OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 4 — Feb. 15, 2010
  • pp: 3370–3378
« Show journal navigation

Artificial metal with effective plasma frequency in near-infrared region

Xingzhan Wei, Haofei Shi, Qiling Deng, Xiaochun Dong, Chunheng Liu, Yueguang Lu, and Chunlei Du  »View Author Affiliations


Optics Express, Vol. 18, Issue 4, pp. 3370-3378 (2010)
http://dx.doi.org/10.1364/OE.18.003370


View Full Text Article

Acrobat PDF (692 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We have proposed and demonstrated an artificial medium consisting of arrays of circular metal rods embedded in a dielectric host, which holds a real metal behavior but the extracted effective plasma frequency is in near-infrared region. The electromagnetic responses of such medium and the retrieved effective material parameters have been particularly shown. In addition, an analytic model about effective plasma frequency is constructed by uniquely considering the skin effect and introducing the parameter-skin depth, whose predicting results are in well accordance with the FDTD simulation. This artificial material may open possibilities for many metal-based applications in near-infrared regime.

© 2010 OSA

1. Introduction

Surface plasmons (SPs), originating from the free electrons of the metal, are electromagnetic surface excitations localizing near the metal/dielectric interface [1

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

]. Due to two key features, namely, local field enhancement and subwavelength resolution capability, SPs has attracted dramatic attentions recently and are known to play a great role in many domains, such as biochemical sensing [2

2. G. Raschke, S. Kowarik, T. Franzl, C. Sönnichsen, T. A. Klar, J. Feldmann, A. Nichtl, and K. Kürzinger, “Bio-molecular recognition based on single gold nanoparticle light scattering,” Nano Lett. 3(7), 935–938 (2003). [CrossRef]

], near-field microscopy and spectroscopy, superlens [3

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

,4

4. H. Lee, Y. Xiong, N. Fang, W. Srituravanich, S. Durant, M. Ambati, C. Sun, and X. Zhang, “Realization of optical superlens imaging below the diffraction limit,” N. J. Phys. 7, 255 (2005). [CrossRef]

] and hyperlens [5

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

] that enable optical imaging with unprecedented resolution, nanolithography [6

6. W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004). [CrossRef]

] at deep subwavelength scale, and highly integrated optical devices and circuits [7

7. P. Andrew and W. L. Barnes, “Energy transfer across a metal film mediated by surface plasmon polaritons,” Science 306(5698), 1002–1005 (2004). [CrossRef] [PubMed]

,8

8. L. Yin, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, J. Hua, U. Welp, D. E. Brown, and C. W. Kimball, “Subwavelength focusing and guiding of surface plasmons,” Nano Lett. 5(7), 1399–1402 (2005). [CrossRef] [PubMed]

]. However, SPs can only be excited and function at frequencies close to the intrinsic plasma frequency, which generally lies in the UV region for natural metals. At lower frequencies, especially in the far-infrared and microwave regions, the metals resemble the perfect conductor which has infinite conductivity and the local fields are only weakly confined in the dielectric, thus SPs are not supported. This restriction apparently limits the aforementioned SPs-based applications to a wider frequency regime. However, by texturing metal or even perfect-conductor surface with subwavelength holes, corrugations, or dimples, the surface wave modes were obtained which can mimic the properties of SPs [9

9. J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking Surface Plasmons with Structured Surfaces,” Science 305(5685), 847–848 (2004). [CrossRef] [PubMed]

,10

10. F. J. Garcia-Vidal, L. Martín-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005). [CrossRef]

].

2. Artificial near-infrared metal

We study an artificial medium consisting of a rectangular array of circular metal rods embedded in a dielectric host, as shown in Fig. 1
Fig. 1 Outline of the geometry under consideration. The basic geometrical parameters are rods period p, rod diameter d, and layer depth a.
. This structure was chosen because it is typical and assumed to be well understood. The rods are parallel with y direction, and are periodically arranged along x direction with a period p. The spatial extension of the layer in the z direction is assumed to be a. The waves illuminate the structure at normal incidence along z direction, with electric fields along the rods (TE mode). Then, the motion of electrons in the metal rods can take place, which creates a magnetic field circling the rod [11

11. 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]

]. Vacuum is taken as the dielectric host first, and then, the influence of dielectric host on effective plasma frequency will be particularly considered in the latter discussion part. We carried out 3D Finite-Difference Fime-Domain (FDTD) calculations. A sufficiently large number of orders were retained in order to ensure convergence of all quantities derived from the calculation. As usual, the silver optical properties are described by the free-electron Drude model [16

16. 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]

] with the parameters plasma frequency ωpl = 1.37 × 1016s−1 and collision frequency ωcol = 8.50 × 1013s−1.

