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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 16 — Jul. 30, 2012
  • pp: 18238–18247
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Experimental verification of spoof surface plasmons in wire metamaterials

Yujiro Kushiyama, Takuji Arima, and Toru Uno  »View Author Affiliations


Optics Express, Vol. 20, Issue 16, pp. 18238-18247 (2012)
http://dx.doi.org/10.1364/OE.20.018238


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Abstract

In this paper, we experimentally demonstrate the excitation of spoof surface plasmon polaritons (SPPs) on a wire-medium metamaterial slab in the microwave region. The spoof SPPs are excited on the opposite side of the slab from the source, which is desirable for applications such as sensing devices. Using the prism coupling method, we verify the excitation of spoof SPPs by measuring the reflection spectrum and near-field enhancement. The excitation of spoof SPPs is also verified by using the grating coupling method, where we demonstrate transmission enhancement through the metamaterial slab by placing diffraction gratings on both sides of the slab. Numerical investigation shows that the enhanced transmission can be attributed to the dispersion relations of the spoof SPPs and the periodicity of the diffraction grating. These properties can be used to realize extraordinary transmission and directional beaming.

© 2012 OSA

1. Introduction

Surface plasmon polaritons (SPPs) have been the focus of much recent research because of the introduction of the concept of a perfect lens by Pendry [1

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

] and the reporting of extraordinary optical transmission (EOT) by Ebbesen [2

2. 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, 667–669 (1998). [CrossRef]

]. Both phenomena are attributable to the SPPs’ bound surface states. The bound waves can preserve the diffracted waves that have large momentum, leading to super-resolution [1

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

] and EOT in which re-radiation of the bounded waves enhances the emission from holes in a metal plate [2

2. 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, 667–669 (1998). [CrossRef]

].

In a bulk metal, SPPs can be excited at only certain optical frequencies where the permittivity of the metal is negative. However, SPPs can be mimicked with structured materials, called spoof SPPs, also introduced by Pendry [3

3. J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847–848 (2004). [CrossRef] [PubMed]

]. This approach opens the possibility of applications of SPP-like phenomena in other frequency regimes (i.e., microwave and terahertz regimes). Therefore, determining how to construct such structured materials (also known as metamaterials) in these regimes is an important research topic in itself.

Early attempts to realize spoof SPPs employed a corrugated perfect electric conductor (PEC) surface and a perforated PEC surface [3

3. J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847–848 (2004). [CrossRef] [PubMed]

]. Reference [4

4. A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science 308, 670–672 (2005). [CrossRef] [PubMed]

] provided experimental verification of spoof SPPs in the microwave region. The same group subsequently reported experimental results in Ref. [5

5. M. J. Lockyear, A. P. Hibbins, and J. R. Sambles, “Microwave surface-plasmon-like modes on thin metamaterials,” Phys. Rev. Lett. 102, 073901 (2009). [CrossRef] [PubMed]

] that the bound state of an electromagnetic band gap (EBG) structure [6

6. D. Sievenpiper, L. Zhang, R. Broas, N. Alexopolous, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microwave Theory Tech. 47, 2059–2074 (1999). [CrossRef]

] can also support surface plasmon-like waves. The EBG structure, which is also referred to as a mushroom structure, is well studied in its equivalent circuit representation, and the structure’s surface plasmon-like behavior is also predicted from circuit representations. The operating bandwidth can be improved by employing the equivalent circuit approach [7

7. M. Navarro-Cía, M. Beruete, S. Agrafiotis, F. Falcone, M. Sorolla, and S. A. Maier, “Broadband spoof plasmons and subwavelength electromagnetic energy confinement on ultrathin metafilms,” Opt. Express 17, 18184–18195 (2009). [CrossRef] [PubMed]

]. However, these structures are fabricated on a ground plane to ensure tight confinement on the surface; their applications are restricted to thin waveguides and cannot be used for sensing or for lenses in which excitation of the SPPs on the back surface of metallic slabs is utilized.

