 (2007).
[CrossRef]

Khanikaev, A. B.

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater.11(1), 69–75 (2011).
[CrossRef] [PubMed]

C. Wu, A. B. Khanikaev, and G. Shvets, “Broadband slow light metamaterial based on a double-continuum fano resonance,” Phys. Rev. Lett.106(10), 107403 (2011).
[CrossRef] [PubMed]

Kim, C. S.

Y. S. Joe, A. M. Satanin, and C. S. Kim, “Classical analogy of Fano resonances,” Phys. Scr.74(2), 259–266 (2006).
[CrossRef]

Kim, J. B.

Koschny, T.

P. Tassin, T. Koschny, and C. M. Soukoulis, “Effective material parameter retrieval for thin sheets: Theory and application to graphene, thin silver films, and single-layer metamaterials,” Physica B407(20), 4062–4065 (2012).
[CrossRef]

Kumar, A.

Y. Cui, J. Xu, K. Hung Fung, Y. Jin, A. Kumar, S. He, and N. X. Fang, “A thin film broadband absorber based on multi-sized nanoantennas,” Appl. Phys. Lett.99(25), 253101 (2011).
[CrossRef]

Kuo, P.

V. A. Fedotov, N. Papasimakis, E. Plum, A. Bitzer, M. Walther, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Spectral collapse in ensembles of metamolecules,” Phys. Rev. Lett.104(22), 223901 (2010).
[CrossRef] [PubMed]

E. Plum, V. A. Fedotov, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Towards the lasing spaser: controlling metamaterial optical response with semiconductor quantum dots,” Opt. Express17(10), 8548–8551 (2009).
[CrossRef] [PubMed]

Lam, V. D.

Lederer, F.

S.-Y. Chiam, R. Singh, C. Rockstuhl, F. Lederer, W. Zhang, and A. A. Bettiol, “Analogue of electromagnetically induced transparency in a terahertz metamaterial,” Phys. Rev. B80(15), 153103 (2009).
[CrossRef]

Lee, H.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science308(5721), 534–537 (2005).
[CrossRef] [PubMed]

Lee, S. J.

Lee, Y. P.

Linden, S.

Liu, N.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett.10(7), 2342–2348 (2010).
[CrossRef] [PubMed]

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater. (Deerfield Beach Fla.)19(21), 3628–3632 (2007).
[CrossRef]

Liu, R.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science323(5912), 366–369 (2009).
[CrossRef] [PubMed]

Luo, X.

Ma, X.

Maier, S. A.

F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett.8(11), 3983–3988 (2008).
[CrossRef] [PubMed]

Martin, O. J. F.

B. Gallinet and O. J. F. Martin, “Ab initio theory of Fano resonances in plasmonic nanostructures and metamaterials,” Phys. Rev. B83(23), 235427 (2011).
[CrossRef]

A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, “Symmetry breaking in a plasmonic metamaterial at optical wavelength,” Nano Lett.8(8), 2171–2175 (2008).
[CrossRef] [PubMed]

Mesch, M.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett.10(7), 2342–2348 (2010).
[CrossRef] [PubMed]

Mock, J. J.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science323(5912), 366–369 (2009).
[CrossRef] [PubMed]

Nordlander, P.

F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett.8(11), 3983–3988 (2008).
[CrossRef] [PubMed]

Papasimakis, N.

V. A. Fedotov, N. Papasimakis, E. Plum, A. Bitzer, M. Walther, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Spectral collapse in ensembles of metamolecules,” Phys. Rev. Lett.104(22), 223901 (2010).
[CrossRef] [PubMed]

N. Papasimakis, V. A. Fedotov, Y. H. Fu, D. P. Tsai, and N. I. Zheludev, “Coherent and incoherent metamaterials and order-disorder transitions,” Phys. Rev. B80(4), 041102 (2009).
[CrossRef]

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics2(6), 351–354 (2008).
[CrossRef]

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett.99(14), 147401 (2007).
[CrossRef] [PubMed]

Plum, E.

V. A. Fedotov, N. Papasimakis, E. Plum, A. Bitzer, M. Walther, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Spectral collapse in ensembles of metamolecules,” Phys. Rev. Lett.104(22), 223901 (2010).
[CrossRef] [PubMed]

E. Plum, V. A. Fedotov, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Towards the lasing spaser: controlling metamaterial optical response with semiconductor quantum dots,” Opt. Express17(10), 8548–8551 (2009).
[CrossRef] [PubMed]

Prosvirnin, S. L.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics2(6), 351–354 (2008).
[CrossRef]

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett.99(14), 147401 (2007).
[CrossRef] [PubMed]

Pu, M.

Rhee, J. Y.

Rockstuhl, C.

S.-Y. Chiam, R. Singh, C. Rockstuhl, F. Lederer, W. Zhang, and A. A. Bettiol, “Analogue of electromagnetically induced transparency in a terahertz metamaterial,” Phys. Rev. B80(15), 153103 (2009).
[CrossRef]

Rose, M.

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett.99(14), 147401 (2007).
[CrossRef] [PubMed]

Satanin, A. M.

Y. S. Joe, A. M. Satanin, and C. S. Kim, “Classical analogy of Fano resonances,” Phys. Scr.74(2), 259–266 (2006).
[CrossRef]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science292(5514), 77–79 (2001).
[CrossRef] [PubMed]

Schweizer, H.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater. (Deerfield Beach Fla.)19(21), 3628–3632 (2007).
[CrossRef]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science292(5514), 77–79 (2001).
[CrossRef] [PubMed]

Shvets, G.

C. Wu and G. Shvets, “Design of metamaterial surfaces with broadband absorbance,” Opt. Lett.37(3), 308–310 (2012).
[CrossRef] [PubMed]

C. Wu, A. B. Khanikaev, and G. Shvets, “Broadband slow light metamaterial based on a double-continuum fano resonance,” Phys. Rev. Lett.106(10), 107403 (2011).
[CrossRef] [PubMed]

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater.11(1), 69–75 (2011).
[CrossRef] [PubMed]

Silveirinha, M.

M. Silveirinha and N. Engheta, “Design of matched zero-index metamaterials using nonmagnetic inclusions in epsilon-near-zero media,” Phys. Rev. B75(7), 075119 (2007).
[CrossRef]

Singh, R.

S.-Y. Chiam, R. Singh, C. Rockstuhl, F. Lederer, W. Zhang, and A. A. Bettiol, “Analogue of electromagnetically induced transparency in a terahertz metamaterial,” Phys. Rev. B80(15), 153103 (2009).
[CrossRef]

Smith, D. R.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science323(5912), 366–369 (2009).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science292(5514), 77–79 (2001).
[CrossRef] [PubMed]

Sonnefraud, Y.

F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett.8(11), 3983–3988 (2008).
[CrossRef] [PubMed]

Soukoulis, C. M.

P. Tassin, T. Koschny, and C. M. Soukoulis, “Effective material parameter retrieval for thin sheets: Theory and application to graphene, thin silver films, and single-layer metamaterials,” Physica B407(20), 4062–4065 (2012).
[CrossRef]

G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett.30(23), 3198–3200 (2005).
[CrossRef] [PubMed]

Sun, C.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science308(5721), 534–537 (2005).
[CrossRef] [PubMed]

Tassin, P.

P. Tassin, T. Koschny, and C. M. Soukoulis, “Effective material parameter retrieval for thin sheets: Theory and application to graphene, thin silver films, and single-layer metamaterials,” Physica B407(20), 4062–4065 (2012).
[CrossRef]

Tikhodeev, S. G.

A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, “Symmetry breaking in a plasmonic metamaterial at optical wavelength,” Nano Lett.8(8), 2171–2175 (2008).
[CrossRef] [PubMed]

Tsai, D. P.

V. A. Fedotov, N. Papasimakis, E. Plum, A. Bitzer, M. Walther, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Spectral collapse in ensembles of metamolecules,” Phys. Rev. Lett.104(22), 223901 (2010).
[CrossRef] [PubMed]

N. Papasimakis, V. A. Fedotov, Y. H. Fu, D. P. Tsai, and N. I. Zheludev, “Coherent and incoherent metamaterials and order-disorder transitions,” Phys. Rev. B80(4), 041102 (2009).
[CrossRef]

E. Plum, V. A. Fedotov, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Towards the lasing spaser: controlling metamaterial optical response with semiconductor quantum dots,” Opt. Express17(10), 8548–8551 (2009).
[CrossRef] [PubMed]

Walther, M.

V. A. Fedotov, N. Papasimakis, E. Plum, A. Bitzer, M. Walther, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Spectral collapse in ensembles of metamolecules,” Phys. Rev. Lett.104(22), 223901 (2010).
[CrossRef] [PubMed]

Wang, C.

Wang, M.

Wegener, M.

Weiss, T.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett.10(7), 2342–2348 (2010).
[CrossRef] [PubMed]

Wu, C.

C. Wu and G. Shvets, “Design of metamaterial surfaces with broadband absorbance,” Opt. Lett.37(3), 308–310 (2012).
[CrossRef] [PubMed]

C. Wu, A. B. Khanikaev, and G. Shvets, “Broadband slow light metamaterial based on a double-continuum fano resonance,” Phys. Rev. Lett.106(10), 107403 (2011).
[CrossRef] [PubMed]

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater.11(1), 69–75 (2011).
[CrossRef] [PubMed]

Xu, J.

Y. Cui, J. Xu, K. Hung Fung, Y. Jin, A. Kumar, S. He, and N. X. Fang, “A thin film broadband absorber based on multi-sized nanoantennas,” Appl. Phys. Lett.99(25), 253101 (2011).
[CrossRef]

Yanik, A. A.

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater.11(1), 69–75 (2011).
[CrossRef] [PubMed]

Zhang, W.

S.-Y. Chiam, R. Singh, C. Rockstuhl, F. Lederer, W. Zhang, and A. A. Bettiol, “Analogue of electromagnetically induced transparency in a terahertz metamaterial,” Phys. Rev. B80(15), 153103 (2009).
[CrossRef]

Zhang, X.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science308(5721), 534–537 (2005).
[CrossRef] [PubMed]

Zhao, Z.

Zheludev, N. I.

V. A. Fedotov, N. Papasimakis, E. Plum, A. Bitzer, M. Walther, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Spectral collapse in ensembles of metamolecules,” Phys. Rev. Lett.104(22), 223901 (2010).
[CrossRef] [PubMed]

N. Papasimakis, V. A. Fedotov, Y. H. Fu, D. P. Tsai, and N. I. Zheludev, “Coherent and incoherent metamaterials and order-disorder transitions,” Phys. Rev. B80(4), 041102 (2009).
[CrossRef]

E. Plum, V. A. Fedotov, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Towards the lasing spaser: controlling metamaterial optical response with semiconductor quantum dots,” Opt. Express17(10), 8548–8551 (2009).
[CrossRef] [PubMed]

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics2(6), 351–354 (2008).
[CrossRef]

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett.99(14), 147401 (2007).
[CrossRef] [PubMed]

Zhou, J. F.

Ziolkowski, R. W.

R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.70(4), 046608 (2004).
[CrossRef] [PubMed]

R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.64(5), 056625 (2001).
[CrossRef] [PubMed]

Adv. Mater. (Deerfield Beach Fla.) (1)

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater. (Deerfield Beach Fla.)19(21), 3628–3632 (2007).
[CrossRef]

Appl. Phys. Lett. (1)

Y. Cui, J. Xu, K. Hung Fung, Y. Jin, A. Kumar, S. He, and N. X. Fang, “A thin film broadband absorber based on multi-sized nanoantennas,” Appl. Phys. Lett.99(25), 253101 (2011).
[CrossRef]

Nano Lett. (3)

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett.10(7), 2342–2348 (2010).
[CrossRef] [PubMed]

F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett.8(11), 3983–3988 (2008).
[CrossRef] [PubMed]

A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, “Symmetry breaking in a plasmonic metamaterial at optical wavelength,” Nano Lett.8(8), 2171–2175 (2008).
[CrossRef] [PubMed]

Nat. Mater. (1)

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater.11(1), 69–75 (2011).
[CrossRef] [PubMed]

Nat. Photonics (1)

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics2(6), 351–354 (2008).
[CrossRef]

Opt. Express (3)

Opt. Lett. (3)

Phys. Rev. B (4)

S.-Y. Chiam, R. Singh, C. Rockstuhl, F. Lederer, W. Zhang, and A. A. Bettiol, “Analogue of electromagnetically induced transparency in a terahertz metamaterial,” Phys. Rev. B80(15), 153103 (2009).
[CrossRef]

B. Gallinet and O. J. F. Martin, “Ab initio theory of Fano resonances in plasmonic nanostructures and metamaterials,” Phys. Rev. B83(23), 235427 (2011).
[CrossRef]

N. Papasimakis, V. A. Fedotov, Y. H. Fu, D. P. Tsai, and N. I. Zheludev, “Coherent and incoherent metamaterials and order-disorder transitions,” Phys. Rev. B80(4), 041102 (2009).
[CrossRef]

M. Silveirinha and N. Engheta, “Design of matched zero-index metamaterials using nonmagnetic inclusions in epsilon-near-zero media,” Phys. Rev. B75(7), 075119 (2007).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (2)

R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.70(4), 046608 (2004).
[CrossRef] [PubMed]

R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.64(5), 056625 (2001).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

V. A. Fedotov, N. Papasimakis, E. Plum, A. Bitzer, M. Walther, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Spectral collapse in ensembles of metamolecules,” Phys. Rev. Lett.104(22), 223901 (2010).
[CrossRef] [PubMed]

C. Wu, A. B. Khanikaev, and G. Shvets, “Broadband slow light metamaterial based on a double-continuum fano resonance,” Phys. Rev. Lett.106(10), 107403 (2011).
[CrossRef] [PubMed]

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett.99(14), 147401 (2007).
[CrossRef] [PubMed]

Phys. Scr. (1)

Y. S. Joe, A. M. Satanin, and C. S. Kim, “Classical analogy of Fano resonances,” Phys. Scr.74(2), 259–266 (2006).
[CrossRef]

Physica B (1)

P. Tassin, T. Koschny, and C. M. Soukoulis, “Effective material parameter retrieval for thin sheets: Theory and application to graphene, thin silver films, and single-layer metamaterials,” Physica B407(20), 4062–4065 (2012).
[CrossRef]

Science (3)

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science323(5912), 366–369 (2009).
[CrossRef] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science308(5721), 534–537 (2005).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science292(5514), 77–79 (2001).
[CrossRef] [PubMed]

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Figures (10)

Fig. 1
Fig. 1

(a) Schematic of the wire pairs with perturbed periodicity. The grey, orange, and red colors depict different widths. (b) Sketch map of the surface current distributions for the two subradiant modes.

Fig. 2
Fig. 2

Transmission coefficients for the symmetric and asymmetric metamaterial slabs. Two regions are highlighted. Region I shows typical asymmetric line shape of Fano resonance. Region II demonstrates the ultra-sharp resonance peak induced by inter-element coupling.

Fig. 3
Fig. 3

Schematic of sheet impedance description for thin metamaterial. The magnetic and electric responses are described by equivalent magnetic and electric sheet currents.

Fig. 4
Fig. 4

(a) The electric admittance and (b) magnetic impedance of the symmetric structure (w1 = w2 = w3 = 4 mm). (c) The transmission coefficients for the real structure and pure magnetic impedance. The fitted magnetic impedance using LC circuit model is also shown in (b).

Fig. 5
Fig. 5

(a) Electric admittance and (b) electric sheet current for the asymmetric structure. (c) The corresponding magnetic impedance and (d) magnetic sheet current.

Fig. 6
Fig. 6

(a) Amplitudes and (b) phases of the effective magnetic sheet current calculated using Eq. (5). The fitted parameters of inductances and capacitors are used (see text). The three frequencies where the phase changes occur are highlighted. At theses frequencies, the corresponding amplitudes are zero.

Fig. 7
Fig. 7

(a) Normalized magnetic fields (Hz) at the center of these resonators. The inset shows the unit cell and the points where the magnetic fields are extracted. (b)(c)(d)(e)(f) Magnetic field distributions at frequencies of f1 = 8 GHz, f2 = 9.79 GHz, f3 = 10.77GHz, f4 = 10.82 GHz and f5 = 10.87 GHz.

Fig. 8
Fig. 8

Transmission spectrum of the metamaterial slab for different asymmetry. Here the geometrical parameters are w1 = w2 = 4 mm, while w3 is variable.

Fig. 9
Fig. 9

(a) Reflection (r), transmission (t) and absorbance (1-r2-t2) of the lossy metamaterial slab. (b) Normalized magnetic fields extracted from Comsol Multiphysics.

Fig. 10
Fig. 10

Absorption of the wideband absorber for different angles of incidence. The absorption for the symmetric structure is also shown for comparison. Inset is schematic of the absorber which is composed of asymmetric wires and a metallic ground plane.

Equations (13)

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E i + E r = E t + n ^ × j m , H i + H r = H t + n ^ × j e .
j e = 1 Z e E average = Y e E average = Y e (1+r+t) E i /2, j m = Z m H average = Z m (1r+t) H i /2.
Y e =2 Y 0 1rt 1+r+t , Z m =2 Z 0 1+rt 1r+t ,
r= 1 2 ( 2 Y 0 Y e 2 Y 0 + Y e + Z m 2 Z 0 Z m +2 Z 0 ), t= 1 2 ( 2 Y 0 Y e 2 Y 0 + Y e Z m 2 Z 0 Z m +2 Z 0 ),
j e = 2 Y 0 Y e 2 Y 0 + Y e E i , j m = 2 Z 0 Z m Z m +2 Z 0 H i .
Z m = 1 1/(iωL)+iωC = iωL 1 ω 2 LC ,
Z m = n=1 3 Z mn = n=1 3 iω L n 1 ω 2 L n C n .
j m = n=1 3 j mn ,
j mn = 2 Z 0 Z mn Z m +2 Z 0 H i , n=1,2,3.
j m1 Z 0 H i j m2 = i L 2 L 3 ( L 2 + L 3 )( C 2 + C 3 ) L 3 C 3 L 2 C 2 H i . j m3 = j m2 = i L 2 L 3 ( L 2 + L 3 )( C 2 + C 3 ) L 2 C 2 L 3 C 3 H i
E i + E r E t = n ^ × j m L E d l = d dt s B d S
n ^ × j m L= d dt ( B LΔ),
| H z |= | j m | iω μ 0 Δ .

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