Abstract

Metamaterials offer the prospect of new science and applications. They have been designed by shaping or changing the material of the individual meta-molecules to achieve properties not naturally attainable. Composite meta-molecules incorporating a magnetic component offer new opportunities. In this work we report on the interaction between a non-magnetic split ring resonator (SRR) and a thin film of yttrium iron garnet (YIG). Strong hybridized resonances are observed. While the SRR is characterized by a magnetic and electric resonance, in practice, it is found that the YIG couples strongly to this symmetric (electric) mode of the SRR. It is also demonstrated that the anti-crossing region provides fertile ground for the creation of elementary excitations such as backward volume magnetostatic waves.

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2012 (1)

2010 (1)

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[CrossRef] [PubMed]

2009 (2)

2008 (3)

L. Kang, Q. Zhao, H. Zhao, and J. Zhou, “Magnetically tunable negative permeability metamaterial composed by split ring resonators and ferrite rods,” Opt. Express 16(12), 8825–8834 (2008).
[CrossRef] [PubMed]

J. M. L. Beaujour, A. D. Kent, D. W. Abraham, and J. Z. Sun, “Ferromagnetic resonance study of polycrystalline Fe1-xVx alloy thin films,” J. Appl. Phys. 103(7), 07B519 (2008).
[CrossRef]

P. He, J. Gao, C. T. Marinis, P. V. Parimi, C. Vittoria, and V. G. Harris, “A microstrip tunable negative refractive index metamaterial and phase shifter,” Appl. Phys. Lett. 93(19), 193505 (2008).
[CrossRef]

2006 (1)

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(5801), 977–980 (2006).
[CrossRef] [PubMed]

2005 (1)

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(33 Pt 2B), 036617 (2005).
[CrossRef] [PubMed]

2004 (2)

F. Falcone, F. Martín, J. Bonache, R. Marqués, and M. Sorolla, “Coplanar waveguide structures loaded with split-ring resonators,” Microw. Opt. Technol. Lett. 40, 3–6 (2004).
[CrossRef]

T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Effective medium theory of left-handed materials,” Phys. Rev. Lett. 93(10), 107402 (2004).
[CrossRef] [PubMed]

2003 (1)

F. Martín, F. Falcone, J. Bonache, R. Marqués, and M. Sorolla, “Miniaturized coplanar waveguide stop band filters based on multiple tuned split ring resonators,” IEEE Microw.Wireless Compon. Lett. 13(12), 511–513 (2003).
[CrossRef]

2001 (2)

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, “Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial,” Appl. Phys. Lett. 78(4), 489–491 (2001).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

2000 (1)

H. How, P. Shi, C. Vittoria, L. C. Kempel, and K. D. Trott, “Single-crystal YIG phase shifter using composite stripline structure at X band,” J. Appl. Phys. 87(9), 4966–4968 (2000).
[CrossRef]

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(11), 2075–2084 (1999).
[CrossRef]

1961 (1)

R. W. Damon and J. R. Eshbach, “Magnetostatic modes of a ferromagnet slab,” J. Phys. Chem. Solids 19(3-4), 308–320 (1961).
[CrossRef]

1960 (1)

J. F. Dillon., “Magnetostatic modes in disks and rods,” J. Appl. Phys. 31(9), 1605–1614 (1960).
[CrossRef]

1958 (1)

L. R. Walker, “Resonant modes of ferromagnetic spheroids,” J. Appl. Phys. 29(3), 318–323 (1958).
[CrossRef]

Abraham, D. W.

J. M. L. Beaujour, A. D. Kent, D. W. Abraham, and J. Z. Sun, “Ferromagnetic resonance study of polycrystalline Fe1-xVx alloy thin films,” J. Appl. Phys. 103(7), 07B519 (2008).
[CrossRef]

Beaujour, J. M. L.

J. M. L. Beaujour, A. D. Kent, D. W. Abraham, and J. Z. Sun, “Ferromagnetic resonance study of polycrystalline Fe1-xVx alloy thin films,” J. Appl. Phys. 103(7), 07B519 (2008).
[CrossRef]

Bonache, J.