A straightforward way of realizing the SPPs at arbitrary frequencies is mimicking the electrical properties of metals at optical frequencies. A structure mimicking these properties has been reported; this structure consists of a metallic wire mesh [8

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

]. However, this approach has two disadvantages [9

9. M. A. Shapiro, G. Shvets, J. R. Sirigiri, and R. J. Temkin, “Spatial dispersion in metamaterials with negative dielectric permittivity and its effect on surface waves,” Opt. Lett. 31, 2051–2053 (2006). [CrossRef] [PubMed]

]. First, the electrical response varies with respect to the direction of the electromagnetic wave. This allows a large leakage of the surface-bound waves. Second, the structured material has no flat cutting plane, requiring extra treatment of the surface. However, the spatial dispersion can be reduced by adding auxiliary elements to the wire-medium [10

10. A. Demetriadou and J. B. Pendry, “Taming spatial dispersion in wire metamaterial,” J. Phys.: Condens. Matter 20, 295222 (2008). [CrossRef]

]. This reduces the expression of the effective permittivity of the metamaterial from a tensor to a scalar. This does not imply that the dispersion relation of the surface is described by the scalar-valued permittivity because the surface structure is not considered in the derivation process of the permittivity. In Ref. [11

11. Y. Kushiyama, T. Uno, and T. Arima, “Novel negative permittivity structure and its application to excitation of surface plasmon in microwave frequency range,” IEICE Trans. Commun. E93-B, 2629–2635 (2010). [CrossRef]

], we found a structure whose surface dispersion almost coincides with the dispersion relation calculated from a scalar-valued permittivity and an assumption that the interface is flat. This allows us to exploit novel applications involving materials that have an intrinsic negative-valued permittivity, at an arbitrary frequency. Using this structure, we have numerically demonstrated the excitation of spoof SPPs on the back surface of the metamaterial slab [11

11. Y. Kushiyama, T. Uno, and T. Arima, “Novel negative permittivity structure and its application to excitation of surface plasmon in microwave frequency range,” IEICE Trans. Commun. E93-B, 2629–2635 (2010). [CrossRef]

] in the Kretschmann configuration [12

12. R. Raether, Surface Plasmons (Springer–Verlag, Berlin, 1988).

].

2. Principle

The metamaterial structure we have previously reported [11

11. Y. Kushiyama, T. Uno, and T. Arima, “Novel negative permittivity structure and its application to excitation of surface plasmon in microwave frequency range,” IEICE Trans. Commun. E93-B, 2629–2635 (2010). [CrossRef]

] is shown in the inset of Fig. 1. The basic structure of the metamaterial consists of a three-dimensionally connected metallic wire lattice. The length of the lattice period is 10 mm, the radius of the wire is rw = 0.3 mm, and the radius of the sphere is rs = 1.73 mm. The dispersion relation of the structure is also shown in Fig. 1. In the calculation of the dispersion diagram, we employed a three-dimensional finite difference frequency domain (FDFD) method [13

13. K. Beilenhoff, W. Heinrich, and H. Hartnagel, “Improved finite-difference formulation in frequency domain for three-dimensional scattering problems,” IEEE Trans. Microwave Theory Tech. 40, 540–546 (1992). [CrossRef]

]. By applying Bloch boundary conditions, the computational domain is restricted to the unit cell of the periodic structure. The resulting matrix of the equation system was solved with the aid of a computational library for large-scale sparse eigenvalue problems [14

14. V. Hernandez, J. E. Roman, and V. Vidal, “SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems,” ACM Trans. Math. Software 31, 351–362 (2005). [CrossRef]

]. The eigenvalues provide the dispersion relation ω(k), where k represents the Bloch wavevector. As we can see in Fig. 1, the two degenerate modes due to the interaction of waves on both sides of the slab will be excited, which is also shown in the inset. It can be also seen that the parallel momentum of the spoof SPPs exceeds any wavenumber that radiative waves can have in the air at the same frequency. This requires momentum-matching methods for coupling the external plane wave to the surface state.

