Abstract

Alternative designs to an electric-LC (ELC) resonator, which is a type of metamaterial inclusion, are presented in this article. Fitting the resonator with an interdigital capacitor (IDC) helps to increase the total capacitance of the structure. In effect, its resonance frequency is shifted downwards. This implies a decreased overall resonator size with respect to its operating wavelength. As a result, the metamaterial, composed of an array of IDC-loaded ELC resonators with their collective electromagnetic response, possesses improved homogeneity and hence is less influenced by diffraction effects of individual cells. The impact of incorporating an IDC into ELC resonators in terms of the electrical size at resonance and other relevant properties are investigated through both simulation and experiment in the microwave regime. The proposed structures can be applied to the terahertz regime via appropriate lithographic scaling.

© 2010 Optical Society of America

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2010 (1)

G. Houzet, X. Melique, and D. Lippens, "Microstrip transmission line loaded by split-ring resonators tuned by ferroelectric thin film," Progress in Electromagnetics Research 12, 225-236 (2010).
[CrossRef]

2009 (2)

W. Withayachumnankul, and D. Abbott, "Metamaterials in the terahertz regime," IEEE Photonics J. 1, 99-118 (2009).
[CrossRef]

E. Lenz, and H. Henke, "Homogenization of metamaterials due to fractaloid structures in the microwave regime," J. Opt. A, Pure Appl. Opt. 11, 114021 (2009).
[CrossRef]

2008 (1)

N. A. Zharova, I. V. Shadrivov, A. A. Zharov, and Y. Kivshar, "Ideal and nonideal invisibility cloaks," Opt. Express 16, 21369-21374 (2008).
[CrossRef] [PubMed]

2007 (4)

W. J. Padilla, M. T. Aronsson, C. Highstrete, M. Lee, A. J. Taylor, and R. D. Averitt, "Electrically resonant terahertz metamaterials: Theoretical and experimental investigations," Phys. Rev. B Condens. Matter 75, 041102 (2007).
[CrossRef]

M. M. Lapine, and S. Tretyakov, "Contemporary notes on metamaterials," IET Microwaves Antennas Propag. 1, 3-11 (2007).
[CrossRef]

K. Aydin, and E. Ozbay, "Capacitor-loaded split ring resonators as tunable metamaterial components," J. Appl. Phys. 101, 024911 (2007).
[CrossRef]

F. Bilotti, A. Toscano, and L. Vegni, "Design of spiral and multiple split-ring resonators for the realization of miniaturized metamaterial samples," IEEE Trans. Antenn. Propag. 55, 2258-2267 (2007).
[CrossRef]

2006 (3)

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

H. Chen, L. Ran, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, "Crankled S-ring resonator with small electrical size," Progress in Electromagnetics Research 66, 179-190 (2006).
[CrossRef]

D. Schurig, J. J. Mock, and D. R. Smith, "Electric-field-coupled resonators for negative permittivity metamaterials," Appl. Phys. Lett. 88, 041109 (2006).
[CrossRef]

2005 (6)

K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Investigation of magnetic resonances for different split-ring resonator parameters and designs," N. J. Phys. 7, 168 (2005).
[CrossRef]

T. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials," Phys. Rev. B Condens. Matter 71, 245105 (2005).
[CrossRef]

C. Caloz, A. Lai, and T. Itoh, "The challenge of homogenization in metamaterials," N. J. Phys. 7, 167 (2005).
[CrossRef]

V. Shalaev, W. Cai, U. Chettiar, H. Yuan, A. Sarychev, V. Drachev, and A. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

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

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Phys. Rev. E 71, 036617 (2005).
[CrossRef]

2004 (5)

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

C. Caloz, and T. Itoh, "Transmission line approach of left-handed (LH) materials and microstrip implementation of an artificial LH transmission line," IEEE Trans. Antenn. Propag. 52, 1159-1166 (2004).
[CrossRef]

