OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 16 — Aug. 12, 2013
  • pp: 19228–19239
« Show journal navigation

Enhancement of Fano resonance in metal/dielectric/metal metamaterials at optical regime

Tun Cao and Lei Zhang  »View Author Affiliations


Optics Express, Vol. 21, Issue 16, pp. 19228-19239 (2013)
http://dx.doi.org/10.1364/OE.21.019228


View Full Text Article

Acrobat PDF (1828 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Fano resonance (FR) within the transmission spectrum is demonstrated in the near infrared (NIR) region using elliptical nanoholes array (ENA) embedding through metal-dielectric-metal (MDM) layers. For the symmetric MDM-ENA, it has been shown that a FR can be excited by the normally incident light. This FR response is attributed to the interplay between the bright modes and dark modes, where the bright modes originate from the electric resonance (localized surface plasmon resonance) caused by the ENA and the dark modes are due to the magnetic resonance (inductive-capacitive resonance) induced by the MDM multilayers. Displacement of the elliptical nanoholes from their centers breaks the structural symmetry to excite a double FR as a result of the coherent interaction of the electric resonance with two splitting sub-magnetic resonances at different wavelengths. Moreover,the degree of the asymmetry allows for the tuning of the amplitude and bandwidth of the double FR window. The sensitivity to the slight variations of the dielectric environment has been calculated and yields a figure-of-merit of 0.8RIU−1 for the symmetric MDM-ENA and 3.0RIU−1 for the asymmetric MDM-ENA.

© 2013 OSA

1. Introduction

Metamaterials (MMs) are manmade engineered material to exhibit fascinating optical properties not occurring in nature, such as negative refractive index [1

1. J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]

4

4. C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics 5, 523–530 (2011).

], perfect lens [5

5. 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]

,6

6. 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]

], electromagnetic cloaking [7

7. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006). [CrossRef] [PubMed]

,8

8. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006). [CrossRef] [PubMed]

],extraordinary transmission [9

9. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]

] and asymmetric transmission [10

10. V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric Propagation of Electromagnetic Waves through a Planar Chiral Structure,” Phys. Rev. Lett. 97(16), 167401 (2006). [CrossRef] [PubMed]

].Recently, MMs have become a flourishing research in the terahertz domain demonstrating application potential in sensing [11

11. N. Soltani, É. Lheurette, and D. Lippens, “Wood anomaly transmission enhancement in fishnet-based metamaterials at terahertz frequencies,” J. Appl. Phys. 112(12), 124509 (2012). [CrossRef]

]. In order to make MMs perform efficiently on biological sensing, a resonance with a high quality factor (defined by the resonant frequency over width of the resonance) is desired [12

12. Y. Ma, Z. Li, Y. Yang, R. Huang, R. Singh, S. Zhang, J. Gu, Z. Tian, J. Han, and W. Zhang, “Plasmon-induced transparency in twisted Fano terahertz metamaterials,” Opt. Mater. Express 1(3), 391–399 (2011). [CrossRef]

,13

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]

].However, conventional planar MMs normally have a modest Q factor due to the rather small volume confinement of electromagnetic fields and strong coupling to vacuum [14

14. M. Pu, C. Hu, C. Huang, C. Wang, Z. Zhao, Y. Wang, and X. Luo, “Investigation of Fano resonance in planar metamaterial with perturbed periodicity,” Opt. Express 21(1), 992–1001 (2013). [CrossRef] [PubMed]

16

16. R. Singh, I. A. I. Al-Naib, M. Koch, and W. Zhang, “Sharp Fano resonances in THz metamaterials,” Opt. Express 19(7), 6312–6319 (2011). [CrossRef] [PubMed]

].Fano resonance (FR) is attributed to the interference of bright (radiating) and dark (non radiating) modes [17

17. N. Papasimakis, V. A. Fedotov, N. I. Zheludev, and S. L. Prosvirnin, “Metamaterial Analog of Electromagnetically Induced Transparency,” Phys. Rev. Lett. 101(25), 253903 (2008). [CrossRef] [PubMed]

21

21. 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]

] and possessing a sharp feature in the transmission spectrum [22

22. P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Low-Loss Metamaterials Based on Classical Electromagnetically Induced Transparency,” Phys. Rev. Lett. 102(5), 053901 (2009). [CrossRef] [PubMed]

].Therefore, the problem of the low sensitivity in MMs sensor can be tackled if MM structural design is engineered in such a way that it could support FRs. FRs were originally considered in the photonics structures such as dielectric photonic crystal slabs [23

23. S. Fan, “Sharp asymmetric line shapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett. 80(6), 908–910 (2002). [CrossRef]

27

27. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59(24), 15882–15892 (1999). [CrossRef]

] and perforated metal films (in the context of extraordinary optical transmission) [28

28. K. A. Tetz, L. Pang, and Y. Fainman, “High-resolution surface plasmon resonance sensor based on linewidth-optimized nanohole array transmittance,” Opt. Lett. 31(10), 1528–1530 (2006). [CrossRef] [PubMed]

]. Another way to obtain FRs is to break the symmetry of MMs [29

29. B. Lahiri, A. Z. Khokhar, R. M. De La Rue, S. G. McMeekin, and N. P. Johnson, “Asymmetric split ring resonators for optical sensing of organic materials,” Opt. Express 17(2), 1107–1115 (2009). [CrossRef] [PubMed]

]. By introducing an asymmetry in the shape of the MM structural element, dark modes (trapped modes) which are not accessible in the symmetric MMs can be evoked [21

21. 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]

]. These dark mode resonances weakly couple to free space and strongly interact with the bright modes thus giving rise to a FR with a steep dispersion.This FR is able to concentrate the electromagnetic field in a small region to interact with the matter strongly, making it suitable for sensitively sensing [30

30. S. A. Maier, “Plasmonics: The Benefits of darkness,” Nat. Mater. 8(9), 699–700 (2009). [CrossRef] [PubMed]

]. Alternatively, FR can also be achieved by the coupling between symmetric and anti-symmetric resonance in symmetric MMs [31

31. N. Papasimakis, Y. H. Fu, V. A. Fedotov, S. L. Prosvirnin, D. P. Tsai, and N. I. Zheludev, “Metamaterial with polarization and direction insensitive resonant transmission response mimicking electromagnetically induced transparency,” Appl. Phys. Lett. 94(21), 211902 (2009). [CrossRef]

]. However, most of the works demonstrate FRs in planar MMs based on a single metallic layer. It has been suggested that multiple layers of perforated metal–dielectric-metal(MDM) stacks (for 100 and 200 layers) along the propagation direction established a promising approach for a three dimensional (3D) optical MM [32

32. S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. Brueck, “Optical negative-index bulk metamaterials consisting of 2D perforated metal-dielectric stacks,” Opt. Express 14(15), 6778–6787 (2006). [CrossRef] [PubMed]

34

34. N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. 7(1), 31–37 (2008). [CrossRef] [PubMed]

].Such a 3D MM can possess a thickness much larger than the free space wavelength in the near infrared(NIR) region and excite a strong magneto-inductive coupling between neighboring functional layers under a normally incident light [33

33. J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008). [CrossRef] [PubMed]

].The tight coupling between adjacent LC resonators through mutual inductance results in a low loss [35

35. T. Li, H. Liu, F. M. Wang, Z. G. Dong, S. N. Zhu, and X. Zhang, “Coupling effect of magnetic polariton in perforated metal/dielectric layered metamaterials and its influence on negative refraction transmission,” Opt. Express 14(23), 11155–11163 (2006). [CrossRef] [PubMed]

].Therefore, achievement of 3D multilayer MMs is an inevitable requirement for nearly all possible applications, like cloaking and invisible materials [33

33. J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008). [CrossRef] [PubMed]

36

36. J. Yang, C. Sauvan, H. T. Liu, and P. Lalanne, “Theory of fishnet negative-index optical metamaterials,” Phys. Rev. Lett. 107(4), 043903 (2011). [CrossRef] [PubMed]

], the observation of FRs [37

37. B. Seo, K. Kim, S. G. Kim, A. Kim, H. Cho, and E. M. Choi, “Observation of trapped-modes excited in double-layered symmetric electric ring resonators,” J. Appl. Phys. 111(11), 113106 (2012). [CrossRef]

] as well as tunable metamaterials [38

38. A. Minovich, D. N. Neshev, D. A. Powell, I. V. Shadrivov, and Y. S. Kivshar, “Tunable fishnet metamaterials infiltrated by liquid crystals,” Appl. Phys. Lett. 96(19), 193103 (2010). [CrossRef]

].

As discussed above, multilayer MMs have strong magnetic responses which can be described by effective magnetic dipoles. In detail, giant magnetic dipolar moments are emerged inside the dielectric interlayer with the formation of closed displacement current (JD) loops [39

39. T. Cao and M. J. Cryan, “Study of incident angle dependence for dual-band double negative-index material using elliptical nanohole arrays,” J. Opt. Soc. Am. A 29(3), 209–215 (2012). [CrossRef] [PubMed]

,40

40. Y. G. Ma, L. Zhao, P. Wang, and C. K. Ong, “Fabrication of negative index materials using dielectric and metallic composite route,” Appl. Phys. Lett. 93(18), 184103 (2008). [CrossRef]

].This phenomenon especially shows the possibility of attaining the double negative index material [41

41. S. Zhang, W. Fan, K. J. Malloy, S. R. J. Brueck, N. C. Paniou, and R. M. Osgood, “Demonstration of metal–dielectric negative index metamaterials with improved performance at optical frequencies,” J. Opt. Soc. Am. B 23(3), 434–438 (2006). [CrossRef]

]. Most notably, several recent works show that magnetic activity in multilayer MMs is also capable of exciting FR. Seo et al. have shown that a FR can be observed in double layer symmetric electric ring resonators at GHz regime [37

37. B. Seo, K. Kim, S. G. Kim, A. Kim, H. Cho, and E. M. Choi, “Observation of trapped-modes excited in double-layered symmetric electric ring resonators,” J. Appl. Phys. 111(11), 113106 (2012). [CrossRef]

]. Soltani et al. have investigated a MDM mulilayer MM with half ellipse patterns, exhibiting a sharp FR around 1THz [11

11. N. Soltani, É. Lheurette, and D. Lippens, “Wood anomaly transmission enhancement in fishnet-based metamaterials at terahertz frequencies,” J. Appl. Phys. 112(12), 124509 (2012). [CrossRef]

]. It is realistic and well known that broken symmetry of the planar MM structures can result in a high order mode thus enhancing the FRs [42

42. R. Singh, I. A. I. Al-Naib, Y. Yang, D. R. Chowdhury, W. Cao, C. Rockstuhl, T. Ozaki, R. Morandotti, and W. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011). [CrossRef]

].However, to the best of our knowledge, limited research work looks at the influence of the symmetry breaking in MDM multilayer MMs on the FRs, specifically in the NIR regime considering the potential of the NIR spectrum for sensing.

Here, we numerically present that a FR in the NIR region can be observed from the symmetric elliptical nanoholes array (ENA) embedding through metal-dielectric-metal layers. This FR response is caused by the interaction between the bright modes and the dark modes. Particularly, the elliptical nanoholes resonator array shows an electric resonance (localized surface plasmon) to excite the bright modes whereas the MDM multilayers support a magnetic resonance (inductive-capacitive resonance) to induce the dark modes [43

43. J. Q. Wang, C. Z. Fan, J. N. He, P. Ding, E. J. Liang, and Q. Z. Xue, “Double Fano resonances due to interplay of electric and magnetic plasmon modes in planar plasmonic structure with high sensing sensitivity,” Opt. Express 21(2), 2236–2244 (2013). [CrossRef] [PubMed]

,44

44. J. Q. Gu, R. J. Singh, X. J. Liu, X. Q. Zhang, Y. F. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. T. Chen, A. J. Taylor, J. G. Han, and W. L. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat Commun 3, 1151 (2012). [CrossRef] [PubMed]

].As soon as the elliptical holes are displaced from their central positions, the single magnetic resonance would be divided into two magnetic resonances at different wavelengths, and a double FR appears owing to the destructive interference between the electric resonance and two magnetic resonances at different wavelengths. This interference leads to a sharp transparency peak for the asymmetric MDM-ENA. Moreover, the degree of the asymmetry allows for the tuning of the amplitude and bandwidth of the double FR window. The sensing capabilities of both the symmetric MDM-ENA and asymmetric MDM-ENA are evaluated through the sensing sensitivity and figure-of-merit (FOM). Our proposed structure possesses a simple geometry which remains compatible with standard photolithography patterning and can be easily experimentally realized at the optical region.

2. Metamaterials design

The proposed MM structures are developed from our previously studied double negative index MMs at optical regime [39

39. T. Cao and M. J. Cryan, “Study of incident angle dependence for dual-band double negative-index material using elliptical nanohole arrays,” J. Opt. Soc. Am. A 29(3), 209–215 (2012). [CrossRef] [PubMed]

] consisting of a two metallic films (30nm thick Au) separated by a dielectric interlayer (60nm thick Al2O3). Here, we simulate two sets of multilayer MMs starting from a symmetric element with both the top and bottom elliptical holes exactly at the centre [see Fig. 1(a)-(b)
Fig. 1 (a) Schematic of the symmetric MDM structure consisting of a 60nm thick Al2O3 dielectric layer between two 30nm thick Au films perforated with a square array of elliptical holes residing on a 200μm thick BK7 glass. (b) Illustration of the symmetric element of ENA, the lattice constant is L = 400nm and hole diameters are d1 = 260nm, d2 = 160nm. (c) Schematic of the asymmetric MDM structure consisting of a 60nm thick Al2O3 dielectric layer between two 30nm thick Au films perforated with a square array of elliptical holes residing on a 200μm thick BK7 glass. (d) Illustration of the asymmetric element of ENA, the lattice constant is L = 400nm, hole diameters are d1 = 260nm, d2 = 160nm, δ is the distance of the upper elliptical hole from the centre. (e) Schematic of the symmetric structure consisting of a 30nm thick Au film perforated with a square array of elliptical holes residing on a 200μm thick BK7 glass. (f) Illustration of the symmetric element of ENA, the lattice constant is L = 400nm and hole diameters are d1 = 260nm, d2 = 160nm.
] and then gradually displaced the upper elliptical hole from the centre by a distance “δ” while keeping the lower elliptical hole fixed at the centre in order to break the symmetry [see Fig. 1(c)-(d)]. For both of the structures, the elliptical nanoholes array (ENA) (lattice constant, L = 400nm; hole diameters, d1 = 260nm, d2 = 160nm) has been perforated through the entire Au/Al2O3/Au structure, β is a cross-section plane of the structure, and the elliptical holes are periodically arranged in both the x and y directions. The Au bottom layer interacts with the upper Au layer to give rise to a closed loop of displacement current (JD) and localize an electromagnetic (EM) field within the dielectric interlayer. The two structures both reside on a 200μm thick BK7 glass. Au is selected as the metal due to its stability and low ohmic loss. The geometry of the unit cell pattern and the thickness of the sandwich layers have been chosen to allow for the impedance matching between the metamaterials and impinging plane wave [45

45. J. Carbonell, C. Croënne, F. Garet, E. Lheurette, J. L. Coutaz, and D. Lippens, “Lumped elements circuit of terahertz fishnet-like arrays with composite dispersion,” J. Appl. Phys. 108(1), 014907 (2010). [CrossRef]

]. In order to justify the influence of magnetic activity on the FR, we have simulated the identical lateral structure to the symmetrical MDM-MMs, however, with a single metal layer (30nm Au) as shown in Fig. 1(e)-(f). The optical properties of the structures are calculated using 3D EM Explorer Studio [46], a commercial Finite Difference Time Domain (FDTD) code. In the simulation, the dielectric properties of Au are described by a drude-type dielectric function, where ωp = 1.37x1016 Hz is the plasma frequency and ωc = 4.08x1013 Hz is the collision frequency for bulk Au [47

47. S. Zhang, W. J. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005). [CrossRef] [PubMed]

]. A plane wave source is simulated at normal incidence to the structure with the electric field direction along the small axis of the elliptical hole. The computational domain (400 nm × 800 nm × 1000 nm) has perfectly match layer (PML), absorbing boundaries, in the z direction and periodic boundaries in the x-y plane [48

48. J. P. Berenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 127(2), 363–379 (1996). [CrossRef]

]. A uniform FDTD mesh size is adopted, the mesh size is the same along all Cartesian axes: ∆x = ∆y = ∆z = 2nm, which is sufficient to minimize the numerical errors arising from the FDTD method.

3. Results and discussions

The ENA has a lower transmission for s polarized light due to the electric field’s orientation with respect to the metallic stripe width hence the polarization of the incident wave was set to be p polarized [39

39. T. Cao and M. J. Cryan, “Study of incident angle dependence for dual-band double negative-index material using elliptical nanohole arrays,” J. Opt. Soc. Am. A 29(3), 209–215 (2012). [CrossRef] [PubMed]

]. Here s polarization means the incident electric field vector is parallel to the long axis of the ENA and p polarization means that the incident electric field vector is parallel to the short axis of the ENA. Figure 2
Fig. 2 3D- FDTD simulation of the transmission spectrum of the symmetric multilayer ENA [see Fig. 1(a)] and its reference structure consisting of the identical ENA embedded through single Au layer [see Fig. 1(e)] for p polarization at normal incidence.
shows the transmissions for both the symmetric MDM-ENA [see Fig. 1(a)] and its reference structure consisting of the identical ENA embedding through a single Au layer [see Fig. 1(e)].In the transmission of the multilayer structure, it is seen that a FR appears at the wavelength of 1284nm [marked as P1 in Fig. 2] possessing a resonance linewidth of 77nm and Q factor of 21,the detailed calculation of which is presented in Section 4. Whereas the single layer ENA structure doesn't have a FR response under the normally incident light owing to the absence of the magnetic dipole resonance. Therefore, the origin of the FR in the symmetric MDM-ENA can be traced to the interaction between the electric resonance and the magnetic resonance, formed by closed loops of displacement current(JD) [40

40. Y. G. Ma, L. Zhao, P. Wang, and C. K. Ong, “Fabrication of negative index materials using dielectric and metallic composite route,” Appl. Phys. Lett. 93(18), 184103 (2008). [CrossRef]

]. Such a magnetic resonance is normally inaccessible but can be excited if, for example, the MMs are based on metal/dielectric/metal films.

To gain further understanding on the nature of the resonance, we look at total electric field intensity distributionsE=|Ex|2+|Ey|2+|Ez|2, total magnetic field intensity distributions H=|Hx|2+|Hy|2+|Hz|2 and JD along the β plane at the resonant wavelength of 1284nm for the symmetric MDM-ENA in Fig. 3(a)-(b)
Fig. 3 3D- FDTD simulation of (a) total electric field intensity distribution, (b) total magnetic field intensity distribution and JD distribution along β plane for the symmetric MDM-ENA, at normal incident angle where λ = 1284nm; Simulation of (c) total electric field intensity distribution, (d) total magnetic field intensity distribution and JD distribution for the symmetric single layer ENA at normal incident angle where λ = 1284nm
, and for the single Au layer ENA in Fig. 3(c)-(d). In the field maps of Fig. 3, the arrows show JD, whereas the colour shows the magnitude of the electric field and magnetic field. In Fig. 3(b), the formation of the closed JD loops is observed to support a magnetic resonance at which light is trapped and strongly absorbed thus the magnetic field can be efficiently confined between two Au layers. However, Fig. 3(a) shows a relatively low concentration of the electric field intensity in the dielectric interlayer and elliptical apertures, indicating a weak electric resonance. The FR (P1) in the symmetric MDM-ENA is caused by the interaction between the bright modes and the dark modes. Particularly, at the wavelength of 1284nm, the ENA resonator shows an electric resonance namely localized surface plasmon resonance whereas the MDM multilayers support a magnetic resonance stemming from the retardation of the wave propagating in the dielectric spacer namely inductive-capacitive resonance [49

49. Ş. E. Kocabaş, G. Veronis, D. A. B. Miller, and S. Fan, “Modal analysis and coupling in metal-insulator-metal waveguides,” Phys. Rev. B 79(3), 035120 (2009). [CrossRef]

].Thus, the ENA resonator and the MDM multilayers serve as the bright modes and dark modes, respectively. Once the configuration changes to the single Au layer in Fig. 3 (c)-(d), it shows that H cannot be trapped in the metal layer since the loops of JD no longer exist hence showing no FR response in the transmission spectrum. To excite the magnetic resonance of such a planar ENA, one may use an oblique incident light which possesses the required magnetic field component [50

50. W. T. Chen, C. J. Chen, P. C. Wu, S. Sun, L. Zhou, G. Y. Guo, C. T. Hsiao, K. Y. Yang, N. I. Zheludev, and D. P. Tsai, “Optical magnetic response in three-dimensional metamaterial of upright plasmonic meta-molecules,” Opt. Express 19(13), 12837–12842 (2011). [CrossRef] [PubMed]

52

52. O. Paul, C. Imhof, B. Reinhard, R. Zengerle, and R. Beigang, “Negative index bulk metamaterial at terahertz frequencies,” Opt. Express 16(9), 6736–6744 (2008). [CrossRef] [PubMed]

]. This restriction will lower the coupling efficiency between the magnetic field of the incident light and the resonant element.

