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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 14 — Jul. 5, 2010
  • pp: 14842–14849
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Modeling and experimental verification of optical materials formed by stacked nanostrips

Xingzhan Wei, Haofei Shi, Guoxing Zheng, Xiaochun Dong, and Chunlei Du  »View Author Affiliations


Optics Express, Vol. 18, Issue 14, pp. 14842-14849 (2010)
http://dx.doi.org/10.1364/OE.18.014842


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Abstract

The effective plasma frequency fp of periodic metallic wires whose characteristic dimensions are comparable to their skin depth has been analyzed. And a relevant analytic model is constructed by considering the skin effect and making a reasonable shape approximation, which is suitable for the case that the cross section of the wire is noncircular. To verify this model, a wires array with rectangle cross section is designed and the corresponding stacked Au-SiO2 nanostrips are fabricated. The experimental and simulational transmittances of the metamaterial have been evaluated with a good agreement, although the presence of quartz substrate and structural imperfections in experiment will have an impact, which validates that the multilayer Au-SiO2 nanostrips could function similarly to a natural bulk metal with discrepancies of fp values less than 8%. It could be confirmed that the theoretic formula is trustworthy in predicting fp for designing and realizing a controllable artificial metal in optical region.

© 2010 OSA

1. Introduction

Early in 1962, periodic arrangements of thin metallic wires were known to use as a negative permittivity medium [1

1. W. Rotman, “Plasma Simulation by Artificial Dielectrics and Parallel-Plate Media,” IRE Trans. Antennas Propag. 10(1), 82–95 (1962). [CrossRef]

]. It was therefore important to understand how the electromagnetic response (especially fp) depends on the structural parameters of the wire system. The early relevant work was proposed by Pendry et al., they demonstrated that the metallic wire-mesh structures have a low frequency stop band from zero frequency up to a cut-off frequency, which was attributed to the motion of electrons in the metal wires [2

2. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs I, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996). [CrossRef] [PubMed]

,3

3. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys. Condens. Matter 10(22), 4785–4809 (1998). [CrossRef]

]. What is more, this artificial material could exhibit novel electromagnetic properties being similar to bulk metals. And fp was depressed into GHz region. The metamaterial of Pendry was composed of very thin wires (namely r<<δ, r and δ is the radius and skin depth of the metal wire, respectively), and the cross section of wire is specifically required to be circular. All electrons would equally participate in the modulation of fp. Thus the skin effect could be ignored, and Pendry’s model was given by
fp2=c022πa2ln(a/r)                                    r<<δ
(1)
where c 0 is the velocity of light in vacuum, and a is the lattice constant of the wire array. Since then several alternative theories have been proposed [4

4. S. I. Maslovski, S. A. Tretyakov, and P. A. Belov, “Wire media with negative effective permittivity: A quasi-static model,” Microw. Opt. Technol. Lett. 35(1), 47–51 (2002). [CrossRef]

6

6. S. Brand, R. A. Abram, and M. A. Kaliteevski, “Complex photonic band structure and effective plasma frequency of a two-dimensional array of metal rods,” Phys. Rev. B 75(3), 035102 (2007). [CrossRef]

]. However, the skin effect which influences to the interaction of the electromagnetic wave with metal is insufficiently considered. With regard to the condition that the wire is thick, namely the radius is relatively larger than the skin depth δ, it has been verified that only the effective active electrons near the wire surface will work and take part in the modulation of fp [7

7. X. Wei, H. Shi, Q. Deng, X. Dong, C. Liu, Y. Lu, and C. Du, “Artificial metal with effective plasma frequency in near-infrared region,” Opt. Express 18(4), 3370–3378 (2010). [CrossRef] [PubMed]

]. In addition, the effects of skin depth on fp were studied for the case of rods with circular cross-section [8

8. M. G. Silveirinha, “Nonlocal homogenization model for a periodic array of epsilon-negative rods,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(4), 046612 (2006). [CrossRef] [PubMed]

,9

9. M. G. Silveirinha, “Artificial plasma formed by connected metallic wires at infrared frequencies,” Phys. Rev. B 79(3), 035118 (2009). [CrossRef]

].

