Abstract

In this paper, we experimentally realize a one-dimensional RHM (Right-handed Material)-LHM (Left-handed Material) multi-frequency resonator that consists of a dual-negative-band LHM and air arranged in an X-band waveguide. Multi-resonant frequencies are observed within two left-handed bands of the LHM. The effects of the loss and the hyperbolic dispersion relation of LHM layer are discussed. The incorporation of such a LHM into the resonator design allows more flexibility to realize multi-resonance.

© 2006 Optical Society of America

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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. A. A. Houck, J. B. Brock, and I. L. Chuang, "Experimental Observations of a Left-Handed Material That Obeys Snell’s Law," Phys. Rev. Lett. 90, 137401 (2003).
    [CrossRef] [PubMed]
  3. Y. Li, L. Ran, H. Chen, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Experimental realization of a one dimensional LHM-RHM Resonator," IEEE Microwave Theory and Tech. special issue on metamaterials 53, 1522 (2005).
  4. Y. Yuan, L. Ran, H. Chen, J. Huangfu, T. M. Grzegorczyk and J. A. Kong, "Backward coupling waveguide coupler using left-handed material," J. Appl. Phys. 88, 211903 (2006).
  5. N. Engheta, "An Idea for Thin Subwavelength Cavity Resonators Using MetamaterialsWith Negative Permittivity and Permeability," IEEE Antennas and Wireless Propagation Lett.,  1, 1 (2002).
  6. L. Ran, J. Huangfu, H. Chen, Y. Li, X. Zhang, K. Chen, and J. A. Kong, "Microwave solid-state left-handed material with a broad bandwidth and an ultralow loss," Phys. Rev. B 70, 073102 (2004).
    [CrossRef]
  7. H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Metamaterial exhibiting left-handed properties over multiple frequency bands," J. Appl. Phys. 96, 5338 (2004).
    [CrossRef]
  8. X. Chen, T. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterial," Phys. Rev. E 70, 016608 (2004).
    [CrossRef]
  9. L. Shen, S. He, S. Xiao, "Stability and quality factor of a one-dimensional subwavelength cavity resonator containing a left-handed material," Phys. Rev. B 69, 115111 (2004).
    [CrossRef]

2006

Y. Yuan, L. Ran, H. Chen, J. Huangfu, T. M. Grzegorczyk and J. A. Kong, "Backward coupling waveguide coupler using left-handed material," J. Appl. Phys. 88, 211903 (2006).

2004

L. Ran, J. Huangfu, H. Chen, Y. Li, X. Zhang, K. Chen, and J. A. Kong, "Microwave solid-state left-handed material with a broad bandwidth and an ultralow loss," Phys. Rev. B 70, 073102 (2004).
[CrossRef]

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Metamaterial exhibiting left-handed properties over multiple frequency bands," J. Appl. Phys. 96, 5338 (2004).
[CrossRef]

X. Chen, T. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterial," Phys. Rev. E 70, 016608 (2004).
[CrossRef]

L. Shen, S. He, S. Xiao, "Stability and quality factor of a one-dimensional subwavelength cavity resonator containing a left-handed material," Phys. Rev. B 69, 115111 (2004).
[CrossRef]

2003

A. A. Houck, J. B. Brock, and I. L. Chuang, "Experimental Observations of a Left-Handed Material That Obeys Snell’s Law," Phys. Rev. Lett. 90, 137401 (2003).
[CrossRef] [PubMed]

2002

N. Engheta, "An Idea for Thin Subwavelength Cavity Resonators Using MetamaterialsWith Negative Permittivity and Permeability," IEEE Antennas and Wireless Propagation Lett.,  1, 1 (2002).

2001

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

Brock, J. B.

A. A. Houck, J. B. Brock, and I. L. Chuang, "Experimental Observations of a Left-Handed Material That Obeys Snell’s Law," Phys. Rev. Lett. 90, 137401 (2003).
[CrossRef] [PubMed]

Chen, H.

Y. Yuan, L. Ran, H. Chen, J. Huangfu, T. M. Grzegorczyk and J. A. Kong, "Backward coupling waveguide coupler using left-handed material," J. Appl. Phys. 88, 211903 (2006).

L. Ran, J. Huangfu, H. Chen, Y. Li, X. Zhang, K. Chen, and J. A. Kong, "Microwave solid-state left-handed material with a broad bandwidth and an ultralow loss," Phys. Rev. B 70, 073102 (2004).
[CrossRef]

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Metamaterial exhibiting left-handed properties over multiple frequency bands," J. Appl. Phys. 96, 5338 (2004).
[CrossRef]

Chen, K.