Calculated transmittance spectrums for TE mode as a function of the number of metal rod layers are shown in Fig. 2(a)
Fig. 2 Transmittances for TE mode (a) and TM mode (b) versus different layer numbers (d = 100nm, a = 300nm, and p = 600nm). (c) Snapshot of electric field at three different frequencies, f = 200, 216, and 240THz, respectively. The wave vector is towards horizontal direction, and a period boundary condition along H direction was selected.
, when d = 100nm, a = 300nm, and p = 600nm. The transmittance is nearly zero in the lower frequency region, and ascends rapidly at about 216THz, which is known as effective plasma frequency or cut-off frequency. When the number of functional layers N changes from 3 to 9, the effective plasma frequency will almost not shift. Thus, we can consider this medium as a high pass filter, that is to say, the electromagnetic wave whose frequency above cut-off frequency is allowed to propagate through the structure. Also, some small dips at higher frequency (above effective plasma frequency) can be observed, and we believe that this phenomenon is due to the F-P cavity effect, arising from multiple reflections in this medium. However, some minima in the transmittance spectrum occur at high frequency domain for TM polarization, as shown in Fig. 2(b). This phenomenon is due to electric and magnetic responses [17

17. 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]

], resulting from the interaction of incident light with the periodical metal rods. Obviously, there is no effective plasma or cut-off frequency for this polarization.

In order to depict the response of our medium with electromagnetic wave vividly, we give the electric distribution patterns at three frequencies as shown in Fig. 2(c). When f = 200ΤΗz, the electric intensity falls off gradually with thickness, and becomes nearly zero in the right side. Therefore, no propagating mode can travel through this structure when the frequency is below effective plasma frequency, which is in well accordance with the transmittance curve depicted in Fig. 2(a). When f = 216ΤΗz, we can find that the effective wavelength in this material is especially large, accordingly there exists a near zero effective refractive index around effective plasma frequency as neff = λvaccum/λeff. When f = 240ΤΗz (above effective plasma frequency), we can find that the effective wavelength is about 2.7μm, and the relevant neff is around 0.46, which is in well accordance with the subsequent retrieved results in Fig. 3 (a)
Fig. 3 Retrieved effective parameters of artificial structure with 3-layers rods. (a) effective refractive index, (b) effective impedance, (c) effective magnetic permeability, (d) effective electric permittivity. The real and imaginary parts of these complex parameters are shown as solid blue and dashed red curves, respectively. (d = 100nm, a = 300nm, and p = 600nm, layers number N = 3).
. Now, the electromagnetic waves are allowed to propagate through the structure. From above mentioned phenomenon, we can find that this structure can be regarded as an artificial metal, but the effective plasma frequency has been modulated into near-infrared region from original ultraviolet domain.

We applied the well-known retrieval procedure [18

18. D. R. Smith, S. Schultz, P. Markoš, and C. 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 refractive index n and the effective wave impedance z from the simulated reflection and transmission data. Then, the effective permittivity ε and permeability μ can be readily obtained in the light of ε = n/z and μ = nz. The retrieved results are depicted in Figs. 3(a)-(d). We can find that the real part of effective refractive index is zero when the frequency of incident light is smaller than effective plasma frequency. Thus, the very low transmittance T shown in Fig. 2(a) can be regarded mainly from the high reflection because of R=(nnvacuumn+nvacuum)(nnvacuumn+nvacuum)*1. Also we can conclude that, when the frequency of incident light is above effective plasma frequency, optical responses are associated with a weak loss as Im(n) = 0, in addition the phase velocity exceeds the speeds of light in vacuum due to 0<Re(n)<1.