Figure 4
Fig. 4 3D-FDTD simulation of the transmission spectrums of symmetric MDM-ENA [see Fig. 1(a)] and asymmetric MDM- ENA [see Fig. 1(c)] for p polarization at normal incidence.
presents the transmissions of the symmetric MDM-ENA and the asymmetric MDM-ENA. Starting from the symmetric MDM-ENA (δ = 0), where only a single FR (P1) is observed at λ = 1284nm, we move to an asymmetric MDM-ENA with δ = 60nm [see Fig. 1(c)]. As can be seen, the single FR (P1) is split in two distinct resonant peaks at 1300nm (marked as P2) and 1228nm (marked as P4) by an asymmetric resonant dip (marked as P3) at 1252nm. Namely, the single magnetic resonance at λ = 1284nm would be divided into two magnetic resonances at different wavelengths of 1228nm and 1300nm by breaking the structural symmetry. The appearance of the double FR is due to the destructive interference between the electric resonance and two magnetic resonances at different wavelengths. In particular, the transmission dip is due to the excitation of the dark mode with a weak coupling to free space, created by a certain weak structural asymmetry of the elements of MMs [19

19. S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008). [CrossRef] [PubMed]

]. As can be seen in Section 4, a narrow transparency sub-band resonance window with a spectral width of 42nm is achieved at P2 mode resulting in a high Q factor of 34.

Figure 5(a)-(f)
Fig. 5 3D-FDTD simulation of (a) total electric field intensity distribution, (b) total magnetic field intensity distribution and JD distribution along β plane for the symmetric multilayer ENA, where λ = 1284nm; Simulation of (c) total electric field intensity distribution, (d) total magnetic field intensity distribution and JD distribution for the asymmetric multilayer ENA where λ = 1300nm. (e) total electric field intensity distribution, (f) total magnetic field intensity distribution and JD distribution for the asymmetric multilayer ENA where λ = 1228nm.
describe the distribution of E field intensity, H field intensity and JD along the β plane at the resonant wavelengths of 1284nm (P1) for the symmetric MDM-ENA and at 1300nm (P2) and 1228nm (P4) for the asymmetric MDM-ENA, respectively. It is obvious that the P2 and P4 modes correspond to different magnetic dipole resonances. Figure 5(c) shows that E field intensity at the P2 mode is efficiently concentrated in both the dielectric interlayer and the elliptical apertures thus giving rise to the strongest electric resonance. As can be seen, the H field intensity distributions are confined well within the dielectric layer for both P1 [see Fig. 5(b)] and P2 modes [see Fig. 5(d)].However, H field intensity at P2 mode is higher than the P1 mode indicating the larger magnetic dipole resonance. Thus, at the P2 mode of the asymmetric MDM-ENA, the interaction of the enhanced magnetic resonances and electric resonances leads to a much narrower FR than the P1 mode of the symmetric MDM-ENA. In Fig. 5(e)-(f), we present the distributions of E field, H field and JD associated with the P4 mode, it demonstrates that the closed JD loops are still maintained to provide the magnetic dipolar moment hence leading to a resonant peak. However, the resonance is broadened owing to the weak magnetic and electric resonances resulted from the low strength of H and E fields in both the dielectric layer and elliptical apertures.

Figure 6
Fig. 6 3D-FDTD simulation of spectrum of transmission of asymmetric multilayer ENA for different values of δ from 10nm to 60nm at normal incidence.
depicts the calculated transmission for different values of from 10nm to 60nm where the splitting of the single resonant peak at λ = 1284nm is observed when the upper elliptical hole's center is shifted by a distance of δ = 20nm. In this graph, the vertical axis describes the center shift of the top elliptical hole as a function of the parameter δ. As the distance δ is increased, the splitting of the resonant peak leading to a transmission dip in the spectrum around 1252nm becomes more obvious since the resonant dip window broadens and its amplitude nearly reaches 0. It can be explained by the fact that the asymmetry increases the free-space coupling and consequently the mode energy losses. Moreover, the asymmetry parameter “δ” leads to the broadening and enhancement on the transmission dip window centered around the same wavelength of 1252nm hence playing a control role in the structure [42

42. R. Singh, I. A. I. Al-Naib, Y. Yang, D. R. Chowdhury, W. Cao, C. Rockstuhl, T. Ozaki, R. Morandotti, and W. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011). [CrossRef]

].

4. Fano formula fitting to the transmission spectrums simulated through FDTD method

In Fig. 7
Fig. 7 (a) 3D-FDTD simulation of the transmission spectrums (red dot) of the symmetric MDM-ENA and best-fits to the single FR lineshape Eq. (1) (blue solid); (b) 3D-FDTD simulation of the transmission spectrums (red dot) of the asymmetric MDM- ENA and best-fits to the double FR lineshape Eq. (2) (blue solid).
, we fit the transmission curves of both the symmetric MDM-ENA and asymmetric MDM-ENA using the single FR lineshape in Eq. (1) [53

53. A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298 (2010). [CrossRef]

,54

54. U. Fano, “Effects of Configuration Interaction on Intensities and Phase Shifts,” Phys. Rev. 124(6), 1866–1878 (1961). [CrossRef]

] and double FR lineshape in Eq. (2) [12

12. Y. Ma, Z. Li, Y. Yang, R. Huang, R. Singh, S. Zhang, J. Gu, Z. Tian, J. Han, and W. Zhang, “Plasmon-induced transparency in twisted Fano terahertz metamaterials,” Opt. Mater. Express 1(3), 391–399 (2011). [CrossRef]

], respectively:

T=A1+F1(ε1+q1)21+ε12
(1)
T=A0+F2(ε2+q2)21+ε22+F4(ε4+q4)21+ε42
(2)

where ε1=2(ωω1)Γ1, ε2=2(ωω2)Γ2, ε4=2(ωω4)Γ4. Particularly, q1, q2, q4 are the phenomenological shape parameters (so-called asymmetry parameter), ω1, ω2, ω4 are the resonance frequencies and Γ1, Γ2, Γ4 are the width of the autoionized state (the resonance linewidth at half maximum, FWHM) of the modes P1, P2, and P4 respectively [54

54. U. Fano, “Effects of Configuration Interaction on Intensities and Phase Shifts,” Phys. Rev. 124(6), 1866–1878 (1961). [CrossRef]

,55

55. B. M. Lagutin, V. L. Sukhorukov, I. D. Petrov, H. Schmoranzer, A. Ehresmann, and K. H. Schartner, “Photoionization of Kr near the 4s threshold. IV. Photoionization through the autoionization of doubly-excited states,” J. Phys. At. Mol. Opt. Phys. 27(21), 5221–5239 (1994). [CrossRef]

]. A0, A1, F1, F2, F4 are constant factors. With the asymmetric parameters shown in Table 1

Table 1. Aymmetric Parameters used in the FR Lineshape to Fit the Transmissions of the Symmetric MDM-ENA and Asymmetric MDM-ENA

table-icon
View This Table
, the calculated transmissions based on Eq. (1) and Eq. (2) approximately reproduce our FDTD simulation data with the different surrounding dielectric refractive index of n = 1.0, 1.2 and 1.4.

For example, in Fig. 7 we use the Fano formula to fit the transmission curves of both the symmetric MDM-ENA and asymmetric MDM-ENA at the surrounding dielectric refractive index of 1.0 as shown by the solid blue curves, respectively. It is found that the Fano formula mostly matches the FDTD simulation data around the resonant modes. Q factor is defined by the resonant frequency over the width of the autoionized state [12

12. Y. Ma, Z. Li, Y. Yang, R. Huang, R. Singh, S. Zhang, J. Gu, Z. Tian, J. Han, and W. Zhang, “Plasmon-induced transparency in twisted Fano terahertz metamaterials,” Opt. Mater. Express 1(3), 391–399 (2011). [CrossRef]

,13

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]

], where the resonant frequency and the width of the autoionized state are obtained from the Fano formula fitting transmission curves shown in Fig. 7.The resonant frequencies, the widths of the autoionized state and Q factors are 1455.6THz and1443.3THz, 67.4THz and 42.3THz, 21 and 34 for both the symmetric MDM-ENA (P1 mode) and asymmetric MDM-ENA (P2 mode), respectively.

