Abstract

Based on the analysis of rectangular periodic structures, the resonance frequency band is found to be shifted and broadened from low frequency to high frequency by adjustment of the corresponding structure size. Computer simulation shows that a miniature split-ring resonator can enhance and broaden resonance frequency without changing the stop-band location. According to the theoretical parameters, different experimental samples can be fabricated. The experimental results are generally the same as those predicted theoretically. A comparison of the experimental and theoretical results concluded that a miniature periodic structure broadened the frequency of the stop band and enhanced the resonance frequency, which are important for the study of left-handed materials.

© 2010 Optical Society of America

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References

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  1. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
  2. R. A. Shelby, D. R. Smith, and S. Schulz, “Experimental verification of a negative index of refraction,” Science 292, 77-79 (2001).
    [CrossRef] [PubMed]
  3. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187 (2000).
    [CrossRef] [PubMed]
  4. T. Jiang, Y. Chen, and Y. J. Feng, “Subwavelength rectangular cavity partially filled with left-handed materials,” Chin. Phys. 15, 1154-1160 (2006).
    [CrossRef]
  5. K. Aydin, K. Guven, M. Kafesaki, L. Zhang, C. M. Soukoulis, and E. Ozbay, “Experimental observation of true left-handed transmission peaks in metamaterials,” Opt. Lett. 29, 2623-2625 (2004).
    [CrossRef] [PubMed]
  6. Y. H. Hu, X. Q. Fu, S. C. Wen, W. H. Su, and D. Y. Fan, “(3+1)-dimensional nonlinear propagation equation for ultrashort pulsed beam in left-handed material,” Chin. Phys. 15, 2970-2976 (2006).
    [CrossRef]
  7. H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M.Grzegorczyk, and J. Au Kong, “Left-handed materials composed of only S-shaped resonators,” Phys. Rev. E 70, 057605 (2004).
    [CrossRef]
  8. J. Huangfu, L. Ran, H. Chen, X. Zhang, K. Chen, T.M. M. Grzegorczyk, and J. Au Kong, “Experimental confirmation of negative refractive index of metamaterial composed of Ω-like metallic patterns,” Appl. Phys. Lett. 84, 1537-1539(2004).
    [CrossRef]
  9. Q. Zheng, X. P. Zhao, Q. H. Fu, Q. Zhao, L. Kang, and M. M. Li, “Reflection and negative refraction of left-handed metematerials at microwave frequencies,” Acta Phys. Sin. 54, 5683-5687 (2005).
  10. M. Sun, C. Zhang, X. Song, G. Liang, and Z. Sun, “Study on new period structures of left- handed material based on rectangular resonators and metal wires,” Acta Phys. Sin. 58, 6179-6184 (2009).
  11. C. Zhang, M. Sun, Z. Yuan, and X. Song, “Study on new period structures of left-handed material composed of hexagonal SRRs and metal wires,” Acta Phys. Sin. 58, 1758-1764 (2009).
  12. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
    [CrossRef]
  13. 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]

2009 (2)

M. Sun, C. Zhang, X. Song, G. Liang, and Z. Sun, “Study on new period structures of left- handed material based on rectangular resonators and metal wires,” Acta Phys. Sin. 58, 6179-6184 (2009).

C. Zhang, M. Sun, Z. Yuan, and X. Song, “Study on new period structures of left-handed material composed of hexagonal SRRs and metal wires,” Acta Phys. Sin. 58, 1758-1764 (2009).

2006 (2)

T. Jiang, Y. Chen, and Y. J. Feng, “Subwavelength rectangular cavity partially filled with left-handed materials,” Chin. Phys. 15, 1154-1160 (2006).
[CrossRef]

Y. H. Hu, X. Q. Fu, S. C. Wen, W. H. Su, and D. Y. Fan, “(3+1)-dimensional nonlinear propagation equation for ultrashort pulsed beam in left-handed material,” Chin. Phys. 15, 2970-2976 (2006).
[CrossRef]

2005 (1)

Q. Zheng, X. P. Zhao, Q. H. Fu, Q. Zhao, L. Kang, and M. M. Li, “Reflection and negative refraction of left-handed metematerials at microwave frequencies,” Acta Phys. Sin. 54, 5683-5687 (2005).

2004 (3)

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M.Grzegorczyk, and J. Au Kong, “Left-handed materials composed of only S-shaped resonators,” Phys. Rev. E 70, 057605 (2004).
[CrossRef]

J. Huangfu, L. Ran, H. Chen, X. Zhang, K. Chen, T.M. M. Grzegorczyk, and J. Au Kong, “Experimental confirmation of negative refractive index of metamaterial composed of Ω-like metallic patterns,” Appl. Phys. Lett. 84, 1537-1539(2004).
[CrossRef]

K. Aydin, K. Guven, M. Kafesaki, L. Zhang, C. M. Soukoulis, and E. Ozbay, “Experimental observation of true left-handed transmission peaks in metamaterials,” Opt. Lett. 29, 2623-2625 (2004).
[CrossRef] [PubMed]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schulz, “Experimental verification of a negative index of refraction,” Science 292, 77-79 (2001).
[CrossRef] [PubMed]

2000 (1)

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

1996 (1)

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]

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Aydin, K.

Chen, H.

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M.Grzegorczyk, and J. Au Kong, “Left-handed materials composed of only S-shaped resonators,” Phys. Rev. E 70, 057605 (2004).
[CrossRef]

J. Huangfu, L. Ran, H. Chen, X. Zhang, K. Chen, T.M. M. Grzegorczyk, and J. Au Kong, “Experimental confirmation of negative refractive index of metamaterial composed of Ω-like metallic patterns,” Appl. Phys. Lett. 84, 1537-1539(2004).
[CrossRef]

Chen, K.

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M.Grzegorczyk, and J. Au Kong, “Left-handed materials composed of only S-shaped resonators,” Phys. Rev. E 70, 057605 (2004).
[CrossRef]

J. Huangfu, L. Ran, H. Chen, X. Zhang, K. Chen, T.M. M. Grzegorczyk, and J. Au Kong, “Experimental confirmation of negative refractive index of metamaterial composed of Ω-like metallic patterns,” Appl. Phys. Lett. 84, 1537-1539(2004).
[CrossRef]

Chen, Y.

T. Jiang, Y. Chen, and Y. J. Feng, “Subwavelength rectangular cavity partially filled with left-handed materials,” Chin. Phys. 15, 1154-1160 (2006).
[CrossRef]

Fan, D. Y.

Y. H. Hu, X. Q. Fu, S. C. Wen, W. H. Su, and D. Y. Fan, “(3+1)-dimensional nonlinear propagation equation for ultrashort pulsed beam in left-handed material,” Chin. Phys. 15, 2970-2976 (2006).
[CrossRef]

Feng, Y. J.

T. Jiang, Y. Chen, and Y. J. Feng, “Subwavelength rectangular cavity partially filled with left-handed materials,” Chin. Phys. 15, 1154-1160 (2006).
[CrossRef]

Fu, Q. H.

Q. Zheng, X. P. Zhao, Q. H. Fu, Q. Zhao, L. Kang, and M. M. Li, “Reflection and negative refraction of left-handed metematerials at microwave frequencies,” Acta Phys. Sin. 54, 5683-5687 (2005).

Fu, X. Q.

Y. H. Hu, X. Q. Fu, S. C. Wen, W. H. Su, and D. Y. Fan, “(3+1)-dimensional nonlinear propagation equation for ultrashort pulsed beam in left-handed material,” Chin. Phys. 15, 2970-2976 (2006).
[CrossRef]

Grzegorczyk, T. M.

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M.Grzegorczyk, and J. Au Kong, “Left-handed materials composed of only S-shaped resonators,” Phys. Rev. E 70, 057605 (2004).
[CrossRef]

Grzegorczyk, T.M. M.

J. Huangfu, L. Ran, H. Chen, X. Zhang, K. Chen, T.M. M. Grzegorczyk, and J. Au Kong, “Experimental confirmation of negative refractive index of metamaterial composed of Ω-like metallic patterns,” Appl. Phys. Lett. 84, 1537-1539(2004).
[CrossRef]

Guven, K.

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

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]

Hu, Y. H.

Y. H. Hu, X. Q. Fu, S. C. Wen, W. H. Su, and D. Y. Fan, “(3+1)-dimensional nonlinear propagation equation for ultrashort pulsed beam in left-handed material,” Chin. Phys. 15, 2970-2976 (2006).
[CrossRef]

Huangfu, J.

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M.Grzegorczyk, and J. Au Kong, “Left-handed materials composed of only S-shaped resonators,” Phys. Rev. E 70, 057605 (2004).
[CrossRef]

J. Huangfu, L. Ran, H. Chen, X. Zhang, K. Chen, T.M. M. Grzegorczyk, and J. Au Kong, “Experimental confirmation of negative refractive index of metamaterial composed of Ω-like metallic patterns,” Appl. Phys. Lett. 84, 1537-1539(2004).
[CrossRef]

Jiang, T.

T. Jiang, Y. Chen, and Y. J. Feng, “Subwavelength rectangular cavity partially filled with left-handed materials,” Chin. Phys. 15, 1154-1160 (2006).
[CrossRef]

Kafesaki, M.

Kang, L.

Q. Zheng, X. P. Zhao, Q. H. Fu, Q. Zhao, L. Kang, and M. M. Li, “Reflection and negative refraction of left-handed metematerials at microwave frequencies,” Acta Phys. Sin. 54, 5683-5687 (2005).