F. Falcone, F. Martín, J. Bonache, R. Marqués, and M. Sorolla, “Coplanar waveguide structures loaded with split-ring resonators,” Microw. Opt. Technol. Lett. 40, 3–6 (2004).
[CrossRef]

F. Martín, F. Falcone, J. Bonache, R. Marqués, and M. Sorolla, “Miniaturized coplanar waveguide stop band filters based on multiple tuned split ring resonators,” IEEE Microw.Wireless Compon. Lett. 13(12), 511–513 (2003).
[CrossRef]

Chin, J. Y.

Chong, C. T.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[CrossRef] [PubMed]

Cui, T. J.

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(5801), 977–980 (2006).
[CrossRef] [PubMed]

Damon, R. W.

R. W. Damon and J. R. Eshbach, “Magnetostatic modes of a ferromagnet slab,” J. Phys. Chem. Solids 19(3-4), 308–320 (1961).
[CrossRef]

Dillon, J. F.

J. F. Dillon., “Magnetostatic modes in disks and rods,” J. Appl. Phys. 31(9), 1605–1614 (1960).
[CrossRef]

Eason, R. W.

Economou, E. N.

T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Effective medium theory of left-handed materials,” Phys. Rev. Lett. 93(10), 107402 (2004).
[CrossRef] [PubMed]

Eshbach, J. R.

R. W. Damon and J. R. Eshbach, “Magnetostatic modes of a ferromagnet slab,” J. Phys. Chem. Solids 19(3-4), 308–320 (1961).
[CrossRef]

Falcone, F.

F. Falcone, F. Martín, J. Bonache, R. Marqués, and M. Sorolla, “Coplanar waveguide structures loaded with split-ring resonators,” Microw. Opt. Technol. Lett. 40, 3–6 (2004).
[CrossRef]

F. Martín, F. Falcone, J. Bonache, R. Marqués, and M. Sorolla, “Miniaturized coplanar waveguide stop band filters based on multiple tuned split ring resonators,” IEEE Microw.Wireless Compon. Lett. 13(12), 511–513 (2003).
[CrossRef]

Feinaeugle, M.

Gao, J.

P. He, J. Gao, C. T. Marinis, P. V. Parimi, C. Vittoria, and V. G. Harris, “A microstrip tunable negative refractive index metamaterial and phase shifter,” Appl. Phys. Lett. 93(19), 193505 (2008).
[CrossRef]

Gholipour, B.

Giessen, H.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[CrossRef] [PubMed]

Gollub, J. N.

Halas, N. J.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[CrossRef] [PubMed]

Harris, V. G.

P. He, J. Gao, C. T. Marinis, P. V. Parimi, C. Vittoria, and V. G. Harris, “A microstrip tunable negative refractive index metamaterial and phase shifter,” Appl. Phys. Lett. 93(19), 193505 (2008).
[CrossRef]

He, P.

P. He, J. Gao, C. T. Marinis, P. V. Parimi, C. Vittoria, and V. G. Harris, “A microstrip tunable negative refractive index metamaterial and phase shifter,” Appl. Phys. Lett. 93(19), 193505 (2008).
[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(11), 2075–2084 (1999).
[CrossRef]

How, H.

H. How, P. Shi, C. Vittoria, L. C. Kempel, and K. D. Trott, “Single-crystal YIG phase shifter using composite stripline structure at X band,” J. Appl. Phys. 87(9), 4966–4968 (2000).
[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(5801), 977–980 (2006).
[CrossRef] [PubMed]

Kafesaki, M.

T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Effective medium theory of left-handed materials,” Phys. Rev. Lett. 93(10), 107402 (2004).
[CrossRef] [PubMed]

Kang, L.

Kempel, L. C.

H. How, P. Shi, C. Vittoria, L. C. Kempel, and K. D. Trott, “Single-crystal YIG phase shifter using composite stripline structure at X band,” J. Appl. Phys. 87(9), 4966–4968 (2000).
[CrossRef]

Kent, A. D.