A. Sanada, C. Caloz, and T. Itoh, "Characteristics of the composite right/left-handed transmission lines," IEEE Microwave Wireless Compon. Lett. 14, 68-70 (2004).
[CrossRef]

J. Dai, J. Zhang, W. Zhang, and D. Grischkowsky, "Terahertz time-domain spectroscopy characterization of the far-infrared absorption and index of refraction of high-resistivity, float-zone silicon," J. Opt. Soc. Am. B 21, 1379-1386 (2004).
[CrossRef]

J. D. Baena, R. Marqués, and F. Medina, "Artificial magnetic metamaterial design by using spiral resonators," Phys. Rev. B Condens. Matter 69, 014402 (2004).
[CrossRef]

2003 (1)

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, "Limitations on subdiffraction imaging with a negative refractive index slab," Appl. Phys. Lett. 82, 1506-1508 (2003).
[CrossRef]

2000 (1)

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (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. Microw. Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

1983 (1)

M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, J. R. W. Alexander, and C. A. Ward, "Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared," Appl. Opt. 22, 1099-1119 (1983).
[CrossRef] [PubMed]

1970 (1)

G. D. Alley, "Interdigital capacitors and their application to lumped-element microwave integrated circuits," IEEE Trans. Microw. Theory Tech. MTT-18, 1028-1033 (1970).
[CrossRef]

1948 (1)

L. J. Chu, "Physical limitations of omni-directional antennas," J. Appl. Phys. 19, 1163-1175 (1948).
[CrossRef]

Abbott, D.

W. Withayachumnankul, and D. Abbott, "Metamaterials in the terahertz regime," IEEE Photonics J. 1, 99-118 (2009).
[CrossRef]

Alexander, J. R. W.

M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, J. R. W. Alexander, and C. A. Ward, "Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared," Appl. Opt. 22, 1099-1119 (1983).
[CrossRef] [PubMed]

Alley, G. D.

G. D. Alley, "Interdigital capacitors and their application to lumped-element microwave integrated circuits," IEEE Trans. Microw. Theory Tech. MTT-18, 1028-1033 (1970).
[CrossRef]

Aronsson, M. T.

W. J. Padilla, M. T. Aronsson, C. Highstrete, M. Lee, A. J. Taylor, and R. D. Averitt, "Electrically resonant terahertz metamaterials: Theoretical and experimental investigations," Phys. Rev. B Condens. Matter 75, 041102 (2007).
[CrossRef]

Averitt, R. D.

W. J. Padilla, M. T. Aronsson, C. Highstrete, M. Lee, A. J. Taylor, and R. D. Averitt, "Electrically resonant terahertz metamaterials: Theoretical and experimental investigations," Phys. Rev. B Condens. Matter 75, 041102 (2007).
[CrossRef]

Aydin, K.

K. Aydin, and E. Ozbay, "Capacitor-loaded split ring resonators as tunable metamaterial components," J. Appl. Phys. 101, 024911 (2007).
[CrossRef]

K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Investigation of magnetic resonances for different split-ring resonator parameters and designs," N. J. Phys. 7, 168 (2005).
[CrossRef]

Baena, J. D.

J. D. Baena, R. Marqués, and F. Medina, "Artificial magnetic metamaterial design by using spiral resonators," Phys. Rev. B Condens. Matter 69, 014402 (2004).
[CrossRef]

Bell, R. J.

M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, J. R. W. Alexander, and C. A. Ward, "Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared," Appl. Opt. 22, 1099-1119 (1983).
[CrossRef] [PubMed]

Bell, R. R.

M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, J. R. W. Alexander, and C. A. Ward, "Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared," Appl. Opt. 22, 1099-1119 (1983).
[CrossRef] [PubMed]

Bell, S. E.

M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, J. R. W. Alexander, and C. A. Ward, "Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared," Appl. Opt. 22, 1099-1119 (1983).
[CrossRef] [PubMed]

Bilotti, F.

F. Bilotti, A. Toscano, and L. Vegni, "Design of spiral and multiple split-ring resonators for the realization of miniaturized metamaterial samples," IEEE Trans. Antenn. Propag. 55, 2258-2267 (2007).
[CrossRef]

Bulu, I.

K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Investigation of magnetic resonances for different split-ring resonator parameters and designs," N. J. Phys. 7, 168 (2005).
[CrossRef]

Cai, W.

V. Shalaev, W. Cai, U. Chettiar, H. Yuan, A. Sarychev, V. Drachev, and A. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

Caloz, C.

C. Caloz, A. Lai, and T. Itoh, "The challenge of homogenization in metamaterials," N. J. Phys. 7, 167 (2005).
[CrossRef]

C. Caloz, and T. Itoh, "Transmission line approach of left-handed (LH) materials and microstrip implementation of an artificial LH transmission line," IEEE Trans. Antenn. Propag. 52, 1159-1166 (2004).
[CrossRef]

A. Sanada, C. Caloz, and T. Itoh, "Characteristics of the composite right/left-handed transmission lines," IEEE Microwave Wireless Compon. Lett. 14, 68-70 (2004).
[CrossRef]

Chen, H.

H. Chen, L. Ran, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, "Crankled S-ring resonator with small electrical size," Progress in Electromagnetics Research 66, 179-190 (2006).
[CrossRef]

Chen, X.

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

Chettiar, U.

V. Shalaev, W. Cai, U. Chettiar, H. Yuan, A. Sarychev, V. Drachev, and A. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

Chu, L. J.

L. J. Chu, "Physical limitations of omni-directional antennas," J. Appl. Phys. 19, 1163-1175 (1948).
[CrossRef]

Cummer, S. A.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

Dai, J.

J. Dai, J. Zhang, W. Zhang, and D. Grischkowsky, "Terahertz time-domain spectroscopy characterization of the far-infrared absorption and index of refraction of high-resistivity, float-zone silicon," J. Opt. Soc. Am. B 21, 1379-1386 (2004).
[CrossRef]

Drachev, V.

V. Shalaev, W. Cai, U. Chettiar, H. Yuan, A. Sarychev, V. Drachev, and A. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

Economou, E. N.

T. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials," Phys. Rev. B Condens. Matter 71, 245105 (2005).
[CrossRef]

Fang, N.

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

Grischkowsky, D.

J. Dai, J. Zhang, W. Zhang, and D. Grischkowsky, "Terahertz time-domain spectroscopy characterization of the far-infrared absorption and index of refraction of high-resistivity, float-zone silicon," J. Opt. Soc. Am. B 21, 1379-1386 (2004).
[CrossRef]

Grzegorczyk, T. M.

H. Chen, L. Ran, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, "Crankled S-ring resonator with small electrical size," Progress in Electromagnetics Research 66, 179-190 (2006).
[CrossRef]

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

Guven, K.

K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Investigation of magnetic resonances for different split-ring resonator parameters and designs," N. J. Phys. 7, 168 (2005).
[CrossRef]

Henke, H.

E. Lenz, and H. Henke, "Homogenization of metamaterials due to fractaloid structures in the microwave regime," J. Opt. A, Pure Appl. Opt. 11, 114021 (2009).
[CrossRef]

Highstrete, C.

W. J. Padilla, M. T. Aronsson, C. Highstrete, M. Lee, A. J. Taylor, and R. D. Averitt, "Electrically resonant terahertz metamaterials: Theoretical and experimental investigations," Phys. Rev. B Condens. Matter 75, 041102 (2007).
[CrossRef]

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. Microw. Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Houzet, G.

G. Houzet, X. Melique, and D. Lippens, "Microstrip transmission line loaded by split-ring resonators tuned by ferroelectric thin film," Progress in Electromagnetics Research 12, 225-236 (2010).
[CrossRef]

Itoh, T.

C. Caloz, A. Lai, and T. Itoh, "The challenge of homogenization in metamaterials," N. J. Phys. 7, 167 (2005).
[CrossRef]

C. Caloz, and T. Itoh, "Transmission line approach of left-handed (LH) materials and microstrip implementation of an artificial LH transmission line," IEEE Trans. Antenn. Propag. 52, 1159-1166 (2004).
[CrossRef]

A. Sanada, C. Caloz, and T. Itoh, "Characteristics of the composite right/left-handed transmission lines," IEEE Microwave Wireless Compon. Lett. 14, 68-70 (2004).
[CrossRef]

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

Kafesaki, M.

K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Investigation of magnetic resonances for different split-ring resonator parameters and designs," N. J. Phys. 7, 168 (2005).
[CrossRef]

Kildishev, A.

V. Shalaev, W. Cai, U. Chettiar, H. Yuan, A. Sarychev, V. Drachev, and A. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

Kivshar, Y.

N. A. Zharova, I. V. Shadrivov, A. A. Zharov, and Y. Kivshar, "Ideal and nonideal invisibility cloaks," Opt. Express 16, 21369-21374 (2008).
[CrossRef] [PubMed]

Kong, J. A.

H. Chen, L. Ran, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, "Crankled S-ring resonator with small electrical size," Progress in Electromagnetics Research 66, 179-190 (2006).
[CrossRef]

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

Koschny, T.

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Phys. Rev. E 71, 036617 (2005).
[CrossRef]

T. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials," Phys. Rev. B Condens. Matter 71, 245105 (2005).
[CrossRef]

Lai, A.

C. Caloz, A. Lai, and T. Itoh, "The challenge of homogenization in metamaterials," N. J. Phys. 7, 167 (2005).
[CrossRef]

Lapine, M. M.

M. M. Lapine, and S. Tretyakov, "Contemporary notes on metamaterials," IET Microwaves Antennas Propag. 1, 3-11 (2007).
[CrossRef]

Lee, H.

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

Lee, M.

W. J. Padilla, M. T. Aronsson, C. Highstrete, M. Lee, A. J. Taylor, and R. D. Averitt, "Electrically resonant terahertz metamaterials: Theoretical and experimental investigations," Phys. Rev. B Condens. Matter 75, 041102 (2007).
[CrossRef]

Lenz, E.

E. Lenz, and H. Henke, "Homogenization of metamaterials due to fractaloid structures in the microwave regime," J. Opt. A, Pure Appl. Opt. 11, 114021 (2009).
[CrossRef]

Lippens, D.

G. Houzet, X. Melique, and D. Lippens, "Microstrip transmission line loaded by split-ring resonators tuned by ferroelectric thin film," Progress in Electromagnetics Research 12, 225-236 (2010).
[CrossRef]

Long, L. L.

M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, J. R. W. Alexander, and C. A. Ward, "Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared," Appl. Opt. 22, 1099-1119 (1983).
[CrossRef] [PubMed]

Markos, P.

T. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials," Phys. Rev. B Condens. Matter 71, 245105 (2005).
[CrossRef]

Marqués, R.

J. D. Baena, R. Marqués, and F. Medina, "Artificial magnetic metamaterial design by using spiral resonators," Phys. Rev. B Condens. Matter 69, 014402 (2004).
[CrossRef]

Medina, F.

J. D. Baena, R. Marqués, and F. Medina, "Artificial magnetic metamaterial design by using spiral resonators," Phys. Rev. B Condens. Matter 69, 014402 (2004).
[CrossRef]

Melique, X.

G. Houzet, X. Melique, and D. Lippens, "Microstrip transmission line loaded by split-ring resonators tuned by ferroelectric thin film," Progress in Electromagnetics Research 12, 225-236 (2010).
[CrossRef]

Mock, J. J.

D. Schurig, J. J. Mock, and D. R. Smith, "Electric-field-coupled resonators for negative permittivity metamaterials," Appl. Phys. Lett. 88, 041109 (2006).
[CrossRef]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

Ordal, M. A.

M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, J. R. W. Alexander, and C. A. Ward, "Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared," Appl. Opt. 22, 1099-1119 (1983).
[CrossRef] [PubMed]

Ozbay, E.

K. Aydin, and E. Ozbay, "Capacitor-loaded split ring resonators as tunable metamaterial components," J. Appl. Phys. 101, 024911 (2007).
[CrossRef]

K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Investigation of magnetic resonances for different split-ring resonator parameters and designs," N. J. Phys. 7, 168 (2005).
[CrossRef]

Pacheco, J. J.

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

Padilla, W. J.

W. J. Padilla, M. T. Aronsson, C. Highstrete, M. Lee, A. J. Taylor, and R. D. Averitt, "Electrically resonant terahertz metamaterials: Theoretical and experimental investigations," Phys. Rev. B Condens. Matter 75, 041102 (2007).
[CrossRef]

Pendry, J. B.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, "Limitations on subdiffraction imaging with a negative refractive index slab," Appl. Phys. Lett. 82, 1506-1508 (2003).
[CrossRef]

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

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

Ramakrishna, S. A.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, "Limitations on subdiffraction imaging with a negative refractive index slab," Appl. Phys. Lett. 82, 1506-1508 (2003).
[CrossRef]

Ran, L.

H. Chen, L. Ran, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, "Crankled S-ring resonator with small electrical size," Progress in Electromagnetics Research 66, 179-190 (2006).
[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. Microw. Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Rosenbluth, M.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, "Limitations on subdiffraction imaging with a negative refractive index slab," Appl. Phys. Lett. 82, 1506-1508 (2003).
[CrossRef]

Sanada, A.

A. Sanada, C. Caloz, and T. Itoh, "Characteristics of the composite right/left-handed transmission lines," IEEE Microwave Wireless Compon. Lett. 14, 68-70 (2004).
[CrossRef]

Sarychev, A.

V. Shalaev, W. Cai, U. Chettiar, H. Yuan, A. Sarychev, V. Drachev, and A. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

Schultz, S.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, "Limitations on subdiffraction imaging with a negative refractive index slab," Appl. Phys. Lett. 82, 1506-1508 (2003).
[CrossRef]

Schurig, D.

D. Schurig, J. J. Mock, and D. R. Smith, "Electric-field-coupled resonators for negative permittivity metamaterials," Appl. Phys. Lett. 88, 041109 (2006).
[CrossRef]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, "Limitations on subdiffraction imaging with a negative refractive index slab," Appl. Phys. Lett. 82, 1506-1508 (2003).
[CrossRef]

Shadrivov, I. V.

N. A. Zharova, I. V. Shadrivov, A. A. Zharov, and Y. Kivshar, "Ideal and nonideal invisibility cloaks," Opt. Express 16, 21369-21374 (2008).
[CrossRef] [PubMed]

Shalaev, V.

V. Shalaev, W. Cai, U. Chettiar, H. Yuan, A. Sarychev, V. Drachev, and A. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

Smith, D. R.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, and D. R. Smith, "Electric-field-coupled resonators for negative permittivity metamaterials," Appl. Phys. Lett. 88, 041109 (2006).
[CrossRef]

T. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials," Phys. Rev. B Condens. Matter 71, 245105 (2005).
[CrossRef]

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Phys. Rev. E 71, 036617 (2005).
[CrossRef]

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, "Limitations on subdiffraction imaging with a negative refractive index slab," Appl. Phys. Lett. 82, 1506-1508 (2003).
[CrossRef]

Soukoulis, C. M.

T. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials," Phys. Rev. B Condens. Matter 71, 245105 (2005).
[CrossRef]

K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Investigation of magnetic resonances for different split-ring resonator parameters and designs," N. J. Phys. 7, 168 (2005).
[CrossRef]

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Phys. Rev. E 71, 036617 (2005).
[CrossRef]

Starr, A. F.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

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. Microw. Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Sun, C.

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

Taylor, A. J.

W. J. Padilla, M. T. Aronsson, C. Highstrete, M. Lee, A. J. Taylor, and R. D. Averitt, "Electrically resonant terahertz metamaterials: Theoretical and experimental investigations," Phys. Rev. B Condens. Matter 75, 041102 (2007).
[CrossRef]

Toscano, A.

F. Bilotti, A. Toscano, and L. Vegni, "Design of spiral and multiple split-ring resonators for the realization of miniaturized metamaterial samples," IEEE Trans. Antenn. Propag. 55, 2258-2267 (2007).
[CrossRef]

Tretyakov, S.

M. M. Lapine, and S. Tretyakov, "Contemporary notes on metamaterials," IET Microwaves Antennas Propag. 1, 3-11 (2007).
[CrossRef]

Vegni, L.

F. Bilotti, A. Toscano, and L. Vegni, "Design of spiral and multiple split-ring resonators for the realization of miniaturized metamaterial samples," IEEE Trans. Antenn. Propag. 55, 2258-2267 (2007).
[CrossRef]

Vier, D. C.

T. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials," Phys. Rev. B Condens. Matter 71, 245105 (2005).
[CrossRef]

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Phys. Rev. E 71, 036617 (2005).
[CrossRef]

Ward, C. A.

M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, J. R. W. Alexander, and C. A. Ward, "Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared," Appl. Opt. 22, 1099-1119 (1983).
[CrossRef] [PubMed]

Withayachumnankul, W.

W. Withayachumnankul, and D. Abbott, "Metamaterials in the terahertz regime," IEEE Photonics J. 1, 99-118 (2009).
[CrossRef]

Wu, B.-I.

H. Chen, L. Ran, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, "Crankled S-ring resonator with small electrical size," Progress in Electromagnetics Research 66, 179-190 (2006).
[CrossRef]

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

Yuan, H.

V. Shalaev, W. Cai, U. Chettiar, H. Yuan, A. Sarychev, V. Drachev, and A. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

Zhang, J.

J. Dai, J. Zhang, W. Zhang, and D. Grischkowsky, "Terahertz time-domain spectroscopy characterization of the far-infrared absorption and index of refraction of high-resistivity, float-zone silicon," J. Opt. Soc. Am. B 21, 1379-1386 (2004).
[CrossRef]

Zhang, W.

J. Dai, J. Zhang, W. Zhang, and D. Grischkowsky, "Terahertz time-domain spectroscopy characterization of the far-infrared absorption and index of refraction of high-resistivity, float-zone silicon," J. Opt. Soc. Am. B 21, 1379-1386 (2004).
[CrossRef]

Zhang, X.

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

Zharov, A. A.

N. A. Zharova, I. V. Shadrivov, A. A. Zharov, and Y. Kivshar, "Ideal and nonideal invisibility cloaks," Opt. Express 16, 21369-21374 (2008).
[CrossRef] [PubMed]

Zharova, N. A.

N. A. Zharova, I. V. Shadrivov, A. A. Zharov, and Y. Kivshar, "Ideal and nonideal invisibility cloaks," Opt. Express 16, 21369-21374 (2008).
[CrossRef] [PubMed]

Appl. Opt. (1)

M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, J. R. W. Alexander, and C. A. Ward, "Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared," Appl. Opt. 22, 1099-1119 (1983).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, "Limitations on subdiffraction imaging with a negative refractive index slab," Appl. Phys. Lett. 82, 1506-1508 (2003).
[CrossRef]