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Metamaterial exhibiting left-handed properties over multiple frequency bands," J. Appl. Phys. 96, 5338 (2004).
[CrossRef]

L. Ran, J. Huangfu, H. Chen, Y. Li, X. Zhang, K. Chen, and J. A. Kong, "Microwave solid-state left-handed material with a broad bandwidth and an ultralow loss," Phys. Rev. B 70, 073102 (2004).
[CrossRef]

Chen, X.

X. Chen, T. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterial," Phys. Rev. E 70, 016608 (2004).
[CrossRef]

Chuang, I. L.

A. A. Houck, J. B. Brock, and I. L. Chuang, "Experimental Observations of a Left-Handed Material That Obeys Snell’s Law," Phys. Rev. Lett. 90, 137401 (2003).
[CrossRef] [PubMed]

Engheta, N.

N. Engheta, "An Idea for Thin Subwavelength Cavity Resonators Using MetamaterialsWith Negative Permittivity and Permeability," IEEE Antennas and Wireless Propagation Lett.,  1, 1 (2002).

Grzegorczyk, T.

X. Chen, T. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterial," Phys. Rev. E 70, 016608 (2004).
[CrossRef]

Grzegorczyk, T. M.

Y. Yuan, L. Ran, H. Chen, J. Huangfu, T. M. Grzegorczyk and J. A. Kong, "Backward coupling waveguide coupler using left-handed material," J. Appl. Phys. 88, 211903 (2006).

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Metamaterial exhibiting left-handed properties over multiple frequency bands," J. Appl. Phys. 96, 5338 (2004).
[CrossRef]

He, S.

L. Shen, S. He, S. Xiao, "Stability and quality factor of a one-dimensional subwavelength cavity resonator containing a left-handed material," Phys. Rev. B 69, 115111 (2004).
[CrossRef]

Houck, A. A.

A. A. Houck, J. B. Brock, and I. L. Chuang, "Experimental Observations of a Left-Handed Material That Obeys Snell’s Law," Phys. Rev. Lett. 90, 137401 (2003).
[CrossRef] [PubMed]

Huangfu, J.

Y. Yuan, L. Ran, H. Chen, J. Huangfu, T. M. Grzegorczyk and J. A. Kong, "Backward coupling waveguide coupler using left-handed material," J. Appl. Phys. 88, 211903 (2006).

L. Ran, J. Huangfu, H. Chen, Y. Li, X. Zhang, K. Chen, and J. A. Kong, "Microwave solid-state left-handed material with a broad bandwidth and an ultralow loss," Phys. Rev. B 70, 073102 (2004).
[CrossRef]

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Metamaterial exhibiting left-handed properties over multiple frequency bands," J. Appl. Phys. 96, 5338 (2004).
[CrossRef]

Kong, J. A.

Y. Yuan, L. Ran, H. Chen, J. Huangfu, T. M. Grzegorczyk and J. A. Kong, "Backward coupling waveguide coupler using left-handed material," J. Appl. Phys. 88, 211903 (2006).

L. Ran, J. Huangfu, H. Chen, Y. Li, X. Zhang, K. Chen, and J. A. Kong, "Microwave solid-state left-handed material with a broad bandwidth and an ultralow loss," Phys. Rev. B 70, 073102 (2004).
[CrossRef]

X. Chen, T. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterial," Phys. Rev. E 70, 016608 (2004).
[CrossRef]

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Metamaterial exhibiting left-handed properties over multiple frequency bands," J. Appl. Phys. 96, 5338 (2004).
[CrossRef]

Li, Y.

L. Ran, J. Huangfu, H. Chen, Y. Li, X. Zhang, K. Chen, and J. A. Kong, "Microwave solid-state left-handed material with a broad bandwidth and an ultralow loss," Phys. Rev. B 70, 073102 (2004).
[CrossRef]

Pacheco, J.

X. Chen, T. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterial," Phys. Rev. E 70, 016608 (2004).
[CrossRef]

Ran, L.

Y. Yuan, L. Ran, H. Chen, J. Huangfu, T. M. Grzegorczyk and J. A. Kong, "Backward coupling waveguide coupler using left-handed material," J. Appl. Phys. 88, 211903 (2006).

L. Ran, J. Huangfu, H. Chen, Y. Li, X. Zhang, K. Chen, and J. A. Kong, "Microwave solid-state left-handed material with a broad bandwidth and an ultralow loss," Phys. Rev. B 70, 073102 (2004).
[CrossRef]

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Metamaterial exhibiting left-handed properties over multiple frequency bands," J. Appl. Phys. 96, 5338 (2004).
[CrossRef]

Schultz, S.

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

Shelby, R. A.

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

Shen, L.

L. Shen, S. He, S. Xiao, "Stability and quality factor of a one-dimensional subwavelength cavity resonator containing a left-handed material," Phys. Rev. B 69, 115111 (2004).
[CrossRef]

Smith, D. R.