One noticeable feature in Fig. 2 (c) is that the electric field amplitudes of the rods center are always zeros at these three frequencies, namely the electrons in these locations cannot “see” the incident electromagnetic waves. Thus, the electromagnetic waves and these aforementioned electrons couldn’t interact, which is quite different from Pendry’s approximation [11

11. 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]

]: all the electrons are uniformly distributed in the cross-section of the thin wire, and entirely attend the modulation of effective plasma frequency. It is no doubt that Pendry’s approximation is not suitable when the rod radius is larger than the skin depth. Therefore, it is very essential to introducing the skin effect. In order to better exhibit the influence of skin effect, we have performed corresponding calculations on the tubes array instead of above rods array as shown in the inset of Fig. 4 (a)
Fig. 4 (a) Transmittances as a function of the tube thickness C. The cross-section of tube is depicted in the inset figure, geometrical parameters used in this simulation are: invariable outside diameter of tube (200nm), layer depth a = 300nm, tube period p = 600nm, and layers number N = 3. (b) Effective plasma frequencies versus tube thickness C by retrieving the calculated transmission and reflection data.
. The outside diameter of tube is unchanged, and we gradually alter the tube thickness C, from below to greatly larger than the skin depth (about 22nm in near-infrared region) [19

19. S. O’Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, “Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials,” Phys. Rev. B 69(24), 241101 (2004). [CrossRef]

]. Figure 4(b) clearly shows that effective plasma frequency increases quickly when the thickness is below 20nm, whereas it nearly doesn’t vary when the thickness is bigger than 40nm. We confirm that this modulation of effective plasma frequency has great relationship with the skin effect. When the metal depth is bigger than the skin depth, only the effective electrons confined at a very thin surface (that is, a little deeper than the skin depth) take part in modulating the effective plasma frequency, and other electrons in the metal cannot “see” the electromagnetic waves and have little effect.

3. Analytical model

We have found that the modulation of effective plasma frequency is greatly influenced by the skin effect. Next, we will derive an approximate analytic formula of effective plasma frequency by considering the skin effect, and the FDTD simulation results are also provided as a criterion to verify this new model. As is well known, the plasma angular frequency ωp is given in terms of the effective active electron density n'eff, the effective electron mass meff and charge e.
ωp2=n'effe2ε0meff
(1)
When the skin effect is considered, supposing n' is the actual conduction electron density in this metal, the amount of the active electrons per unit length of the wire can be immediately expressed to be
N'=n'0Rexp(Rr)/δ2πrdr=n'δ2π(Rδ+δexp(R/δ))=n'δ2πreff=n'δleff
(2)
Here R is rods radius, δ is the skin depth, reff and leff are effective radius and perimeter, respectively. Then, the effective active electron density can be written as
n'eff=n'δleffap
(3)
From Ampere’s circuital law, here the rectangle approximately is regarded as a circle with the same area (ap=b2), and the vector magnetic potential A at a given point outside the wire is [12

12. 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]

]:
A(R')=μ0δleffn'ev2π[ln(R'πb)πR'22b2+12]
(4)
Where R' is the distance between wire center and above interesting point. Therefore, with the same principle as in Pendry’s work [11

11. 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]

], the momentum per unit length of the rod is
P=δleffn'eA(reff)=δleffn'eμ0δleffn'ev2π[ln(reffπb)πreff22b2+12]=meffδleffn'v
(5)
then the effective electrons mass meff is
meff=μ0leffδn'e22π[ln(leff2πb)leff28πb2+12]
(6)
Bringing Eq. (2) and (5) into (1), and we can finally yield
fp2=(ωp2π)2=c022πb2[ln(leff2πb)leff28πb2+12]
(7)
Note that the skin depth, acts as a crucial factor in the modulation of effective plasma frequency, has been involved in the effective perimeter leff. In Fig. 5
Fig. 5 Comparison of effective plasma frequencies yielded by FDTD simulation, our analytic model and Pendry’s model. Purple solid line represents the simulation results, cyan dash line shows our model results, and pink dot line represents Pendry’s model results. (a = 300nm, P = 600nm layers number N = 3).
, the effective plasma frequency values derived by the combination of FDTD simulation and standard S-parameter retrieval method, are provided and compared with the predicting results calculated by our and Pendry’s model [11

11. 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]

]. Our model results are in well accordance with the simulation results (discrepancy is less than 3%), thus it certainly confirms that our formula is very trustworthy in predicting effective plasma frequency.