Kong, J. Au

J. Huangfu, L. Ran, H. Chen, X. Zhang, K. Chen, T.M. M. Grzegorczyk, and J. Au Kong, “Experimental confirmation of negative refractive index of metamaterial composed of Ω-like metallic patterns,” Appl. Phys. Lett. 84, 1537-1539(2004).
[CrossRef]

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M.Grzegorczyk, and J. Au Kong, “Left-handed materials composed of only S-shaped resonators,” Phys. Rev. E 70, 057605 (2004).
[CrossRef]

Li, M. M.

Q. Zheng, X. P. Zhao, Q. H. Fu, Q. Zhao, L. Kang, and M. M. Li, “Reflection and negative refraction of left-handed metematerials at microwave frequencies,” Acta Phys. Sin. 54, 5683-5687 (2005).

Liang, G.

M. Sun, C. Zhang, X. Song, G. Liang, and Z. Sun, “Study on new period structures of left- handed material based on rectangular resonators and metal wires,” Acta Phys. Sin. 58, 6179-6184 (2009).

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Ozbay, E.

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Pendry, J. B.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

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]

Ran, L.

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M.Grzegorczyk, and J. Au Kong, “Left-handed materials composed of only S-shaped resonators,” Phys. Rev. E 70, 057605 (2004).
[CrossRef]

J. Huangfu, L. Ran, H. Chen, X. Zhang, K. Chen, T.M. M. Grzegorczyk, and J. Au Kong, “Experimental confirmation of negative refractive index of metamaterial composed of Ω-like metallic patterns,” Appl. Phys. Lett. 84, 1537-1539(2004).
[CrossRef]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Schultz, S.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Schulz, S.

R. A. Shelby, D. R. Smith, and S. Schulz, “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. Schulz, “Experimental verification of a negative index of refraction,” Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Smith, D. R.

R. A. Shelby, D. R. Smith, and S. Schulz, “Experimental verification of a negative index of refraction,” Science 292, 77-79 (2001).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Song, X.

M. Sun, C. Zhang, X. Song, G. Liang, and Z. Sun, “Study on new period structures of left- handed material based on rectangular resonators and metal wires,” Acta Phys. Sin. 58, 6179-6184 (2009).

C. Zhang, M. Sun, Z. Yuan, and X. Song, “Study on new period structures of left-handed material composed of hexagonal SRRs and metal wires,” Acta Phys. Sin. 58, 1758-1764 (2009).

Soukoulis, C. M.

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

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]

Su, W. H.

Y. H. Hu, X. Q. Fu, S. C. Wen, W. H. Su, and D. Y. Fan, “(3+1)-dimensional nonlinear propagation equation for ultrashort pulsed beam in left-handed material,” Chin. Phys. 15, 2970-2976 (2006).
[CrossRef]

Sun, M.

C. Zhang, M. Sun, Z. Yuan, and X. Song, “Study on new period structures of left-handed material composed of hexagonal SRRs and metal wires,” Acta Phys. Sin. 58, 1758-1764 (2009).

M. Sun, C. Zhang, X. Song, G. Liang, and Z. Sun, “Study on new period structures of left- handed material based on rectangular resonators and metal wires,” Acta Phys. Sin. 58, 6179-6184 (2009).

Sun, Z.

M. Sun, C. Zhang, X. Song, G. Liang, and Z. Sun, “Study on new period structures of left- handed material based on rectangular resonators and metal wires,” Acta Phys. Sin. 58, 6179-6184 (2009).

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Wen, S. C.

Y. H. Hu, X. Q. Fu, S. C. Wen, W. H. Su, and D. Y. Fan, “(3+1)-dimensional nonlinear propagation equation for ultrashort pulsed beam in left-handed material,” Chin. Phys. 15, 2970-2976 (2006).
[CrossRef]

Youngs, I.

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]

Yuan, Z.

C. Zhang, M. Sun, Z. Yuan, and X. Song, “Study on new period structures of left-handed material composed of hexagonal SRRs and metal wires,” Acta Phys. Sin. 58, 1758-1764 (2009).

Zhang, C.

C. Zhang, M. Sun, Z. Yuan, and X. Song, “Study on new period structures of left-handed material composed of hexagonal SRRs and metal wires,” Acta Phys. Sin. 58, 1758-1764 (2009).

M. Sun, C. Zhang, X. Song, G. Liang, and Z. Sun, “Study on new period structures of left- handed material based on rectangular resonators and metal wires,” Acta Phys. Sin. 58, 6179-6184 (2009).

Zhang, L.

Zhang, X.

J. Huangfu, L. Ran, H. Chen, X. Zhang, K. Chen, T.M. M. Grzegorczyk, and J. Au Kong, “Experimental confirmation of negative refractive index of metamaterial composed of Ω-like metallic patterns,” Appl. Phys. Lett. 84, 1537-1539(2004).
[CrossRef]

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M.Grzegorczyk, and J. Au Kong, “Left-handed materials composed of only S-shaped resonators,” Phys. Rev. E 70, 057605 (2004).
[CrossRef]

Zhao, Q.

Q. Zheng, X. P. Zhao, Q. H. Fu, Q. Zhao, L. Kang, and M. M. Li, “Reflection and negative refraction of left-handed metematerials at microwave frequencies,” Acta Phys. Sin. 54, 5683-5687 (2005).

Zhao, X. P.

Q. Zheng, X. P. Zhao, Q. H. Fu, Q. Zhao, L. Kang, and M. M. Li, “Reflection and negative refraction of left-handed metematerials at microwave frequencies,” Acta Phys. Sin. 54, 5683-5687 (2005).

Zheng, Q.

Q. Zheng, X. P. Zhao, Q. H. Fu, Q. Zhao, L. Kang, and M. M. Li, “Reflection and negative refraction of left-handed metematerials at microwave frequencies,” Acta Phys. Sin. 54, 5683-5687 (2005).

Acta Phys. Sin. (3)

Q. Zheng, X. P. Zhao, Q. H. Fu, Q. Zhao, L. Kang, and M. M. Li, “Reflection and negative refraction of left-handed metematerials at microwave frequencies,” Acta Phys. Sin. 54, 5683-5687 (2005).

M. Sun, C. Zhang, X. Song, G. Liang, and Z. Sun, “Study on new period structures of left- handed material based on rectangular resonators and metal wires,” Acta Phys. Sin. 58, 6179-6184 (2009).

C. Zhang, M. Sun, Z. Yuan, and X. Song, “Study on new period structures of left-handed material composed of hexagonal SRRs and metal wires,” Acta Phys. Sin. 58, 1758-1764 (2009).

Appl. Phys. Lett. (1)

J. Huangfu, L. Ran, H. Chen, X. Zhang, K. Chen, T.M. M. Grzegorczyk, and J. Au Kong, “Experimental confirmation of negative refractive index of metamaterial composed of Ω-like metallic patterns,” Appl. Phys. Lett. 84, 1537-1539(2004).
[CrossRef]

Chin. Phys. (2)

Y. H. Hu, X. Q. Fu, S. C. Wen, W. H. Su, and D. Y. Fan, “(3+1)-dimensional nonlinear propagation equation for ultrashort pulsed beam in left-handed material,” Chin. Phys. 15, 2970-2976 (2006).
[CrossRef]

T. Jiang, Y. Chen, and Y. J. Feng, “Subwavelength rectangular cavity partially filled with left-handed materials,” Chin. Phys. 15, 1154-1160 (2006).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. E (1)

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M.Grzegorczyk, and J. Au Kong, “Left-handed materials composed of only S-shaped resonators,” Phys. Rev. E 70, 057605 (2004).
[CrossRef]

Phys. Rev. Lett. (2)

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187 (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]

Science (1)

R. A. Shelby, D. R. Smith, and S. Schulz, “Experimental verification of a negative index of refraction,” Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

(a)  Rectangular and (b) side view SRRs.

Fig. 2
Fig. 2

Left-handed materials (C-shaped): (a)  plane structures and (b) spatial structures.

Fig. 3
Fig. 3

(a) Large and (b) small rectangular SRRs.

Fig. 4
Fig. 4

Model of rectangular SRR spatial structures.

Fig. 5
Fig. 5

S21 curves for (a) large and (b) small rectangular SRRs; (c) large CSRRs.

Fig. 6
Fig. 6

Experimental (a)  device, (b)  samples, (c)  measure.

Fig. 7
Fig. 7

Experimental results of the (a) original and (b) miniature structures.

Tables (1)

Tables Icon

Table 1 Parameters of the Simulation

Equations (8)

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

L = μ 0 π ( b / a + a / b ) 2 a 2 + b 2 S .
C = Q U = Q E d = σ S E d = 4 π ε 0 ln ( b + b 2 + a 2 2 b + b 2 + a 2 2 b + b 2 + a 1 2 b + b 2 + a 1 2 ) S d .
ω m 0 = 1 L C , ω m p = 1 1 F ω m 0 ,
ω m 0 2 = 3 l c 0 2 π In 2 c d r 3 ,
ω m p 2 = 1 1 π r 2 a 2 ω 0 2 ,
μ ( ω ) μ 0 = 1 ω m p 2 ω m 0 2 ω 2 ω m 0 2 + i γ ω ,
ω m 0 = 1 LC = 2 π × 8.52 GHz , ω m p = 1 1 F ω m 0 = 2 π × 12.2 GHz .
ω m 0 = 1 LC = 2 π × 8.02 GHz , ω m p = 1 1 F ω m 0 = 2 π × 13.2 GHz .

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