However, for creating artificial structured material in the optical region, besides the lattice period is reduced to the nanoscale level, the dimension of the metal wire is very close to the skin depth and the cross section of the metal wire can normally not be formed in a circular shape by present nano-fabrication means. It is very important to develop a relevant method for predicting fp of the optical structured material with above requirement.

In this paper, we demonstrate a design for predicting fp of the structured material in optical region with a noncircular cross section being comparable to the skin depth δ. Accordingly, an improved model is deduced by considering the skin effect and making a reasonable shape approximation. The noncircular wires could be approximated into circular ones by keeping the total amount of the electrons invariable which determines fp. For instance, the design is given for wires array with rectangle cross section. According to the theoretic investigation of fp, we report a successful fabrication of an elementary artificial metal composed of multilayer Au-SiO2 nanostrips whose fp is in optical region. The experimental and simulational transmittance results have been evaluated with a good agreement. It is validated that the multilayer Au-SiO2 nanostrips could function similarly to a natural bulk metal based on the model. This metamaterial may lead to various plasmonics-based applications such as subwavelength waveguides and antennas [10

10. S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89(21), 213902 (2002). [CrossRef] [PubMed]

,11

11. R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100(2), 023903–023907 (2008). [CrossRef] [PubMed]

], spectral selective filters [12

12. S. Zhang, W. 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]

], superlens [13

13. 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]

,14

14. Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. 7(2), 403–408 (2007). [CrossRef] [PubMed]

] and negative refraction [15

15. G. Dolling, M. Wegener, and S. Linden, “Realization of a three-functional-layer negative-index photonic metamaterial,” Opt. Lett. 32(5), 551–553 (2007). [CrossRef] [PubMed]

].

2. Modeling of effective plasma frequency

In Fig. 1
Fig. 1 Schematic view of the geometry under consideration. The basic geometrical parameters are wire period a, skin depth δ and effective radius reff.
, an array of infinitely long, parallel metal wires with noncircular cross section is placed periodically in a square lattice with distance a. The electric field is applied parallel to the wires (along the y axis). When the waves impinge this system, the electrons are confined to move within the wires. Thus, two vital consequences are brought: the first is the decrease of the average electrons density due to diluting of the metal by the air space; the second is the distinct enhancement of the effective mass of the electrons caused by magnetic effects [2

2. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs I, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996). [CrossRef] [PubMed]

].

In order to test the improved model, we first carried out 3D Finite-Difference Time-Domain (FDTD) calculations for Au wire with a circular cross section. Au could be well described by the free-electron Drude model [16

16. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312(5775), 892–894 (2006). [CrossRef] [PubMed]

] with the parameters plasma frequency ωpl = 1.32 × 1016s−1 and collision frequency ωcol = 1.2 × 1014s−1. Note that the skin depth of Au is frequency dependent, whereas the change is not obvious. Therefore, we consider it as an invariable parameter with the value of 20 nm in the visible and near-infrared region [17

17. V. Shrotriya, E. H. Wu, G. Li, Y. Yao, and Y. Yang, “Efficient light harvesting in multiple-device stacked structure for polymer solar cells,” Appl. Phys. Lett. 88(6), 064104 (2006). [CrossRef]

]. As the cross section is circular, Eq. (3) can be specifically expressed as
N'=n'0rexp(rr')/δ2πr'dr'=n'δ2π(rδ+δexp(r/δ))
(9)
where r is the radius of the original circular wire, which is comparable to δ. When r = 25 nm, reff can be obtained to be 20.7 nm through solving Eqs. (4) and (9). To obtain fp through simulation, we applied the well known retrieval procedure [18

18. D. R. Smith, S. Schultz, P. Markos, 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]

] to calculate the effective permittivity εeff from the simulated reflection and transmission data. And fp can be determined at the frequency where εeff = 0. Figure 2
Fig. 2 fp values yielded by FDTD simulation and our analytic model (r = 25 nm and reff = 20.7 nm). Dark solid line and red dash line represents fp values by simulation and model, respectively.
shows the comparisons of fp values, which are derived by the FDTD simulation and our analytic model, separately. The discrepancies between the simulation and our model are small, and the maximum value is less than 8%.

The rectangular cross section of wire is considered as shown in Fig. 3
Fig. 3 fp values yielded by FDTD simulation and our analytic model (w = 70 nm, t = 30 nm and reff = 21.7 nm). Green solid line and purple dash line represents fp values by simulation and model, respectively.
, where the width and height of the rectangle is w and t, respectively. For this case, N' can be formulated as the following expression corresponding to the Eq. (3). Here t is comparable to δ and much smaller than w,
N'=n'2w0t2exp(t2x)/δdx
(10)
By solving Eqs. (4) and (10), the rectangular cross section with w = 70 nm and t = 30 nm can be replaced by an equivalent circle with reff = 21.7 nm. In Fig. 3, the simulation results by FDTD as the criterion are compared with the predicting ones by model which indicates the validity of the improved model for the rectangle wire. Similarly, this model could be suitable for many other shapes, such as ellipse, square and irregular shape through above reasonable approximation.

3. Experiment

In what follows, the fabrication is described for the artificial metal whose fp is in optical region by using Au strip surrounded by SiO2. An elementary bulk metamaterial composed of triple Au strips has been designed, as shown in Fig. 4(a)
Fig. 4 (a) Scheme of the multilayer nanostrips. The geometrical parameters are indicated and given by strip width w, strip period p, metal depth t, and SiO2 depth s. (b) Schematic view of the processes of fabricating the Au-SiO2 composite metamaterials.
. We have actualized an etching-based procedure [19

19. A. Boltasseva and V. M. Shalaev, “Fabrication of optical negative-index metamaterials: Recent advances and outlook,” Metamaterials (Amst.) 2(1), 1–17 (2008). [CrossRef]

] to fabricate these multilayer materials. Figure 4(b) shows the major fabrication processes.

The first approach was to evaporate Au and SiO2 layer by layer (Au-SiO2-Au-SiO2-Au) onto the SiO2 substrate at pressures about 4 mTorr by magnetron sputtering (LAB-18, Kutt. J. Lesker). The depths of Au and SiO2 were 20 nm and 40 nm, respectively. Subsequently, 200 nm thick poly(methy lmethacrylate) (PMMA) was spun on the top of the upper Au film. And then, lithography was performed by using standard electron beam exposure apparatus (JBX5500ZA), followed by an appropriate development for 90 s in a solution of methyl isobutyl ketone (MIBK) diluted 1:3 by volume with isopropyl alcohol (IPA) at 21°C. For achieving the artificial metal with excellent performance, the results of electron beam lithography were examined using field emission scanning electron microscope (Quanta 400 FEG) to confirm the fine quality. Although the sample of 40nm minimum lateral feature size and 200 nm thickness were fabricated, some parts of the PMMA patterns collapsed as shown in Fig. 5(a)
Fig. 5 (a) Top-view electron micrograph of the PMMA patterns with geometrical parameters p = 250 nm, w = 40 nm and thickness 200 nm. The collapsed patterns are shown in the dot frame. (b) Electron micrograph of the good sample fabricated by the etching-based procedure. Inset, magnified view. p = 250 nm, w = 70 nm.
because of the high aspect ratio (i.e., height/width). Obviously, this result would not meet the requirement for the following etching step. However, the unwanted effect could be avoided by extending the strip width w to 70 nm. Next, the PMMA pattern was transferred into the multilayer Au and SiO2 film using deep anisotropic etching in LKJ-1C-150 IBE system with Ar at pressures below 2 × 10−2 Pa. The samples were rotated to achieve uniform etching rate in various directions. The cooling system of etching device could help to control working temperature to avoid the PMMA deformation caused by ion bombardment. The etching rates of Au, SiO2, and PMMA were beforehand stabilized at 30 nm/min, 15 nm/min, and 23 nm/min, respectively, with 80 mA ion beam, 300 eV ion energy, 180 V acceleration voltage, and 2 mA neutralization current. After 8 min etching, the pre-patterned PMMA topography could be perfectly transferred into the alternating Au-SiO2 layers. The electron micrograph of the best sample (500 μm × 500 μm footprint) shown in Fig. 5(b) reveals a good large-scale homogeneity with the feature dimension about 70 nm line width and 250 nm period, and the sidewall roughness is about 10 nm. With these experimental parameters, the effective plasma wavelength can be estimated by our model. We can obtain reff = 18.7 nm through solving Eqs. (4) and (10) and a can be appropriately decided to be p(s+t)123nm. Since the dielectric material is composed by air and SiO2, the modulation factor could be effectively decided to be εr(SiO2)g+εr(air)(1g)1.3by effective medium theory, where g represents the ratio of the area of SiO2 to the whole filling layer, εr(SiO2)2.31 and εr(air)1. Then, the effective plasma wavelength of λp=c/fp=483nm can be calculated by using Eq. (8).