4. Discussion

As is well known, metamaterials exhibit their properties through sub-wavelength structures rather than chemical and physical composition. Here, we demonstrate two dominant geometrical parameters for modulating the effective plasma frequency, namely, the rod period p and rod diameter d. Figure 6
Fig. 6 Transmittances for different rod periods, when d = 100nm, a = 300nm and layers number N = 3. Inset graph shows effective plasma frequencies versus rod period p.
shows the transmittances as functions of different rod periods, and the inserted picture displays the corresponding effective plasma frequency variation. We can find that effective plasma frequency red shifts as p increases. This phenomenon can be well explained by the effects of reducing the active effective electrons density and increasing their effective mass [11

11. 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]

].

The diameter of silver rod is an equally important parameter to modulate effective plasma frequency. Figure 7
Fig. 7 Transmittances for different rods diameters, when a = 300nm, p = 600nm and layers number N = 3. In the inset, we show effective plasma frequencies versus rods diameter.
shows the transmittances of this artificial medium versus different rod diameters. When the diameter becomes bigger, a blue-shift of effective plasma frequency occurs as expected, which can be attributed to the increase of effective electrons density and the decrease of effective electrons mass.

In our simulation and analytic model, the circular rods were chosen for simplicity. Actually, many other shapes, such as rectangle and ellipse, even arbitrary shape are all suitable for constructing this artificial metal. Besides, we just focus on the near-infrared region in this paper, actually our model can be applicable in other spectrum range, for instance, GHz region [20

20. L. Liu, H. Shi, X. Luo, X. Wei, and C. Du, “A plasma frequency modulation model for constructing structure material with arbitrary cross-section thin metallic wires,” Appl. Phys., A Mater. Sci. Process. 95(2), 563–566 (2009). [CrossRef]

], and here we will not give more discussions. Considering the realistic fabrication, vacuum cannot be employed as the dielectric host, instead, other materials such as SiO2 and MgF2 can well act as the filling layer. Accordingly, a modulation factor εr called the relative permittivity is added. The ultimate expression of effective plasma frequency can be expressed as

fp2=c022πb2εr[ln(leff2πb)leff28πb2+12]
(8)

In Fig. 8
Fig. 8 The effective plasma frequencies as a function of rod diameters as obtained in simulation and model with realistic dielectric host. The solid and dash lines represent the simulation and model results, respectively. (a = 300nm, p = 600nm and layers number N = 3).
, the simulated results are provided as the criterion and compared with the results calculated with Eq. (8). The relative permittivity of SiO2 and MgF2 is 2.31 and 1.9, respectively. We can find that the calculated results by our model are in well accordance with simulation. As for realistic manufacture, we confirm it is not difficult to meet the requirement of critical dimension and fabrication uniformity. These artificial structures can be realized by many different fabrication techniques, for example, standard electron-beam lithography, laser beam interference lithography and our localized surface plasmon nanolithography [21

21. X. Wei, X. Luo, X. Dong, and C. Du, “Localized surface plasmon nanolithography with ultrahigh resolution,” Opt. Express 15(21), 14177–14183 (2007). [CrossRef] [PubMed]

], which have to be combined with lift-off and other assistant procedures. Relevant experimental work is currently underway in an attempt to verify our theoretical predictions for the detailed artificial structures.

In our above simulation, two-dimensional rods array was proposed and demonstrated by FDTD simulation to modulate effective plasma frequency into near-infrared spectrum region. Note that only the modes whose electric fields are parallel to the rods will play a great role in the modulation of effective plasma frequency. When electric field is perpendicular to the axis of the rods, there is no effective plasma frequency. Actually, we have only considered the electric field is parallel to the metal rods, and this artificial medium is anisotropic. However, this medium can be made to represent an approximately isotropic response by considering a lattice of rods oriented along the three orthogonal directions.

5.Conclusions

Acknowledgment

This work was supported by the National Basic Research Program (2006CB302900) and High Tech. Program of China (2007AA03Z332). The authors thank Dr. Shaoyun Yin and Ms. Lifang Shi for their kind contributions to the work.

References and links

1.

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

2.

G. Raschke, S. Kowarik, T. Franzl, C. Sönnichsen, T. A. Klar, J. Feldmann, A. Nichtl, and K. Kürzinger, “Bio-molecular recognition based on single gold nanoparticle light scattering,” Nano Lett. 3(7), 935–938 (2003). [CrossRef]

3.

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

4.

