Abstract

Responses of plasmonic magneto-optical (MO) (gold–garnet) systems in different regimes of light propagation to identify the features of plasmon-modified MO responses are demonstrated. The absorption band associated with excitation of the localized plasmon resonance in gold is shown to influence a cumulative angle of polarization rotation of the considered systems. The resonance is responsible for enhanced polarization rotation when gold–garnet systems are magnetized; however, this enhancement is found to be the reciprocal effect, with no influence on the inherent properties of garnet from the near field. The experimental results are in good agreement with the numerical analysis results.

© 2013 Optical Society of America

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2012 (2)

A. V. Chetvertukhin, A. V. Baryshev, H. Uchida, M. Inoue, and A. Fedyanin, “Resonant surface magnetoplasmons in two-dimensional magnetoplasmonic crystals excited in Faraday configuration,” J. Appl. Phys. 111, 07A946 (2012).
[CrossRef]

A. V. Baryshev, K. Kawasaki, P. B. Lim, and M. Inoue, “Interplay of surface resonances in one-dimensional plasmonic magnetophotonic crystal slabs,” Phys. Rev. B 85, 205130 (2012).
[CrossRef]

2011 (3)

A. V. Baryshev, M. E. Dokukin, A. M. Merzlikin, and M. Inoue, “Propagation of polarized light in opals: amplitude and phase anisotropy,” JETP 112, 361–369 (2011).
[CrossRef]

J. B. González-Díaz, A. García-Martín, and G. A. Reig, “Unusual magneto-optical behavior induced by local dielectric variations under localized surface plasmon excitations,” Nanoscale Res. Lett. 6, 408 (2011).
[CrossRef]

L. Wang, C. Clavero, Z. Huba, K. J. Carroll, E. E. Carpenter, D. Gu, and R. A. Lukaszew, “Plasmonics and enhanced magneto-optics in core-shell Co–Ag nanoparticles,” Nano Lett. 11, 1237–1240 (2011).
[CrossRef]

2010 (1)

B. Sepúlveda, J. B. González-Díaz, A. García-Martín, L. M. Lechuga, and G. Armelles, “Plasmon-induced magneto-optical activity in nanosized gold disks,” Phys. Rev. Lett. 104, 147401 (2010).
[CrossRef]

2009 (3)

P. K. Jain, Y. Xiao, R. Walsworth, and A. E. Cohen, “Surface plasmon resonance enhanced magneto-optics (SuPREMO): Faraday rotation enhancement in gold-coated iron oxide nanocrystals,” Nano Lett. 9, 1644–1650 (2009).
[CrossRef]

Y. Mizutani, H. Uchida, Y. Masuda, A. V. Baryshev, and M. Inoue, “Magneto-optical plasmonic Bi:YIG composite films with Ag and Au–Ag alloy particles,” J. Magn. Soc. Jpn. 33, 481–484 (2009).
[CrossRef]

S. Ozaki, H. Kura, H. Maki, and T. Sato, “Size effect in magneto-optical properties of Co nanoparticles dispersed systems,” J. Appl. Phys. 106, 123530 (2009).
[CrossRef]

2008 (1)

R. Fujikawa, A. V. Baryshev, J. Kim, H. Uchida, and M. Inoue, “Contribution of the surface plasmon resonance to optical and magneto-optical properties of a Bi:YIG–Au nanostructure,” J. Appl. Phys. 103, 07D301 (2008).
[CrossRef]

2007 (5)

J. B. González-Díaz, A. García-Martín, G. Armelles, J. M. García-Martín, C. Clavero, A. Cebollada, R. A. Lukaszew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76, 153402 (2007).
[CrossRef]

S. Tomita, M. Fujii, S. Hayashi, A. Terai, and N. Nabatova-Gabain, “Spectroscopic ellipsometry of yttrium–iron garnet thin films containing gold nanoparticles,” Jpn. J. Appl. Phys. 46, L1032–L1034 (2007).
[CrossRef]

J. B. González-Díaz, A. García-Martín, G. Armelles, D. Navas, M. Vázquez, K. Nielsch, R. B. Wehrspohn, and U. Gösele, “Enhanced magneto-optics and size effects in ferromagnetic nanowire arrays,” Adv. Mater. 19, 2643–2647 (2007).
[CrossRef]

V. I. Belotelov, L. L. Doskolovich, and A. K. Zvezdin, “Extraordinary magneto-optical effects and transmission through metal–dielectric plasmonic systems,” Phys. Rev. Lett. 98, 077401 (2007).
[CrossRef]

A. B. Khanikaev, A. V. Baryshev, A. A. Fedyanin, A. B. Granovsky, and M. Inoue, “Anomalous Faraday effect of a system with extraordinary optical transmittance,” Opt. Express 15, 6612–6622 (2007).
[CrossRef]

2006 (3)

D. A. Smith and K. L. Stokes, “Discrete dipole approximation for magneto-optical scattering calculations,” Opt. Express 14, 5746–5754 (2006).
[CrossRef]

M. Inoue, R. Fujikawa, A. Baryshev, A. Khanikaev, P. B. Lim, H. Uchida, O. Aktsipetrov, A. Fedyanin, T. Murzina, and A. Granovsky, “Magnetophotonic crystals,” J. Phys. D 39, R151–R161 (2006).
[CrossRef]

S. Tomita, T. Kato, S. Tsunashima, S. Iwata, M. Fujii, and S. Hayashi, “Magneto-optical Kerr effects of yttrium–iron garnet thin films incorporating gold nanoparticles,” Phys. Rev. Lett. 96, 167402 (2006).
[CrossRef]

2005 (3)

Y. Li, Q. Zhang, A. V. Nurmikko, and S. Sun, “Enhanced magneto-optical response in dumbbell-like Ag–CoFe2O4 nanoparticle pairs,” Nano Lett. 5, 1689–1692 (2005).
[CrossRef]

M. Abe and T. Suwa, “Magneto-optical enhancement by surface plasmon resonance in magnetic “nano-onions” with multicore-shell structures,” J. Appl. Phys. 97, 10M514 (2005).
[CrossRef]