Fig. 1 Dispersion relation of the spoof SPPs for a half-plane and finite slab of the meta-material. The slab has two unit cells along the thickness direction, and the cutting plane of the surface is chosen as shown in the inset. The geometrical parameters are defined with respect to the unit length a as the radius of the sphere rs = 0.173a and the radius of the wire rw = 0.03a. In the experiment, the unit length was fixed at a = 10 mm. The shaded region represents the inside of the light cone. The spatial distributions of the electric field Ex corresponding to the lowest two modes are shown in the inset.

A well-known method for compensating the momentum mismatch between the incident wave and the SPPs is attenuated total reflection (ATR) using a dielectric prism. The parallel component of the wavevector in the prism is given by
Re(kspp)=nk0sinθinc,
(1)
where k0 is the wavenumber in free space and n is the refractive index of the dielectric prism. Therefore, if n is sufficiently large, the left-hand side of the equation matches the dispersion relation of the SPPs. The parallel component of the wavevector is also controlled by diffraction gratings, as given by
Re(kspp)=kx+m2πΛ,
(2)
where kx = k0 sinθinc, m is a diffraction order, and Λ is the grating period. The diffraction grating is placed near the surface of the metamaterial. This grating layer can be considered as an additional surface structure of the metamaterial. We computed the dispersion relation of the surface with such a grating layer in Section 4.

3. Prism coupling

Figure 2 depicts the measurement setup using the ATR prism coupling method. The prism is a 77-mm-thick 45°–45°–90° triangle made by stacking FR4 dielectric substrates with relative permittivity of 4.9. The metamaterial consists of three-dimensionally connected brass wires with auxiliary spheres made of brass. The structure has dimensions of 11 unit cells in height, 70 unit cells in length, and 2 unit cells in thickness. The TM-polarized electromagnetic wave is incident on one face of the prism with different angles of incidence. The reflection from the prism is used to normalize subsequent measurements of the metamaterial. In the experimental setup, a metal-backed microwave absorber with an aperture is placed in front of the prism to suppress interference. The electric field intensity is measured using a probe mounted on an X–Y position controller. The source and the receiver horn or the probe are connected to a vector network analyzer (VNA). The VNA and X–Y position controller are controlled by an in-house program for recording electric field values.

Fig. 2 Schematic representation of a prism coupling experiment setup. Numerical simulation of the experiment by using the finite difference time domain (FDTD) method is also conducted with the same parameters as this setup, except for the height dimension; in the computation, we employed a periodic boundary condition along the height direction.

Fig. 3 Experimentally determined dispersion relations for internal angles between 41.6° and 48.4°. The distance between the face of the prism and the metamaterial is d = 7.0 mm. Black dots represent the positions of reflection minima. The inset shows measured reflection spectra for an angle of incidence of 45°. The distance d is varied as follows: d = 3.5, 5.0, 7.0 and 8.5 mm.
Fig. 4 Electric field intensity spectra measured by scanning using a monopole probe. The probe was moved along the lateral line depicted in Fig. 2. (a) shows the experimental result and (b) shows the simulated result. In both cases, the distance between the prism and the metamaterial is d = 3.5 mm, the angle of incidence is 45°. (c) shows the calculated spatial distributions of the electric field for 5.37 and 4.40 GHz.
Fig. 5 Electric field intensity recorded with a monopole probe at the frequency of 5.50 GHz. The calculated results at the frequency of 5.37 GHz are also shown. The field intensity for the metamaterial face is scaled with respect to the field intensity for the prism face.

4. Grating coupling and plasmon-induced transmission

Fig. 6 (a) Schematic representation of the metamaterial and the grating. The period of the grating is equal to three periods of the unit length of the metamaterial. This introduces modes folded at kxa/π = 1/3 into the dispersion relation. (b) The dispersion relation for the metamaterial slab, in which folding lines kxa/π = n/3 are also depicted. This dispersion relation is normalized with respect to the unit length of the metamaterial. In the experiment described later, the unit length of the metamaterial is fixed at a = 23 mm, and the distance between the grating and the metamaterial face is d = 3.5 mm. (c) The calculated transmission spectra as a function of frequency and wave number parallel to the surface. This dispersion relation is normalized with respect to the period of the grating.