H. Lee, Y. Xiong, N. Fang, W. Srituravanich, S. Durant, M. Ambati, C. Sun, and X. Zhang, “Realization of optical superlens imaging below the diffraction limit,” N. J. Phys. 7, 255 (2005). [CrossRef]

5.

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

6.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004). [CrossRef]

7.

P. Andrew and W. L. Barnes, “Energy transfer across a metal film mediated by surface plasmon polaritons,” Science 306(5698), 1002–1005 (2004). [CrossRef] [PubMed]

8.

L. Yin, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, J. Hua, U. Welp, D. E. Brown, and C. W. Kimball, “Subwavelength focusing and guiding of surface plasmons,” Nano Lett. 5(7), 1399–1402 (2005). [CrossRef] [PubMed]

9.

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking Surface Plasmons with Structured Surfaces,” Science 305(5685), 847–848 (2004). [CrossRef] [PubMed]

10.

F. J. Garcia-Vidal, L. Martín-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005). [CrossRef]

11.

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]

12.

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]

13.

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]

14.

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]

15.

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]

16.

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]

17.

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]

18.

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

19.

S. O’Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, “Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials,” Phys. Rev. B 69(24), 241101 (2004). [CrossRef]

20.

L. Liu, H. Shi, X. Luo, X. Wei, and C. Du, “A plasma frequency modulation model for constructing structure material with arbitrary cross-section thin metallic wires,” Appl. Phys., A Mater. Sci. Process. 95(2), 563–566 (2009). [CrossRef]

21.

X. Wei, X. Luo, X. Dong, and C. Du, “Localized surface plasmon nanolithography with ultrahigh resolution,” Opt. Express 15(21), 14177–14183 (2007). [CrossRef] [PubMed]

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: October 30, 2009
Revised Manuscript: January 17, 2010
Manuscript Accepted: January 18, 2010
Published: February 2, 2010

Citation
Xingzhan Wei, Haofei Shi, Qiling Deng, Xiaochun Dong, Chunheng Liu, Yueguang Lu, and Chunlei Du, "Artificial metal with effective plasma frequency in near-infrared region," Opt. Express 18, 3370-3378 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-4-3370


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]
  2. G. Raschke, S. Kowarik, T. Franzl, C. Sönnichsen, T. A. Klar, J. Feldmann, A. Nichtl, and K. Kürzinger, “Bio-molecular recognition based on single gold nanoparticle light scattering,” Nano Lett. 3(7), 935–938 (2003). [CrossRef]
  3. N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005). [CrossRef] [PubMed]
  4. H. Lee, Y. Xiong, N. Fang, W. Srituravanich, S. Durant, M. Ambati, C. Sun, and X. Zhang, “Realization of optical superlens imaging below the diffraction limit,” N. J. Phys. 7, 255 (2005). [CrossRef]
  5. N. Fang, H. Lee, C. Sun, X. Zhang, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005). [CrossRef] [PubMed]
  6. W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004). [CrossRef]
  7. P. Andrew and W. L. Barnes, “Energy transfer across a metal film mediated by surface plasmon polaritons,” Science 306(5698), 1002–1005 (2004). [CrossRef] [PubMed]
  8. L. Yin, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, J. Hua, U. Welp, D. E. Brown, and C. W. Kimball, “Subwavelength focusing and guiding of surface plasmons,” Nano Lett. 5(7), 1399–1402 (2005). [CrossRef] [PubMed]
  9. J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking Surface Plasmons with Structured Surfaces,” Science 305(5685), 847–848 (2004). [CrossRef] [PubMed]
  10. F. J. Garcia-Vidal, L. Martín-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005). [CrossRef]
  11. 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]
  12. 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]
  13. 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]
  14. 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]
  15. 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]
  16. 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]
  17. 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]
  18. D. R. Smith, S. Schultz, P. Markoš, and C. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002). [CrossRef]
  19. S. O’Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, “Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials,” Phys. Rev. B 69(24), 241101 (2004). [CrossRef]
  20. L. Liu, H. Shi, X. Luo, X. Wei, and C. Du, “A plasma frequency modulation model for constructing structure material with arbitrary cross-section thin metallic wires,” Appl. Phys., A Mater. Sci. Process. 95(2), 563–566 (2009). [CrossRef]
  21. X. Wei, X. Luo, X. Dong, and C. Du, “Localized surface plasmon nanolithography with ultrahigh resolution,” Opt. Express 15(21), 14177–14183 (2007). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

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


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited