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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 23 — Nov. 7, 2011
  • pp: 22942–22949
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Exchange of electric and magnetic resonances in multilayered metal/dielectric nanoplates

De Li, Ling Qin, Xiang Xiong, Ru-Wen Peng, Qing Hu, Guo-Bin Ma, Hao-Shen Zhou, and Mu Wang  »View Author Affiliations


Optics Express, Vol. 19, Issue 23, pp. 22942-22949 (2011)
http://dx.doi.org/10.1364/OE.19.022942


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Abstract

In this work, we have experimentally demonstrated that in a rectangular multilayered Ag/SiO2 nanoplate array, electric and magnetic resonances are exchanged at the same frequency simply by changing the polarization of incident light for 90°. Both electric and magnetic resonances originate from localized surface plasmons, and lead to negative permittivity and permeability, respectively. The numerical calculations on electromagnetic fields agree with the experiments. The investigations provide a simple building block for a metamaterial to switch electric and magnetic resonances by external excitation field.

© 2011 OSA

In the past decade, metamaterials have drivingly developed, which provides a new paradigm to control the electromagnetic properties of materials beyond the nature. With deliberately designed metallic microstructures, specific electromagnetic responses are realized, such as artificial magnetism [1

1. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from Conductors and Enhanced Nonlinear Phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999). [CrossRef]

, 2

2. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000). [CrossRef] [PubMed]

], extraordinary optical transmission [3

3. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]

5

5. Y. J. Bao, R. W. Peng, D. J. Shu, M. Wang, X. Lu, J. Shao, W. Lu, and N. B. Ming, “Role of interference between localized and propagating surface waves on the extraordinary optical transmission through a subwavelength-aperture array,” Phys. Rev. Lett. 101(8), 087401 (2008). [CrossRef] [PubMed]

], optical antenna [6

6. Z. J. Zhang, R. W. Peng, Z. Wang, F. Gao, X. R. Huang, W. H. Sun, Q. J. Wang, and M. Wang, “Plasmonic antenna array at optical frequency made by nanoapertures,” Appl. Phys. Lett. 93(17), 171110 (2008). [CrossRef]

], subwavelength imaging [7

7. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]

, 8

8. X. Zhang and Z. W. Liu, “Superlenses to overcome the diffraction limit,” Nat. Mater. 7(6), 435–441 (2008). [CrossRef] [PubMed]

] and invisible cloaking [9

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

]. As we know, there are no high-frequency magnetic materials in nature. However, the high-frequency magnetic response of a metamaterial can be achieved by the interaction of magnetic component of incident light and induced magnetic dipole moment. Recently, some engineered metallic structures have been investigated, in which magnetic resonances can be excited from microwave to optical frequencies, such as double split-ring resonators (SRRs) [1

1. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from Conductors and Enhanced Nonlinear Phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999). [CrossRef]

, 10

10. T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004). [CrossRef] [PubMed]

], coupled metal nano-strips [11

11. S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004). [CrossRef] [PubMed]

], the metal wire pairs [12

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

], gold nanosandwiches [13

13. 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]

], fishnet structures [14

14. 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]

] and so on. At optical frequencies, the metal-dielectric-metal nanosandwich is very common as a resonant magnetic structure, however, few efforts have been made to exploit multilayerd metal/dielectric nanostructures [15

15. K. H. Su, Q. H. Wei, and X. Zhang, “Tunable and augmented plasmon resonances of Au/SiO2 /Au nanodisks,” Appl. Phys. Lett. 88(6), 063118 (2006). [CrossRef]

, 16

16. X. Z. Wei, H. F. Shi, X. C. Dong, Y. G. Lu, and C. L. Du, “A high refractive index metamaterial at visible frequencies formed by stacked cut-wire plasmonic structures,” Appl. Phys. Lett. 97(1), 011904 (2010). [CrossRef]

], where the coupling of surface plasmons may play an important role [17

17. Z. H. Tang, R. W. Peng, Z. Wang, X. Wu, Y. J. Bao, Q. J. Wang, Z. J. Zhang, W. H. Sun, and M. Wang, “Coupling of surface plasmons in nanostructured metal/dielectric multilayers with subwavelength hole arrays,” Phys. Rev. B 76(19), 195405 (2007). [CrossRef]

].

Firstly, we have designed a rectangular multilayered Ag/SiO2 nanoplate array (as shown in Fig. 1(a)
Fig. 1 (a) Schematic view of multilayered Ag/SiO2 nanoplates on a glass substrate with periodicities of the square lattice ax=ay=400nm, and widths of the rectangular nanoplate ux=220nm and uy=110nm. The layer sequence from the glass substrate to the top is Ag/SiO2/Ag/SiO2/Ag/SiO2/Ag/SiO2 with a total thickness d=160nm, where all Ag layers are 25 nm thick and SiO2 layers are 13.3 nm thick except the topmost SiO2 layer of 20 nm thick. (b) The calculated normal transmission spectra for the structure described in (a), which is illuminated from the glass substrate by the x-polarized (black curve) and y-polarized (red curve) incident light, respectively. The x-z plane cross section of (c) the electric field distribution E where the arrows represent direction and the color map represents intensity and (d) the magnetic field distribution Hy for the electric resonance (Mode #1) in the x-polarized incidence. The y-z plane cross section of (e) the electric field distribution E and (f) the magnetic field distribution Hx for the magnetic resonance (Mode #2) in the y-polarized incidence. Here, the black boxes and the white line represent Ag layers and the boundary of air, respectively. (g) Schematics of the effective currents induced in multiple Ag layers for the four optical modes marked in (b), respectively.
). Optical properties of this nanoplate array are calculated based on the full-vectorial three-dimensional finite-difference time-domain (FDTD) method. In the simulations, the frequency-dependent permittivity of Ag is obtained from the Lorentz-Drude model [21

21. A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37(22), 5271–5283 (1998). [CrossRef] [PubMed]

]. Figure 1(b) shows the normal transmission spectra when the light along z axis illuminates this structure from the glass substrate. In the x-polarized incidence (black curve), there is a broad transmission dip (marked as Mode #1) at the wavelength λ=789nm, while there is a narrow dip (marked as Mode #2) at λ=794nm in the y-polarized incidence (red curve). Although two dips are located at the same wavelength λ800nm, they originate from the electric and magnetic resonances, respectively. Figures 1(c) and (d) illustrate the electric field distribution E and the magnetic field distribution Hy in the x-z plane for the electric resonance (Mode #1). The electric fields in all Ag layers are in the same directions, and the electric field around the nanoplate is very strong, especially at four corners. The magnetic field Hy in the center of the nanoplate is weak while those on top and bottom of the nanoplate are quite strong with opposite directions. Obviously, the LSPs on multiple Ag layers are in-phase coupled, which lead to the electric resonance. In contrast, the magnetic resonance results from the out-of-phase coupling of LSPs on multiple Ag layers [20

20. D. Li, L. Qin, D. X. Qi, F. Gao, R. W. Peng, J. Zou, Q. J. Wang, and M. Wang, “Tunable electric and magnetic resonances in multilayered metal/dielectric nanoplates at optical frequencies,” J. Phys. D Appl. Phys. 43(34), 345102 (2010). [CrossRef]

]. For Mode #2, as shown in Figs. 1(e) and (f), the electric fields in the upper and lower Ag layers are in the opposite directions, and the electric fields are very strong with opposite directions between left and right sides in SiO2 layers; while the magnetic fields are strong within the multiayer structure. All these phenomena indicate that the Mode #2 comes from the magnetic resonance.

It is interestingly noted that there are more than two optical modes excited in the structure (as shown in Fig. 1(b)). Due to the fact that the diffraction is strong enough and optical excitation becomes complicated when the wavelength is less than 600nm or so, we simply pay attention to the cases when the wavelength is larger than 600nm. As marked in Fig. 1(b), four transmission dips appear in both x-polarized and y-polarized incidences when λ>600nm. By calculating the electromagnetic filed distributions at these dips, the local currents in the layer structure can be obtained, which are effectively illustrated by the highlighted arrows in Fig. 1(g). For Mode #1, the effective currents in four Ag layers are in parallel and form the effective electric dipoles, which is the symmetric excitation corresponding to the electric resonance (as discussed above); while for Mode #2, the effective currents in the upper two Ag layers are in parallel, and the currents in lower two Ag layers are in anti-parallel with those in upper two layers. Therefore, the effective circular currents are induced and form the effective magnetic dipole, that is, Mode #2 is antisymmetric excitation corresponding to the magnetic resonance (as discussed above). Mode #1 and Mode #2 are similar to the excitations in two-Ag-layer-coupled systems [22

22. V. M. Shalaev, W. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30(24), 3356–3358 (2005). [CrossRef] [PubMed]

]. As for Mode #3 and Mode #4, both of them are antisymmetric excitations. The magnetic fields induced by circular currents in Mode #3 and Mode #4 may cancel each other, thereafter, these two excitations becomes weak.

Now we try to give more evidence to illustrate the electric resonance (Mode #1) and the magnetic resonance (Mode #2) at λ800nm. We consider the whole structure effectively as a homogeneous slab with the thickness d=160nm between the glass substrate and the air, and derive the effective permittivity εand permeability μ from normal reflection and transmission coefficients, analysed by a robust retrieval algorithm [23

23. D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002). [CrossRef]

]. In the x-polarized incidence, there is a relatively wide negative electric response around the wavelengthλ800nm, as shown in Fig. 2(a)
Fig. 2 (a) The retrieved permittivity εx and (b) permeability μyfor the nanoplates illuminated by the x-polarized normal incidence, while (c) εy and (d) μx for the y-polarized incidence. Here, the black solid and red dashed curves stand for the real and imaginary parts, respectively.
. Meanwhile, the electric resonance introduces a magnetic anti-resonance response [24

24. T. Koschny, P. Markoš, D. R. Smith, and C. M. Soukoulis, “Resonant and antiresonant frequency dependence of the effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(6), 065602 (2003). [CrossRef] [PubMed]

], as an evident drop of Re(μy) and a negative value of Im(μy) in Fig. 2(b). Actually, the magnetic anti-resonance always accompanies with the electric resonance, because the anti-resonance is intrinsic in a metamaterial owing to the finite spatial periodicity. During the resonance, the magnetic field is gained with negative Im(μy), but the electric filed is attenuated with positive Im(εx), as shown in Fig. 2(a). Thereafter, the total energy is not gained and the system still obeys the conversation of energy. While in the y-polarized incidence, the magnetic resonance results in a narrow band of negative magnetic response and introduces a weak electric anti-resonance response at the wavelength λ800nm, as shown in Fig. 2(d) and (c) respectively. (Here, the electric anti-resonance can be analog to the above magnetic anti-resonance.) These properties confirm the electric and magnetic resonances, which can be switched at the same frequency by changing the polarization of incident light for 90°.

It should be mentioned that only by optimizing the widths of the nanoplates, the electric and magnetic resonances coincide at the same wavelength λ800nmin different polarization excitations. The electric and magnetic resonances are tuned by changing the widths of the nanoplates (as shown in Fig. 3
Fig. 3 The calculated normal transmission spectra of rectangular nanoplates with varying the long width ux for (a) x-polarization and (b) y-polarization, and varying the short width uy for (c) x-polarization and (d) y-polarization. Here, ux=220,230and240nm and uy=110nm for (a) and (b), and uy=110,120and130nm and ux=220nm for (c) and (d).
). When the short width is fixed as uy=110nm but the long width is varied as ux=220,230and240nm, the electric resonance shifts a little to the red for the x-polarization as shown in Fig. 3(a), and the magnetic resonance does not move for the y-polarization as shown in Fig. 3(b). In contrast, when the long width is fixed as ux=220nm and the short width is tuned as uy=110,120and130nm, the electric resonance shifts a little to the blue for the x-polarization as shown in Fig. 3(c), while the magnetic resonance dramatically shift to the red for the y-polarization as shown in Fig. 3(d). Therefore, the electric resonance depends on both widths of the nanoplates differently, while the magnetic resonance only determined by the width along polarization, as discussed in Ref. 20

20. D. Li, L. Qin, D. X. Qi, F. Gao, R. W. Peng, J. Zou, Q. J. Wang, and M. Wang, “Tunable electric and magnetic resonances in multilayered metal/dielectric nanoplates at optical frequencies,” J. Phys. D Appl. Phys. 43(34), 345102 (2010). [CrossRef]

.

In experiments, a nanoplate array was fabricated by using magnetron sputtering and focused-ion-beam (FIB) facility, and its optical spectra were measured by a micro-spectrophotometer. First, a multilayered Ag/SiO2 film was coated on a piece of glass substrate by magnetron sputtering, then an array of nanoplates was fabricated on the film by focused-ion-beam facility (strata FIB 201, FEI company, 30 keV Ga ions). Figures 4(a) and (b)
Fig. 4 (a) and (b) The SEM images of multilayered Ag/SiO2 nanoplates on a glass substrate, where the bars represent 1μm and 200 nm, respectively. (c) and (d) The SEM images of side view with a 30° tilt-angle, where both the bars represent 100 nm. Here, the parameters of this sample are nearly the same as that model. (e) and (f) the measured normal transmission spectra for the incident polarization parallel and perpendicular to the long width, respectively, where the red dashed curves are calculated spectra in Fig. 1(b).
shows the field-emission scanning electronic microscope (SEM) images of the sample, where the bars represent 1μm and 200 nm, respectively. And the layer sequence is revealed by the SEM images of side view with a 30° tilt-angle, as shown in Figs. 4(c) and (d) where both the bars represent 100 nm. The average parameters of this sample are close to the theoretical design. However, the nanoplates are a little nonuniform in the array with the sidewall angle of about 15°, and some of the glass substrate is sculpted by the ion beam.

In order to understand the measured data better, we also carried out the calculations for the nanoplates with oblique side walls (schematically shown in Fig. 5(a)
Fig. 5 (a) Configuration of a unit cell with vertical wall as designed, which becomes oblique in fabrication. (b) The calculated normal transmission spectra for the incident polarization (black solid) parallel and (red dashed) perpendicular to the long width, where the side wall of the unit cell is oblique with a tilt angle of about 15°. (c) Schematics of the effective currents induced in multiple Ag layers for the four optical modes marked in (b), respectively.
). For example, in a tapered nanoplate, the top widths of the rectangular nanoplate are set as ux=199nm and uy=89nm, and the bottom widths are set as ux=241nm and uy=131nm, respectively. The tilt angle of the side wall is about 15°. Except for the widths, the other parameters are kept the same as the straight nanoplate array. Figure 5(b) shows the calculated transmission of the tapered nanoplate array for both polarizations, where all the dips are changed a little owing to the variation of widths. Corresponding to four typical modes marked in Fig. 5(b), the effective currents induced in multiple Ag layers are illustrated in Fig. 5(c), respectively. We find that both the electric resonance (Mode #1) and the magnetic resonance (Mode #2) depend on the average width in the tapered nanoplate. The dips of electric and magnetic resonances keep at λ800nm, as the average widths in each direction are just ux=220nm and uy=110nm, respectively. Thus, the straight nanoplate can be adopted in calculations when we focus on switching the electric and magnetic resonances by polarization. Additionally, Mode #3 and Mode #4 are antisymmetric excitations. Comparing the cases of straight nanoplates, the magnetic fields induced by circular currents are cancelled partly in tapered nanoplates, thereafter, these two excitations becomes much more obvious in tapered nanoplates.

Furthermore, we try to experimentally demonstrate the electric and magnetic resonances by varying the incident angle. For the incident polarization perpendicular to the short width, the transmission dip at λ800nm shifts to the red as the incident angle θ increases, while the dip at λ550nm disappears, as shown in Figs. 6(a) and (b)
Fig. 6 The measured oblique transmission spectra in the following cases. The polarization is perpendicular to the short width: (a) TE and (b) TM; while the polarization perpendicular to the long width: (c) TE and (d) TM case. The insets schematically illustrate each oblique incidence.
. For the electric resonance, the electromagnetic field dominates outside the nanoplate, and the interactions between different units are considerable. At the oblique incidence, these interactions will be influenced by phase differences between polarized nanoplates, which lead to the redshift of electric resonance. Contrastively, the magnetic resonance does not shift for the incident polarization perpendicular to the long width, as the transmission dip at λ800nm in Figs. 6(c) and (d). Additionally, this dip becomes shallow when increasing the incident angle θ in the transverse-electric (TE) case, because the in-plane component of incident magnetic field decreases.

In conclusion, we have demonstrated that in a rectangular multilayered Ag/SiO2 nanoplate array, the electric and magnetic resonances are switched at the same frequency by changing the polarization of incident light. Actually, two resonances originate from the in-phase and out-of-phase couplings of LSPs on multiple Ag layers respectively, and they are experimentally discriminable in the oblique incidence. The investigations may provide another way to achieve optical magnetism by switching electric resonance to magnetic one, which may be used to construct specific negative-index materials.

Acknowledgments

This work was supported by the State Key Program for Basic Research from the Ministry of Science and Technology of China (Grant Nos. 2012CB921502 and 2010CB630705), the National Natural Science Foundation of China (Grant Nos.11034005, 61077023, and 11021403), and partly by Jiangsu Province (Grant No. BK2008012) and Ministry of Education of China (Grant No. 20100091110029).

References and links

1.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from Conductors and Enhanced Nonlinear Phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999). [CrossRef]

2.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000). [CrossRef] [PubMed]

3.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]

4.

A. Battula, S. Chen, Y. Lu, R. J. Knize, and K. Reinhardt, “Tuning the extraordinary optical transmission through subwavelength hole array by applying a magnetic field,” Opt. Lett. 32(18), 2692–2694 (2007). [CrossRef] [PubMed]

5.

Y. J. Bao, R. W. Peng, D. J. Shu, M. Wang, X. Lu, J. Shao, W. Lu, and N. B. Ming, “Role of interference between localized and propagating surface waves on the extraordinary optical transmission through a subwavelength-aperture array,” Phys. Rev. Lett. 101(8), 087401 (2008). [CrossRef] [PubMed]

6.

Z. J. Zhang, R. W. Peng, Z. Wang, F. Gao, X. R. Huang, W. H. Sun, Q. J. Wang, and M. Wang, “Plasmonic antenna array at optical frequency made by nanoapertures,” Appl. Phys. Lett. 93(17), 171110 (2008). [CrossRef]

7.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]

8.

X. Zhang and Z. W. Liu, “Superlenses to overcome the diffraction limit,” Nat. Mater. 7(6), 435–441 (2008). [CrossRef] [PubMed]

9.

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

10.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004). [CrossRef] [PubMed]

11.

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004). [CrossRef] [PubMed]

12.

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

13.

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]

14.

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]

15.

K. H. Su, Q. H. Wei, and X. Zhang, “Tunable and augmented plasmon resonances of Au/SiO2 /Au nanodisks,” Appl. Phys. Lett. 88(6), 063118 (2006). [CrossRef]

16.

X. Z. Wei, H. F. Shi, X. C. Dong, Y. G. Lu, and C. L. Du, “A high refractive index metamaterial at visible frequencies formed by stacked cut-wire plasmonic structures,” Appl. Phys. Lett. 97(1), 011904 (2010). [CrossRef]

17.

Z. H. Tang, R. W. Peng, Z. Wang, X. Wu, Y. J. Bao, Q. J. Wang, Z. J. Zhang, W. H. Sun, and M. Wang, “Coupling of surface plasmons in nanostructured metal/dielectric multilayers with subwavelength hole arrays,” Phys. Rev. B 76(19), 195405 (2007). [CrossRef]

18.

X. Xiong, W. H. Sun, Y. J. Bao, R. W. Peng, M. Wang, C. Sun, X. Lu, J. Shao, Z. F. Li, and N. B. Ming, “Switching the electric and magnetic responses in a metamaterial,” Phys. Rev. B 80(20), 201105 (2009). [CrossRef]

19.

X. Xiong, X.-C. Chen, M. Wang, R.-W. Peng, D.-J. Shu, and C. Sun, “Optically nonactive assorted helix array with interchangeable magnetic/electric resonance,” Appl. Phys. Lett. 98(7), 071901 (2011). [CrossRef]

20.

D. Li, L. Qin, D. X. Qi, F. Gao, R. W. Peng, J. Zou, Q. J. Wang, and M. Wang, “Tunable electric and magnetic resonances in multilayered metal/dielectric nanoplates at optical frequencies,” J. Phys. D Appl. Phys. 43(34), 345102 (2010). [CrossRef]

21.

A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37(22), 5271–5283 (1998). [CrossRef] [PubMed]

22.

V. M. Shalaev, W. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30(24), 3356–3358 (2005). [CrossRef] [PubMed]

23.

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002). [CrossRef]

24.

T. Koschny, P. Markoš, D. R. Smith, and C. M. Soukoulis, “Resonant and antiresonant frequency dependence of the effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(6), 065602 (2003). [CrossRef] [PubMed]

25.

M. Meier, A. Wokaun, and P. F. Liao, “Enhanced fields on rough surfaces: dipolar interactions among particles of sizes exceeding the Rayleigh limit,” J. Opt. Soc. Am. B 2(6), 931–949 (1985). [CrossRef]

OCIS Codes
(260.5740) Physical optics : Resonance
(350.3618) Other areas of optics : Left-handed materials
(160.3918) Materials : Metamaterials
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Metamaterials

History
Original Manuscript: September 16, 2011
Revised Manuscript: October 16, 2011
Manuscript Accepted: October 16, 2011
Published: October 27, 2011

Citation
De Li, Ling Qin, Xiang Xiong, Ru-Wen Peng, Qing Hu, Guo-Bin Ma, Hao-Shen Zhou, and Mu Wang, "Exchange of electric and magnetic resonances in multilayered metal/dielectric nanoplates," Opt. Express 19, 22942-22949 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-23-22942


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References

  1. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from Conductors and Enhanced Nonlinear Phenomena,” IEEE Trans. Microw. Theory Tech.47(11), 2075–2084 (1999). [CrossRef]
  2. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett.84(18), 4184–4187 (2000). [CrossRef] [PubMed]
  3. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391(6668), 667–669 (1998). [CrossRef]
  4. A. Battula, S. Chen, Y. Lu, R. J. Knize, and K. Reinhardt, “Tuning the extraordinary optical transmission through subwavelength hole array by applying a magnetic field,” Opt. Lett.32(18), 2692–2694 (2007). [CrossRef] [PubMed]
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