Abstract

We apply an analytic theory [New J. Phys. 12, 093010 (2010)] toward the design of varactor-loaded split-ring resonator metacrystals, having nonlinear electromagnetic properties on demand. The design methodology here is shown to be efficient and is validated by the excellent agreement between the analytically predicted and experimentally measured harmonic generation. The analytic formulas enable a path toward optimization of nonlinear properties, which we demonstrate by varying the spacing of the metamaterial elements to maximize the second-order nonlinear susceptibility of the system.

© 2011 Optical Society of America

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  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]
  2. N. M. Litchinitser, I. R. Gabitov, and A. I. Maimistov, “Optical bistability in a nonlinear optical coupler with a negative index channel,” Phys. Rev. Lett. 99, 113902 (2007).
    [CrossRef] [PubMed]
  3. S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306, 1351–1353 (2004).
    [CrossRef] [PubMed]
  4. D. A. Powell, I. V. Shadrivov, Y. S. Kivshar, and M. V. Gorkunov, “Self-tuning mechanisms of nonlinear split-ring resonators,” Appl. Phys. Lett. 91, 144107 (2007).
    [CrossRef]
  5. B. Wang, J. Zhou, T. Koschny, and C. M. Soukoulis, “Nonlinear properties of split-ring resonators” Opt. Express 16, 16058–16063 (2008).
    [CrossRef] [PubMed]
  6. D. Huang, E. Poutrina, and D. R. Smith, “Analysis of the power dependent tuning of a varactor-loaded metamaterial at microwave frequencies,” Appl. Phys. Lett. 96, 104104 (2010).
    [CrossRef]
  7. T. H. Hand and S. A. Cummer, “Frequency tunable electromagnetic metamaterial using ferroelectric loaded split rings,” J. Appl. Phys. 103, 066105 (2008).
    [CrossRef]
  8. N. M. Litchinitser, I. R. Gabitov, A. I. Maimistov, and V. M. Shalaev, “Effect of an optical negative index thin film on optical bistability,” Opt. Lett. 32, 151–153 (2007).
    [CrossRef]
  9. I. Gabitov, R. Indik, L. Mollenauer, M. Shkarayev, M. Stepanov, and P. M. Lushnikov, “Twin families of bisolitons in dispersion-managed systems,” Opt. Lett. 32, 605–607 (2007).
    [CrossRef] [PubMed]
  10. A. Peleg, M. Chertkov, and I. Gabitov, “Inelastic interchannel collisions of pulses in optical fibers in the presence of third-order dispersion,” J. Opt. Soc. Am. B 21, 18–23 (2004).
    [CrossRef]
  11. Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99, 153901 (2007).
    [CrossRef] [PubMed]
  12. A. R. Katko, S. Gu, J. P. Barrett, B.-I. Popa, G. Shvets, and S. A. Cummer, “Phase conjugation and negative refraction using nonlinear active metamaterials,” Phys. Rev. Lett. 105, 123905(2010).
    [CrossRef] [PubMed]
  13. D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71, 36617 (2005).
    [CrossRef]
  14. M. Lapine, M. Gorkunov, and K. H. Ringhofer, “Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements,” Phys. Rev. E 67, 065601 (2003).
    [CrossRef]
  15. E. Poutrina, D. Huang, and D. R. Smith, “Analysis of nonlinear electromagnetic metamaterials,” New J. Phys. 12, 093010(2010).
    [CrossRef]
  16. S. Larouche and D. R. Smith, “A retrieval method for nonlinear metamaterials,” Opt. Commun. 283, 1621–1627 (2010).
    [CrossRef]
  17. A. Rose, S. Larouche, D. Huang, E. Poutrina, and D. R. Smith, “Nonlinear parameter retrieval from three- and four-wave mixing in metamaterials,” Phys. Rev. E 82 (2010).
    [CrossRef]
  18. J. Pendry, A. Holden, D. Robbins, and W. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
    [CrossRef]
  19. D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88, 041109 (2006).
    [CrossRef]
  20. A. Zharov, I. Shadrivov, and Y. Kivshar, “Nonlinear properties of left-handed metamaterials,” Phys. Rev. Lett. 91 (2003).
    [CrossRef] [PubMed]
  21. A. I. Maimistov and I. R. Gabitov, “Nonlinear response of a thin metamaterial film containing Josephson junctions,” Opt. Commun. 283, 1633–1639 (2010).
    [CrossRef]
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  23. K. Aydin and E. Ozbay, “Capacitor-loaded split ring resonators as tunable metamaterial components,” J. Appl. Phys. 101, 024911 (2007).
    [CrossRef]
  24. D. R. Smith, “Analytic expressions for the constitutive parameters of magnetoelectric metamaterials,” Phys. Rev. E 81, 036605 (2010).
    [CrossRef]
  25. C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).
  26. A. Rose and D. R. Smith, “Broadly tunable quasi-phase-matching in nonlinear metamaterials,” Phys. Rev. A 84, 013823(2011).
    [CrossRef]
  27. E. Poutrina, D. Huang, Y. Urzhumov, and D. R. Smith, “Nonlinear oscillator metamaterial model: numerical and experimental verification,” Opt. Express 19, 8312–8319 (2011).
    [CrossRef] [PubMed]

2011 (2)

2010 (7)

D. R. Smith, “Analytic expressions for the constitutive parameters of magnetoelectric metamaterials,” Phys. Rev. E 81, 036605 (2010).
[CrossRef]

D. Huang, E. Poutrina, and D. R. Smith, “Analysis of the power dependent tuning of a varactor-loaded metamaterial at microwave frequencies,” Appl. Phys. Lett. 96, 104104 (2010).
[CrossRef]

A. R. Katko, S. Gu, J. P. Barrett, B.-I. Popa, G. Shvets, and S. A. Cummer, “Phase conjugation and negative refraction using nonlinear active metamaterials,” Phys. Rev. Lett. 105, 123905(2010).
[CrossRef] [PubMed]

E. Poutrina, D. Huang, and D. R. Smith, “Analysis of nonlinear electromagnetic metamaterials,” New J. Phys. 12, 093010(2010).
[CrossRef]

S. Larouche and D. R. Smith, “A retrieval method for nonlinear metamaterials,” Opt. Commun. 283, 1621–1627 (2010).
[CrossRef]

A. Rose, S. Larouche, D. Huang, E. Poutrina, and D. R. Smith, “Nonlinear parameter retrieval from three- and four-wave mixing in metamaterials,” Phys. Rev. E 82 (2010).
[CrossRef]

A. I. Maimistov and I. R. Gabitov, “Nonlinear response of a thin metamaterial film containing Josephson junctions,” Opt. Commun. 283, 1633–1639 (2010).
[CrossRef]

2008 (2)

T. H. Hand and S. A. Cummer, “Frequency tunable electromagnetic metamaterial using ferroelectric loaded split rings,” J. Appl. Phys. 103, 066105 (2008).
[CrossRef]

B. Wang, J. Zhou, T. Koschny, and C. M. Soukoulis, “Nonlinear properties of split-ring resonators” Opt. Express 16, 16058–16063 (2008).
[CrossRef] [PubMed]

2007 (6)

N. M. Litchinitser, I. R. Gabitov, A. I. Maimistov, and V. M. Shalaev, “Effect of an optical negative index thin film on optical bistability,” Opt. Lett. 32, 151–153 (2007).
[CrossRef]

I. Gabitov, R. Indik, L. Mollenauer, M. Shkarayev, M. Stepanov, and P. M. Lushnikov, “Twin families of bisolitons in dispersion-managed systems,” Opt. Lett. 32, 605–607 (2007).
[CrossRef] [PubMed]

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99, 153901 (2007).
[CrossRef] [PubMed]

N. M. Litchinitser, I. R. Gabitov, and A. I. Maimistov, “Optical bistability in a nonlinear optical coupler with a negative index channel,” Phys. Rev. Lett. 99, 113902 (2007).
[CrossRef] [PubMed]

D. A. Powell, I. V. Shadrivov, Y. S. Kivshar, and M. V. Gorkunov, “Self-tuning mechanisms of nonlinear split-ring resonators,” Appl. Phys. Lett. 91, 144107 (2007).
[CrossRef]

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

2006 (1)

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 (1)

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71, 36617 (2005).
[CrossRef]

2004 (2)

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306, 1351–1353 (2004).
[CrossRef] [PubMed]

A. Peleg, M. Chertkov, and I. Gabitov, “Inelastic interchannel collisions of pulses in optical fibers in the presence of third-order dispersion,” J. Opt. Soc. Am. B 21, 18–23 (2004).
[CrossRef]

2003 (2)

M. Lapine, M. Gorkunov, and K. H. Ringhofer, “Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements,” Phys. Rev. E 67, 065601 (2003).
[CrossRef]

A. Zharov, I. Shadrivov, and Y. Kivshar, “Nonlinear properties of left-handed metamaterials,” Phys. Rev. Lett. 91 (2003).
[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. Pendry, A. Holden, D. Robbins, and W. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
[CrossRef]

Aydin, K.

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

Balanis, C. A.

C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).

Barrett, J. P.

A. R. Katko, S. Gu, J. P. Barrett, B.-I. Popa, G. Shvets, and S. A. Cummer, “Phase conjugation and negative refraction using nonlinear active metamaterials,” Phys. Rev. Lett. 105, 123905(2010).
[CrossRef] [PubMed]

Bartal, G.

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99, 153901 (2007).
[CrossRef] [PubMed]

Chertkov, M.

Cummer, S. A.

A. R. Katko, S. Gu, J. P. Barrett, B.-I. Popa, G. Shvets, and S. A. Cummer, “Phase conjugation and negative refraction using nonlinear active metamaterials,” Phys. Rev. Lett. 105, 123905(2010).
[CrossRef] [PubMed]

T. H. Hand and S. A. Cummer, “Frequency tunable electromagnetic metamaterial using ferroelectric loaded split rings,” J. Appl. Phys. 103, 066105 (2008).
[CrossRef]

Enkrich, C.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306, 1351–1353 (2004).
[CrossRef] [PubMed]

Gabitov, I.

Gabitov, I. R.

A. I. Maimistov and I. R. Gabitov, “Nonlinear response of a thin metamaterial film containing Josephson junctions,” Opt. Commun. 283, 1633–1639 (2010).
[CrossRef]

N. M. Litchinitser, I. R. Gabitov, and A. I. Maimistov, “Optical bistability in a nonlinear optical coupler with a negative index channel,” Phys. Rev. Lett. 99, 113902 (2007).
[CrossRef] [PubMed]

N. M. Litchinitser, I. R. Gabitov, A. I. Maimistov, and V. M. Shalaev, “Effect of an optical negative index thin film on optical bistability,” Opt. Lett. 32, 151–153 (2007).
[CrossRef]

Genov, D. A.

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99, 153901 (2007).
[CrossRef] [PubMed]

Gorkunov, M.

M. Lapine, M. Gorkunov, and K. H. Ringhofer, “Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements,” Phys. Rev. E 67, 065601 (2003).
[CrossRef]

Gorkunov, M. V.

D. A. Powell, I. V. Shadrivov, Y. S. Kivshar, and M. V. Gorkunov, “Self-tuning mechanisms of nonlinear split-ring resonators,” Appl. Phys. Lett. 91, 144107 (2007).
[CrossRef]

Gu, S.

A. R. Katko, S. Gu, J. P. Barrett, B.-I. Popa, G. Shvets, and S. A. Cummer, “Phase conjugation and negative refraction using nonlinear active metamaterials,” Phys. Rev. Lett. 105, 123905(2010).
[CrossRef] [PubMed]

Hand, T. H.

T. H. Hand and S. A. Cummer, “Frequency tunable electromagnetic metamaterial using ferroelectric loaded split rings,” J. Appl. Phys. 103, 066105 (2008).
[CrossRef]

Holden, A.

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

Huang, D.

E. Poutrina, D. Huang, Y. Urzhumov, and D. R. Smith, “Nonlinear oscillator metamaterial model: numerical and experimental verification,” Opt. Express 19, 8312–8319 (2011).
[CrossRef] [PubMed]

D. Huang, E. Poutrina, and D. R. Smith, “Analysis of the power dependent tuning of a varactor-loaded metamaterial at microwave frequencies,” Appl. Phys. Lett. 96, 104104 (2010).
[CrossRef]

E. Poutrina, D. Huang, and D. R. Smith, “Analysis of nonlinear electromagnetic metamaterials,” New J. Phys. 12, 093010(2010).
[CrossRef]

A. Rose, S. Larouche, D. Huang, E. Poutrina, and D. R. Smith, “Nonlinear parameter retrieval from three- and four-wave mixing in metamaterials,” Phys. Rev. E 82 (2010).
[CrossRef]

Indik, R.

Katko, A. R.

A. R. Katko, S. Gu, J. P. Barrett, B.-I. Popa, G. Shvets, and S. A. Cummer, “Phase conjugation and negative refraction using nonlinear active metamaterials,” Phys. Rev. Lett. 105, 123905(2010).
[CrossRef] [PubMed]

Kivshar, Y.

A. Zharov, I. Shadrivov, and Y. Kivshar, “Nonlinear properties of left-handed metamaterials,” Phys. Rev. Lett. 91 (2003).
[CrossRef] [PubMed]

Kivshar, Y. S.

D. A. Powell, I. V. Shadrivov, Y. S. Kivshar, and M. V. Gorkunov, “Self-tuning mechanisms of nonlinear split-ring resonators,” Appl. Phys. Lett. 91, 144107 (2007).
[CrossRef]

Koschny, T.

B. Wang, J. Zhou, T. Koschny, and C. M. Soukoulis, “Nonlinear properties of split-ring resonators” Opt. Express 16, 16058–16063 (2008).
[CrossRef] [PubMed]

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71, 36617 (2005).
[CrossRef]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306, 1351–1353 (2004).
[CrossRef] [PubMed]

Lapine, M.

M. Lapine, M. Gorkunov, and K. H. Ringhofer, “Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements,” Phys. Rev. E 67, 065601 (2003).
[CrossRef]

Larouche, S.

A. Rose, S. Larouche, D. Huang, E. Poutrina, and D. R. Smith, “Nonlinear parameter retrieval from three- and four-wave mixing in metamaterials,” Phys. Rev. E 82 (2010).
[CrossRef]

S. Larouche and D. R. Smith, “A retrieval method for nonlinear metamaterials,” Opt. Commun. 283, 1621–1627 (2010).
[CrossRef]

Linden, S.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306, 1351–1353 (2004).
[CrossRef] [PubMed]

Litchinitser, N. M.

N. M. Litchinitser, I. R. Gabitov, and A. I. Maimistov, “Optical bistability in a nonlinear optical coupler with a negative index channel,” Phys. Rev. Lett. 99, 113902 (2007).
[CrossRef] [PubMed]

N. M. Litchinitser, I. R. Gabitov, A. I. Maimistov, and V. M. Shalaev, “Effect of an optical negative index thin film on optical bistability,” Opt. Lett. 32, 151–153 (2007).
[CrossRef]

Liu, Y.

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99, 153901 (2007).
[CrossRef] [PubMed]

Lushnikov, P. M.

Maimistov, A. I.

A. I. Maimistov and I. R. Gabitov, “Nonlinear response of a thin metamaterial film containing Josephson junctions,” Opt. Commun. 283, 1633–1639 (2010).
[CrossRef]

N. M. Litchinitser, I. R. Gabitov, and A. I. Maimistov, “Optical bistability in a nonlinear optical coupler with a negative index channel,” Phys. Rev. Lett. 99, 113902 (2007).
[CrossRef] [PubMed]

N. M. Litchinitser, I. R. Gabitov, A. I. Maimistov, and V. M. Shalaev, “Effect of an optical negative index thin film on optical bistability,” Opt. Lett. 32, 151–153 (2007).
[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]

Mollenauer, L.

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.

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

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]

Peleg, A.

Pendry, J.

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

Popa, B.-I.

A. R. Katko, S. Gu, J. P. Barrett, B.-I. Popa, G. Shvets, and S. A. Cummer, “Phase conjugation and negative refraction using nonlinear active metamaterials,” Phys. Rev. Lett. 105, 123905(2010).
[CrossRef] [PubMed]

Poutrina, E.

E. Poutrina, D. Huang, Y. Urzhumov, and D. R. Smith, “Nonlinear oscillator metamaterial model: numerical and experimental verification,” Opt. Express 19, 8312–8319 (2011).
[CrossRef] [PubMed]

D. Huang, E. Poutrina, and D. R. Smith, “Analysis of the power dependent tuning of a varactor-loaded metamaterial at microwave frequencies,” Appl. Phys. Lett. 96, 104104 (2010).
[CrossRef]

E. Poutrina, D. Huang, and D. R. Smith, “Analysis of nonlinear electromagnetic metamaterials,” New J. Phys. 12, 093010(2010).
[CrossRef]

A. Rose, S. Larouche, D. Huang, E. Poutrina, and D. R. Smith, “Nonlinear parameter retrieval from three- and four-wave mixing in metamaterials,” Phys. Rev. E 82 (2010).
[CrossRef]

Powell, D. A.

D. A. Powell, I. V. Shadrivov, Y. S. Kivshar, and M. V. Gorkunov, “Self-tuning mechanisms of nonlinear split-ring resonators,” Appl. Phys. Lett. 91, 144107 (2007).
[CrossRef]

Ringhofer, K. H.

M. Lapine, M. Gorkunov, and K. H. Ringhofer, “Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements,” Phys. Rev. E 67, 065601 (2003).
[CrossRef]

Robbins, D.

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

Rose, A.

A. Rose and D. R. Smith, “Broadly tunable quasi-phase-matching in nonlinear metamaterials,” Phys. Rev. A 84, 013823(2011).
[CrossRef]

A. Rose, S. Larouche, D. Huang, E. Poutrina, and D. R. Smith, “Nonlinear parameter retrieval from three- and four-wave mixing in metamaterials,” Phys. Rev. E 82 (2010).
[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]

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]

Shadrivov, I.

A. Zharov, I. Shadrivov, and Y. Kivshar, “Nonlinear properties of left-handed metamaterials,” Phys. Rev. Lett. 91 (2003).
[CrossRef] [PubMed]

Shadrivov, I. V.

D. A. Powell, I. V. Shadrivov, Y. S. Kivshar, and M. V. Gorkunov, “Self-tuning mechanisms of nonlinear split-ring resonators,” Appl. Phys. Lett. 91, 144107 (2007).
[CrossRef]

Shalaev, V. M.

Shkarayev, M.

Shvets, G.

A. R. Katko, S. Gu, J. P. Barrett, B.-I. Popa, G. Shvets, and S. A. Cummer, “Phase conjugation and negative refraction using nonlinear active metamaterials,” Phys. Rev. Lett. 105, 123905(2010).
[CrossRef] [PubMed]

Smith, D. R.

A. Rose and D. R. Smith, “Broadly tunable quasi-phase-matching in nonlinear metamaterials,” Phys. Rev. A 84, 013823(2011).
[CrossRef]

E. Poutrina, D. Huang, Y. Urzhumov, and D. R. Smith, “Nonlinear oscillator metamaterial model: numerical and experimental verification,” Opt. Express 19, 8312–8319 (2011).
[CrossRef] [PubMed]

D. Huang, E. Poutrina, and D. R. Smith, “Analysis of the power dependent tuning of a varactor-loaded metamaterial at microwave frequencies,” Appl. Phys. Lett. 96, 104104 (2010).
[CrossRef]

E. Poutrina, D. Huang, and D. R. Smith, “Analysis of nonlinear electromagnetic metamaterials,” New J. Phys. 12, 093010(2010).
[CrossRef]

S. Larouche and D. R. Smith, “A retrieval method for nonlinear metamaterials,” Opt. Commun. 283, 1621–1627 (2010).
[CrossRef]

A. Rose, S. Larouche, D. Huang, E. Poutrina, and D. R. Smith, “Nonlinear parameter retrieval from three- and four-wave mixing in metamaterials,” Phys. Rev. E 82 (2010).
[CrossRef]

D. R. Smith, “Analytic expressions for the constitutive parameters of magnetoelectric metamaterials,” Phys. Rev. E 81, 036605 (2010).
[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]

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71, 36617 (2005).
[CrossRef]

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]

Soukoulis, C. M.

B. Wang, J. Zhou, T. Koschny, and C. M. Soukoulis, “Nonlinear properties of split-ring resonators” Opt. Express 16, 16058–16063 (2008).
[CrossRef] [PubMed]

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71, 36617 (2005).
[CrossRef]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306, 1351–1353 (2004).
[CrossRef] [PubMed]

Stepanov, M.

Stewart, W.

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

Urzhumov, Y.

Vier, D. C.

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71, 36617 (2005).
[CrossRef]

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]

Wang, B.

Wegener, M.

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Figures (4)

Fig. 1
Fig. 1

(a) Geometry of a single VLSRR unit; (b) the equivalent circuit model for the VLSRR unit in (a); (c) the artificial medium with arrays of VLSRR units; (d) the effective medium model for the array composite in (c).

Fig. 2
Fig. 2

(a), (b) Real and imaginary parts of the effective permittivity; (c), (d) real and imaginary parts of the effective permeability; (e), (f) real and imaginary parts of the effective second-order nonlinear susceptibility.

Fig. 3
Fig. 3

Comparison of the transmission curves obtained experimentally (dotted red curve) and numerically (solid black and dashed black curves). The numerical curves are calculated using the Lorentz parameters given in Table 1 for the 10 mm spacing.

Fig. 4
Fig. 4

(a) Experiment setup; (b) magnitude of effective second-order nonlinear susceptibility; (c) analytical (solid curves) and experimental (dashed curves) result of the norm of the generated second harmonic magnetic field (in mA / m ) at different artificial medium configurations.

Tables (1)

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Table 1 Retrieved Lorentz Parameters in Different Spacing Configurations

Equations (2)

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μ eff = 1 + N ω 0 2 μ 0 A 2 C 0 ω 2 ω 0 2 ω 2 i γ ω = 1 + F ω 2 D ( ω ) ,
χ eff ( 2 ) = i a 2 N ω 0 6 μ 0 2 A 3 C 0 ω 3 ( ω 0 2 ω 2 i γ ω ) 2 ( ω 0 2 4 ω 2 i 2 γ ω ) i a 2 μ 0 A F ω 0 4 ω 3 D ( ω ) 2 D ( 2 ω ) .

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