Fig. 7 (a) The electric Ex field distributions at the frequencies corresponding to four distinct peaks in Fig. 6(c). (b) The electric |Ex| field distributions at the same frequencies, when the grating is placed only on the source side. A, B, C, and D are the 1st, 2nd, 3rd, and 4th lowest modes in Fig. 6(c), respectively.

To verify this phenomenon experimentally, we conducted an experiment using a parallel-plate waveguide (PPW). The height of the PPW corresponds to three periods of the metamaterial, which also corresponds to the period of the gratings. Therefore, the cutting plane of the PPW along the height direction and the thickness of the metamaterial is identical to the plane shown in Fig. 7. The PPW section that embedded thirteen periods of the metamaterial in the width direction is made as a separable section. An identical PPW section without the metamaterial is also made for normalizing the transmission spectrum. In the experiment, the lattice constant of the metamaterial is a = 23 mm. The gratings are made of a 23-mm-wide aluminum sheet put on a 3.5-mm-thick foam board. The foam boards are placed tight against the metamaterial face. Figure 8 shows the transmission for the metamaterial and the grating–metamaterial–grating configuration installed in the PPW. A large transmission is found around 2.45 GHz in the measured result and around 2.35 GHz in the simulated result. An enhanced transmission of 12 dB, achieved by inserting the gratings on both sides of the slab, is observed in the experiment. In the simulated result, four distinct peaks and two band gaps can be seen, while no such distinctions are found in the measured result. As we have seen, these distinctive peaks involve highly symmetrical spatial distributions. The experimental observation of such details requires more careful fabrication of the metamaterial. It is worth noting that the spatial symmetry can be exploited; the even symmetric modes can be reproduced by placing the PEC plane in the middle of the metamaterial. This can provide another means of experimentally verifying the numerical results and more opportunities for practical applications like frequency dependent beam steering.

Fig. 8 Measured transmittance for the metamaterial and grating–metamaterial–grating configuration installed in the parallel plate waveguide (PPW). The height of the PPW corresponds to three periods of the metamaterial in the x direction. Therefore, the cutting plane of the PPW along the xz plane is identical to the plane shown in Fig. 7.

5. Conclusions

In this paper, we have experimentally demonstrated the excitation of spoof SPPs on a metamaterial slab. A metamaterial slab consisting of a metallic wire-medium with auxiliary metallic spheres was fabricated. By employing the ATR prism coupling method, the excitation of spoof SPPs on the back surface of the metamaterial slab was observed. We have also shown transmission enhancement through the metamaterial slab due to the excitation of spoof SPPs by placing the diffraction gratings on both sides of the slab. Our results show two essential properties of the SPPs for practical applications: the field localization on the back surface and the coupling ability between the SPPs and diffracted waves. Therefore, we believe that our results have potential for plasmonic sensing, waveguiding, and configurable beam forming.

References and links

1.

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

2.

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, 667–669 (1998). [CrossRef]

3.

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847–848 (2004). [CrossRef] [PubMed]

4.

A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science 308, 670–672 (2005). [CrossRef] [PubMed]

5.

M. J. Lockyear, A. P. Hibbins, and J. R. Sambles, “Microwave surface-plasmon-like modes on thin metamaterials,” Phys. Rev. Lett. 102, 073901 (2009). [CrossRef] [PubMed]

6.

D. Sievenpiper, L. Zhang, R. Broas, N. Alexopolous, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microwave Theory Tech. 47, 2059–2074 (1999). [CrossRef]

7.

M. Navarro-Cía, M. Beruete, S. Agrafiotis, F. Falcone, M. Sorolla, and S. A. Maier, “Broadband spoof plasmons and subwavelength electromagnetic energy confinement on ultrathin metafilms,” Opt. Express 17, 18184–18195 (2009). [CrossRef] [PubMed]

8.

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

9.

M. A. Shapiro, G. Shvets, J. R. Sirigiri, and R. J. Temkin, “Spatial dispersion in metamaterials with negative dielectric permittivity and its effect on surface waves,” Opt. Lett. 31, 2051–2053 (2006). [CrossRef] [PubMed]

10.

A. Demetriadou and J. B. Pendry, “Taming spatial dispersion in wire metamaterial,” J. Phys.: Condens. Matter 20, 295222 (2008). [CrossRef]

11.

Y. Kushiyama, T. Uno, and T. Arima, “Novel negative permittivity structure and its application to excitation of surface plasmon in microwave frequency range,” IEICE Trans. Commun. E93-B, 2629–2635 (2010). [CrossRef]

12.

R. Raether, Surface Plasmons (Springer–Verlag, Berlin, 1988).

13.

K. Beilenhoff, W. Heinrich, and H. Hartnagel, “Improved finite-difference formulation in frequency domain for three-dimensional scattering problems,” IEEE Trans. Microwave Theory Tech. 40, 540–546 (1992). [CrossRef]

14.

V. Hernandez, J. E. Roman, and V. Vidal, “SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems,” ACM Trans. Math. Software 31, 351–362 (2005). [CrossRef]

15.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, Third Edition (Artech House Publishers, 2000).

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(240.6680) Optics at surfaces : Surface plasmons
(240.6690) Optics at surfaces : Surface waves
(160.1245) Materials : Artificially engineered materials
(160.3918) Materials : Metamaterials
(050.6624) Diffraction and gratings : Subwavelength structures

ToC Category:
Metamaterials

History
Original Manuscript: April 11, 2012
Revised Manuscript: July 14, 2012
Manuscript Accepted: July 15, 2012
Published: July 25, 2012

Citation
Yujiro Kushiyama, Takuji Arima, and Toru Uno, "Experimental verification of spoof surface plasmons in wire metamaterials," Opt. Express 20, 18238-18247 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-16-18238


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References

  1. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett.85, 3966–3969 (2000). [CrossRef] [PubMed]
  2. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391, 667–669 (1998). [CrossRef]
  3. J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science305, 847–848 (2004). [CrossRef] [PubMed]
  4. A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science308, 670–672 (2005). [CrossRef] [PubMed]
  5. M. J. Lockyear, A. P. Hibbins, and J. R. Sambles, “Microwave surface-plasmon-like modes on thin metamaterials,” Phys. Rev. Lett.102, 073901 (2009). [CrossRef] [PubMed]
  6. D. Sievenpiper, L. Zhang, R. Broas, N. Alexopolous, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microwave Theory Tech.47, 2059–2074 (1999). [CrossRef]
  7. M. Navarro-Cía, M. Beruete, S. Agrafiotis, F. Falcone, M. Sorolla, and S. A. Maier, “Broadband spoof plasmons and subwavelength electromagnetic energy confinement on ultrathin metafilms,” Opt. Express17, 18184–18195 (2009). [CrossRef] [PubMed]
  8. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely-low-frequency plasmons in metallic mesostructures,” Phys. Rev. Lett.76, 4773–4776 (1996). [CrossRef] [PubMed]
  9. M. A. Shapiro, G. Shvets, J. R. Sirigiri, and R. J. Temkin, “Spatial dispersion in metamaterials with negative dielectric permittivity and its effect on surface waves,” Opt. Lett.31, 2051–2053 (2006). [CrossRef] [PubMed]
  10. A. Demetriadou and J. B. Pendry, “Taming spatial dispersion in wire metamaterial,” J. Phys.: Condens. Matter20, 295222 (2008). [CrossRef]
  11. Y. Kushiyama, T. Uno, and T. Arima, “Novel negative permittivity structure and its application to excitation of surface plasmon in microwave frequency range,” IEICE Trans. Commun.E93-B, 2629–2635 (2010). [CrossRef]
  12. R. Raether, Surface Plasmons (Springer–Verlag, Berlin, 1988).
  13. K. Beilenhoff, W. Heinrich, and H. Hartnagel, “Improved finite-difference formulation in frequency domain for three-dimensional scattering problems,” IEEE Trans. Microwave Theory Tech.40, 540–546 (1992). [CrossRef]
  14. V. Hernandez, J. E. Roman, and V. Vidal, “SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems,” ACM Trans. Math. Software31, 351–362 (2005). [CrossRef]
  15. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, Third Edition (Artech House Publishers, 2000).

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