Abstract

A band separating device that uses an anisotropic metamaterial exhibiting negative refraction is designed and measured. The metamaterial has frequency dispersion in one component of the permeability tensor. A beam is incident onto the metamaterial and undergoes frequency dependent reflection and refraction directing different bandwidths towards three distinct measurement ports. Design issues are discussed, and measurement results are presented.

© 2005 Optical Society of America

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References

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  1. R. A. Shelby, D. R. Smith, and S. Schultz, �??Experimental Verification of a Negative Index of Refraction,�?? Science 292, 77�??79 (2001).
    [CrossRef] [PubMed]
  2. 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]
  3. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, �??Magnetism from Conductors and Enhanced Nonlinear Phenomena,�?? IEEE Trans. Microwave Thoery Tech. 47, 2075�??2084 (1999).
    [CrossRef]
  4. D. R. Smith and N. Kroll, �??Negative Refractive Index in Left-Handed Materials,�?? Phys. Rev. Lett. 85, 2933�??2936 (2000).
    [CrossRef] [PubMed]
  5. H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, �??T-junction waveguide experiment to characterize left-handed properties of metamaterials,�?? J. Appl. Phys. 94, 3712�??3716 (2003).
    [CrossRef]
  6. C. Caloz, C.-C. Chang, and T. Itoh, �??Full-wave verification of the fundamental properties of left-handed materials in waveguide configurations,�?? J. Appl. Phys. 90, 5483�??5486 (2001).
    [CrossRef]
  7. J. A. Kong, Electromagnetic Wave Theory (EMW, 2000).
  8. D. R. Smith and D. Schurig, �??Electromagnetic Wave Propagation in Media with Indefinite Permittivity and Permeability Tensors,�?? Phys. Rev. Lett. 90, 77405 (2003).
    [CrossRef]
  9. D. R. Smith, P. Rye, J. J. Mock, D. C. Vier, and A. F. Starr, �??Enhanced Diffraction from a Grating on the Surface of a Negative-Index Metamaterial,�?? Phys. Rev. Lett. 93, 137405 (2004).
    [CrossRef] [PubMed]
  10. S. O' Brien and J. B. Pendry, �??Magnetic activity at infrared frequencies in structured metallic photonic crystals,�?? J. Phys.: Condens. Matter pp. 6383�??6394 (2002).
    [CrossRef]
  11. W. Wang, �??Directive Antenna Using Metamaterial Substrates,�?? MIT Masters Thesis (2004).
  12. X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. P. Jr., and J. A. Kong, �??Improved Method to Retrieve the Constitutive Effective Parameters of Metamaterials,�?? Phys. Rev. E 70, 016608 (2004).
    [CrossRef]
  13. T. M. Grzegorczyk, M. Nikku, X. Chen, B.-I. Wu, and J. A. Kong, �??Refraction laws for anisotropic media and their application to left-handed metamaterials,�?? IEEE Trans. Microwave Thoery Tech. 53, 1443�??1450 (2005).
    [CrossRef]
  14. L. Ran, J. Huangfu, H. Chen, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, �??Beam shifting experiment for the characterization of left-handed properties,�?? J. Appl. Phys. 95, 2238�??2241 (2004).
    [CrossRef]
  15. J. A. Kong, B.-I. Wu, and Y. Zhang, �??Lateral Displacement of a Gaussian Beam Reflected from a Grounded Slab with Negative Permittivity and Permeability,�?? Appl. Phys. Lett. 80, 2084�??2086 (2002).
    [CrossRef]
  16. J. A. Kong, B.-I. Wu, and Y. Zhang, �??A Unique Lateral Displacement of a Gaussian Beam Transmitted Through a Slab with Negative Permittivity and Permeability,�?? Microwave Opt. Technol. Lett. 33, 136�??139 (2002).
    [CrossRef]
  17. T. M. Grzegorczyk, X. Chen, J. P. Jr., J. Chen, B.-I. Wu, and J. A. Kong, �??Reflection Coefficients and Goos-Hänchen Shifts in Anisotropic and Bianisotropic Left-Handed Metamaterials,�?? Progress in Electromagnetic Research 51, 83�??113 (2005).
    [CrossRef]
  18. J. A. Kong, �??Electromagnetic Wave Interaction With Stratified Negative Isotropic Media,�?? Progress in Electromagnetic Research 35, 1�??52 (2002).
    [CrossRef]
  19. H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, �??Left-handed Metamaterials composed of only S-shaped Resonators,�?? Phys. Rev. E 70, 057605 (2004)
    [CrossRef]
  20. H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, �??Magnetic properties of S-shaped split-ring resonators,�?? Progress in Electromagnetic Research 51, 231�??247 (2005).
    [CrossRef]

Appl. Phys. Lett. (1)

J. A. Kong, B.-I. Wu, and Y. Zhang, �??Lateral Displacement of a Gaussian Beam Reflected from a Grounded Slab with Negative Permittivity and Permeability,�?? Appl. Phys. Lett. 80, 2084�??2086 (2002).
[CrossRef]

IEEE Trans. Microwave Thoery Tech. (2)

T. M. Grzegorczyk, M. Nikku, X. Chen, B.-I. Wu, and J. A. Kong, �??Refraction laws for anisotropic media and their application to left-handed metamaterials,�?? IEEE Trans. Microwave Thoery Tech. 53, 1443�??1450 (2005).
[CrossRef]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, �??Magnetism from Conductors and Enhanced Nonlinear Phenomena,�?? IEEE Trans. Microwave Thoery Tech. 47, 2075�??2084 (1999).
[CrossRef]

J. Appl. Phys. (3)

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, �??T-junction waveguide experiment to characterize left-handed properties of metamaterials,�?? J. Appl. Phys. 94, 3712�??3716 (2003).
[CrossRef]

C. Caloz, C.-C. Chang, and T. Itoh, �??Full-wave verification of the fundamental properties of left-handed materials in waveguide configurations,�?? J. Appl. Phys. 90, 5483�??5486 (2001).
[CrossRef]

L. Ran, J. Huangfu, H. Chen, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, �??Beam shifting experiment for the characterization of left-handed properties,�?? J. Appl. Phys. 95, 2238�??2241 (2004).
[CrossRef]

J. Phys.: Condens. Matter (1)

S. O' Brien and J. B. Pendry, �??Magnetic activity at infrared frequencies in structured metallic photonic crystals,�?? J. Phys.: Condens. Matter pp. 6383�??6394 (2002).
[CrossRef]

Microwave Opt. Technol. Lett. (1)

J. A. Kong, B.-I. Wu, and Y. Zhang, �??A Unique Lateral Displacement of a Gaussian Beam Transmitted Through a Slab with Negative Permittivity and Permeability,�?? Microwave Opt. Technol. Lett. 33, 136�??139 (2002).
[CrossRef]

Phys. Rev. E (2)

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, �??Left-handed Metamaterials composed of only S-shaped Resonators,�?? Phys. Rev. E 70, 057605 (2004)
[CrossRef]

X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. P. Jr., and J. A. Kong, �??Improved Method to Retrieve the Constitutive Effective Parameters of Metamaterials,�?? Phys. Rev. E 70, 016608 (2004).
[CrossRef]

Phys. Rev. Lett. (4)

D. R. Smith and D. Schurig, �??Electromagnetic Wave Propagation in Media with Indefinite Permittivity and Permeability Tensors,�?? Phys. Rev. Lett. 90, 77405 (2003).
[CrossRef]

D. R. Smith, P. Rye, J. J. Mock, D. C. Vier, and A. F. Starr, �??Enhanced Diffraction from a Grating on the Surface of a Negative-Index Metamaterial,�?? Phys. Rev. Lett. 93, 137405 (2004).
[CrossRef] [PubMed]

D. R. Smith and N. Kroll, �??Negative Refractive Index in Left-Handed Materials,�?? Phys. Rev. Lett. 85, 2933�??2936 (2000).
[CrossRef] [PubMed]

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]

Progress in Electromagnetic Research (3)

T. M. Grzegorczyk, X. Chen, J. P. Jr., J. Chen, B.-I. Wu, and J. A. Kong, �??Reflection Coefficients and Goos-Hänchen Shifts in Anisotropic and Bianisotropic Left-Handed Metamaterials,�?? Progress in Electromagnetic Research 51, 83�??113 (2005).
[CrossRef]

J. A. Kong, �??Electromagnetic Wave Interaction With Stratified Negative Isotropic Media,�?? Progress in Electromagnetic Research 35, 1�??52 (2002).
[CrossRef]

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, �??Magnetic properties of S-shaped split-ring resonators,�?? Progress in Electromagnetic Research 51, 231�??247 (2005).
[CrossRef]

Science (1)

R. A. Shelby, D. R. Smith, and S. Schultz, �??Experimental Verification of a Negative Index of Refraction,�?? Science 292, 77�??79 (2001).
[CrossRef] [PubMed]

Other (2)

J. A. Kong, Electromagnetic Wave Theory (EMW, 2000).

W. Wang, �??Directive Antenna Using Metamaterial Substrates,�?? MIT Masters Thesis (2004).

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Figures (6)

Fig. 1.
Fig. 1.

Four-Port Concept Design: An electromagnetic wave excited at the incident port (1) is reflected (port 2), positively refracted (“RH” port 3), or negatively refracted (“LH” port 4) at the surface of a metamaterial prism as a function of frequency.

Fig. 2.
Fig. 2.

Symmetric SRR unit cell with superimposed photograph. The labeled dimensions are: a=0.24 mm, b=1.56 mm, c=1.2 mm, d=3.12 mm, e=2.25 mm, f=5 mm, and g=0.5 mm. The substrate has εr ≈4. The remaining volume is air-filled.

Fig. 3.
Fig. 3.

Metamaterial Design Parameters: θi - incidence angle; ϕ 3 - rotation angle at port 3; ϕ 4 - rotation angle at port 4; S - metamaterial size. The material axes are shown. Dashed lines indicate port boundaries as absorbing material has been suppressed for clarity. The gray lines forming the material indicate the orientation of the dielectric cards with SRRs for reference.

Fig. 4.
Fig. 4.

Refraction to Port 4 when µz =-0.5, with ϕ 4=60° and θi =15°. Refraction at the port 1 and port 4 boundaries are shown with the dispersion relations superimposed. The dashed line indicates the phase matching component of the suppressed k vector. The small and large arrows indicate the direction of energy flow in air and in the negative medium, respectively. The inset figures detail the dispersion relation in the area of interest. The thick line in the detail of the second interface indicates the possible k vectors in the negative medium that meet the transmission requirement.

Fig. 5.
Fig. 5.

Top view of experimental setup with top plate removed. The bottom plate is shown in gray. Microwave absorbing material is represented by the black wedges. The material axes are shown. The final design angles are used: ϕ 4=60° and θi =5°. S=6 cm (12 unit cells).

Fig. 6.
Fig. 6.

(a) Experimental measurement results. The 3 dB passbands are indicated by shading. (b) Simulation results. Magenta — Reflection Port 2. Green — RH Port 3. Red — LH Port 4.

Tables (1)

Tables Icon

Table 1. Refraction Properties for Anisotropic Materials

Equations (3)

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ε ̿ = diag [ ε x ( ω ) , ε y ( ω ) , ε z ( ω ) ] ε o
μ ̿ = diag [ μ x ( ω ) , μ y ( ω ) , μ z ( ω ) ] μ o
k z 2 = ω 2 c 2 μ x ( ω ) ε y ( ω ) μ x ( ω ) μ z ( ω ) k x 2

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