D. Schurig, J. J. Mock, and D. R. Smith, "Electric-field-coupled resonators for negative permittivity metamaterials," Appl. Phys. Lett. 88, 041109 (2006).
[CrossRef]

IEEE Microwave Wireless Compon. Lett. (1)

A. Sanada, C. Caloz, and T. Itoh, "Characteristics of the composite right/left-handed transmission lines," IEEE Microwave Wireless Compon. Lett. 14, 68-70 (2004).
[CrossRef]

IEEE Photonics J. (1)

W. Withayachumnankul, and D. Abbott, "Metamaterials in the terahertz regime," IEEE Photonics J. 1, 99-118 (2009).
[CrossRef]

IEEE Trans. Antenn. Propag. (2)

C. Caloz, and T. Itoh, "Transmission line approach of left-handed (LH) materials and microstrip implementation of an artificial LH transmission line," IEEE Trans. Antenn. Propag. 52, 1159-1166 (2004).
[CrossRef]

F. Bilotti, A. Toscano, and L. Vegni, "Design of spiral and multiple split-ring resonators for the realization of miniaturized metamaterial samples," IEEE Trans. Antenn. Propag. 55, 2258-2267 (2007).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (2)

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

G. D. Alley, "Interdigital capacitors and their application to lumped-element microwave integrated circuits," IEEE Trans. Microw. Theory Tech. MTT-18, 1028-1033 (1970).
[CrossRef]

IET Microwaves Antennas Propag. (1)

M. M. Lapine, and S. Tretyakov, "Contemporary notes on metamaterials," IET Microwaves Antennas Propag. 1, 3-11 (2007).
[CrossRef]

J. Appl. Phys. (2)

K. Aydin, and E. Ozbay, "Capacitor-loaded split ring resonators as tunable metamaterial components," J. Appl. Phys. 101, 024911 (2007).
[CrossRef]

L. J. Chu, "Physical limitations of omni-directional antennas," J. Appl. Phys. 19, 1163-1175 (1948).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

E. Lenz, and H. Henke, "Homogenization of metamaterials due to fractaloid structures in the microwave regime," J. Opt. A, Pure Appl. Opt. 11, 114021 (2009).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Dai, J. Zhang, W. Zhang, and D. Grischkowsky, "Terahertz time-domain spectroscopy characterization of the far-infrared absorption and index of refraction of high-resistivity, float-zone silicon," J. Opt. Soc. Am. B 21, 1379-1386 (2004).
[CrossRef]

N. J. Phys. (2)

C. Caloz, A. Lai, and T. Itoh, "The challenge of homogenization in metamaterials," N. J. Phys. 7, 167 (2005).
[CrossRef]

K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Investigation of magnetic resonances for different split-ring resonator parameters and designs," N. J. Phys. 7, 168 (2005).
[CrossRef]

Opt. Express (1)

N. A. Zharova, I. V. Shadrivov, A. A. Zharov, and Y. Kivshar, "Ideal and nonideal invisibility cloaks," Opt. Express 16, 21369-21374 (2008).
[CrossRef] [PubMed]

Opt. Lett. (1)

V. Shalaev, W. Cai, U. Chettiar, H. Yuan, A. Sarychev, V. Drachev, and A. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

Phys. Rev. B Condens. Matter (3)

T. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials," Phys. Rev. B Condens. Matter 71, 245105 (2005).
[CrossRef]

J. D. Baena, R. Marqués, and F. Medina, "Artificial magnetic metamaterial design by using spiral resonators," Phys. Rev. B Condens. Matter 69, 014402 (2004).
[CrossRef]

W. J. Padilla, M. T. Aronsson, C. Highstrete, M. Lee, A. J. Taylor, and R. D. Averitt, "Electrically resonant terahertz metamaterials: Theoretical and experimental investigations," Phys. Rev. B Condens. Matter 75, 041102 (2007).
[CrossRef]

Phys. Rev. E (2)

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

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Phys. Rev. E 71, 036617 (2005).
[CrossRef]

Phys. Rev. Lett. (1)

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

Progress in Electromagnetics Research (2)

H. Chen, L. Ran, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, "Crankled S-ring resonator with small electrical size," Progress in Electromagnetics Research 66, 179-190 (2006).
[CrossRef]

G. Houzet, X. Melique, and D. Lippens, "Microstrip transmission line loaded by split-ring resonators tuned by ferroelectric thin film," Progress in Electromagnetics Research 12, 225-236 (2010).
[CrossRef]

Science (2)

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

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

Other (7)

D. Rialet, A. Sharaiha, A.-C. Tarot, and C. Delaveaud, "Characterization of antennas on dielectric and magnetic substrates effective medium approximation," in "Third European Conference on Antennas and Propagation (EuCAP)," (2009), pp. 3163-3166.

K. C. Gupta, R. Garg, I. Bahl, and P. Bhartia, Microstrip Lines and Slotlines (Artech House, 1996), 2nd ed.

I. J. Bahl, Lumped Element for RF and Microwave Circuits (Artech House, 2003).

J. Zhang, and Z. R. Hu, "A novel broadband metamaterial resonator with negative permittivity," in "PIERS Proceedings, Xi’an, China," (2010), pp. 1346-1348.

H. A. Wheeler, "Fundamental limits of small antennas," Proc. IRE. 35, 1479-1484 (1947).
[CrossRef]

K. Takano, T. Kawabata, C.-F. Hsieh, K. Akiyama, F. Miyamaru, Y. Abe, Y. Tokuda, R.-P. Pan, C.-L. Pan, and M. Hangyo, "Fabrication of terahertz planar metamaterials using a super-fine ink-jet printer," Appl. Phys. Express, art. no. 016701 (2010).
[CrossRef]

R. F. Harrington, "Effect of antenna size on gain, bandwidth, and efficiency," J. Research National Bureau of Standards—D. Radio Propagation 64D (1960).
[PubMed]

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Figures (6)

Fig. 1
Fig. 1

Electric-LC resonator. (a) A typical ELC resonator is composed of a center capacitive gap connected to two inductive loops. (b) An equivalent circuit of the resonator constitutes an LC resonator (the resistance is neglected here) [18].

Fig. 2
Fig. 2

Interdigital capacitor (IDC) with 6 fingers. The finger length lIDC extends over the overlapping portion of all fingers.

Fig. 3
Fig. 3

Two variants of IDC-loaded ELC resonators. The IDC’s gaps align (a,c) in perpendicular to and (b,d) in parallel with the direction of an incident electric field.

Fig. 4
Fig. 4

ELC resonator arrays forming planar metamaterials used in the experiment. Each sample is fabricated from copper on an FR4 substrate. The photos show 3 by 3 arrays of resonators for convenience, however the actual array size used in the experiment was 9 by 9.

Fig. 5
Fig. 5

Transmission profiles of the resonators from (top) the experiment and (bottom) the simulation. The two graphs share the horizontal scale.

Fig. 6
Fig. 6

The simulated effective medium properties of the samples; (top) the effective permittivity, and (bottom) the effective permeability. The two graphs share the horizontal scale.

Tables (1)

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Table 1 The structural parameters and resonance frequency of the samples under test.

Equations (5)

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C IDC = ɛ re 10 3 18 π K ( k ) K ( k ) ( N 1 ) l IDC ( pF ) ,
K ( k ) K ( k ) = { 1 π ln [ 2 1 + k 1 k ] for 0.707 k 1 π ln [ 2 1 + k 1 k ] for 0 k < 0.707 ,
C 0 = ɛ re 10 3 18 π K ( k ) K ( k ) l 0 ( pF ) ,
C IDC = ( N 1 ) l IDC l 0 C 0 .
f 0 , new = l 0 l IDC ( N 1 ) f 0 ,

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