5. Sensitivity to the dielectric environment

The dependence of the spectral position of surface plasmon resonance (SPR) on the permittivity of the surrounding medium environment is important for the refractive index sensor [56

56. N. Liu, T. Weiss, M. Mesch, L. Langguth, U. Eigenthaler, M. Hirscher, C. Sönnichsen, and H. Giessen, “Planar Metamaterial Analogue of Electromagnetically Induced Transparency for Plasmonic Sensing,” Nano Lett. 10(4), 1103–1107 (2010). [CrossRef] [PubMed]

]. Developing from the SPR technologies, the multilayer MMs proposed here have the sharp FR making them interesting for sensor applications. We evaluate the sensing performance of the symmetric MDM-ENA and asymmetric MDM-ENA by testing the index of the medium surrounding the structures varied from n = 1.0 to n = 1.4. Here, the test samples with the different refractive index is placed on the top of the MM sensor [28

28. K. A. Tetz, L. Pang, and Y. Fainman, “High-resolution surface plasmon resonance sensor based on linewidth-optimized nanohole array transmittance,” Opt. Lett. 31(10), 1528–1530 (2006). [CrossRef] [PubMed]

,57

57. L. Zhu, L. Dong, F. Y. Meng, J. H. Fu, and Q. Wu, “Influence of symmetry breaking in a planar metamaterial on transparency effect and sensing application,” Appl. Opt. 51(32), 7794–7799 (2012). [CrossRef] [PubMed]

]. The sensing capability of our multilayer fishnet MMs can be understood by the fact that the resonance wavelength is proportional to the square root of capacitance between the top and bottom Au films according to LC circuit resonance model, which is in turn proportional to the surrounding dielectric constant [43

43. J. Q. Wang, C. Z. Fan, J. N. He, P. Ding, E. J. Liang, and Q. Z. Xue, “Double Fano resonances due to interplay of electric and magnetic plasmon modes in planar plasmonic structure with high sensing sensitivity,” Opt. Express 21(2), 2236–2244 (2013). [CrossRef] [PubMed]

]. As can be seen in Fig. 8(a) and (b)
Fig. 8 3D-FDTD simulation of (a)transmission spectra of symmetric MDM-ENA for different values of the refractive index of the surrounding medium; (b)transmission spectra of asymmetric MDM-ENA for different values of the refractive index of the surrounding medium; (c)wavelength shift of symmetric MDM-ENA and asymmetric MDM-ENA as a function of the surrounding dielectric; (d)change of the phenomenological shape parameter as a function of the surrounding dielectric.
, both the single FR and the double FR exhibit a resonance red shift with respect to the increment of the surrounding material index. Figure 8(c) presents the refractive index sensitivityS=ΔλΔn of the MM sensors, where ∆λ is the resonant wavelength shift obtained for the refractive index variation(∆n) of the media surrounding the MMs sensors. It shows that the resonant wavelength shift dependences are linear.The double FR reveals a higher response to change in the dielectric environment compared to the single FR.The calculated sensitivity is 120nm/ RIU for the P2 mode and 60nm/RIU for the P1 mode.The resonance linewidth directly dictates the MM sensor’s minimum resolution [58

58. H. M. Chen, L. Pang, A. Kher, and Y. Fainman, “Three-dimensional composite metallodielectric nanostructure for enhanced surface plasmon resonance sensing,” Appl. Phys. Lett. 94(7), 073117 (2009). [CrossRef]

].Hence, a higher Q factor or narrower resonance linewidth are desired to yield a higher sensitivity. Only then small analyte induced shifts of a resonance wavelength can be accurately measured. As we presented in this work, upon the symmetry breaking between the neighboring holes, the single FR(P1) splits into two plasmon modes (P2 and P4) resulting in an increase in the strength of the resonance at the P2 mode shown in Fig. 5. The interaction between the enhanced magnetic resonance and electric resonance leads to a FR with a narrower linewidth and higher Q factor thus leading to a higher sensitivity.

In order to provide better quantification of the spectroscopic sensors operating at the different regime, the sensing performance in terms of the figure of merit (FOM) is defined as follows [58

58. H. M. Chen, L. Pang, A. Kher, and Y. Fainman, “Three-dimensional composite metallodielectric nanostructure for enhanced surface plasmon resonance sensing,” Appl. Phys. Lett. 94(7), 073117 (2009). [CrossRef]

]:

FOM=S(nm/RIU)Γ(nm)
(3)

where Γ is the width of the autoionized state (FWHM) of the resonant feature [54

54. U. Fano, “Effects of Configuration Interaction on Intensities and Phase Shifts,” Phys. Rev. 124(6), 1866–1878 (1961). [CrossRef]

,56

56. N. Liu, T. Weiss, M. Mesch, L. Langguth, U. Eigenthaler, M. Hirscher, C. Sönnichsen, and H. Giessen, “Planar Metamaterial Analogue of Electromagnetically Induced Transparency for Plasmonic Sensing,” Nano Lett. 10(4), 1103–1107 (2010). [CrossRef] [PubMed]

]. Γ is 77nm at the P1 mode leading to FOM of 0.8 RIU−1. However, at the P2 mode of the asymmetric MDM-ENA, it possesses a higher FOM of 3.0 RIU−1 with Γ = 42nm, which is close to the measurement results of FOM in the NIR region in [56

56. N. Liu, T. Weiss, M. Mesch, L. Langguth, U. Eigenthaler, M. Hirscher, C. Sönnichsen, and H. Giessen, “Planar Metamaterial Analogue of Electromagnetically Induced Transparency for Plasmonic Sensing,” Nano Lett. 10(4), 1103–1107 (2010). [CrossRef] [PubMed]

,59

59. J. Zhao, C. J. Zhang, P. V. Braun, and H. Giessen, “Large-Area Low-Cost Plasmonic Nanostructures in the NIR for Fano Resonant Sensing,” Adv. Mater. 24(35), OP247–OP252 (2012). [CrossRef] [PubMed]

]. Therefore a weakly asymmetric MDM-ENA appears more suitable for the development of a simple spectroscopic sensor, given the higher values of both sensitivity and FOM. After extracting the asymmetric parameters q1, q2, q4 fitted by the Fano functions in Table 1, we present the variation of the asymmetric parameters to the change of the surrounding dielectric in Fig. 8(d). It is found that the absolute values of the asymmetric parameters of q1 and q2 decrease when altering the surrounding dielectric refractive index from 1.0 to 1.4. Specifically, for the case of q4 at the refractive index of 1.4, the resonance linewidth increases to a large value thus leading to the degeneration of the P4 resonant mode [shown by the red dot line in Fig. 8(b)] as well as a worse fitting through the Fano formula.

6. Conclusion

In conclusion, we show that a FR can be obtained using the symmetric multilayer MMs. This fact is due to the interplay between the bright modes and the dark modes. The bright modes are induced by the elliptical nanoholes resonator array which shows a typical localized surface plasmon resonance, whereas the dark modes correspond to the inductive-capacitive resonance excited by the closed loops of JD from the MDM multilayers. Furthermore, by setting a low degree of the structural asymmetry in the ENA element, the single FR from the symmetric MDM-ENA splits in two resonant peaks, resulting in a double FR. It is concluded that the strong interaction between the electric resonance and two magnetic resonances at different wavelengths plays the key role to produce the enhanced double FR.This interference leads to a sharp transparency peak with ultrahigh Q factor in the NIR regime for the asymmetric MDM-ENA. Moreover, the degree of asymmetry allows for the tuning of the amplitude and bandwidth of the double FR window. Finally, the sensitivity and FOM of the MDM-ENA to the external dielectric environment are calculated to show the possibilities of sensing application in the NIR region.