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

Wu, B.-I.

X. Chen, T. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterial," Phys. Rev. E 70, 016608 (2004).
[CrossRef]

Xiao, S.

L. Shen, S. He, S. Xiao, "Stability and quality factor of a one-dimensional subwavelength cavity resonator containing a left-handed material," Phys. Rev. B 69, 115111 (2004).
[CrossRef]

Yuan, Y.

Y. Yuan, L. Ran, H. Chen, J. Huangfu, T. M. Grzegorczyk and J. A. Kong, "Backward coupling waveguide coupler using left-handed material," J. Appl. Phys. 88, 211903 (2006).

Zhang, X.

L. Ran, J. Huangfu, H. Chen, Y. Li, X. Zhang, K. Chen, and J. A. Kong, "Microwave solid-state left-handed material with a broad bandwidth and an ultralow loss," Phys. Rev. B 70, 073102 (2004).
[CrossRef]

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Metamaterial exhibiting left-handed properties over multiple frequency bands," J. Appl. Phys. 96, 5338 (2004).
[CrossRef]

IEEE Antennas and Wireless Propagation Lett.

N. Engheta, "An Idea for Thin Subwavelength Cavity Resonators Using MetamaterialsWith Negative Permittivity and Permeability," IEEE Antennas and Wireless Propagation Lett.,  1, 1 (2002).

J. Appl. Phys.

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Metamaterial exhibiting left-handed properties over multiple frequency bands," J. Appl. Phys. 96, 5338 (2004).
[CrossRef]

Y. Yuan, L. Ran, H. Chen, J. Huangfu, T. M. Grzegorczyk and J. A. Kong, "Backward coupling waveguide coupler using left-handed material," J. Appl. Phys. 88, 211903 (2006).

Phys. Rev. B

L. Ran, J. Huangfu, H. Chen, Y. Li, X. Zhang, K. Chen, and J. A. Kong, "Microwave solid-state left-handed material with a broad bandwidth and an ultralow loss," Phys. Rev. B 70, 073102 (2004).
[CrossRef]

L. Shen, S. He, S. Xiao, "Stability and quality factor of a one-dimensional subwavelength cavity resonator containing a left-handed material," Phys. Rev. B 69, 115111 (2004).
[CrossRef]

Phys. Rev. E

X. Chen, T. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterial," Phys. Rev. E 70, 016608 (2004).
[CrossRef]

Phys. Rev. Lett.

A. A. Houck, J. B. Brock, and I. L. Chuang, "Experimental Observations of a Left-Handed Material That Obeys Snell’s Law," Phys. Rev. Lett. 90, 137401 (2003).
[CrossRef] [PubMed]

Science

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

Y. Li, L. Ran, H. Chen, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Experimental realization of a one dimensional LHM-RHM Resonator," IEEE Microwave Theory and Tech. special issue on metamaterials 53, 1522 (2005).

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Figures (8)

Fig. 1.
Fig. 1.

The resonant scheme proposed in [5].

Fig. 2.
Fig. 2.

The experimental setup. d is the total length of the resonator. d 1 and d 2 are the thicknesses of the LHM and RHM layers, respectively. a=22.86mm and h=10.16mm represent the cross section of the resonator.

Fig. 3.
Fig. 3.

Experimental transmission property of the two-bands S-shaped LHM sample from 7GHz to 16GHz.

Fig. 4.
Fig. 4.

The extracted refractive indexes of the dual-band S shaped LHM from prism experiment and prism simulation

Fig. 5.
Fig. 5.

The measured S 11 curve of the RHM-LHM resonator from 9GHz to 13.5GHz. The total length of the resonator is 11mm.

Fig. 6.
Fig. 6.

The retrieval (simulation) and estimated permeabilities (μy ).

Fig. 7.
Fig. 7.

k surface of air (circle) and LHM sample (hyperbola). k i1 and k i2 are the incident wave vectors, k t1 and k t2 are the transmitted wave vectors at 12.5GHz and 12GHz respectively, k z1 and k z2 are the z components of k t1 and k t2, correspondingly.

Fig. 8.
Fig. 8.

The value of Eq. (2) left side for three loss cases. δm =1×103×2πrads/s, δm =1×105×2πrads/s, δm =1×106×2πrads/s for blue, red and green curves, correspondingly. For all the three cases, δe =1×107×2πrads/s.

Tables (1)

Tables Icon

Table 1. Experimental resonant frequencies of the multi-resonant RHM-LHM resonator at different total lengthes.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

n 2 μ 2 tan ( n 1 k 0 t 1 ) + n 1 μ 1 tan ( n 2 k 0 t 2 ) = 0 ,
μ 1 y k 2 z tan k 1 z d 1 + μ 2 y k 1 z tan k 2 z d 2 = 0 ,

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