D. A. Smith, Yu. A. Barnakov, B. L. Scott, S. A. White, and K. L. Stokes, “Magneto-optical spectra of closely spaced magnetite nanoparticles,” J. Appl. Phys. 97, 10M504 (2005).
[CrossRef]

2002 (1)

G. Shemer and G. Markovich, “Enhancement of magneto-optical effects in magnetite near gold surfaces,” J. Phys. Chem. B 106, 9195–9197 (2002).
[CrossRef]

2001 (1)

C. Hermann, V. A. Kosobukin, G. Lampel, J. Peretti, V. I. Safarov, and P. Bertrand, “Surface-enhanced magneto-optics in metallic multilayer films,” Phys. Rev. B 64, 235422 (2001).
[CrossRef]

1998 (1)

V. E. Kochergin, A. Yu. Toporov, and M. Valeiko, “Polariton enhancement of the Faraday magneto-optic effect,” JETP Lett. 68, 400–403 (1998).
[CrossRef]

1997 (1)

M. R. Pufall, A. Berger, and S. Schultz, “Measurement of the scattered light magneto-optical Kerr effect from plasmon–resonant Ag particles near a magnetic film,” J. Appl. Phys. 81, 5689 (1997).
[CrossRef]

1994 (1)

V. I. Safarov, V. A. Kosobukin, C. Hermann, G. Lampel, and J. Peretti, “Magneto-optical effects enhanced by surface plasmons in metallic multilayer films,” Phys. Rev. Lett. 73, 3584–3587 (1994).
[CrossRef]

1990 (1)

T. K. Xia, P. M. Hui, and D. Stroud, “Theory of Faraday rotation in granular magnetic materials,” J. Appl. Phys. 67, 2736 (1990).
[CrossRef]

1988 (1)

T. Katayama, Y. Suzuki, H. Awano, Y. Nishihara, and N. Koshizuka, “Enhancement of the magneto-optical Kerr rotation in Fe/Cu bilayered films,” Phys. Rev. Lett. 60, 1426–1429 (1988).
[CrossRef]

1987 (1)

H. Feil and C. Haas, “Magneto-optical Kerr effect, enhanced by the plasma resonance of charge carriers,” Phys. Rev. Lett. 58, 65–68 (1987).
[CrossRef]

Abe, M.

M. Abe and T. Suwa, “Magneto-optical enhancement by surface plasmon resonance in magnetic “nano-onions” with multicore-shell structures,” J. Appl. Phys. 97, 10M514 (2005).
[CrossRef]

Aktsipetrov, O.

M. Inoue, R. Fujikawa, A. Baryshev, A. Khanikaev, P. B. Lim, H. Uchida, O. Aktsipetrov, A. Fedyanin, T. Murzina, and A. Granovsky, “Magnetophotonic crystals,” J. Phys. D 39, R151–R161 (2006).
[CrossRef]

Armelles, G.

B. Sepúlveda, J. B. González-Díaz, A. García-Martín, L. M. Lechuga, and G. Armelles, “Plasmon-induced magneto-optical activity in nanosized gold disks,” Phys. Rev. Lett. 104, 147401 (2010).
[CrossRef]

J. B. González-Díaz, A. García-Martín, G. Armelles, D. Navas, M. Vázquez, K. Nielsch, R. B. Wehrspohn, and U. Gösele, “Enhanced magneto-optics and size effects in ferromagnetic nanowire arrays,” Adv. Mater. 19, 2643–2647 (2007).
[CrossRef]

J. B. González-Díaz, A. García-Martín, G. Armelles, J. M. García-Martín, C. Clavero, A. Cebollada, R. A. Lukaszew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76, 153402 (2007).
[CrossRef]

Awano, H.

T. Katayama, Y. Suzuki, H. Awano, Y. Nishihara, and N. Koshizuka, “Enhancement of the magneto-optical Kerr rotation in Fe/Cu bilayered films,” Phys. Rev. Lett. 60, 1426–1429 (1988).
[CrossRef]

Barnakov, Yu. A.

D. A. Smith, Yu. A. Barnakov, B. L. Scott, S. A. White, and K. L. Stokes, “Magneto-optical spectra of closely spaced magnetite nanoparticles,” J. Appl. Phys. 97, 10M504 (2005).
[CrossRef]

Baryshev, A.

M. Inoue, R. Fujikawa, A. Baryshev, A. Khanikaev, P. B. Lim, H. Uchida, O. Aktsipetrov, A. Fedyanin, T. Murzina, and A. Granovsky, “Magnetophotonic crystals,” J. Phys. D 39, R151–R161 (2006).
[CrossRef]

Baryshev, A. V.

A. V. Baryshev, K. Kawasaki, P. B. Lim, and M. Inoue, “Interplay of surface resonances in one-dimensional plasmonic magnetophotonic crystal slabs,” Phys. Rev. B 85, 205130 (2012).
[CrossRef]

A. V. Chetvertukhin, A. V. Baryshev, H. Uchida, M. Inoue, and A. Fedyanin, “Resonant surface magnetoplasmons in two-dimensional magnetoplasmonic crystals excited in Faraday configuration,” J. Appl. Phys. 111, 07A946 (2012).
[CrossRef]

A. V. Baryshev, M. E. Dokukin, A. M. Merzlikin, and M. Inoue, “Propagation of polarized light in opals: amplitude and phase anisotropy,” JETP 112, 361–369 (2011).
[CrossRef]

Y. Mizutani, H. Uchida, Y. Masuda, A. V. Baryshev, and M. Inoue, “Magneto-optical plasmonic Bi:YIG composite films with Ag and Au–Ag alloy particles,” J. Magn. Soc. Jpn. 33, 481–484 (2009).
[CrossRef]

R. Fujikawa, A. V. Baryshev, J. Kim, H. Uchida, and M. Inoue, “Contribution of the surface plasmon resonance to optical and magneto-optical properties of a Bi:YIG–Au nanostructure,” J. Appl. Phys. 103, 07D301 (2008).
[CrossRef]

A. B. Khanikaev, A. V. Baryshev, A. A. Fedyanin, A. B. Granovsky, and M. Inoue, “Anomalous Faraday effect of a system with extraordinary optical transmittance,” Opt. Express 15, 6612–6622 (2007).
[CrossRef]

Belotelov, V. I.