Acknowledgments

We acknowledge the financial support from National Natural Science Foundation of China (Grant No. 61172059), Ph.D Programs Foundation of Ministry of Education of China (Grant No. 20110041120015), Postdoctoral Gathering Project of Liaoning Province (Grant No. 2011921008), and The Fundamental Research for the Central University (Grant No. DUT12JB01).

References and links

1.

J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]

2.

C. W. Qiu, A. Akbarzadeh, T. C. Han, and A. J. Danner, “Photorealistic rendering of a graded negative-index metamaterial magnifier,” New J. Phys. 14(3), 033024 (2012). [CrossRef]

3.

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007). [CrossRef]

4.

C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics 5, 523–530 (2011).

5.

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]

6.

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]

7.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006). [CrossRef] [PubMed]

8.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006). [CrossRef] [PubMed]

9.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]

10.

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric Propagation of Electromagnetic Waves through a Planar Chiral Structure,” Phys. Rev. Lett. 97(16), 167401 (2006). [CrossRef] [PubMed]

11.

N. Soltani, É. Lheurette, and D. Lippens, “Wood anomaly transmission enhancement in fishnet-based metamaterials at terahertz frequencies,” J. Appl. Phys. 112(12), 124509 (2012). [CrossRef]

12.

Y. Ma, Z. Li, Y. Yang, R. Huang, R. Singh, S. Zhang, J. Gu, Z. Tian, J. Han, and W. Zhang, “Plasmon-induced transparency in twisted Fano terahertz metamaterials,” Opt. Mater. Express 1(3), 391–399 (2011). [CrossRef]

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.

M. Pu, C. Hu, C. Huang, C. Wang, Z. Zhao, Y. Wang, and X. Luo, “Investigation of Fano resonance in planar metamaterial with perturbed periodicity,” Opt. Express 21(1), 992–1001 (2013). [CrossRef] [PubMed]

15.

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]

16.

R. Singh, I. A. I. Al-Naib, M. Koch, and W. Zhang, “Sharp Fano resonances in THz metamaterials,” Opt. Express 19(7), 6312–6319 (2011). [CrossRef] [PubMed]

17.

N. Papasimakis, V. A. Fedotov, N. I. Zheludev, and S. L. Prosvirnin, “Metamaterial Analog of Electromagnetically Induced Transparency,” Phys. Rev. Lett. 101(25), 253903 (2008). [CrossRef] [PubMed]

18.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009). [CrossRef] [PubMed]

19.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008). [CrossRef] [PubMed]

20.

F. Hao, Y. Sonnefraud, P. Van 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]

21.

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]

22.

P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Low-Loss Metamaterials Based on Classical Electromagnetically Induced Transparency,” Phys. Rev. Lett. 102(5), 053901 (2009). [CrossRef] [PubMed]

23.

S. Fan, “Sharp asymmetric line shapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett. 80(6), 908–910 (2002). [CrossRef]

24.

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002). [CrossRef]

25.

S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A 20(3), 569–572 (2003). [CrossRef] [PubMed]

26.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80(5), 960–963 (1998). [CrossRef]

27.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59(24), 15882–15892 (1999). [CrossRef]

28.

K. A. Tetz, L. Pang, and Y. Fainman, “High-resolution surface plasmon resonance sensor based on linewidth-optimized nanohole array transmittance,” Opt. Lett. 31(10), 1528–1530 (2006). [CrossRef] [PubMed]

29.

B. Lahiri, A. Z. Khokhar, R. M. De La Rue, S. G. McMeekin, and N. P. Johnson, “Asymmetric split ring resonators for optical sensing of organic materials,” Opt. Express 17(2), 1107–1115 (2009). [CrossRef] [PubMed]

30.

S. A. Maier, “Plasmonics: The Benefits of darkness,” Nat. Mater. 8(9), 699–700 (2009). [CrossRef] [PubMed]

31.

N. Papasimakis, Y. H. Fu, V. A. Fedotov, S. L. Prosvirnin, D. P. Tsai, and N. I. Zheludev, “Metamaterial with polarization and direction insensitive resonant transmission response mimicking electromagnetically induced transparency,” Appl. Phys. Lett. 94(21), 211902 (2009). [CrossRef]

32.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. Brueck, “Optical negative-index bulk metamaterials consisting of 2D perforated metal-dielectric stacks,” Opt. Express 14(15), 6778–6787 (2006). [CrossRef] [PubMed]

33.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008). [CrossRef] [PubMed]

34.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. 7(1), 31–37 (2008). [CrossRef] [PubMed]

35.

T. Li, H. Liu, F. M. Wang, Z. G. Dong, S. N. Zhu, and X. Zhang, “Coupling effect of magnetic polariton in perforated metal/dielectric layered metamaterials and its influence on negative refraction transmission,” Opt. Express 14(23), 11155–11163 (2006). [CrossRef] [PubMed]

36.

J. Yang, C. Sauvan, H. T. Liu, and P. Lalanne, “Theory of fishnet negative-index optical metamaterials,” Phys. Rev. Lett. 107(4), 043903 (2011). [CrossRef] [PubMed]

37.

B. Seo, K. Kim, S. G. Kim, A. Kim, H. Cho, and E. M. Choi, “Observation of trapped-modes excited in double-layered symmetric electric ring resonators,” J. Appl. Phys. 111(11), 113106 (2012). [CrossRef]

38.

A. Minovich, D. N. Neshev, D. A. Powell, I. V. Shadrivov, and Y. S. Kivshar, “Tunable fishnet metamaterials infiltrated by liquid crystals,” Appl. Phys. Lett. 96(19), 193103 (2010). [CrossRef]

39.

T. Cao and M. J. Cryan, “Study of incident angle dependence for dual-band double negative-index material using elliptical nanohole arrays,” J. Opt. Soc. Am. A 29(3), 209–215 (2012). [CrossRef] [PubMed]

40.

Y. G. Ma, L. Zhao, P. Wang, and C. K. Ong, “Fabrication of negative index materials using dielectric and metallic composite route,” Appl. Phys. Lett. 93(18), 184103 (2008). [CrossRef]

41.

S. Zhang, W. Fan, K. J. Malloy, S. R. J. Brueck, N. C. Paniou, and R. M. Osgood, “Demonstration of metal–dielectric negative index metamaterials with improved performance at optical frequencies,” J. Opt. Soc. Am. B 23(3), 434–438 (2006). [CrossRef]

42.

R. Singh, I. A. I. Al-Naib, Y. Yang, D. R. Chowdhury, W. Cao, C. Rockstuhl, T. Ozaki, R. Morandotti, and W. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011). [CrossRef]

43.

J. Q. Wang, C. Z. Fan, J. N. He, P. Ding, E. J. Liang, and Q. Z. Xue, “Double Fano resonances due to interplay of electric and magnetic plasmon modes in planar plasmonic structure with high sensing sensitivity,” Opt. Express 21(2), 2236–2244 (2013). [CrossRef] [PubMed]

44.

J. Q. Gu, R. J. Singh, X. J. Liu, X. Q. Zhang, Y. F. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. T. Chen, A. J. Taylor, J. G. Han, and W. L. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat Commun 3, 1151 (2012). [CrossRef] [PubMed]

45.

J. Carbonell, C. Croënne, F. Garet, E. Lheurette, J. L. Coutaz, and D. Lippens, “Lumped elements circuit of terahertz fishnet-like arrays with composite dispersion,” J. Appl. Phys. 108(1), 014907 (2010). [CrossRef]

46.

http://www.emexplorer.net

47.

S. Zhang, W. J. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005). [CrossRef] [PubMed]

48.

J. P. Berenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 127(2), 363–379 (1996). [CrossRef]

49.

Ş. E. Kocabaş, G. Veronis, D. A. B. Miller, and S. Fan, “Modal analysis and coupling in metal-insulator-metal waveguides,” Phys. Rev. B 79(3), 035120 (2009). [CrossRef]

50.

W. T. Chen, C. J. Chen, P. C. Wu, S. Sun, L. Zhou, G. Y. Guo, C. T. Hsiao, K. Y. Yang, N. I. Zheludev, and D. P. Tsai, “Optical magnetic response in three-dimensional metamaterial of upright plasmonic meta-molecules,” Opt. Express 19(13), 12837–12842 (2011). [CrossRef] [PubMed]

51.

C. Rockstuhl, F. Lederer, C. Etrich, T. Zentgraf, J. Kuhl, and H. Giessen, “On the reinterpretation of resonances in split-ring-resonators at normal incidence,” Opt. Express 14(19), 8827–8836 (2006). [CrossRef] [PubMed]

52.

O. Paul, C. Imhof, B. Reinhard, R. Zengerle, and R. Beigang, “Negative index bulk metamaterial at terahertz frequencies,” Opt. Express 16(9), 6736–6744 (2008). [CrossRef] [PubMed]

53.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298 (2010). [CrossRef]

54.

U. Fano, “Effects of Configuration Interaction on Intensities and Phase Shifts,” Phys. Rev. 124(6), 1866–1878 (1961). [CrossRef]

55.

B. M. Lagutin, V. L. Sukhorukov, I. D. Petrov, H. Schmoranzer, A. Ehresmann, and K. H. Schartner, “Photoionization of Kr near the 4s threshold. IV. Photoionization through the autoionization of doubly-excited states,” J. Phys. At. Mol. Opt. Phys. 27(21), 5221–5239 (1994). [CrossRef]

56.

N. Liu, T. Weiss, M. Mesch, L. Langguth, U. Eigenthaler, M. Hirscher, C. Sönnichsen, and H. Giessen, “Planar Metamaterial Analogue of Electromagnetically Induced Transparency for Plasmonic Sensing,” Nano Lett. 10(4), 1103–1107 (2010). [CrossRef] [PubMed]

57.

L. Zhu, L. Dong, F. Y. Meng, J. H. Fu, and Q. Wu, “Influence of symmetry breaking in a planar metamaterial on transparency effect and sensing application,” Appl. Opt. 51(32), 7794–7799 (2012). [CrossRef] [PubMed]

58.

H. M. Chen, L. Pang, A. Kher, and Y. Fainman, “Three-dimensional composite metallodielectric nanostructure for enhanced surface plasmon resonance sensing,” Appl. Phys. Lett. 94(7), 073117 (2009). [CrossRef]

59.

J. Zhao, C. J. Zhang, P. V. Braun, and H. Giessen, “Large-Area Low-Cost Plasmonic Nanostructures in the NIR for Fano Resonant Sensing,” Adv. Mater. 24(35), OP247–OP252 (2012). [CrossRef] [PubMed]

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(260.5740) Physical optics : Resonance
(160.3918) Materials : Metamaterials

ToC Category:
Metamaterials

History
Original Manuscript: May 24, 2013
Revised Manuscript: July 11, 2013
Manuscript Accepted: July 31, 2013
Published: August 6, 2013

Citation
Tun Cao and Lei Zhang, "Enhancement of Fano resonance in metal/dielectric/metal metamaterials at optical regime," Opt. Express 21, 19228-19239 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-16-19228


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett.85(18), 3966–3969 (2000). [CrossRef] [PubMed]
  2. C. W. Qiu, A. Akbarzadeh, T. C. Han, and A. J. Danner, “Photorealistic rendering of a graded negative-index metamaterial magnifier,” New J. Phys.14(3), 033024 (2012). [CrossRef]
  3. V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics1(1), 41–48 (2007). [CrossRef]
  4. C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics5, 523–530 (2011).
  5. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science292(5514), 77–79 (2001). [CrossRef] [PubMed]
  6. 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]
  7. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006). [CrossRef] [PubMed]
  8. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314(5801), 977–980 (2006). [CrossRef] [PubMed]
  9. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003). [CrossRef] [PubMed]
  10. V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric Propagation of Electromagnetic Waves through a Planar Chiral Structure,” Phys. Rev. Lett.97(16), 167401 (2006). [CrossRef] [PubMed]
  11. N. Soltani, É. Lheurette, and D. Lippens, “Wood anomaly transmission enhancement in fishnet-based metamaterials at terahertz frequencies,” J. Appl. Phys.112(12), 124509 (2012). [CrossRef]
  12. Y. Ma, Z. Li, Y. Yang, R. Huang, R. Singh, S. Zhang, J. Gu, Z. Tian, J. Han, and W. Zhang, “Plasmon-induced transparency in twisted Fano terahertz metamaterials,” Opt. Mater. Express1(3), 391–399 (2011). [CrossRef]
  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. M. Pu, C. Hu, C. Huang, C. Wang, Z. Zhao, Y. Wang, and X. Luo, “Investigation of Fano resonance in planar metamaterial with perturbed periodicity,” Opt. Express21(1), 992–1001 (2013). [CrossRef] [PubMed]
  15. 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]
  16. R. Singh, I. A. I. Al-Naib, M. Koch, and W. Zhang, “Sharp Fano resonances in THz metamaterials,” Opt. Express19(7), 6312–6319 (2011). [CrossRef] [PubMed]
  17. N. Papasimakis, V. A. Fedotov, N. I. Zheludev, and S. L. Prosvirnin, “Metamaterial Analog of Electromagnetically Induced Transparency,” Phys. Rev. Lett.101(25), 253903 (2008). [CrossRef] [PubMed]
  18. N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater.8(9), 758–762 (2009). [CrossRef] [PubMed]
  19. S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett.101(4), 047401 (2008). [CrossRef] [PubMed]
  20. F. Hao, Y. Sonnefraud, P. Van 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]
  21. 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]
  22. P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Low-Loss Metamaterials Based on Classical Electromagnetically Induced Transparency,” Phys. Rev. Lett.102(5), 053901 (2009). [CrossRef] [PubMed]
  23. S. Fan, “Sharp asymmetric line shapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett.80(6), 908–910 (2002). [CrossRef]
  24. S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B65(23), 235112 (2002). [CrossRef]
  25. S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A20(3), 569–572 (2003). [CrossRef] [PubMed]
  26. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett.80(5), 960–963 (1998). [CrossRef]
  27. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B59(24), 15882–15892 (1999). [CrossRef]
  28. K. A. Tetz, L. Pang, and Y. Fainman, “High-resolution surface plasmon resonance sensor based on linewidth-optimized nanohole array transmittance,” Opt. Lett.31(10), 1528–1530 (2006). [CrossRef] [PubMed]
  29. B. Lahiri, A. Z. Khokhar, R. M. De La Rue, S. G. McMeekin, and N. P. Johnson, “Asymmetric split ring resonators for optical sensing of organic materials,” Opt. Express17(2), 1107–1115 (2009). [CrossRef] [PubMed]
  30. S. A. Maier, “Plasmonics: The Benefits of darkness,” Nat. Mater.8(9), 699–700 (2009). [CrossRef] [PubMed]
  31. N. Papasimakis, Y. H. Fu, V. A. Fedotov, S. L. Prosvirnin, D. P. Tsai, and N. I. Zheludev, “Metamaterial with polarization and direction insensitive resonant transmission response mimicking electromagnetically induced transparency,” Appl. Phys. Lett.94(21), 211902 (2009). [CrossRef]
  32. S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. Brueck, “Optical negative-index bulk metamaterials consisting of 2D perforated metal-dielectric stacks,” Opt. Express14(15), 6778–6787 (2006). [CrossRef] [PubMed]
  33. J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature455(7211), 376–379 (2008). [CrossRef] [PubMed]
  34. N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater.7(1), 31–37 (2008). [CrossRef] [PubMed]
  35. T. Li, H. Liu, F. M. Wang, Z. G. Dong, S. N. Zhu, and X. Zhang, “Coupling effect of magnetic polariton in perforated metal/dielectric layered metamaterials and its influence on negative refraction transmission,” Opt. Express14(23), 11155–11163 (2006). [CrossRef] [PubMed]
  36. J. Yang, C. Sauvan, H. T. Liu, and P. Lalanne, “Theory of fishnet negative-index optical metamaterials,” Phys. Rev. Lett.107(4), 043903 (2011). [CrossRef] [PubMed]
  37. B. Seo, K. Kim, S. G. Kim, A. Kim, H. Cho, and E. M. Choi, “Observation of trapped-modes excited in double-layered symmetric electric ring resonators,” J. Appl. Phys.111(11), 113106 (2012). [CrossRef]
  38. A. Minovich, D. N. Neshev, D. A. Powell, I. V. Shadrivov, and Y. S. Kivshar, “Tunable fishnet metamaterials infiltrated by liquid crystals,” Appl. Phys. Lett.96(19), 193103 (2010). [CrossRef]
  39. T. Cao and M. J. Cryan, “Study of incident angle dependence for dual-band double negative-index material using elliptical nanohole arrays,” J. Opt. Soc. Am. A29(3), 209–215 (2012). [CrossRef] [PubMed]
  40. Y. G. Ma, L. Zhao, P. Wang, and C. K. Ong, “Fabrication of negative index materials using dielectric and metallic composite route,” Appl. Phys. Lett.93(18), 184103 (2008). [CrossRef]
  41. S. Zhang, W. Fan, K. J. Malloy, S. R. J. Brueck, N. C. Paniou, and R. M. Osgood, “Demonstration of metal–dielectric negative index metamaterials with improved performance at optical frequencies,” J. Opt. Soc. Am. B23(3), 434–438 (2006). [CrossRef]
  42. R. Singh, I. A. I. Al-Naib, Y. Yang, D. R. Chowdhury, W. Cao, C. Rockstuhl, T. Ozaki, R. Morandotti, and W. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett.99(20), 201107 (2011). [CrossRef]
  43. J. Q. Wang, C. Z. Fan, J. N. He, P. Ding, E. J. Liang, and Q. Z. Xue, “Double Fano resonances due to interplay of electric and magnetic plasmon modes in planar plasmonic structure with high sensing sensitivity,” Opt. Express21(2), 2236–2244 (2013). [CrossRef] [PubMed]
  44. J. Q. Gu, R. J. Singh, X. J. Liu, X. Q. Zhang, Y. F. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. T. Chen, A. J. Taylor, J. G. Han, and W. L. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat Commun3, 1151 (2012). [CrossRef] [PubMed]
  45. J. Carbonell, C. Croënne, F. Garet, E. Lheurette, J. L. Coutaz, and D. Lippens, “Lumped elements circuit of terahertz fishnet-like arrays with composite dispersion,” J. Appl. Phys.108(1), 014907 (2010). [CrossRef]
  46. http://www.emexplorer.net
  47. S. Zhang, W. J. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett.95(13), 137404 (2005). [CrossRef] [PubMed]
  48. J. P. Berenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys.127(2), 363–379 (1996). [CrossRef]
  49. Ş. E. Kocabaş, G. Veronis, D. A. B. Miller, and S. Fan, “Modal analysis and coupling in metal-insulator-metal waveguides,” Phys. Rev. B79(3), 035120 (2009). [CrossRef]
  50. W. T. Chen, C. J. Chen, P. C. Wu, S. Sun, L. Zhou, G. Y. Guo, C. T. Hsiao, K. Y. Yang, N. I. Zheludev, and D. P. Tsai, “Optical magnetic response in three-dimensional metamaterial of upright plasmonic meta-molecules,” Opt. Express19(13), 12837–12842 (2011). [CrossRef] [PubMed]
  51. C. Rockstuhl, F. Lederer, C. Etrich, T. Zentgraf, J. Kuhl, and H. Giessen, “On the reinterpretation of resonances in split-ring-resonators at normal incidence,” Opt. Express14(19), 8827–8836 (2006). [CrossRef] [PubMed]
  52. O. Paul, C. Imhof, B. Reinhard, R. Zengerle, and R. Beigang, “Negative index bulk metamaterial at terahertz frequencies,” Opt. Express16(9), 6736–6744 (2008). [CrossRef] [PubMed]
  53. A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys.82(3), 2257–2298 (2010). [CrossRef]
  54. U. Fano, “Effects of Configuration Interaction on Intensities and Phase Shifts,” Phys. Rev.124(6), 1866–1878 (1961). [CrossRef]
  55. B. M. Lagutin, V. L. Sukhorukov, I. D. Petrov, H. Schmoranzer, A. Ehresmann, and K. H. Schartner, “Photoionization of Kr near the 4s threshold. IV. Photoionization through the autoionization of doubly-excited states,” J. Phys. At. Mol. Opt. Phys.27(21), 5221–5239 (1994). [CrossRef]
  56. N. Liu, T. Weiss, M. Mesch, L. Langguth, U. Eigenthaler, M. Hirscher, C. Sönnichsen, and H. Giessen, “Planar Metamaterial Analogue of Electromagnetically Induced Transparency for Plasmonic Sensing,” Nano Lett.10(4), 1103–1107 (2010). [CrossRef] [PubMed]
  57. L. Zhu, L. Dong, F. Y. Meng, J. H. Fu, and Q. Wu, “Influence of symmetry breaking in a planar metamaterial on transparency effect and sensing application,” Appl. Opt.51(32), 7794–7799 (2012). [CrossRef] [PubMed]
  58. H. M. Chen, L. Pang, A. Kher, and Y. Fainman, “Three-dimensional composite metallodielectric nanostructure for enhanced surface plasmon resonance sensing,” Appl. Phys. Lett.94(7), 073117 (2009). [CrossRef]
  59. J. Zhao, C. J. Zhang, P. V. Braun, and H. Giessen, “Large-Area Low-Cost Plasmonic Nanostructures in the NIR for Fano Resonant Sensing,” Adv. Mater.24(35), OP247–OP252 (2012). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited