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Optical Materials Express

Optical Materials Express

  • Editor: David J. Hagan
  • Vol. 2, Iss. 10 — Oct. 1, 2012
  • pp: 1407–1415
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Magnetic-electric interference in metal-dielectric-metal oligomers: generation of magneto-electric Fano resonance

J. Yang, M. Rahmani, J. H. Teng, and M. H. Hong  »View Author Affiliations


Optical Materials Express, Vol. 2, Issue 10, pp. 1407-1415 (2012)
http://dx.doi.org/10.1364/OME.2.001407


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Abstract

The existence of magnetic resonance in designed Metal-Dielectric-Metal (MDM) oligomers is investigated. Via angling the incident light it is found that in the MDM oligomers, not only the E-component of incident field drives plasmon oscillations, but the H-component also plays an important role to excite magnetic plasmons. These magnetic plasmons give rise to a magnetic resonance in addition to classical Fano Resonance (FR). Importantly, unlike regular MDM structures which exhibit separate magnetic and electric resonances, the MDM oligomers possess the capability to exhibit both magnetic and electric resonances in the same wavelength window with proper metallic and dielectric thicknesses. It leads to the appearance of an additional FR as a result of interference between magnetic-electric plasmonic resonances rather than electric-electric resonances with a clear proof of remarkable absorption enhancement. The unique capability of MDM oligomers exhibiting both electric and magneto-electric FRs can realize many potential applications of FR.

© 2012 OSA

1. Introduction

Recent development in the fabrication, simulation and the optical characterization of metallic nanostructures has provided rich opportunities to study behaviors of collective oscillations of surface free electrons, known as surface plasmons, excited by incident electromagnetic waves [1

1. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

]. In complex plasmonic nanostructures, many intriguing optical responses are results of hybridization among plasmons arising from individual components of the nanostructures [2

2. V. Giannini, A. I. Fernández-Domínguez, S. C. Heck, and S. A. Maier, “Plasmonic nanoantennas: fundamentals and their use in controlling the radiative properties of nanoemitters,” Chem. Rev. 111(6), 3888–3912 (2011). [CrossRef] [PubMed]

,3

3. N. J. Halas, S. Lal, W. S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev. 111(6), 3913–3961 (2011). [CrossRef] [PubMed]

]. This hybridization has been shown to give rise to a wide range of coherent phenomena, such as artificial magnetism [4

4. A. Dmitriev, T. Pakizeh, M. Käll, and D. S. Sutherland, “Gold-silica-gold nanosandwiches: tunable bimodal plasmonic resonators,” Small 3(2), 294–299 (2007). [CrossRef] [PubMed]

13

13. Y. Ekinci, A. Christ, M. Agio, O. J. F. Martin, H. H. Solak, and J. F. Löffler, “Electric and magnetic resonances in arrays of coupled gold nanoparticle in-tandem pairs,” Opt. Express 16(17), 13287–13295 (2008). [CrossRef] [PubMed]

], electromagnetically induced transparency (EIT) [14

14. 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]

] and Fano Resonances (FRs) [15

15. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010). [CrossRef] [PubMed]

,16

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

] which can find analogues in systems as diverse as atomic physics [3

3. N. J. Halas, S. Lal, W. S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev. 111(6), 3913–3961 (2011). [CrossRef] [PubMed]

], coupled mechanical oscillators [17

17. S. Mukherjee, H. Sobhani, J. B. Lassiter, R. Bardhan, P. Nordlander, and N. J. Halas, “Fanoshells: nanoparticles with built-in Fano resonances,” Nano Lett. 10(7), 2694–2701 (2010). [CrossRef] [PubMed]

] and resonant electrical circuits [18

18. F. Hao, C. L. Nehl, J. H. Hafner, and P. Nordlander, “Plasmon resonances of a gold nanostar,” Nano Lett. 7(3), 729–732 (2007). [CrossRef] [PubMed]

]. Novel optical properties of these phenomena in plasmonic structures provide great prospects for various nanophotonics applications.

Metal-Dielectric-Metal (MDM) structures are widely used in obtaining artificial magnetism [4

4. A. Dmitriev, T. Pakizeh, M. Käll, and D. S. Sutherland, “Gold-silica-gold nanosandwiches: tunable bimodal plasmonic resonators,” Small 3(2), 294–299 (2007). [CrossRef] [PubMed]

13

13. Y. Ekinci, A. Christ, M. Agio, O. J. F. Martin, H. H. Solak, and J. F. Löffler, “Electric and magnetic resonances in arrays of coupled gold nanoparticle in-tandem pairs,” Opt. Express 16(17), 13287–13295 (2008). [CrossRef] [PubMed]

,19

19. G. Dolling, M. Wegener, A. Schadle, S. Burger, and S. Linden, “Observation of magnetization waves in negative-index photonic metamaterials,” Appl. Phys. Lett. 89(23), 231118 (2006). [CrossRef]

21

21. Y. L. Zhang, W. Jin, X. Z. Dong, Z. S. Zhao, and X. M. Duan, “Asymmetric fishnet metamaterials with strong optical activity,” Opt. Express 20(10), 10776–10787 (2012). [CrossRef] [PubMed]

]. Well studied MDM structures are nanosandwiches [4

4. A. Dmitriev, T. Pakizeh, M. Käll, and D. S. Sutherland, “Gold-silica-gold nanosandwiches: tunable bimodal plasmonic resonators,” Small 3(2), 294–299 (2007). [CrossRef] [PubMed]

,6

6. T. Pakizeh, M. S. Abrishamian, N. Granpayeh, A. Dmitriev, and M. Käll, “Magnetic-field enhancement in gold nanosandwiches,” Opt. Express 14(18), 8240–8246 (2006). [CrossRef] [PubMed]

,7

7. C. Tserkezis, N. Papanikolaou, G. Gantzounis, and N. Stefanou, “Understanding artificial optical magnetism of periodic metal-dielectric-metal layered structures,” Phys. Rev. B 78(16), 165114 (2008). [CrossRef]

,9

9. T. Pakizeh, A. Dmitriev, M. S. Abrishamian, N. Granpayeh, and M. Käll, “Structural asymmetry and induced optical magnetism in plasmonic nanosandwiches,” J. Opt. Soc. Am. B 25(4), 659–667 (2008). [CrossRef]

,13

13. Y. Ekinci, A. Christ, M. Agio, O. J. F. Martin, H. H. Solak, and J. F. Löffler, “Electric and magnetic resonances in arrays of coupled gold nanoparticle in-tandem pairs,” Opt. Express 16(17), 13287–13295 (2008). [CrossRef] [PubMed]

], photonic cavities [10

10. R. Ameling and H. Giessen, “Cavity plasmonics: large normal mode splitting of electric and magnetic particle plasmons induced by a photonic microcavity,” Nano Lett. 10(11), 4394–4398 (2010). [CrossRef] [PubMed]

], metamaterial molecules [8

8. S. Wu, G. Wang, Q. Wang, L. Zhou, J. Zhao, C. Huang, and Y. Zhu, “Novel optical transmission property of metal–dielectric multilayered structure,” J. Phys. D Appl. Phys. 42(22), 225406 (2009). [CrossRef]

,12

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

] and fishnets [11

11. N. Liu, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmonic building blocks for magnetic molecules in three-dimensional optical metamaterials,” Adv. Mater. 20(20), 3859–3865 (2008). [CrossRef]

,19

19. G. Dolling, M. Wegener, A. Schadle, S. Burger, and S. Linden, “Observation of magnetization waves in negative-index photonic metamaterials,” Appl. Phys. Lett. 89(23), 231118 (2006). [CrossRef]

21

21. Y. L. Zhang, W. Jin, X. Z. Dong, Z. S. Zhao, and X. M. Duan, “Asymmetric fishnet metamaterials with strong optical activity,” Opt. Express 20(10), 10776–10787 (2012). [CrossRef] [PubMed]

]. In such structures, when anti-parallel moments in the top and bottom metallic layers oscillate out of phase, the electric fields are very strong with opposite directions at two sides of the dielectric layer. Therefore, a magnetic moment appears inside the dielectric layer and pushes magnetic resonance to emerge. This phenomenon leads to another type of plasmon oscillation, so called magnetic plasmons. On the other hand, 2D planar structures, such as ring-disk cavities, Dolmen structures, and nanoshells, being introduced to show coherent phenomena, such as EIT and FR [14

14. 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]

,15

15. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010). [CrossRef] [PubMed]

,18

18. F. Hao, C. L. Nehl, J. H. Hafner, and P. Nordlander, “Plasmon resonances of a gold nanostar,” Nano Lett. 7(3), 729–732 (2007). [CrossRef] [PubMed]

], are based on the electric plasmons driven by an electric field. Such structures are usually used to generate dipole and high order electric modes, which can have constructive and destructive interferences.

Among planar plasmonic structures, plasmonic oligomers are of high interest [22

22. M. Rahmani, B. Lukiyanchuk, T. T. V. Nguyen, T. Tahmasebi, Y. Lin, T. Y. F. Liew, and M. H. Hong, “Influence of symmetry breaking in pentamers on Fano resonance and near-field energy localization,” Opt. Mater. Express 1(8), 1409–1415 (2011). [CrossRef]

33

33. J. A. Fan, K. Bao, C. Wu, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, G. Shvets, P. Nordlander, and F. Capasso, “Fano-like interference in self-assembled plasmonic quadrumer clusters,” Nano Lett. 10(11), 4680–4685 (2010). [CrossRef] [PubMed]

]. Oligomers are aggregated nanoparticles with sufficiently small inter-particle gaps, which have been proved as excellent candidates to generate FR in visible and near infra-red (NIR) range. Such effect is due to the coupling among anti-parallel modes arisen from the neighboring metallic nanoparticles along the lateral direction at certain wavelength ranges. In fact, this classical FR in oligomers is a result of hybridization among electric plasmons. Such FRs in this paper are called as electric FRs. Recently, Halas and associates have shown that certain arrangement of planar oligomers can also be used to excite a magnetic resonance [34

34. N. Liu, S. Mukherjee, K. Bao, L. V. Brown, J. Dorfmüller, P. Nordlander, and N. J. Halas, “Magnetic plasmon formation and propagation in artificial aromatic molecules,” Nano Lett. 12(1), 364–369 (2012). [CrossRef] [PubMed]

,35

35. N. Liu, S. Mukherjee, K. Bao, Y. Li, L. V. Brown, P. Nordlander, and N. J. Halas, “Manipulating magnetic plasmon propagation in metallic nanocluster networks,” ACS Nano 6(6), 5482–5488 (2012). [CrossRef] [PubMed]

] in addition to the electric FR. Multi-heptamers investigated by Liu et al. [34

34. N. Liu, S. Mukherjee, K. Bao, L. V. Brown, J. Dorfmüller, P. Nordlander, and N. J. Halas, “Magnetic plasmon formation and propagation in artificial aromatic molecules,” Nano Lett. 12(1), 364–369 (2012). [CrossRef] [PubMed]

,35

35. N. Liu, S. Mukherjee, K. Bao, Y. Li, L. V. Brown, P. Nordlander, and N. J. Halas, “Manipulating magnetic plasmon propagation in metallic nanocluster networks,” ACS Nano 6(6), 5482–5488 (2012). [CrossRef] [PubMed]

] give rise to anti-parallel magnetic dipole moments [36

36. N. Liu, S. Kaiser, and H. Giessen, “Magnetoinductive and electroinductive coupling in plasmonic metamaterial molecules,” Adv. Mater. 20(23), 4521–4525 (2008). [CrossRef]

], which are attributed to the circulating current in each individual heptamer.

2. Methodology

In the present work, the optical properties of the MDM oligomers were investigated through numerical simulations. Lumerical FDTD solutions were used for the 3D finite-difference time-domain (FDTD) simulations. Cross section spectra of various MDM oligomers on glass substrates were studied at wavelength ranging from 400 to 1300 nm. A total field scattered field (TFSF) plane wave was applied as the source. Two boxes of monitors, one in the total field region and the other in the scattered field region, were defined to calculate the absorption and scattering cross sections. The extinction cross section is defined as the sum of absorption and scattering cross sections. Therefore, the extinction cross section is equal to 1- transmission [22

22. M. Rahmani, B. Lukiyanchuk, T. T. V. Nguyen, T. Tahmasebi, Y. Lin, T. Y. F. Liew, and M. H. Hong, “Influence of symmetry breaking in pentamers on Fano resonance and near-field energy localization,” Opt. Mater. Express 1(8), 1409–1415 (2011). [CrossRef]

35

35. N. Liu, S. Mukherjee, K. Bao, Y. Li, L. V. Brown, P. Nordlander, and N. J. Halas, “Manipulating magnetic plasmon propagation in metallic nanocluster networks,” ACS Nano 6(6), 5482–5488 (2012). [CrossRef] [PubMed]

]. Meanwhile, in order to avoid coupling among optical diffraction arising from individual unit cells with periodic-type boundary [38

38. Z. S. Zhang, Z. J. Yang, J. B. Li, Z. H. Hao, and Q. Q. Wang, “Plasmonic interferences in two-dimensional stacked double-disk array,” Appl. Phys. Lett. 98(17), 173111 (2011). [CrossRef]

], optical properties of the MDM oligomers in this research were investigated in isolated boundary. Perfect matched layers were used as an effective absorbing boundary condition. The dielectric functions of Au structures and glass substrate are referred to the experimental data of Johnson and Christy [39

39. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]

] and Palik book [40

40. E. D. Palik, Handbook of Optical Constants of Solids, Academic Press handbook series (Academic Press, 1997).

], respectively.

3. Results and discussion

In order to get physical insight into this magnetic resonance and the contribution of E- and H-components of incident light on electric and magnetic plasmons, we applied a simple but clear proof. With pentamers as an example, we changed the incident light angle to study the contribution of E- and H-components of incident light in exciting electric and magnetic resonances. Figure 2(a)
Fig. 2 (a) Extinction cross section spectra of the MDM pentamer with of 20 nm Au layers at the bottom and top and 10 nm dielectric SiO2 layer in the middle at incident light angle of 0, 30, 60 and 90 degrees. Magnetic field intensity accompanied with its x and y components corresponding to (b) 0 degree and (c) 90 degree of incidence.
illustrates the extinction cross section spectra of the MDM pentamers with the same dimensions as shown in Fig. 1 but different incident angles. To avoid the influence from the substrate [41

41. S. Zhang, K. Bao, N. J. Halas, H. Xu, and P. Nordlander, “Substrate-induced Fano resonances of a plasmonic nanocube: a route to increased-sensitivity localized surface plasmon resonance sensors revealed,” Nano Lett. 11(4), 1657–1663 (2011). [CrossRef] [PubMed]

,42

42. M. W. Knight, Y. Wu, J. B. Lassiter, P. Nordlander, and N. J. Halas, “Substrates matter: influence of an adjacent dielectric on an individual plasmonic nanoparticle,” Nano Lett. 9(5), 2188–2192 (2009). [CrossRef] [PubMed]

], the glass substrate is removed temporarily in this simulation. Extinction spectra at different incident angles are shown in Fig. 2(a). As it has been shown previously [22

22. M. Rahmani, B. Lukiyanchuk, T. T. V. Nguyen, T. Tahmasebi, Y. Lin, T. Y. F. Liew, and M. H. Hong, “Influence of symmetry breaking in pentamers on Fano resonance and near-field energy localization,” Opt. Mater. Express 1(8), 1409–1415 (2011). [CrossRef]

,28

28. M. Rahmani, B. Lukiyanchuk, B. Ng, A. Tavakkoli K. G, Y. F. Liew, and M. H. Hong, “Generation of pronounced Fano resonances and tuning of subwavelength spatial light distribution in plasmonic pentamers,” Opt. Express 19(6), 4949–4956 (2011). [CrossRef] [PubMed]

] at normal incidence, E-components of light excite electric plasmons in each metallic layer of pentamers, which leads to the appearance of electric FR around 700 nm (see black curve). Meanwhile, the H field intensities plots at the magnetic resonance of 1130 nm in the middle dielectric layer as shown in Fig. 2(b), reveals that at normal incidence, H and Hy intensities of magnetic field are identical while Hz intensity is very small. It agrees well with H-component of incident light along y-axis at normal incidence.

Extensionally, we found that the MDM oligomers possess an excellent capability to tune the spectral position of magnetic resonance by changing the thickness of consisting layers while the spectral position of electric FR is kept constant. It provides a rich opportunity to induce an overlap between magnetic and electric resonances. It is a rare potential which allows not only exciting both FR and artificial magnetic resonance together, but also induces hybridization of these resonances for novel optical properties. Geometrical manipulation of other proposed structures, which exhibit magnetic resonance, can also tune the position of magnetic resonance, but simultaneously it changes the position of electric resonance [4

4. A. Dmitriev, T. Pakizeh, M. Käll, and D. S. Sutherland, “Gold-silica-gold nanosandwiches: tunable bimodal plasmonic resonators,” Small 3(2), 294–299 (2007). [CrossRef] [PubMed]

9

9. T. Pakizeh, A. Dmitriev, M. S. Abrishamian, N. Granpayeh, and M. Käll, “Structural asymmetry and induced optical magnetism in plasmonic nanosandwiches,” J. Opt. Soc. Am. B 25(4), 659–667 (2008). [CrossRef]

,13

13. Y. Ekinci, A. Christ, M. Agio, O. J. F. Martin, H. H. Solak, and J. F. Löffler, “Electric and magnetic resonances in arrays of coupled gold nanoparticle in-tandem pairs,” Opt. Express 16(17), 13287–13295 (2008). [CrossRef] [PubMed]

], which prevents spectral overlap of electric and magnetic resonances. Figure 3
Fig. 3 (a) Extinction and (b) absorption cross section spectra of the MDM pentamers consisting of 20, 30 and 40 nm thick Au layer, respectively. Each set shows spectra corresponding to 10 (red curve), 20 (blue curve) and 30 (cyan curve) nm thick middle SiO2 layers.
reveals the capability of hybridization of magnetic and electric resonances among MDM pentamers. Detail studies on planar single layer pentamers can be found in [22

22. M. Rahmani, B. Lukiyanchuk, T. T. V. Nguyen, T. Tahmasebi, Y. Lin, T. Y. F. Liew, and M. H. Hong, “Influence of symmetry breaking in pentamers on Fano resonance and near-field energy localization,” Opt. Mater. Express 1(8), 1409–1415 (2011). [CrossRef]

,27

27. M. Rahmani, D. Y. Lei, V. Giannini, B. Lukiyanchuk, M. Ranjbar, T. Y. F. Liew, M. Hong, and S. A. Maier, “Subgroup decomposition of plasmonic resonances in hybrid oligomers: modeling the resonance lineshape,” Nano Lett. 12(4), 2101–2106 (2012). [CrossRef] [PubMed]

,28

28. M. Rahmani, B. Lukiyanchuk, B. Ng, A. Tavakkoli K. G, Y. F. Liew, and M. H. Hong, “Generation of pronounced Fano resonances and tuning of subwavelength spatial light distribution in plasmonic pentamers,” Opt. Express 19(6), 4949–4956 (2011). [CrossRef] [PubMed]

], where, it has been shown that around the position of electric FR in the extinction spectra, a weak fluctuation can be seen in absorption curve [27

27. M. Rahmani, D. Y. Lei, V. Giannini, B. Lukiyanchuk, M. Ranjbar, T. Y. F. Liew, M. Hong, and S. A. Maier, “Subgroup decomposition of plasmonic resonances in hybrid oligomers: modeling the resonance lineshape,” Nano Lett. 12(4), 2101–2106 (2012). [CrossRef] [PubMed]

]. This trend is similar to asymmetric quadrumers [33

33. J. A. Fan, K. Bao, C. Wu, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, G. Shvets, P. Nordlander, and F. Capasso, “Fano-like interference in self-assembled plasmonic quadrumer clusters,” Nano Lett. 10(11), 4680–4685 (2010). [CrossRef] [PubMed]

] in which the existence of these absorption fluctuations are regarded as an evidence of FR. It has been shown that such absorption increase comes to existence due to the nature of appeared subradiant dark mode which is weakly lifetime broadened with a small decay rate due to nonradiative loss [3

3. N. J. Halas, S. Lal, W. S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev. 111(6), 3913–3961 (2011). [CrossRef] [PubMed]

,15

15. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010). [CrossRef] [PubMed]

,16

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

,27

27. M. Rahmani, D. Y. Lei, V. Giannini, B. Lukiyanchuk, M. Ranjbar, T. Y. F. Liew, M. Hong, and S. A. Maier, “Subgroup decomposition of plasmonic resonances in hybrid oligomers: modeling the resonance lineshape,” Nano Lett. 12(4), 2101–2106 (2012). [CrossRef] [PubMed]

,33

33. J. A. Fan, K. Bao, C. Wu, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, G. Shvets, P. Nordlander, and F. Capasso, “Fano-like interference in self-assembled plasmonic quadrumer clusters,” Nano Lett. 10(11), 4680–4685 (2010). [CrossRef] [PubMed]

]. For the case of planar pentamers, a weak fluctuation can only be observed around FR since signature of FR is mostly formed by subgroups, which are efficiently excited at their spectral peak positions [27

27. M. Rahmani, D. Y. Lei, V. Giannini, B. Lukiyanchuk, M. Ranjbar, T. Y. F. Liew, M. Hong, and S. A. Maier, “Subgroup decomposition of plasmonic resonances in hybrid oligomers: modeling the resonance lineshape,” Nano Lett. 12(4), 2101–2106 (2012). [CrossRef] [PubMed]

].

We found that the interference between magnetic and electric resonances leads to emergence of another FR with much more obvious signature in absorption spectra. Figure 3(a) shows three different sets of MDM pentamers at different thicknesses of Au and dielectric layers. In all sets, an increase in the dielectric thickness leads to significant blue shift in magnetic resonance. Due to the similarity of the MDM structures with LC resonator models, a recall of basic LC rules can be used to explain the mechanism of this shift simply. It is well known that the resonant frequency of a LC resonator can be calculated by ω=1/LC, where C is capacitance and L the inductance of magnetic coil. An increase in the gap among coils leads to reduction in C value [43

43. R. C. Dorf and J. A. Svoboda, Introduction to Electric Circuits, 5th ed. (Wiley, 2001).

], increasing ω value. With this analogy, one can summarize that when the gap among metallic layers of MDM structures increases, the wavelength of magnetic resonance decreases.

On the other hand, the position and intensity of this absorption peak prove clearly that when the magnetic resonance gets closer to the wing of electric resonance, the interference between these two resonances gets stronger, which enhances dark mode. Therefore, more portion of incident light gets absorbed. It introduces a new family of FRs in plasmonic oligomers based on the interference between magnetic-electric resonances rather than electric-electric resonances. When the thickness of dielectric layer is equal to 10 nm (see red curves), the magnetic resonance and electric resonance are very far from each other. Both extinction and absorption spectra experience a weak spectral peak due to the nature of magnetic resonance [4

4. A. Dmitriev, T. Pakizeh, M. Käll, and D. S. Sutherland, “Gold-silica-gold nanosandwiches: tunable bimodal plasmonic resonators,” Small 3(2), 294–299 (2007). [CrossRef] [PubMed]

,6

6. T. Pakizeh, M. S. Abrishamian, N. Granpayeh, A. Dmitriev, and M. Käll, “Magnetic-field enhancement in gold nanosandwiches,” Opt. Express 14(18), 8240–8246 (2006). [CrossRef] [PubMed]

,7

7. C. Tserkezis, N. Papanikolaou, G. Gantzounis, and N. Stefanou, “Understanding artificial optical magnetism of periodic metal-dielectric-metal layered structures,” Phys. Rev. B 78(16), 165114 (2008). [CrossRef]

,9

9. T. Pakizeh, A. Dmitriev, M. S. Abrishamian, N. Granpayeh, and M. Käll, “Structural asymmetry and induced optical magnetism in plasmonic nanosandwiches,” J. Opt. Soc. Am. B 25(4), 659–667 (2008). [CrossRef]

,10

10. R. Ameling and H. Giessen, “Cavity plasmonics: large normal mode splitting of electric and magnetic particle plasmons induced by a photonic microcavity,” Nano Lett. 10(11), 4394–4398 (2010). [CrossRef] [PubMed]

,13

13. Y. Ekinci, A. Christ, M. Agio, O. J. F. Martin, H. H. Solak, and J. F. Löffler, “Electric and magnetic resonances in arrays of coupled gold nanoparticle in-tandem pairs,” Opt. Express 16(17), 13287–13295 (2008). [CrossRef] [PubMed]

]. This trend can be seen in all sets of studied MDM oligomers with different thicknesses of Au layers. But when the thickness of dielectric layer increases to 20 nm, the magnetic resonance becomes sufficiently close to the electric resonance, which results in interference between these resonances (see blue curves). In these MDM pentamers with 30 and 40 nm thick Au layers, more intense absorption peaks can be observed around the second dip positions of extinction spectra at 857 and 818 nm, respectively. It is a signature of dark mode which is due to the coupling between superradiant and subradiant modes with less radiative loss and a small decay rate. It is in direct agreement with physics behind FR [15

15. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010). [CrossRef] [PubMed]

,16

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

,27

27. M. Rahmani, D. Y. Lei, V. Giannini, B. Lukiyanchuk, M. Ranjbar, T. Y. F. Liew, M. Hong, and S. A. Maier, “Subgroup decomposition of plasmonic resonances in hybrid oligomers: modeling the resonance lineshape,” Nano Lett. 12(4), 2101–2106 (2012). [CrossRef] [PubMed]

,33

33. J. A. Fan, K. Bao, C. Wu, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, G. Shvets, P. Nordlander, and F. Capasso, “Fano-like interference in self-assembled plasmonic quadrumer clusters,” Nano Lett. 10(11), 4680–4685 (2010). [CrossRef] [PubMed]

]. This trend can be seen in MDM pentamers with 30 nm dielectric thicknesses (see green curves) as well. Small observed differences between positions of absorption peak and extinction dip are due to the oligomeric configuration in which the interference among modes starts a few tens of nanometres before extinction dip [27

27. M. Rahmani, D. Y. Lei, V. Giannini, B. Lukiyanchuk, M. Ranjbar, T. Y. F. Liew, M. Hong, and S. A. Maier, “Subgroup decomposition of plasmonic resonances in hybrid oligomers: modeling the resonance lineshape,” Nano Lett. 12(4), 2101–2106 (2012). [CrossRef] [PubMed]

,32

32. M. Rahmani, B. Luk'yanchuk, and M. Hong, “Fano resonance in novel plasmonic nanostructures,” Laser Photonics Rev. , doi: (2012). [CrossRef]

]. Meanwhile, as can be seen, since the thicknesses of all Au layers are more than skin depth of Au (12 ~15nm [44

44. Z. Iluz and A. Boag, “Dual-Vivaldi wideband nanoantenna with high radiation efficiency over the infrared frequency band,” Opt. Lett. 36(15), 2773–2775 (2011). [CrossRef] [PubMed]

]), the thickness of Au layers does not play as a significant role as the thickness of dielectric layer.

As can be observed, proposed MDM oligomers exhibit second FR with more observable signature in the absorption responses rather than extinction responses. It can find high potential applications as FR slow light devices, which are mostly based on the absorption enhancement. Meanwhile, such oligomers still exhibit regular classic electric FR which can find potential applications as filters. One should be noted here that, further increase in the thickness of dielectric layers will push the magnetic resonance to the wavelength window in which electric FR appears. Therefore, the complex resulting spectra may avoid MDM oligomers to be unique devices with capability to exhibit both electric and magneto-electric FRs.

4. Conclusions

In summary, magnetic resonance in the MDM oligomers is investigated. It is shown that in addition to E-component of incident light which drives electric plasmons, H-component of incident light also has a remarkable contribution to the emergence of magnetic flux in middle dielectric layer of MDM structures. It is established by angling the incident light which affects H-component contribution in plasmons excitations while E-component contribution remains constant. It is found that at 90 degree incident light, pure E-component is not able to induce magnetic flux since H-component is no longer effective. Furthermore, it is shown that changing the thickness of metallic and dielectric layers provides an opportunity to shift the magnetic resonance, while the position of classical electric FR of oligomers remains constant. It is in contrary with regular MDM structures in which typically magnetic and electric resonances are separated. Therefore, interference between magnetic and electric resonances in the MDM oligomers can be induced artificially. It gives rise to another FR, which possesses novel magneto-electric characteristics. The evidence of this magneto-electric FR in absorption response is much more observable than classic electric FR in planar oligomers. It makes the MDM oligomers as unique plasmonic devices, which possess both electric and magneto-electric FRs at the same time.

Acknowledgments

The authors would like to acknowledge the financial support from the Temasek Defence Systems Institute (TDSI) Optical Limiters Project (Project code: R-263-000-687-232 TDSI/11-013/1A), and the National Research Foundation and the Economic Development Board (SPORE, COY-15-EWI-RCFSA/N197-1).

References and links

1.

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

2.

V. Giannini, A. I. Fernández-Domínguez, S. C. Heck, and S. A. Maier, “Plasmonic nanoantennas: fundamentals and their use in controlling the radiative properties of nanoemitters,” Chem. Rev. 111(6), 3888–3912 (2011). [CrossRef] [PubMed]

3.

N. J. Halas, S. Lal, W. S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev. 111(6), 3913–3961 (2011). [CrossRef] [PubMed]

4.

A. Dmitriev, T. Pakizeh, M. Käll, and D. S. Sutherland, “Gold-silica-gold nanosandwiches: tunable bimodal plasmonic resonators,” Small 3(2), 294–299 (2007). [CrossRef] [PubMed]

5.

W. Cai, U. K. Chettiar, H. K. Yuan, V. C. de Silva, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Metamagnetics with rainbow colors,” Opt. Express 15(6), 3333–3341 (2007). [CrossRef] [PubMed]

6.

T. Pakizeh, M. S. Abrishamian, N. Granpayeh, A. Dmitriev, and M. Käll, “Magnetic-field enhancement in gold nanosandwiches,” Opt. Express 14(18), 8240–8246 (2006). [CrossRef] [PubMed]

7.

C. Tserkezis, N. Papanikolaou, G. Gantzounis, and N. Stefanou, “Understanding artificial optical magnetism of periodic metal-dielectric-metal layered structures,” Phys. Rev. B 78(16), 165114 (2008). [CrossRef]

8.

S. Wu, G. Wang, Q. Wang, L. Zhou, J. Zhao, C. Huang, and Y. Zhu, “Novel optical transmission property of metal–dielectric multilayered structure,” J. Phys. D Appl. Phys. 42(22), 225406 (2009). [CrossRef]

9.

T. Pakizeh, A. Dmitriev, M. S. Abrishamian, N. Granpayeh, and M. Käll, “Structural asymmetry and induced optical magnetism in plasmonic nanosandwiches,” J. Opt. Soc. Am. B 25(4), 659–667 (2008). [CrossRef]

10.

R. Ameling and H. Giessen, “Cavity plasmonics: large normal mode splitting of electric and magnetic particle plasmons induced by a photonic microcavity,” Nano Lett. 10(11), 4394–4398 (2010). [CrossRef] [PubMed]

11.

N. Liu, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmonic building blocks for magnetic molecules in three-dimensional optical metamaterials,” Adv. Mater. 20(20), 3859–3865 (2008). [CrossRef]

12.

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

13.

Y. Ekinci, A. Christ, M. Agio, O. J. F. Martin, H. H. Solak, and J. F. Löffler, “Electric and magnetic resonances in arrays of coupled gold nanoparticle in-tandem pairs,” Opt. Express 16(17), 13287–13295 (2008). [CrossRef] [PubMed]

14.

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]

15.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010). [CrossRef] [PubMed]

16.

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

17.

S. Mukherjee, H. Sobhani, J. B. Lassiter, R. Bardhan, P. Nordlander, and N. J. Halas, “Fanoshells: nanoparticles with built-in Fano resonances,” Nano Lett. 10(7), 2694–2701 (2010). [CrossRef] [PubMed]

18.

F. Hao, C. L. Nehl, J. H. Hafner, and P. Nordlander, “Plasmon resonances of a gold nanostar,” Nano Lett. 7(3), 729–732 (2007). [CrossRef] [PubMed]

19.

G. Dolling, M. Wegener, A. Schadle, S. Burger, and S. Linden, “Observation of magnetization waves in negative-index photonic metamaterials,” Appl. Phys. Lett. 89(23), 231118 (2006). [CrossRef]

20.

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]

21.

Y. L. Zhang, W. Jin, X. Z. Dong, Z. S. Zhao, and X. M. Duan, “Asymmetric fishnet metamaterials with strong optical activity,” Opt. Express 20(10), 10776–10787 (2012). [CrossRef] [PubMed]

22.

M. Rahmani, B. Lukiyanchuk, T. T. V. Nguyen, T. Tahmasebi, Y. Lin, T. Y. F. Liew, and M. H. Hong, “Influence of symmetry breaking in pentamers on Fano resonance and near-field energy localization,” Opt. Mater. Express 1(8), 1409–1415 (2011). [CrossRef]

23.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010). [CrossRef] [PubMed]

24.

M. Hentschel, M. Saliba, R. Vogelgesang, H. Giessen, A. P. Alivisatos, and N. Liu, “Transition from isolated to collective modes in plasmonic oligomers,” Nano Lett. 10(7), 2721–2726 (2010). [CrossRef] [PubMed]

25.

M. Rahmani, B. Lukiyanchuk, T. Tahmasebi, Y. Lin, T. Liew, and M. Hong, “Polarization-controlled spatial localization of near-field energy in planar symmetric coupled oligomers,” Appl. Phys., A Mater. Sci. Process. 107(1), 23–30 (2012). [CrossRef]

26.

J. B. Lassiter, H. Sobhani, M. W. Knight, W. S. Mielczarek, P. Nordlander, and N. J. Halas, “Designing and deconstructing the Fano lineshape in plasmonic nanoclusters,” Nano Lett. 12(2), 1058–1062 (2012). [CrossRef] [PubMed]

27.

M. Rahmani, D. Y. Lei, V. Giannini, B. Lukiyanchuk, M. Ranjbar, T. Y. F. Liew, M. Hong, and S. A. Maier, “Subgroup decomposition of plasmonic resonances in hybrid oligomers: modeling the resonance lineshape,” Nano Lett. 12(4), 2101–2106 (2012). [CrossRef] [PubMed]

28.

M. Rahmani, B. Lukiyanchuk, B. Ng, A. Tavakkoli K. G, Y. F. Liew, and M. H. Hong, “Generation of pronounced Fano resonances and tuning of subwavelength spatial light distribution in plasmonic pentamers,” Opt. Express 19(6), 4949–4956 (2011). [CrossRef] [PubMed]

29.

M. Rahmani, T. Tahmasebi, Y. Lin, B. Lukiyanchuk, T. Y. F. Liew, and M. H. Hong, “Influence of plasmon destructive interferences on optical properties of gold planar quadrumers,” Nanotechnology 22(24), 245204 (2011). [CrossRef] [PubMed]

30.

D. Dregely, M. Hentschel, and H. Giessen, “Excitation and tuning of higher-order Fano resonances in plasmonic oligomer clusters,” ACS Nano 5(10), 8202–8211 (2011). [CrossRef] [PubMed]

31.

M. Hentschel, D. Dregely, R. Vogelgesang, H. Giessen, and N. Liu, “Plasmonic oligomers: the role of individual particles in collective behavior,” ACS Nano 5(3), 2042–2050 (2011). [CrossRef] [PubMed]

32.

M. Rahmani, B. Luk'yanchuk, and M. Hong, “Fano resonance in novel plasmonic nanostructures,” Laser Photonics Rev. , doi: (2012). [CrossRef]

33.

J. A. Fan, K. Bao, C. Wu, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, G. Shvets, P. Nordlander, and F. Capasso, “Fano-like interference in self-assembled plasmonic quadrumer clusters,” Nano Lett. 10(11), 4680–4685 (2010). [CrossRef] [PubMed]

34.

N. Liu, S. Mukherjee, K. Bao, L. V. Brown, J. Dorfmüller, P. Nordlander, and N. J. Halas, “Magnetic plasmon formation and propagation in artificial aromatic molecules,” Nano Lett. 12(1), 364–369 (2012). [CrossRef] [PubMed]

35.

N. Liu, S. Mukherjee, K. Bao, Y. Li, L. V. Brown, P. Nordlander, and N. J. Halas, “Manipulating magnetic plasmon propagation in metallic nanocluster networks,” ACS Nano 6(6), 5482–5488 (2012). [CrossRef] [PubMed]

36.

N. Liu, S. Kaiser, and H. Giessen, “Magnetoinductive and electroinductive coupling in plasmonic metamaterial molecules,” Adv. Mater. 20(23), 4521–4525 (2008). [CrossRef]

37.

S. Kim, J. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453(7196), 757–760 (2008). [CrossRef] [PubMed]

38.

Z. S. Zhang, Z. J. Yang, J. B. Li, Z. H. Hao, and Q. Q. Wang, “Plasmonic interferences in two-dimensional stacked double-disk array,” Appl. Phys. Lett. 98(17), 173111 (2011). [CrossRef]

39.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]

40.

E. D. Palik, Handbook of Optical Constants of Solids, Academic Press handbook series (Academic Press, 1997).

41.

S. Zhang, K. Bao, N. J. Halas, H. Xu, and P. Nordlander, “Substrate-induced Fano resonances of a plasmonic nanocube: a route to increased-sensitivity localized surface plasmon resonance sensors revealed,” Nano Lett. 11(4), 1657–1663 (2011). [CrossRef] [PubMed]

42.

M. W. Knight, Y. Wu, J. B. Lassiter, P. Nordlander, and N. J. Halas, “Substrates matter: influence of an adjacent dielectric on an individual plasmonic nanoparticle,” Nano Lett. 9(5), 2188–2192 (2009). [CrossRef] [PubMed]

43.

R. C. Dorf and J. A. Svoboda, Introduction to Electric Circuits, 5th ed. (Wiley, 2001).

44.

Z. Iluz and A. Boag, “Dual-Vivaldi wideband nanoantenna with high radiation efficiency over the infrared frequency band,” Opt. Lett. 36(15), 2773–2775 (2011). [CrossRef] [PubMed]

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(260.2110) Physical optics : Electromagnetic optics
(260.5740) Physical optics : Resonance
(310.6628) Thin films : Subwavelength structures, nanostructures

ToC Category:
Plasmonics

History
Original Manuscript: August 7, 2012
Revised Manuscript: September 8, 2012
Manuscript Accepted: September 10, 2012
Published: September 20, 2012

Citation
J. Yang, M. Rahmani, J. H. Teng, and M. H. Hong, "Magnetic-electric interference in metal-dielectric-metal oligomers: generation of magneto-electric Fano resonance," Opt. Mater. Express 2, 1407-1415 (2012)
http://www.opticsinfobase.org/ome/abstract.cfm?URI=ome-2-10-1407


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References

  1. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
  2. V. Giannini, A. I. Fernández-Domínguez, S. C. Heck, and S. A. Maier, “Plasmonic nanoantennas: fundamentals and their use in controlling the radiative properties of nanoemitters,” Chem. Rev.111(6), 3888–3912 (2011). [CrossRef] [PubMed]
  3. N. J. Halas, S. Lal, W. S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev.111(6), 3913–3961 (2011). [CrossRef] [PubMed]
  4. A. Dmitriev, T. Pakizeh, M. Käll, and D. S. Sutherland, “Gold-silica-gold nanosandwiches: tunable bimodal plasmonic resonators,” Small3(2), 294–299 (2007). [CrossRef] [PubMed]
  5. W. Cai, U. K. Chettiar, H. K. Yuan, V. C. de Silva, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Metamagnetics with rainbow colors,” Opt. Express15(6), 3333–3341 (2007). [CrossRef] [PubMed]
  6. T. Pakizeh, M. S. Abrishamian, N. Granpayeh, A. Dmitriev, and M. Käll, “Magnetic-field enhancement in gold nanosandwiches,” Opt. Express14(18), 8240–8246 (2006). [CrossRef] [PubMed]
  7. C. Tserkezis, N. Papanikolaou, G. Gantzounis, and N. Stefanou, “Understanding artificial optical magnetism of periodic metal-dielectric-metal layered structures,” Phys. Rev. B78(16), 165114 (2008). [CrossRef]
  8. S. Wu, G. Wang, Q. Wang, L. Zhou, J. Zhao, C. Huang, and Y. Zhu, “Novel optical transmission property of metal–dielectric multilayered structure,” J. Phys. D Appl. Phys.42(22), 225406 (2009). [CrossRef]
  9. T. Pakizeh, A. Dmitriev, M. S. Abrishamian, N. Granpayeh, and M. Käll, “Structural asymmetry and induced optical magnetism in plasmonic nanosandwiches,” J. Opt. Soc. Am. B25(4), 659–667 (2008). [CrossRef]
  10. R. Ameling and H. Giessen, “Cavity plasmonics: large normal mode splitting of electric and magnetic particle plasmons induced by a photonic microcavity,” Nano Lett.10(11), 4394–4398 (2010). [CrossRef] [PubMed]
  11. N. Liu, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmonic building blocks for magnetic molecules in three-dimensional optical metamaterials,” Adv. Mater.20(20), 3859–3865 (2008). [CrossRef]
  12. N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater.19(21), 3628–3632 (2007). [CrossRef]
  13. Y. Ekinci, A. Christ, M. Agio, O. J. F. Martin, H. H. Solak, and J. F. Löffler, “Electric and magnetic resonances in arrays of coupled gold nanoparticle in-tandem pairs,” Opt. Express16(17), 13287–13295 (2008). [CrossRef] [PubMed]
  14. 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]
  15. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater.9(9), 707–715 (2010). [CrossRef] [PubMed]
  16. A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys.82(3), 2257–2298 (2010). [CrossRef]
  17. S. Mukherjee, H. Sobhani, J. B. Lassiter, R. Bardhan, P. Nordlander, and N. J. Halas, “Fanoshells: nanoparticles with built-in Fano resonances,” Nano Lett.10(7), 2694–2701 (2010). [CrossRef] [PubMed]
  18. F. Hao, C. L. Nehl, J. H. Hafner, and P. Nordlander, “Plasmon resonances of a gold nanostar,” Nano Lett.7(3), 729–732 (2007). [CrossRef] [PubMed]
  19. G. Dolling, M. Wegener, A. Schadle, S. Burger, and S. Linden, “Observation of magnetization waves in negative-index photonic metamaterials,” Appl. Phys. Lett.89(23), 231118 (2006). [CrossRef]
  20. 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]
  21. Y. L. Zhang, W. Jin, X. Z. Dong, Z. S. Zhao, and X. M. Duan, “Asymmetric fishnet metamaterials with strong optical activity,” Opt. Express20(10), 10776–10787 (2012). [CrossRef] [PubMed]
  22. M. Rahmani, B. Lukiyanchuk, T. T. V. Nguyen, T. Tahmasebi, Y. Lin, T. Y. F. Liew, and M. H. Hong, “Influence of symmetry breaking in pentamers on Fano resonance and near-field energy localization,” Opt. Mater. Express1(8), 1409–1415 (2011). [CrossRef]
  23. J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science328(5982), 1135–1138 (2010). [CrossRef] [PubMed]
  24. M. Hentschel, M. Saliba, R. Vogelgesang, H. Giessen, A. P. Alivisatos, and N. Liu, “Transition from isolated to collective modes in plasmonic oligomers,” Nano Lett.10(7), 2721–2726 (2010). [CrossRef] [PubMed]
  25. M. Rahmani, B. Lukiyanchuk, T. Tahmasebi, Y. Lin, T. Liew, and M. Hong, “Polarization-controlled spatial localization of near-field energy in planar symmetric coupled oligomers,” Appl. Phys., A Mater. Sci. Process.107(1), 23–30 (2012). [CrossRef]
  26. J. B. Lassiter, H. Sobhani, M. W. Knight, W. S. Mielczarek, P. Nordlander, and N. J. Halas, “Designing and deconstructing the Fano lineshape in plasmonic nanoclusters,” Nano Lett.12(2), 1058–1062 (2012). [CrossRef] [PubMed]
  27. M. Rahmani, D. Y. Lei, V. Giannini, B. Lukiyanchuk, M. Ranjbar, T. Y. F. Liew, M. Hong, and S. A. Maier, “Subgroup decomposition of plasmonic resonances in hybrid oligomers: modeling the resonance lineshape,” Nano Lett.12(4), 2101–2106 (2012). [CrossRef] [PubMed]
  28. M. Rahmani, B. Lukiyanchuk, B. Ng, A. Tavakkoli K. G, Y. F. Liew, and M. H. Hong, “Generation of pronounced Fano resonances and tuning of subwavelength spatial light distribution in plasmonic pentamers,” Opt. Express19(6), 4949–4956 (2011). [CrossRef] [PubMed]
  29. M. Rahmani, T. Tahmasebi, Y. Lin, B. Lukiyanchuk, T. Y. F. Liew, and M. H. Hong, “Influence of plasmon destructive interferences on optical properties of gold planar quadrumers,” Nanotechnology22(24), 245204 (2011). [CrossRef] [PubMed]
  30. D. Dregely, M. Hentschel, and H. Giessen, “Excitation and tuning of higher-order Fano resonances in plasmonic oligomer clusters,” ACS Nano5(10), 8202–8211 (2011). [CrossRef] [PubMed]
  31. M. Hentschel, D. Dregely, R. Vogelgesang, H. Giessen, and N. Liu, “Plasmonic oligomers: the role of individual particles in collective behavior,” ACS Nano5(3), 2042–2050 (2011). [CrossRef] [PubMed]
  32. M. Rahmani, B. Luk'yanchuk, and M. Hong, “Fano resonance in novel plasmonic nanostructures,” Laser Photonics Rev., doi: (2012). [CrossRef]
  33. J. A. Fan, K. Bao, C. Wu, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, G. Shvets, P. Nordlander, and F. Capasso, “Fano-like interference in self-assembled plasmonic quadrumer clusters,” Nano Lett.10(11), 4680–4685 (2010). [CrossRef] [PubMed]
  34. N. Liu, S. Mukherjee, K. Bao, L. V. Brown, J. Dorfmüller, P. Nordlander, and N. J. Halas, “Magnetic plasmon formation and propagation in artificial aromatic molecules,” Nano Lett.12(1), 364–369 (2012). [CrossRef] [PubMed]
  35. N. Liu, S. Mukherjee, K. Bao, Y. Li, L. V. Brown, P. Nordlander, and N. J. Halas, “Manipulating magnetic plasmon propagation in metallic nanocluster networks,” ACS Nano6(6), 5482–5488 (2012). [CrossRef] [PubMed]
  36. N. Liu, S. Kaiser, and H. Giessen, “Magnetoinductive and electroinductive coupling in plasmonic metamaterial molecules,” Adv. Mater.20(23), 4521–4525 (2008). [CrossRef]
  37. S. Kim, J. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature453(7196), 757–760 (2008). [CrossRef] [PubMed]
  38. Z. S. Zhang, Z. J. Yang, J. B. Li, Z. H. Hao, and Q. Q. Wang, “Plasmonic interferences in two-dimensional stacked double-disk array,” Appl. Phys. Lett.98(17), 173111 (2011). [CrossRef]
  39. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972). [CrossRef]
  40. E. D. Palik, Handbook of Optical Constants of Solids, Academic Press handbook series (Academic Press, 1997).
  41. S. Zhang, K. Bao, N. J. Halas, H. Xu, and P. Nordlander, “Substrate-induced Fano resonances of a plasmonic nanocube: a route to increased-sensitivity localized surface plasmon resonance sensors revealed,” Nano Lett.11(4), 1657–1663 (2011). [CrossRef] [PubMed]
  42. M. W. Knight, Y. Wu, J. B. Lassiter, P. Nordlander, and N. J. Halas, “Substrates matter: influence of an adjacent dielectric on an individual plasmonic nanoparticle,” Nano Lett.9(5), 2188–2192 (2009). [CrossRef] [PubMed]
  43. R. C. Dorf and J. A. Svoboda, Introduction to Electric Circuits, 5th ed. (Wiley, 2001).
  44. Z. Iluz and A. Boag, “Dual-Vivaldi wideband nanoantenna with high radiation efficiency over the infrared frequency band,” Opt. Lett.36(15), 2773–2775 (2011). [CrossRef] [PubMed]

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