In order to test the effective plasma wavelength and the properties of the artificial structure, we measured the transmission spectra of the nanostrips sample for two orthogonal polarizations (parallel and perpendicular to the strips) over a broad spectral range. For the optical characteristic evaluation, a commercial ellipsometer (MD2000D, J. A. Woollam) which could provide and collect a linearly polarized broadband light with the range from visible to near-infrared were employed. By complementing with a home-built setup (Diaphragm and travel translation stage), only the lights that passed through the sample were collected. Normalization was performed with respect to the bare quartz substrate.

4. Results and discussion

These measured spectra [dash lines in Fig. 6(a)
Fig. 6 (a) Measured normal-incidence transmittance spectrum (dashed curves) and corresponding simulated results (solid curves) for two orthogonal polarizations. (b) Complex permittivity retrieved from the phase and amplitude data of the simulated transmission and reflection. Solid curves, real parts; dashed curves, imaginary parts. (p = 250 nm, w = 70 nm, s = 40 nm and t = 20 nm).
] are directly compared with numerical calculations [solid lines in Fig. 6(a)]. For the perpendicular polarization, this metamaterial can be regarded as an effective medium [20

20. J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94(19), 197401 (2005). [CrossRef] [PubMed]

]. A transmission coefficient with the value of 100% at 725 nm is presented in the simulation curve, as the Fabry-Perot resonance condition is well fulfilled. However, this condition is destroyed due to the existence of quartz substrate in the experiment, so the transmittance peak is not exhibited in the measured spectrum. We can also find that two minima occur at around 570 nm in the transmittance spectrums of the experiment and simulation. This phenomenon results from an anti-symmetric current from in the upper and lower strips, which forms a circular current and gives rise to a magnetic response [21

21. J. Zhou, E. N. Economon, T. Koschny, and C. M. Soukoulis, “Unifying approach to left-handed material design,” Opt. Lett. 31(24), 3620–3622 (2006). [CrossRef] [PubMed]

]. The magnetic resonance is greatly sensitive to the geometrical parameters [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]

]. So, the minima positions which have a minor discrepancy (about 23 nm) between experiment and simulation are responsible for the sidewall roughness of the structure. Anyway the experimental and simulational transmittances reveal a good agreement. For the polarization parallel to the strips, the spectrum displays a diluted metal with λp = 524 nm as shown in Fig. 6(b). And the discrepancy of the effective plasma wavelength between above-mentioned prediction by model and the experiment is below 8%. Above the interested plasma wavelength, the real part of effective permittivity is regularly negative. Note that only the modes whose electric fields are parallel to the strips will play a great role in the modulation of fp.

5. Conclusion

In summary, we have demonstrated a metamaterial composed of Au-SiO2 nanostrips numerically and experimentally to create diluted plasma responses in the visible spectrum. Also, we have proposed an improved analytical model to predict fp, which is suitable for the case that the characteristic dimension of the metal wire is comparable to δ. The dependence of fp on the geometric parameters, which can be predicted by the model, provides us with a general recipe for designing and fabricating such artificial metal at desired frequency. This new artificial material may open new possibilities for many plasmonics-based applications in much wider regime, and the fascinating electrodynamic effects of such metamaterials are expected to be investigated further.

Acknowledgment

This work was supported by the National Basic Research Program (2006CB302900), High Tech. Program of China (2007AA03Z332) and the Chinese Nature Science Grant (10904118, 60727006). We thank Wenhua Shi, Qiang Zha, Baoshun Zhang, Yongxin Qiu, Kai Huang and Xionghui Zeng of Suzhou Institute of Nano-tech and Nano-bionics, Chinese Academy of Sciences, for assisting in experiment.

References and links

1.

W. Rotman, “Plasma Simulation by Artificial Dielectrics and Parallel-Plate Media,” IRE Trans. Antennas Propag. 10(1), 82–95 (1962). [CrossRef]

2.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs I, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996). [CrossRef] [PubMed]

3.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys. Condens. Matter 10(22), 4785–4809 (1998). [CrossRef]

4.

S. I. Maslovski, S. A. Tretyakov, and P. A. Belov, “Wire media with negative effective permittivity: A quasi-static model,” Microw. Opt. Technol. Lett. 35(1), 47–51 (2002). [CrossRef]

5.

M. Silveirinha and C. Fernandes, “A Hybrid Method for the Efficient Calculation of the Band Structure of 3-D Metallic Crystals,” IEEE Trans. Microw. Theory Tech. 52(3), 889–902 (2004). [CrossRef]

6.

S. Brand, R. A. Abram, and M. A. Kaliteevski, “Complex photonic band structure and effective plasma frequency of a two-dimensional array of metal rods,” Phys. Rev. B 75(3), 035102 (2007). [CrossRef]

7.

X. Wei, H. Shi, Q. Deng, X. Dong, C. Liu, Y. Lu, and C. Du, “Artificial metal with effective plasma frequency in near-infrared region,” Opt. Express 18(4), 3370–3378 (2010). [CrossRef] [PubMed]

8.

M. G. Silveirinha, “Nonlocal homogenization model for a periodic array of epsilon-negative rods,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(4), 046612 (2006). [CrossRef] [PubMed]

9.

M. G. Silveirinha, “Artificial plasma formed by connected metallic wires at infrared frequencies,” Phys. Rev. B 79(3), 035118 (2009). [CrossRef]

10.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89(21), 213902 (2002). [CrossRef] [PubMed]

11.

R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100(2), 023903–023907 (2008). [CrossRef] [PubMed]

12.

S. Zhang, W. 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]

13.

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]

14.

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. 7(2), 403–408 (2007). [CrossRef] [PubMed]

15.

G. Dolling, M. Wegener, and S. Linden, “Realization of a three-functional-layer negative-index photonic metamaterial,” Opt. Lett. 32(5), 551–553 (2007). [CrossRef] [PubMed]

16.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312(5775), 892–894 (2006). [CrossRef] [PubMed]

17.

V. Shrotriya, E. H. Wu, G. Li, Y. Yao, and Y. Yang, “Efficient light harvesting in multiple-device stacked structure for polymer solar cells,” Appl. Phys. Lett. 88(6), 064104 (2006). [CrossRef]

18.

D. R. Smith, S. Schultz, P. Markos, 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]

19.

A. Boltasseva and V. M. Shalaev, “Fabrication of optical negative-index metamaterials: Recent advances and outlook,” Metamaterials (Amst.) 2(1), 1–17 (2008). [CrossRef]

20.

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94(19), 197401 (2005). [CrossRef] [PubMed]

21.

J. Zhou, E. N. Economon, T. Koschny, and C. M. Soukoulis, “Unifying approach to left-handed material design,” Opt. Lett. 31(24), 3620–3622 (2006). [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]

OCIS Codes
(160.4670) Materials : Optical materials
(160.4760) Materials : Optical properties
(260.5740) Physical optics : Resonance
(350.4238) Other areas of optics : Nanophotonics and photonic crystals

ToC Category:
Metamaterials

History
Original Manuscript: April 27, 2010
Revised Manuscript: June 5, 2010
Manuscript Accepted: June 16, 2010
Published: June 28, 2010

Citation
Xingzhan Wei, Haofei Shi, Guoxing Zheng, Xiaochun Dong, and Chunlei Du, "Modeling and experimental verification of optical materials formed by stacked nanostrips," Opt. Express 18, 14842-14849 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-14-14842


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References

  1. W. Rotman, “Plasma Simulation by Artificial Dielectrics and Parallel-Plate Media,” IRE Trans. Antennas Propag. 10(1), 82–95 (1962). [CrossRef]
  2. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996). [CrossRef] [PubMed]
  3. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys. Condens. Matter 10(22), 4785–4809 (1998). [CrossRef]
  4. S. I. Maslovski, S. A. Tretyakov, and P. A. Belov, “Wire media with negative effective permittivity: A quasi-static model,” Microw. Opt. Technol. Lett. 35(1), 47–51 (2002). [CrossRef]
  5. M. Silveirinha and C. Fernandes, “A Hybrid Method for the Efficient Calculation of the Band Structure of 3-D Metallic Crystals,” IEEE Trans. Microw. Theory Tech. 52(3), 889–902 (2004). [CrossRef]
  6. S. Brand, R. A. Abram, and M. A. Kaliteevski, “Complex photonic band structure and effective plasma frequency of a two-dimensional array of metal rods,” Phys. Rev. B 75(3), 035102 (2007). [CrossRef]
  7. X. Wei, H. Shi, Q. Deng, X. Dong, C. Liu, Y. Lu, and C. Du, “Artificial metal with effective plasma frequency in near-infrared region,” Opt. Express 18(4), 3370–3378 (2010). [CrossRef] [PubMed]
  8. M. G. Silveirinha, “Nonlocal homogenization model for a periodic array of epsilon-negative rods,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(4), 046612 (2006). [CrossRef] [PubMed]
  9. M. G. Silveirinha, “Artificial plasma formed by connected metallic wires at infrared frequencies,” Phys. Rev. B 79(3), 035118 (2009). [CrossRef]
  10. S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89(21), 213902 (2002). [CrossRef] [PubMed]
  11. R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100(2), 023903–023907 (2008). [CrossRef] [PubMed]
  12. S. Zhang, W. 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]
  13. 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]
  14. Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. 7(2), 403–408 (2007). [CrossRef] [PubMed]
  15. G. Dolling, M. Wegener, and S. Linden, “Realization of a three-functional-layer negative-index photonic metamaterial,” Opt. Lett. 32(5), 551–553 (2007). [CrossRef] [PubMed]
  16. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312(5775), 892–894 (2006). [CrossRef] [PubMed]
  17. V. Shrotriya, E. H. Wu, G. Li, Y. Yao, and Y. Yang, “Efficient light harvesting in multiple-device stacked structure for polymer solar cells,” Appl. Phys. Lett. 88(6), 064104 (2006). [CrossRef]
  18. D. R. Smith, S. Schultz, P. Markos, 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]
  19. A. Boltasseva and V. M. Shalaev, “Fabrication of optical negative-index metamaterials: Recent advances and outlook,” Metamaterials (Amst.) 2(1), 1–17 (2008). [CrossRef]
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