V. I. Belotelov, L. L. Doskolovich, and A. K. Zvezdin, “Extraordinary magneto-optical effects and transmission through metal–dielectric plasmonic systems,” Phys. Rev. Lett. 98, 077401 (2007).
[CrossRef]

Berger, A.

M. R. Pufall, A. Berger, and S. Schultz, “Measurement of the scattered light magneto-optical Kerr effect from plasmon–resonant Ag particles near a magnetic film,” J. Appl. Phys. 81, 5689 (1997).
[CrossRef]

Bertrand, P.

C. Hermann, V. A. Kosobukin, G. Lampel, J. Peretti, V. I. Safarov, and P. Bertrand, “Surface-enhanced magneto-optics in metallic multilayer films,” Phys. Rev. B 64, 235422 (2001).
[CrossRef]

Carpenter, E. E.

L. Wang, C. Clavero, Z. Huba, K. J. Carroll, E. E. Carpenter, D. Gu, and R. A. Lukaszew, “Plasmonics and enhanced magneto-optics in core-shell Co–Ag nanoparticles,” Nano Lett. 11, 1237–1240 (2011).
[CrossRef]

Carroll, K. J.

L. Wang, C. Clavero, Z. Huba, K. J. Carroll, E. E. Carpenter, D. Gu, and R. A. Lukaszew, “Plasmonics and enhanced magneto-optics in core-shell Co–Ag nanoparticles,” Nano Lett. 11, 1237–1240 (2011).
[CrossRef]

Cebollada, A.

J. B. González-Díaz, A. García-Martín, G. Armelles, J. M. García-Martín, C. Clavero, A. Cebollada, R. A. Lukaszew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76, 153402 (2007).
[CrossRef]

Chetvertukhin, A. V.

A. V. Chetvertukhin, A. V. Baryshev, H. Uchida, M. Inoue, and A. Fedyanin, “Resonant surface magnetoplasmons in two-dimensional magnetoplasmonic crystals excited in Faraday configuration,” J. Appl. Phys. 111, 07A946 (2012).
[CrossRef]

Clarke, R.

J. B. González-Díaz, A. García-Martín, G. Armelles, J. M. García-Martín, C. Clavero, A. Cebollada, R. A. Lukaszew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76, 153402 (2007).
[CrossRef]

Clavero, C.

L. Wang, C. Clavero, Z. Huba, K. J. Carroll, E. E. Carpenter, D. Gu, and R. A. Lukaszew, “Plasmonics and enhanced magneto-optics in core-shell Co–Ag nanoparticles,” Nano Lett. 11, 1237–1240 (2011).
[CrossRef]

J. B. González-Díaz, A. García-Martín, G. Armelles, J. M. García-Martín, C. Clavero, A. Cebollada, R. A. Lukaszew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76, 153402 (2007).
[CrossRef]

Cohen, A. E.

P. K. Jain, Y. Xiao, R. Walsworth, and A. E. Cohen, “Surface plasmon resonance enhanced magneto-optics (SuPREMO): Faraday rotation enhancement in gold-coated iron oxide nanocrystals,” Nano Lett. 9, 1644–1650 (2009).
[CrossRef]

Dokukin, M. E.

A. V. Baryshev, M. E. Dokukin, A. M. Merzlikin, and M. Inoue, “Propagation of polarized light in opals: amplitude and phase anisotropy,” JETP 112, 361–369 (2011).
[CrossRef]

Doskolovich, L. L.

V. I. Belotelov, L. L. Doskolovich, and A. K. Zvezdin, “Extraordinary magneto-optical effects and transmission through metal–dielectric plasmonic systems,” Phys. Rev. Lett. 98, 077401 (2007).
[CrossRef]

Fedyanin, A.

A. V. Chetvertukhin, A. V. Baryshev, H. Uchida, M. Inoue, and A. Fedyanin, “Resonant surface magnetoplasmons in two-dimensional magnetoplasmonic crystals excited in Faraday configuration,” J. Appl. Phys. 111, 07A946 (2012).
[CrossRef]

M. Inoue, R. Fujikawa, A. Baryshev, A. Khanikaev, P. B. Lim, H. Uchida, O. Aktsipetrov, A. Fedyanin, T. Murzina, and A. Granovsky, “Magnetophotonic crystals,” J. Phys. D 39, R151–R161 (2006).
[CrossRef]

Fedyanin, A. A.

Feil, H.

H. Feil and C. Haas, “Magneto-optical Kerr effect, enhanced by the plasma resonance of charge carriers,” Phys. Rev. Lett. 58, 65–68 (1987).
[CrossRef]

Fujii, M.

S. Tomita, M. Fujii, S. Hayashi, A. Terai, and N. Nabatova-Gabain, “Spectroscopic ellipsometry of yttrium–iron garnet thin films containing gold nanoparticles,” Jpn. J. Appl. Phys. 46, L1032–L1034 (2007).
[CrossRef]

S. Tomita, T. Kato, S. Tsunashima, S. Iwata, M. Fujii, and S. Hayashi, “Magneto-optical Kerr effects of yttrium–iron garnet thin films incorporating gold nanoparticles,” Phys. Rev. Lett. 96, 167402 (2006).
[CrossRef]

Fujikawa, R.

R. Fujikawa, A. V. Baryshev, J. Kim, H. Uchida, and M. Inoue, “Contribution of the surface plasmon resonance to optical and magneto-optical properties of a Bi:YIG–Au nanostructure,” J. Appl. Phys. 103, 07D301 (2008).
[CrossRef]

M. Inoue, R. Fujikawa, A. Baryshev, A. Khanikaev, P. B. Lim, H. Uchida, O. Aktsipetrov, A. Fedyanin, T. Murzina, and A. Granovsky, “Magnetophotonic crystals,” J. Phys. D 39, R151–R161 (2006).
[CrossRef]

García-Martín, A.

J. B. González-Díaz, A. García-Martín, and G. A. Reig, “Unusual magneto-optical behavior induced by local dielectric variations under localized surface plasmon excitations,” Nanoscale Res. Lett. 6, 408 (2011).
[CrossRef]

B. Sepúlveda, J. B. González-Díaz, A. García-Martín, L. M. Lechuga, and G. Armelles, “Plasmon-induced magneto-optical activity in nanosized gold disks,” Phys. Rev. Lett. 104, 147401 (2010).
[CrossRef]

J. B. González-Díaz, A. García-Martín, G. Armelles, D. Navas, M. Vázquez, K. Nielsch, R. B. Wehrspohn, and U. Gösele, “Enhanced magneto-optics and size effects in ferromagnetic nanowire arrays,” Adv. Mater. 19, 2643–2647 (2007).
[CrossRef]

J. B. González-Díaz, A. García-Martín, G. Armelles, J. M. García-Martín, C. Clavero, A. Cebollada, R. A. Lukaszew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76, 153402 (2007).
[CrossRef]

García-Martín, J. M.

J. B. González-Díaz, A. García-Martín, G. Armelles, J. M. García-Martín, C. Clavero, A. Cebollada, R. A. Lukaszew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76, 153402 (2007).
[CrossRef]

González-Díaz, J. B.

J. B. González-Díaz, A. García-Martín, and G. A. Reig, “Unusual magneto-optical behavior induced by local dielectric variations under localized surface plasmon excitations,” Nanoscale Res. Lett. 6, 408 (2011).
[CrossRef]

B. Sepúlveda, J. B. González-Díaz, A. García-Martín, L. M. Lechuga, and G. Armelles, “Plasmon-induced magneto-optical activity in nanosized gold disks,” Phys. Rev. Lett. 104, 147401 (2010).
[CrossRef]

J. B. González-Díaz, A. García-Martín, G. Armelles, D. Navas, M. Vázquez, K. Nielsch, R. B. Wehrspohn, and U. Gösele, “Enhanced magneto-optics and size effects in ferromagnetic nanowire arrays,” Adv. Mater. 19, 2643–2647 (2007).
[CrossRef]

J. B. González-Díaz, A. García-Martín, G. Armelles, J. M. García-Martín, C. Clavero, A. Cebollada, R. A. Lukaszew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76, 153402 (2007).
[CrossRef]

Gösele, U.

J. B. González-Díaz, A. García-Martín, G. Armelles, D. Navas, M. Vázquez, K. Nielsch, R. B. Wehrspohn, and U. Gösele, “Enhanced magneto-optics and size effects in ferromagnetic nanowire arrays,” Adv. Mater. 19, 2643–2647 (2007).
[CrossRef]

Granovsky, A.

M. Inoue, R. Fujikawa, A. Baryshev, A. Khanikaev, P. B. Lim, H. Uchida, O. Aktsipetrov, A. Fedyanin, T. Murzina, and A. Granovsky, “Magnetophotonic crystals,” J. Phys. D 39, R151–R161 (2006).
[CrossRef]

Granovsky, A. B.

Gu, D.

L. Wang, C. Clavero, Z. Huba, K. J. Carroll, E. E. Carpenter, D. Gu, and R. A. Lukaszew, “Plasmonics and enhanced magneto-optics in core-shell Co–Ag nanoparticles,” Nano Lett. 11, 1237–1240 (2011).
[CrossRef]

Haas, C.

H. Feil and C. Haas, “Magneto-optical Kerr effect, enhanced by the plasma resonance of charge carriers,” Phys. Rev. Lett. 58, 65–68 (1987).
[CrossRef]

Hayashi, S.

S. Tomita, M. Fujii, S. Hayashi, A. Terai, and N. Nabatova-Gabain, “Spectroscopic ellipsometry of yttrium–iron garnet thin films containing gold nanoparticles,” Jpn. J. Appl. Phys. 46, L1032–L1034 (2007).
[CrossRef]

S. Tomita, T. Kato, S. Tsunashima, S. Iwata, M. Fujii, and S. Hayashi, “Magneto-optical Kerr effects of yttrium–iron garnet thin films incorporating gold nanoparticles,” Phys. Rev. Lett. 96, 167402 (2006).
[CrossRef]

Hermann, C.

C. Hermann, V. A. Kosobukin, G. Lampel, J. Peretti, V. I. Safarov, and P. Bertrand, “Surface-enhanced magneto-optics in metallic multilayer films,” Phys. Rev. B 64, 235422 (2001).
[CrossRef]

V. I. Safarov, V. A. Kosobukin, C. Hermann, G. Lampel, and J. Peretti, “Magneto-optical effects enhanced by surface plasmons in metallic multilayer films,” Phys. Rev. Lett. 73, 3584–3587 (1994).
[CrossRef]

Huba, Z.

L. Wang, C. Clavero, Z. Huba, K. J. Carroll, E. E. Carpenter, D. Gu, and R. A. Lukaszew, “Plasmonics and enhanced magneto-optics in core-shell Co–Ag nanoparticles,” Nano Lett. 11, 1237–1240 (2011).
[CrossRef]

Hui, P. M.

T. K. Xia, P. M. Hui, and D. Stroud, “Theory of Faraday rotation in granular magnetic materials,” J. Appl. Phys. 67, 2736 (1990).
[CrossRef]

Inoue, M.

A. V. Baryshev, K. Kawasaki, P. B. Lim, and M. Inoue, “Interplay of surface resonances in one-dimensional plasmonic magnetophotonic crystal slabs,” Phys. Rev. B 85, 205130 (2012).
[CrossRef]

A. V. Chetvertukhin, A. V. Baryshev, H. Uchida, M. Inoue, and A. Fedyanin, “Resonant surface magnetoplasmons in two-dimensional magnetoplasmonic crystals excited in Faraday configuration,” J. Appl. Phys. 111, 07A946 (2012).
[CrossRef]

A. V. Baryshev, M. E. Dokukin, A. M. Merzlikin, and M. Inoue, “Propagation of polarized light in opals: amplitude and phase anisotropy,” JETP 112, 361–369 (2011).
[CrossRef]

Y. Mizutani, H. Uchida, Y. Masuda, A. V. Baryshev, and M. Inoue, “Magneto-optical plasmonic Bi:YIG composite films with Ag and Au–Ag alloy particles,” J. Magn. Soc. Jpn. 33, 481–484 (2009).
[CrossRef]

R. Fujikawa, A. V. Baryshev, J. Kim, H. Uchida, and M. Inoue, “Contribution of the surface plasmon resonance to optical and magneto-optical properties of a Bi:YIG–Au nanostructure,” J. Appl. Phys. 103, 07D301 (2008).
[CrossRef]

A. B. Khanikaev, A. V. Baryshev, A. A. Fedyanin, A. B. Granovsky, and M. Inoue, “Anomalous Faraday effect of a system with extraordinary optical transmittance,” Opt. Express 15, 6612–6622 (2007).
[CrossRef]

M. Inoue, R. Fujikawa, A. Baryshev, A. Khanikaev, P. B. Lim, H. Uchida, O. Aktsipetrov, A. Fedyanin, T. Murzina, and A. Granovsky, “Magnetophotonic crystals,” J. Phys. D 39, R151–R161 (2006).
[CrossRef]

Iwata, S.

S. Tomita, T. Kato, S. Tsunashima, S. Iwata, M. Fujii, and S. Hayashi, “Magneto-optical Kerr effects of yttrium–iron garnet thin films incorporating gold nanoparticles,” Phys. Rev. Lett. 96, 167402 (2006).
[CrossRef]

Jain, P. K.

P. K. Jain, Y. Xiao, R. Walsworth, and A. E. Cohen, “Surface plasmon resonance enhanced magneto-optics (SuPREMO): Faraday rotation enhancement in gold-coated iron oxide nanocrystals,” Nano Lett. 9, 1644–1650 (2009).
[CrossRef]

Katayama, T.

T. Katayama, Y. Suzuki, H. Awano, Y. Nishihara, and N. Koshizuka, “Enhancement of the magneto-optical Kerr rotation in Fe/Cu bilayered films,” Phys. Rev. Lett. 60, 1426–1429 (1988).
[CrossRef]

Kato, T.

S. Tomita, T. Kato, S. Tsunashima, S. Iwata, M. Fujii, and S. Hayashi, “Magneto-optical Kerr effects of yttrium–iron garnet thin films incorporating gold nanoparticles,” Phys. Rev. Lett. 96, 167402 (2006).
[CrossRef]

Kawasaki, K.

A. V. Baryshev, K. Kawasaki, P. B. Lim, and M. Inoue, “Interplay of surface resonances in one-dimensional plasmonic magnetophotonic crystal slabs,” Phys. Rev. B 85, 205130 (2012).
[CrossRef]

Khanikaev, A.

M. Inoue, R. Fujikawa, A. Baryshev, A. Khanikaev, P. B. Lim, H. Uchida, O. Aktsipetrov, A. Fedyanin, T. Murzina, and A. Granovsky, “Magnetophotonic crystals,” J. Phys. D 39, R151–R161 (2006).
[CrossRef]

Khanikaev, A. B.

Kim, J.

R. Fujikawa, A. V. Baryshev, J. Kim, H. Uchida, and M. Inoue, “Contribution of the surface plasmon resonance to optical and magneto-optical properties of a Bi:YIG–Au nanostructure,” J. Appl. Phys. 103, 07D301 (2008).
[CrossRef]

Kochergin, V. E.

V. E. Kochergin, A. Yu. Toporov, and M. Valeiko, “Polariton enhancement of the Faraday magneto-optic effect,” JETP Lett. 68, 400–403 (1998).
[CrossRef]

Koshizuka, N.

T. Katayama, Y. Suzuki, H. Awano, Y. Nishihara, and N. Koshizuka, “Enhancement of the magneto-optical Kerr rotation in Fe/Cu bilayered films,” Phys. Rev. Lett. 60, 1426–1429 (1988).
[CrossRef]

Kosobukin, V. A.

C. Hermann, V. A. Kosobukin, G. Lampel, J. Peretti, V. I. Safarov, and P. Bertrand, “Surface-enhanced magneto-optics in metallic multilayer films,” Phys. Rev. B 64, 235422 (2001).
[CrossRef]

V. I. Safarov, V. A. Kosobukin, C. Hermann, G. Lampel, and J. Peretti, “Magneto-optical effects enhanced by surface plasmons in metallic multilayer films,” Phys. Rev. Lett. 73, 3584–3587 (1994).
[CrossRef]

Kumah, D. P.

J. B. González-Díaz, A. García-Martín, G. Armelles, J. M. García-Martín, C. Clavero, A. Cebollada, R. A. Lukaszew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76, 153402 (2007).
[CrossRef]

Kura, H.

S. Ozaki, H. Kura, H. Maki, and T. Sato, “Size effect in magneto-optical properties of Co nanoparticles dispersed systems,” J. Appl. Phys. 106, 123530 (2009).
[CrossRef]

Lampel, G.

C. Hermann, V. A. Kosobukin, G. Lampel, J. Peretti, V. I. Safarov, and P. Bertrand, “Surface-enhanced magneto-optics in metallic multilayer films,” Phys. Rev. B 64, 235422 (2001).
[CrossRef]

V. I. Safarov, V. A. Kosobukin, C. Hermann, G. Lampel, and J. Peretti, “Magneto-optical effects enhanced by surface plasmons in metallic multilayer films,” Phys. Rev. Lett. 73, 3584–3587 (1994).
[CrossRef]

Lechuga, L. M.

B. Sepúlveda, J. B. González-Díaz, A. García-Martín, L. M. Lechuga, and G. Armelles, “Plasmon-induced magneto-optical activity in nanosized gold disks,” Phys. Rev. Lett. 104, 147401 (2010).
[CrossRef]

Li, Y.

Y. Li, Q. Zhang, A. V. Nurmikko, and S. Sun, “Enhanced magneto-optical response in dumbbell-like Ag–CoFe2O4 nanoparticle pairs,” Nano Lett. 5, 1689–1692 (2005).
[CrossRef]

Lim, P. B.

A. V. Baryshev, K. Kawasaki, P. B. Lim, and M. Inoue, “Interplay of surface resonances in one-dimensional plasmonic magnetophotonic crystal slabs,” Phys. Rev. B 85, 205130 (2012).
[CrossRef]

M. Inoue, R. Fujikawa, A. Baryshev, A. Khanikaev, P. B. Lim, H. Uchida, O. Aktsipetrov, A. Fedyanin, T. Murzina, and A. Granovsky, “Magnetophotonic crystals,” J. Phys. D 39, R151–R161 (2006).
[CrossRef]

Lukaszew, R. A.

L. Wang, C. Clavero, Z. Huba, K. J. Carroll, E. E. Carpenter, D. Gu, and R. A. Lukaszew, “Plasmonics and enhanced magneto-optics in core-shell Co–Ag nanoparticles,” Nano Lett. 11, 1237–1240 (2011).
[CrossRef]

J. B. González-Díaz, A. García-Martín, G. Armelles, J. M. García-Martín, C. Clavero, A. Cebollada, R. A. Lukaszew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76, 153402 (2007).
[CrossRef]

Maki, H.

S. Ozaki, H. Kura, H. Maki, and T. Sato, “Size effect in magneto-optical properties of Co nanoparticles dispersed systems,” J. Appl. Phys. 106, 123530 (2009).
[CrossRef]

Markovich, G.

G. Shemer and G. Markovich, “Enhancement of magneto-optical effects in magnetite near gold surfaces,” J. Phys. Chem. B 106, 9195–9197 (2002).
[CrossRef]

Masuda, Y.

Y. Mizutani, H. Uchida, Y. Masuda, A. V. Baryshev, and M. Inoue, “Magneto-optical plasmonic Bi:YIG composite films with Ag and Au–Ag alloy particles,” J. Magn. Soc. Jpn. 33, 481–484 (2009).
[CrossRef]

Merzlikin, A. M.

A. V. Baryshev, M. E. Dokukin, A. M. Merzlikin, and M. Inoue, “Propagation of polarized light in opals: amplitude and phase anisotropy,” JETP 112, 361–369 (2011).
[CrossRef]

Mizutani, Y.

Y. Mizutani, H. Uchida, Y. Masuda, A. V. Baryshev, and M. Inoue, “Magneto-optical plasmonic Bi:YIG composite films with Ag and Au–Ag alloy particles,” J. Magn. Soc. Jpn. 33, 481–484 (2009).
[CrossRef]

Murzina, T.

M. Inoue, R. Fujikawa, A. Baryshev, A. Khanikaev, P. B. Lim, H. Uchida, O. Aktsipetrov, A. Fedyanin, T. Murzina, and A. Granovsky, “Magnetophotonic crystals,” J. Phys. D 39, R151–R161 (2006).
[CrossRef]

Nabatova-Gabain, N.

S. Tomita, M. Fujii, S. Hayashi, A. Terai, and N. Nabatova-Gabain, “Spectroscopic ellipsometry of yttrium–iron garnet thin films containing gold nanoparticles,” Jpn. J. Appl. Phys. 46, L1032–L1034 (2007).
[CrossRef]

Navas, D.

J. B. González-Díaz, A. García-Martín, G. Armelles, D. Navas, M. Vázquez, K. Nielsch, R. B. Wehrspohn, and U. Gösele, “Enhanced magneto-optics and size effects in ferromagnetic nanowire arrays,” Adv. Mater. 19, 2643–2647 (2007).
[CrossRef]

Nielsch, K.

J. B. González-Díaz, A. García-Martín, G. Armelles, D. Navas, M. Vázquez, K. Nielsch, R. B. Wehrspohn, and U. Gösele, “Enhanced magneto-optics and size effects in ferromagnetic nanowire arrays,” Adv. Mater. 19, 2643–2647 (2007).
[CrossRef]

Nishihara, Y.

T. Katayama, Y. Suzuki, H. Awano, Y. Nishihara, and N. Koshizuka, “Enhancement of the magneto-optical Kerr rotation in Fe/Cu bilayered films,” Phys. Rev. Lett. 60, 1426–1429 (1988).
[CrossRef]

Nurmikko, A. V.

Y. Li, Q. Zhang, A. V. Nurmikko, and S. Sun, “Enhanced magneto-optical response in dumbbell-like Ag–CoFe2O4 nanoparticle pairs,” Nano Lett. 5, 1689–1692 (2005).
[CrossRef]

Ozaki, S.

S. Ozaki, H. Kura, H. Maki, and T. Sato, “Size effect in magneto-optical properties of Co nanoparticles dispersed systems,” J. Appl. Phys. 106, 123530 (2009).
[CrossRef]

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1985).

Peretti, J.

C. Hermann, V. A. Kosobukin, G. Lampel, J. Peretti, V. I. Safarov, and P. Bertrand, “Surface-enhanced magneto-optics in metallic multilayer films,” Phys. Rev. B 64, 235422 (2001).
[CrossRef]

V. I. Safarov, V. A. Kosobukin, C. Hermann, G. Lampel, and J. Peretti, “Magneto-optical effects enhanced by surface plasmons in metallic multilayer films,” Phys. Rev. Lett. 73, 3584–3587 (1994).
[CrossRef]

Pufall, M. R.

M. R. Pufall, A. Berger, and S. Schultz, “Measurement of the scattered light magneto-optical Kerr effect from plasmon–resonant Ag particles near a magnetic film,” J. Appl. Phys. 81, 5689 (1997).
[CrossRef]

Raether, H.

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Grating (Springer, 1988).

Reig, G. A.

J. B. González-Díaz, A. García-Martín, and G. A. Reig, “Unusual magneto-optical behavior induced by local dielectric variations under localized surface plasmon excitations,” Nanoscale Res. Lett. 6, 408 (2011).
[CrossRef]

Safarov, V. I.

C. Hermann, V. A. Kosobukin, G. Lampel, J. Peretti, V. I. Safarov, and P. Bertrand, “Surface-enhanced magneto-optics in metallic multilayer films,” Phys. Rev. B 64, 235422 (2001).
[CrossRef]

V. I. Safarov, V. A. Kosobukin, C. Hermann, G. Lampel, and J. Peretti, “Magneto-optical effects enhanced by surface plasmons in metallic multilayer films,” Phys. Rev. Lett. 73, 3584–3587 (1994).
[CrossRef]

Sato, T.

S. Ozaki, H. Kura, H. Maki, and T. Sato, “Size effect in magneto-optical properties of Co nanoparticles dispersed systems,” J. Appl. Phys. 106, 123530 (2009).
[CrossRef]

Schultz, S.

M. R. Pufall, A. Berger, and S. Schultz, “Measurement of the scattered light magneto-optical Kerr effect from plasmon–resonant Ag particles near a magnetic film,” J. Appl. Phys. 81, 5689 (1997).
[CrossRef]

Scott, B. L.

D. A. Smith, Yu. A. Barnakov, B. L. Scott, S. A. White, and K. L. Stokes, “Magneto-optical spectra of closely spaced magnetite nanoparticles,” J. Appl. Phys. 97, 10M504 (2005).
[CrossRef]

Sepúlveda, B.

B. Sepúlveda, J. B. González-Díaz, A. García-Martín, L. M. Lechuga, and G. Armelles, “Plasmon-induced magneto-optical activity in nanosized gold disks,” Phys. Rev. Lett. 104, 147401 (2010).
[CrossRef]

Shemer, G.

G. Shemer and G. Markovich, “Enhancement of magneto-optical effects in magnetite near gold surfaces,” J. Phys. Chem. B 106, 9195–9197 (2002).
[CrossRef]

Skuza, J. R.

J. B. González-Díaz, A. García-Martín, G. Armelles, J. M. García-Martín, C. Clavero, A. Cebollada, R. A. Lukaszew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76, 153402 (2007).
[CrossRef]

Smith, D. A.

D. A. Smith and K. L. Stokes, “Discrete dipole approximation for magneto-optical scattering calculations,” Opt. Express 14, 5746–5754 (2006).
[CrossRef]

D. A. Smith, Yu. A. Barnakov, B. L. Scott, S. A. White, and K. L. Stokes, “Magneto-optical spectra of closely spaced magnetite nanoparticles,” J. Appl. Phys. 97, 10M504 (2005).
[CrossRef]

Stokes, K. L.

D. A. Smith and K. L. Stokes, “Discrete dipole approximation for magneto-optical scattering calculations,” Opt. Express 14, 5746–5754 (2006).
[CrossRef]

D. A. Smith, Yu. A. Barnakov, B. L. Scott, S. A. White, and K. L. Stokes, “Magneto-optical spectra of closely spaced magnetite nanoparticles,” J. Appl. Phys. 97, 10M504 (2005).
[CrossRef]

Stroud, D.

T. K. Xia, P. M. Hui, and D. Stroud, “Theory of Faraday rotation in granular magnetic materials,” J. Appl. Phys. 67, 2736 (1990).
[CrossRef]

Sun, S.

Y. Li, Q. Zhang, A. V. Nurmikko, and S. Sun, “Enhanced magneto-optical response in dumbbell-like Ag–CoFe2O4 nanoparticle pairs,” Nano Lett. 5, 1689–1692 (2005).
[CrossRef]

Suwa, T.

M. Abe and T. Suwa, “Magneto-optical enhancement by surface plasmon resonance in magnetic “nano-onions” with multicore-shell structures,” J. Appl. Phys. 97, 10M514 (2005).
[CrossRef]

Suzuki, Y.

T. Katayama, Y. Suzuki, H. Awano, Y. Nishihara, and N. Koshizuka, “Enhancement of the magneto-optical Kerr rotation in Fe/Cu bilayered films,” Phys. Rev. Lett. 60, 1426–1429 (1988).
[CrossRef]

Terai, A.

S. Tomita, M. Fujii, S. Hayashi, A. Terai, and N. Nabatova-Gabain, “Spectroscopic ellipsometry of yttrium–iron garnet thin films containing gold nanoparticles,” Jpn. J. Appl. Phys. 46, L1032–L1034 (2007).
[CrossRef]

Tomita, S.

S. Tomita, M. Fujii, S. Hayashi, A. Terai, and N. Nabatova-Gabain, “Spectroscopic ellipsometry of yttrium–iron garnet thin films containing gold nanoparticles,” Jpn. J. Appl. Phys. 46, L1032–L1034 (2007).
[CrossRef]

S. Tomita, T. Kato, S. Tsunashima, S. Iwata, M. Fujii, and S. Hayashi, “Magneto-optical Kerr effects of yttrium–iron garnet thin films incorporating gold nanoparticles,” Phys. Rev. Lett. 96, 167402 (2006).
[CrossRef]

Toporov, A. Yu.

V. E. Kochergin, A. Yu. Toporov, and M. Valeiko, “Polariton enhancement of the Faraday magneto-optic effect,” JETP Lett. 68, 400–403 (1998).
[CrossRef]

Tsunashima, S.

S. Tomita, T. Kato, S. Tsunashima, S. Iwata, M. Fujii, and S. Hayashi, “Magneto-optical Kerr effects of yttrium–iron garnet thin films incorporating gold nanoparticles,” Phys. Rev. Lett. 96, 167402 (2006).
[CrossRef]

Uchida, H.

A. V. Chetvertukhin, A. V. Baryshev, H. Uchida, M. Inoue, and A. Fedyanin, “Resonant surface magnetoplasmons in two-dimensional magnetoplasmonic crystals excited in Faraday configuration,” J. Appl. Phys. 111, 07A946 (2012).
[CrossRef]

Y. Mizutani, H. Uchida, Y. Masuda, A. V. Baryshev, and M. Inoue, “Magneto-optical plasmonic Bi:YIG composite films with Ag and Au–Ag alloy particles,” J. Magn. Soc. Jpn. 33, 481–484 (2009).
[CrossRef]

R. Fujikawa, A. V. Baryshev, J. Kim, H. Uchida, and M. Inoue, “Contribution of the surface plasmon resonance to optical and magneto-optical properties of a Bi:YIG–Au nanostructure,” J. Appl. Phys. 103, 07D301 (2008).
[CrossRef]

M. Inoue, R. Fujikawa, A. Baryshev, A. Khanikaev, P. B. Lim, H. Uchida, O. Aktsipetrov, A. Fedyanin, T. Murzina, and A. Granovsky, “Magnetophotonic crystals,” J. Phys. D 39, R151–R161 (2006).
[CrossRef]

Valeiko, M.

V. E. Kochergin, A. Yu. Toporov, and M. Valeiko, “Polariton enhancement of the Faraday magneto-optic effect,” JETP Lett. 68, 400–403 (1998).
[CrossRef]

Vázquez, M.

J. B. González-Díaz, A. García-Martín, G. Armelles, D. Navas, M. Vázquez, K. Nielsch, R. B. Wehrspohn, and U. Gösele, “Enhanced magneto-optics and size effects in ferromagnetic nanowire arrays,” Adv. Mater. 19, 2643–2647 (2007).
[CrossRef]

Walsworth, R.

P. K. Jain, Y. Xiao, R. Walsworth, and A. E. Cohen, “Surface plasmon resonance enhanced magneto-optics (SuPREMO): Faraday rotation enhancement in gold-coated iron oxide nanocrystals,” Nano Lett. 9, 1644–1650 (2009).
[CrossRef]

Wang, L.

L. Wang, C. Clavero, Z. Huba, K. J. Carroll, E. E. Carpenter, D. Gu, and R. A. Lukaszew, “Plasmonics and enhanced magneto-optics in core-shell Co–Ag nanoparticles,” Nano Lett. 11, 1237–1240 (2011).
[CrossRef]

Wehrspohn, R. B.

J. B. González-Díaz, A. García-Martín, G. Armelles, D. Navas, M. Vázquez, K. Nielsch, R. B. Wehrspohn, and U. Gösele, “Enhanced magneto-optics and size effects in ferromagnetic nanowire arrays,” Adv. Mater. 19, 2643–2647 (2007).
[CrossRef]

White, S. A.

D. A. Smith, Yu. A. Barnakov, B. L. Scott, S. A. White, and K. L. Stokes, “Magneto-optical spectra of closely spaced magnetite nanoparticles,” J. Appl. Phys. 97, 10M504 (2005).
[CrossRef]

Xia, T. K.

T. K. Xia, P. M. Hui, and D. Stroud, “Theory of Faraday rotation in granular magnetic materials,” J. Appl. Phys. 67, 2736 (1990).
[CrossRef]

Xiao, Y.

P. K. Jain, Y. Xiao, R. Walsworth, and A. E. Cohen, “Surface plasmon resonance enhanced magneto-optics (SuPREMO): Faraday rotation enhancement in gold-coated iron oxide nanocrystals,” Nano Lett. 9, 1644–1650 (2009).
[CrossRef]

Zhang, Q.

Y. Li, Q. Zhang, A. V. Nurmikko, and S. Sun, “Enhanced magneto-optical response in dumbbell-like Ag–CoFe2O4 nanoparticle pairs,” Nano Lett. 5, 1689–1692 (2005).
[CrossRef]

Zvezdin, A. K.

V. I. Belotelov, L. L. Doskolovich, and A. K. Zvezdin, “Extraordinary magneto-optical effects and transmission through metal–dielectric plasmonic systems,” Phys. Rev. Lett. 98, 077401 (2007).
[CrossRef]

Adv. Mater. (1)

J. B. González-Díaz, A. García-Martín, G. Armelles, D. Navas, M. Vázquez, K. Nielsch, R. B. Wehrspohn, and U. Gösele, “Enhanced magneto-optics and size effects in ferromagnetic nanowire arrays,” Adv. Mater. 19, 2643–2647 (2007).
[CrossRef]

J. Appl. Phys. (7)

D. A. Smith, Yu. A. Barnakov, B. L. Scott, S. A. White, and K. L. Stokes, “Magneto-optical spectra of closely spaced magnetite nanoparticles,” J. Appl. Phys. 97, 10M504 (2005).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

(a) SEM image of a 2D lattice of Au disks and a sketch of an Au–Bi:YIG layer; (b), (c) geometry of experiments for the multipass regime; (d) sketch of MPC having defect Au–Bi:YIG layers; the Au lattice was 1D. The system of coordinates is shown for defining polarization planes; Ex and Ez are for polarizations across and along Au rods, respectively.

Fig. 2.
Fig. 2.

(a) Transmission and (b) Faraday rotation spectra of Bi:YIG and Au–Bi:YIG layers, α=0. In plot (b), spectral dependencies of θ(H) are shown. Spectral positions of LSPRs of the lattice of Au discs due to facing Bi:YIG and quartz are shown by dashed lines. Inset to plot (b): cumulative polarization rotation together with the ellipticity of transmitted light for the Au–Bi:YIG sample; both spectra were measured for a magnetic field applied along the direction of light propagation, H+.

Fig. 3.
Fig. 3.

(a), (b) Single-pass polarization rotation spectra of the Au–Bi:YIG layer at normal incidence when the external magnetic field is applied or not: H+ and H stand for the opposite fields. Polarization rotation spectra measured as shown in Fig. 1(b): α=7°, plot (c) for the Bi:YIG and plot (d) for Au–Bi:YIG layer. Solid lines show the rotation angle of θ(H).

Fig. 4.
Fig. 4.

Transmission (a) and polarization rotation spectra (b): the Au–Bi:YIG layer in the single-pass regime at normal incidence (squares) and multipass regime at α=40° (circles) and α=20° (triangles).

Fig. 5.
Fig. 5.

Polarization-resolved absorbance (a) and polarization rotation (b) spectra of an Au–Bi:YIG layer; the dotted curves show spectra of a reference Bi:YIG layer. Transmittance (c) and polarization rotation (d) spectra of MPC: MPCs 1 and 2 having Au–Bi:YIG defect layers as shown in Fig. 1(d), and reference MPC 3 having a Bi:YIG defect layer (solid line). All spectra were calculated for normal incidence.

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