J. M. L. Beaujour, A. D. Kent, D. W. Abraham, and J. Z. Sun, “Ferromagnetic resonance study of polycrystalline Fe1-xVx alloy thin films,” J. Appl. Phys. 103(7), 07B519 (2008).
[CrossRef]

Koschny, T.

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(33 Pt 2B), 036617 (2005).
[CrossRef] [PubMed]

T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Effective medium theory of left-handed materials,” Phys. Rev. Lett. 93(10), 107402 (2004).
[CrossRef] [PubMed]

Luk’yanchuk, B.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[CrossRef] [PubMed]

Maier, S. A.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[CrossRef] [PubMed]

Marinis, C. T.

P. He, J. Gao, C. T. Marinis, P. V. Parimi, C. Vittoria, and V. G. Harris, “A microstrip tunable negative refractive index metamaterial and phase shifter,” Appl. Phys. Lett. 93(19), 193505 (2008).
[CrossRef]

Marqués, R.

F. Falcone, F. Martín, J. Bonache, R. Marqués, and M. Sorolla, “Coplanar waveguide structures loaded with split-ring resonators,” Microw. Opt. Technol. Lett. 40, 3–6 (2004).
[CrossRef]

F. Martín, F. Falcone, J. Bonache, R. Marqués, and M. Sorolla, “Miniaturized coplanar waveguide stop band filters based on multiple tuned split ring resonators,” IEEE Microw.Wireless Compon. Lett. 13(12), 511–513 (2003).
[CrossRef]

Martín, F.

F. Falcone, F. Martín, J. Bonache, R. Marqués, and M. Sorolla, “Coplanar waveguide structures loaded with split-ring resonators,” Microw. Opt. Technol. Lett. 40, 3–6 (2004).
[CrossRef]

F. Martín, F. Falcone, J. Bonache, R. Marqués, and M. Sorolla, “Miniaturized coplanar waveguide stop band filters based on multiple tuned split ring resonators,” IEEE Microw.Wireless Compon. Lett. 13(12), 511–513 (2003).
[CrossRef]

Mock, J. 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(5801), 977–980 (2006).
[CrossRef] [PubMed]

Nemat-Nasser, S. C.

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, “Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial,” Appl. Phys. Lett. 78(4), 489–491 (2001).
[CrossRef]

Nordlander, P.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[CrossRef] [PubMed]

Parimi, P. V.

P. He, J. Gao, C. T. Marinis, P. V. Parimi, C. Vittoria, and V. G. Harris, “A microstrip tunable negative refractive index metamaterial and phase shifter,” Appl. Phys. Lett. 93(19), 193505 (2008).
[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(5801), 977–980 (2006).
[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(11), 2075–2084 (1999).
[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(11), 2075–2084 (1999).
[CrossRef]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, “Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial,” Appl. Phys. Lett. 78(4), 489–491 (2001).
[CrossRef]

Schurig, D.

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(5801), 977–980 (2006).
[CrossRef] [PubMed]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, “Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial,” Appl. Phys. Lett. 78(4), 489–491 (2001).
[CrossRef]

Shi, P.

H. How, P. Shi, C. Vittoria, L. C. Kempel, and K. D. Trott, “Single-crystal YIG phase shifter using composite stripline structure at X band,” J. Appl. Phys. 87(9), 4966–4968 (2000).
[CrossRef]

Smith, D. R.

J. N. Gollub, J. Y. Chin, T. J. Cui, and D. R. Smith, “Hybrid resonant phenomena in a SRR/YIG metamaterial structure,” Opt. Express 17(4), 2122–2131 (2009).
[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(5801), 977–980 (2006).
[CrossRef] [PubMed]

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(33 Pt 2B), 036617 (2005).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, “Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial,” Appl. Phys. Lett. 78(4), 489–491 (2001).
[CrossRef]

Sones, C. L.

Sorolla, M.

F. Falcone, F. Martín, J. Bonache, R. Marqués, and M. Sorolla, “Coplanar waveguide structures loaded with split-ring resonators,” Microw. Opt. Technol. Lett. 40, 3–6 (2004).
[CrossRef]

F. Martín, F. Falcone, J. Bonache, R. Marqués, and M. Sorolla, “Miniaturized coplanar waveguide stop band filters based on multiple tuned split ring resonators,” IEEE Microw.Wireless Compon. Lett. 13(12), 511–513 (2003).
[CrossRef]

Soukoulis, C. M.

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(33 Pt 2B), 036617 (2005).
[CrossRef] [PubMed]

T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Effective medium theory of left-handed materials,” Phys. Rev. Lett. 93(10), 107402 (2004).
[CrossRef] [PubMed]

Sposito, A.

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(5801), 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(11), 2075–2084 (1999).
[CrossRef]

Sun, J. Z.

J. M. L. Beaujour, A. D. Kent, D. W. Abraham, and J. Z. Sun, “Ferromagnetic resonance study of polycrystalline Fe1-xVx alloy thin films,” J. Appl. Phys. 103(7), 07B519 (2008).
[CrossRef]

Trott, K. D.

H. How, P. Shi, C. Vittoria, L. C. Kempel, and K. D. Trott, “Single-crystal YIG phase shifter using composite stripline structure at X band,” J. Appl. Phys. 87(9), 4966–4968 (2000).
[CrossRef]

Vier, D. C.

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(33 Pt 2B), 036617 (2005).
[CrossRef] [PubMed]

Vittoria, C.

P. He, J. Gao, C. T. Marinis, P. V. Parimi, C. Vittoria, and V. G. Harris, “A microstrip tunable negative refractive index metamaterial and phase shifter,” Appl. Phys. Lett. 93(19), 193505 (2008).
[CrossRef]

H. How, P. Shi, C. Vittoria, L. C. Kempel, and K. D. Trott, “Single-crystal YIG phase shifter using composite stripline structure at X band,” J. Appl. Phys. 87(9), 4966–4968 (2000).
[CrossRef]

Walker, L. R.

L. R. Walker, “Resonant modes of ferromagnetic spheroids,” J. Appl. Phys. 29(3), 318–323 (1958).
[CrossRef]

Zhao, H.

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Figures (6)

Fig. 1
Fig. 1

Schematic view of a) Top view of the CPW. b) SRRs (metamaterial) located on the underside of the CPW substrate. The YIG film is placed directly on top of one SRR. c) Single split ring resonator (SRR). Dimensions of, a = 3.93 mm, c = 0.375 mm, d = 0.45 mm, g = 0.69 mm. Field direction as shown by Ba.

Fig. 2
Fig. 2

The (ν-Ba) map of the YIG-SRR anti-crossing modes. The transmission colour-bar on the right represents transmission (positive values/blue) and absorption (negative values/red). Satellites of the FMR are visible to the right of the anti-crossing and FMR shown by the black arrow. These arise from the creation of BVMSWs.

Fig. 3
Fig. 3

Normalized transmission SN21 vs frequency (ν) at three fixed fields from Fig. 2 (a) Ba = 0.2777 T, (b) 0.306 T and (c) 0.3202 T, blue, red and black respectively. For clarity, each frequency trace is vertically offset by 2 dB.

Fig. 4
Fig. 4

Unnormalized data (S21) for two orientations of the SRR. The blue arrow represents the electric field polarization as supplied by the CPW. The resonance S21 curves blue, red and black were obtained for applied fields of 0.27 T, 0.30 T and 0.33 T, respectively. The dashed circles indicate the YIG resonance, with vertical black lines representing the reduction in microwave losses. Each frequency trace has been offset vertically by 4 dB.

Fig. 5
Fig. 5

Anti-crossing of the SRR and YIG modes, obtained using a simple two-level model. Dotted lines show the effects of discrete spin-wave, MSSW and BVMSW excitations.

Fig. 6
Fig. 6

As per Fig. 2 but with a 5 × 5 × 0.5 mm3 thick bulk YIG crystal.

Equations (4)

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

M=[ ν SRR δ δ ν YIG ]
ν YIG =γ B a ( B a + μ 0 M 0 )
λ ± = 1 2 ( ν SRR + ν YIG )± 1 2 ( ν SRR ν YIG ) 2 +4 δ 2
ν YIG =γ ( B a +D k s 2 )( B a + μ 0 M 0 +D k s 2 )

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