Abstract

Giant enhancement of the magneto-optical Kerr effect (MOKE) by surface plasmon polaritons (SPPs) is theoretically shown in a trilayer structure consisting of double-layer dielectrics and a ferromagnetic metal (Al2O3/SiO2/Fe). We calculated the resonant enhancement of the transverse MOKE (TMOKE) and polar MOKE (PMOKE) using the attenuated total reflection (ATR) configuration with the transfer matrix method using a 4 × 4 scattering matrix. At a specific film thickness of the low-index SiO2 layer, where confinement of the SPPs on the Fe surface becomes close to the cutoff condition, the incident light from the Al2O3 couples with the SPPs at the SiO2/Fe boundary most efficiently, resulting in resonant enhancement of the MOKE at an incident angle corresponding to the wave vector of the SPPs. The calculated PMOKE showed orthogonal transformation (90°-rotation) and almost full-orbed deformation (44°-ellipticity) of the polarization, and the TMOKE showed a change in reflectance of about 34 dB upon magnetization reversal.

© 2015 Optical Society of America

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References

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2014 (3)

Y. Shoji, Y. Shirato, and T. Mizumoto, “Silicon Mach–Zehnder interferometer optical isolator having 8 nm bandwidth for over 20 dB isolation,” Jpn. J. Appl. Phys. 53(2), 022202 (2014).
[Crossref]

S. M. Hamidi, M. A. Oskuei, S. Sadeghi, and M. M. Tehranchi, “Enhanced polar magneto-optical Kerr rotation in cobalt thin film incorporating Ag nanoparticles,” J. Supercond. Novel Magn. 27(3), 867–870 (2014).
[Crossref]

H.-T. Huang, P.-J. Chen, T.-R. Ger, Y.-J. Chi, C.-W. Huang, K.-T. Liao, J.-Y. Lai, J.-Y. Chen, W.-Y. Peng, Q. Zhang, T.-F. Hsieh, W.-J. Sheu, and Z.-H. Wei, “Magneto-optical Kerr effect enhanced by surface plasmon resonance and its application on biological detection,” IEEE Trans. Magn. 50(1), 1001604 (2014).
[Crossref]

2013 (5)

S. Zhang, S. Tang, J. Gao, X. Luo, W. Xia, and Y. Du, “Theoretical calculation of magneto-optical properties in cobalt nanotube array with hexagonal symmetry,” Solid State Commun. 170, 19–23 (2013).
[Crossref]

L. E. Kreilkamp, V. I. Belotelov, J. Y. Chin, S. Neutzner, D. Dregely, T. Wehlus, I. A. Akimov, M. Bayer, B. Stritzker, and H. Giessen, “Waveguide-plasmon polaritons enhance transverse magneto-optical Kerr effect,” Phys. Rev. X 3, 041019 (2013).

Y. Sobu, Y. Shoji, K. Sakurai, and T. Mizumoto, “GaInAsP/InP MZI waveguide optical isolator integrated with spot size converter,” Opt. Express 21(13), 15373–15381 (2013).
[Crossref] [PubMed]

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is — and what is not — an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

G. Armelles, A. Cebollada, A. García-Martín, and M. U. González, “Magnetoplasmonics: combining magnetic and plasmonic functionalities,” Adv. Opt. Mater. 1(1), 10–35 (2013).
[Crossref]

2012 (4)

G. Armelles, A. Cebollada, A. García-Martín, J. M. Montero-Moreno, M. Waleczek, and K. Nielsch, “Magneto-optical Properties of Core-Shell Magneto-plasmonic Au-CoxFe3 - xO4 Nanowires,” Langmuir 28(24), 9127–9130 (2012).
[Crossref] [PubMed]

B. Caballero, A. García-Martín, and J. C. Cuevas, “Generalized scattering-matrix approach for magneto-optics in periodically patterned multilayer systems,” Phys. Rev. B 85(24), 245103 (2012).
[Crossref]

V. Zayets, H. Saito, S. Yuasa, and K. Ando, “Enhancement of the transverse non-reciprocal magneto-optical effect,” J. Appl. Phys. 111(2), 023103 (2012).
[Crossref]

V. Zayets, H. Saito, K. Ando, and S. Yuasa, “Optical isolator utilizing surface plasmons,” Materials (Basel) 5(5), 857–871 (2012).
[Crossref]

2011 (5)

H. Uchida, Y. Mizutani, Y. Nakai, A. A. Fedyanin, and M. Inoue, “Garnet composite films with Au particles fabricated by repetitive formation for enhancement of Faraday effect,” J. Phys. D Appl. Phys. 44(6), 064014 (2011).
[Crossref]

D. Meneses-Rodríguez, E. Ferreiro-Vila, P. Prieto, J. Anguita, M. U. González, J. M. García-Martín, A. Cebollada, A. García-Martín, and G. Armelles, “Probing the Electromagnetic Field Distribution within a Metallic Nanodisk,” Small 7(23), 3317–3323 (2011).
[Crossref] [PubMed]

D. Regatos, B. Sepúlveda, D. Fariña, L. G. Carrascosa, and L. M. Lechuga, “Suitable combination of noble/ferromagnetic metal multilayers for enhanced magneto-plasmonic biosensing,” Opt. Express 19(9), 8336–8346 (2011).
[Crossref] [PubMed]

R. C. Rumpf, “Improved formulation of scattering matrices for semi-analytical methods that is consistent with convention,” Prog. Electromagn. Res. B 35, 241–261 (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(3), 1237–1240 (2011).
[Crossref] [PubMed]

2010 (1)

V. I. Belotelov, D. A. Bykov, L. L. Doskolovich, A. N. Kalish, and A. K. Zvezdin, “Giant transversal Kerr effect in magneto-plasmonic heterostructures: The scattering-matrix method,” Sov. Phys. JETP 110(5), 816–824 (2010).
[Crossref]

2009 (1)

H. Uchida, Y. Masuda, R. Fujikawa, A. V. Baryshev, and M. Inoue, “Large enhancement of Faraday rotation by localized surface plasmon resonance in Au nanoparticles embedded in Bi:YIG film,” J. Magn. Magn. Mater. 321(7), 843–845 (2009).
[Crossref]

2008 (3)

J. B. González-Díaz, A. García-Martín, J. M. García-Martín, A. Cebollada, G. Armelles, B. Sepúlveda, Y. Alaverdyan, and M. Käll, “Plasmonic Au/Co/Au Nanosandwiches with Enhanced Magneto-Optical Activity,” Small 4(2), 202–205 (2008).
[Crossref] [PubMed]

J. Homola, “Surface plasmon resonance sensors for detection of chemical and biological species,” Chem. Rev. 108(2), 462–493 (2008).
[Crossref] [PubMed]

K. Hering, D. Cialla, K. Ackermann, T. Dörfer, R. Möller, H. Schneidewind, R. Mattheis, W. Fritzsche, P. Rösch, and J. Popp, “SERS: a versatile tool in chemical and biochemical diagnostics,” Anal. Bioanal. Chem. 390(1), 113–124 (2008).
[Crossref] [PubMed]

2007 (2)

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(18), 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(15), 153402 (2007).
[Crossref]

2006 (2)

2004 (1)

H. Shimizu and Y. Nakano, “First Demonstration of TE Mode Nonreciprocal Propagation in an InGaAsP/InP Active Waveguide for an Integratable Optical Isolator,” Jpn. J. Appl. Phys. 43(12A12A), L1561–L1563 (2004).
[Crossref]

2001 (1)

P. Bertrand, C. Hermann, G. Lampel, J. Peretti, and V. I. Safarov, “General analytical treatment of optics in layered structures: Application to magneto-optics,” Phys. Rev. B 64(23), 235421 (2001).
[Crossref]

1998 (1)

T. Shintaku, “Integrated optical isolator based on efficient nonreciprocal radiation mode conversion,” Appl. Phys. Lett. 73(14), 1946–1948 (1998).
[Crossref]

1994 (1)

T. Shintaku and T. Uno, “Optical waveguide isolator based on nonreciprocal radiation,” J. Appl. Phys. 76(12), 8155–8159 (1994).
[Crossref]

1987 (1)

P. M. Hui and D. Stroud, “Theory of Faraday rotation by dilute suspensions of small particles,” Appl. Phys. Lett. 50(15), 950–952 (1987).
[Crossref]

1982 (1)

C. Nylander, B. Liedberg, and T. Lind, “Gas detection by means of surface plasmon resonance,” Sens. Actuators 3, 79–88 (1982).
[Crossref]

1976 (1)

1974 (1)

M. Fleischmann, P. J. Hendra, and A. J. McQuillan, “Raman spectra of pyridine adsorbed at a silver electrode,” Chem. Phys. Lett. 26(2), 163–166 (1974).
[Crossref]

1957 (1)

H. J. Williams, R. C. Sherwood, F. G. Foster, and E. M. Kelley, “Magnetic Writing on Thin Films of MnBi,” J. Appl. Phys. 28(10), 1181–1184 (1957).
[Crossref]

Ackermann, K.

K. Hering, D. Cialla, K. Ackermann, T. Dörfer, R. Möller, H. Schneidewind, R. Mattheis, W. Fritzsche, P. Rösch, and J. Popp, “SERS: a versatile tool in chemical and biochemical diagnostics,” Anal. Bioanal. Chem. 390(1), 113–124 (2008).
[Crossref] [PubMed]

Akimov, I. A.

L. E. Kreilkamp, V. I. Belotelov, J. Y. Chin, S. Neutzner, D. Dregely, T. Wehlus, I. A. Akimov, M. Bayer, B. Stritzker, and H. Giessen, “Waveguide-plasmon polaritons enhance transverse magneto-optical Kerr effect,” Phys. Rev. X 3, 041019 (2013).

Alaverdyan, Y.

J. B. González-Díaz, A. García-Martín, J. M. García-Martín, A. Cebollada, G. Armelles, B. Sepúlveda, Y. Alaverdyan, and M. Käll, “Plasmonic Au/Co/Au Nanosandwiches with Enhanced Magneto-Optical Activity,” Small 4(2), 202–205 (2008).
[Crossref] [PubMed]

Ando, K.

V. Zayets, H. Saito, S. Yuasa, and K. Ando, “Enhancement of the transverse non-reciprocal magneto-optical effect,” J. Appl. Phys. 111(2), 023103 (2012).
[Crossref]

V. Zayets, H. Saito, K. Ando, and S. Yuasa, “Optical isolator utilizing surface plasmons,” Materials (Basel) 5(5), 857–871 (2012).
[Crossref]

Anguita, J.

D. Meneses-Rodríguez, E. Ferreiro-Vila, P. Prieto, J. Anguita, M. U. González, J. M. García-Martín, A. Cebollada, A. García-Martín, and G. Armelles, “Probing the Electromagnetic Field Distribution within a Metallic Nanodisk,” Small 7(23), 3317–3323 (2011).
[Crossref] [PubMed]

Armelles, G.

G. Armelles, A. Cebollada, A. García-Martín, and M. U. González, “Magnetoplasmonics: combining magnetic and plasmonic functionalities,” Adv. Opt. Mater. 1(1), 10–35 (2013).
[Crossref]

G. Armelles, A. Cebollada, A. García-Martín, J. M. Montero-Moreno, M. Waleczek, and K. Nielsch, “Magneto-optical Properties of Core-Shell Magneto-plasmonic Au-CoxFe3 - xO4 Nanowires,” Langmuir 28(24), 9127–9130 (2012).
[Crossref] [PubMed]

D. Meneses-Rodríguez, E. Ferreiro-Vila, P. Prieto, J. Anguita, M. U. González, J. M. García-Martín, A. Cebollada, A. García-Martín, and G. Armelles, “Probing the Electromagnetic Field Distribution within a Metallic Nanodisk,” Small 7(23), 3317–3323 (2011).
[Crossref] [PubMed]

J. B. González-Díaz, A. García-Martín, J. M. García-Martín, A. Cebollada, G. Armelles, B. Sepúlveda, Y. Alaverdyan, and M. Käll, “Plasmonic Au/Co/Au Nanosandwiches with Enhanced Magneto-Optical Activity,” Small 4(2), 202–205 (2008).
[Crossref] [PubMed]

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(18), 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(15), 153402 (2007).
[Crossref]

B. Sepúlveda, A. Calle, L. M. Lechuga, and G. Armelles, “Highly sensitive detection of biomolecules with the magneto-optic surface-plasmon-resonance sensor,” Opt. Lett. 31(8), 1085–1087 (2006).
[Crossref] [PubMed]

Baets, R.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is — and what is not — an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

Baryshev, A. V.

H. Uchida, Y. Masuda, R. Fujikawa, A. V. Baryshev, and M. Inoue, “Large enhancement of Faraday rotation by localized surface plasmon resonance in Au nanoparticles embedded in Bi:YIG film,” J. Magn. Magn. Mater. 321(7), 843–845 (2009).
[Crossref]

Bayer, M.

L. E. Kreilkamp, V. I. Belotelov, J. Y. Chin, S. Neutzner, D. Dregely, T. Wehlus, I. A. Akimov, M. Bayer, B. Stritzker, and H. Giessen, “Waveguide-plasmon polaritons enhance transverse magneto-optical Kerr effect,” Phys. Rev. X 3, 041019 (2013).

Belotelov, V. I.

L. E. Kreilkamp, V. I. Belotelov, J. Y. Chin, S. Neutzner, D. Dregely, T. Wehlus, I. A. Akimov, M. Bayer, B. Stritzker, and H. Giessen, “Waveguide-plasmon polaritons enhance transverse magneto-optical Kerr effect,” Phys. Rev. X 3, 041019 (2013).

V. I. Belotelov, D. A. Bykov, L. L. Doskolovich, A. N. Kalish, and A. K. Zvezdin, “Giant transversal Kerr effect in magneto-plasmonic heterostructures: The scattering-matrix method,” Sov. Phys. JETP 110(5), 816–824 (2010).
[Crossref]

Bertrand, P.

P. Bertrand, C. Hermann, G. Lampel, J. Peretti, and V. I. Safarov, “General analytical treatment of optics in layered structures: Application to magneto-optics,” Phys. Rev. B 64(23), 235421 (2001).
[Crossref]

Bykov, D. A.

V. I. Belotelov, D. A. Bykov, L. L. Doskolovich, A. N. Kalish, and A. K. Zvezdin, “Giant transversal Kerr effect in magneto-plasmonic heterostructures: The scattering-matrix method,” Sov. Phys. JETP 110(5), 816–824 (2010).
[Crossref]

Caballero, B.

B. Caballero, A. García-Martín, and J. C. Cuevas, “Generalized scattering-matrix approach for magneto-optics in periodically patterned multilayer systems,” Phys. Rev. B 85(24), 245103 (2012).
[Crossref]

Calle, A.

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(3), 1237–1240 (2011).
[Crossref] [PubMed]

Carrascosa, L. G.

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(3), 1237–1240 (2011).
[Crossref] [PubMed]

Cebollada, A.

G. Armelles, A. Cebollada, A. García-Martín, and M. U. González, “Magnetoplasmonics: combining magnetic and plasmonic functionalities,” Adv. Opt. Mater. 1(1), 10–35 (2013).
[Crossref]

G. Armelles, A. Cebollada, A. García-Martín, J. M. Montero-Moreno, M. Waleczek, and K. Nielsch, “Magneto-optical Properties of Core-Shell Magneto-plasmonic Au-CoxFe3 - xO4 Nanowires,” Langmuir 28(24), 9127–9130 (2012).
[Crossref] [PubMed]

D. Meneses-Rodríguez, E. Ferreiro-Vila, P. Prieto, J. Anguita, M. U. González, J. M. García-Martín, A. Cebollada, A. García-Martín, and G. Armelles, “Probing the Electromagnetic Field Distribution within a Metallic Nanodisk,” Small 7(23), 3317–3323 (2011).
[Crossref] [PubMed]

J. B. González-Díaz, A. García-Martín, J. M. García-Martín, A. Cebollada, G. Armelles, B. Sepúlveda, Y. Alaverdyan, and M. Käll, “Plasmonic Au/Co/Au Nanosandwiches with Enhanced Magneto-Optical Activity,” Small 4(2), 202–205 (2008).
[Crossref] [PubMed]

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(15), 153402 (2007).
[Crossref]

Chen, J.-Y.

H.-T. Huang, P.-J. Chen, T.-R. Ger, Y.-J. Chi, C.-W. Huang, K.-T. Liao, J.-Y. Lai, J.-Y. Chen, W.-Y. Peng, Q. Zhang, T.-F. Hsieh, W.-J. Sheu, and Z.-H. Wei, “Magneto-optical Kerr effect enhanced by surface plasmon resonance and its application on biological detection,” IEEE Trans. Magn. 50(1), 1001604 (2014).
[Crossref]

Chen, P.-J.

H.-T. Huang, P.-J. Chen, T.-R. Ger, Y.-J. Chi, C.-W. Huang, K.-T. Liao, J.-Y. Lai, J.-Y. Chen, W.-Y. Peng, Q. Zhang, T.-F. Hsieh, W.-J. Sheu, and Z.-H. Wei, “Magneto-optical Kerr effect enhanced by surface plasmon resonance and its application on biological detection,” IEEE Trans. Magn. 50(1), 1001604 (2014).
[Crossref]

Chi, Y.-J.

H.-T. Huang, P.-J. Chen, T.-R. Ger, Y.-J. Chi, C.-W. Huang, K.-T. Liao, J.-Y. Lai, J.-Y. Chen, W.-Y. Peng, Q. Zhang, T.-F. Hsieh, W.-J. Sheu, and Z.-H. Wei, “Magneto-optical Kerr effect enhanced by surface plasmon resonance and its application on biological detection,” IEEE Trans. Magn. 50(1), 1001604 (2014).
[Crossref]

Chin, J. Y.

L. E. Kreilkamp, V. I. Belotelov, J. Y. Chin, S. Neutzner, D. Dregely, T. Wehlus, I. A. Akimov, M. Bayer, B. Stritzker, and H. Giessen, “Waveguide-plasmon polaritons enhance transverse magneto-optical Kerr effect,” Phys. Rev. X 3, 041019 (2013).

Cialla, D.

K. Hering, D. Cialla, K. Ackermann, T. Dörfer, R. Möller, H. Schneidewind, R. Mattheis, W. Fritzsche, P. Rösch, and J. Popp, “SERS: a versatile tool in chemical and biochemical diagnostics,” Anal. Bioanal. Chem. 390(1), 113–124 (2008).
[Crossref] [PubMed]

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(15), 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(3), 1237–1240 (2011).
[Crossref] [PubMed]

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(15), 153402 (2007).
[Crossref]

Cuevas, J. C.

B. Caballero, A. García-Martín, and J. C. Cuevas, “Generalized scattering-matrix approach for magneto-optics in periodically patterned multilayer systems,” Phys. Rev. B 85(24), 245103 (2012).
[Crossref]

Doerr, C. R.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is — and what is not — an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

Dörfer, T.

K. Hering, D. Cialla, K. Ackermann, T. Dörfer, R. Möller, H. Schneidewind, R. Mattheis, W. Fritzsche, P. Rösch, and J. Popp, “SERS: a versatile tool in chemical and biochemical diagnostics,” Anal. Bioanal. Chem. 390(1), 113–124 (2008).
[Crossref] [PubMed]

Doskolovich, L. L.

V. I. Belotelov, D. A. Bykov, L. L. Doskolovich, A. N. Kalish, and A. K. Zvezdin, “Giant transversal Kerr effect in magneto-plasmonic heterostructures: The scattering-matrix method,” Sov. Phys. JETP 110(5), 816–824 (2010).
[Crossref]

Dregely, D.

L. E. Kreilkamp, V. I. Belotelov, J. Y. Chin, S. Neutzner, D. Dregely, T. Wehlus, I. A. Akimov, M. Bayer, B. Stritzker, and H. Giessen, “Waveguide-plasmon polaritons enhance transverse magneto-optical Kerr effect,” Phys. Rev. X 3, 041019 (2013).

Du, Y.

S. Zhang, S. Tang, J. Gao, X. Luo, W. Xia, and Y. Du, “Theoretical calculation of magneto-optical properties in cobalt nanotube array with hexagonal symmetry,” Solid State Commun. 170, 19–23 (2013).
[Crossref]

Eich, M.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is — and what is not — an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

Fan, S.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is — and what is not — an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

Fariña, D.

Fedyanin, A. A.

H. Uchida, Y. Mizutani, Y. Nakai, A. A. Fedyanin, and M. Inoue, “Garnet composite films with Au particles fabricated by repetitive formation for enhancement of Faraday effect,” J. Phys. D Appl. Phys. 44(6), 064014 (2011).
[Crossref]

Ferreiro-Vila, E.

D. Meneses-Rodríguez, E. Ferreiro-Vila, P. Prieto, J. Anguita, M. U. González, J. M. García-Martín, A. Cebollada, A. García-Martín, and G. Armelles, “Probing the Electromagnetic Field Distribution within a Metallic Nanodisk,” Small 7(23), 3317–3323 (2011).
[Crossref] [PubMed]

Fleischmann, M.

M. Fleischmann, P. J. Hendra, and A. J. McQuillan, “Raman spectra of pyridine adsorbed at a silver electrode,” Chem. Phys. Lett. 26(2), 163–166 (1974).
[Crossref]

Foster, F. G.

H. J. Williams, R. C. Sherwood, F. G. Foster, and E. M. Kelley, “Magnetic Writing on Thin Films of MnBi,” J. Appl. Phys. 28(10), 1181–1184 (1957).
[Crossref]

Freude, W.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is — and what is not — an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

Fritzsche, W.

K. Hering, D. Cialla, K. Ackermann, T. Dörfer, R. Möller, H. Schneidewind, R. Mattheis, W. Fritzsche, P. Rösch, and J. Popp, “SERS: a versatile tool in chemical and biochemical diagnostics,” Anal. Bioanal. Chem. 390(1), 113–124 (2008).
[Crossref] [PubMed]

Fujikawa, R.

H. Uchida, Y. Masuda, R. Fujikawa, A. V. Baryshev, and M. Inoue, “Large enhancement of Faraday rotation by localized surface plasmon resonance in Au nanoparticles embedded in Bi:YIG film,” J. Magn. Magn. Mater. 321(7), 843–845 (2009).
[Crossref]

Gao, J.

S. Zhang, S. Tang, J. Gao, X. Luo, W. Xia, and Y. Du, “Theoretical calculation of magneto-optical properties in cobalt nanotube array with hexagonal symmetry,” Solid State Commun. 170, 19–23 (2013).
[Crossref]

García-Martín, A.

G. Armelles, A. Cebollada, A. García-Martín, and M. U. González, “Magnetoplasmonics: combining magnetic and plasmonic functionalities,” Adv. Opt. Mater. 1(1), 10–35 (2013).
[Crossref]

G. Armelles, A. Cebollada, A. García-Martín, J. M. Montero-Moreno, M. Waleczek, and K. Nielsch, “Magneto-optical Properties of Core-Shell Magneto-plasmonic Au-CoxFe3 - xO4 Nanowires,” Langmuir 28(24), 9127–9130 (2012).
[Crossref] [PubMed]

B. Caballero, A. García-Martín, and J. C. Cuevas, “Generalized scattering-matrix approach for magneto-optics in periodically patterned multilayer systems,” Phys. Rev. B 85(24), 245103 (2012).
[Crossref]

D. Meneses-Rodríguez, E. Ferreiro-Vila, P. Prieto, J. Anguita, M. U. González, J. M. García-Martín, A. Cebollada, A. García-Martín, and G. Armelles, “Probing the Electromagnetic Field Distribution within a Metallic Nanodisk,” Small 7(23), 3317–3323 (2011).
[Crossref] [PubMed]

J. B. González-Díaz, A. García-Martín, J. M. García-Martín, A. Cebollada, G. Armelles, B. Sepúlveda, Y. Alaverdyan, and M. Käll, “Plasmonic Au/Co/Au Nanosandwiches with Enhanced Magneto-Optical Activity,” Small 4(2), 202–205 (2008).
[Crossref] [PubMed]

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(18), 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(15), 153402 (2007).
[Crossref]

García-Martín, J. M.

D. Meneses-Rodríguez, E. Ferreiro-Vila, P. Prieto, J. Anguita, M. U. González, J. M. García-Martín, A. Cebollada, A. García-Martín, and G. Armelles, “Probing the Electromagnetic Field Distribution within a Metallic Nanodisk,” Small 7(23), 3317–3323 (2011).
[Crossref] [PubMed]

J. B. González-Díaz, A. García-Martín, J. M. García-Martín, A. Cebollada, G. Armelles, B. Sepúlveda, Y. Alaverdyan, and M. Käll, “Plasmonic Au/Co/Au Nanosandwiches with Enhanced Magneto-Optical Activity,” Small 4(2), 202–205 (2008).
[Crossref] [PubMed]

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(15), 153402 (2007).
[Crossref]

Ger, T.-R.

H.-T. Huang, P.-J. Chen, T.-R. Ger, Y.-J. Chi, C.-W. Huang, K.-T. Liao, J.-Y. Lai, J.-Y. Chen, W.-Y. Peng, Q. Zhang, T.-F. Hsieh, W.-J. Sheu, and Z.-H. Wei, “Magneto-optical Kerr effect enhanced by surface plasmon resonance and its application on biological detection,” IEEE Trans. Magn. 50(1), 1001604 (2014).
[Crossref]

Giessen, H.

L. E. Kreilkamp, V. I. Belotelov, J. Y. Chin, S. Neutzner, D. Dregely, T. Wehlus, I. A. Akimov, M. Bayer, B. Stritzker, and H. Giessen, “Waveguide-plasmon polaritons enhance transverse magneto-optical Kerr effect,” Phys. Rev. X 3, 041019 (2013).

González, M. U.

G. Armelles, A. Cebollada, A. García-Martín, and M. U. González, “Magnetoplasmonics: combining magnetic and plasmonic functionalities,” Adv. Opt. Mater. 1(1), 10–35 (2013).
[Crossref]

D. Meneses-Rodríguez, E. Ferreiro-Vila, P. Prieto, J. Anguita, M. U. González, J. M. García-Martín, A. Cebollada, A. García-Martín, and G. Armelles, “Probing the Electromagnetic Field Distribution within a Metallic Nanodisk,” Small 7(23), 3317–3323 (2011).
[Crossref] [PubMed]

González-Díaz, J. B.

J. B. González-Díaz, A. García-Martín, J. M. García-Martín, A. Cebollada, G. Armelles, B. Sepúlveda, Y. Alaverdyan, and M. Käll, “Plasmonic Au/Co/Au Nanosandwiches with Enhanced Magneto-Optical Activity,” Small 4(2), 202–205 (2008).
[Crossref] [PubMed]

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(18), 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(15), 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(18), 2643–2647 (2007).
[Crossref]

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(3), 1237–1240 (2011).
[Crossref] [PubMed]

Hamidi, S. M.

S. M. Hamidi, M. A. Oskuei, S. Sadeghi, and M. M. Tehranchi, “Enhanced polar magneto-optical Kerr rotation in cobalt thin film incorporating Ag nanoparticles,” J. Supercond. Novel Magn. 27(3), 867–870 (2014).
[Crossref]

Hendra, P. J.

M. Fleischmann, P. J. Hendra, and A. J. McQuillan, “Raman spectra of pyridine adsorbed at a silver electrode,” Chem. Phys. Lett. 26(2), 163–166 (1974).
[Crossref]

Hering, K.

K. Hering, D. Cialla, K. Ackermann, T. Dörfer, R. Möller, H. Schneidewind, R. Mattheis, W. Fritzsche, P. Rösch, and J. Popp, “SERS: a versatile tool in chemical and biochemical diagnostics,” Anal. Bioanal. Chem. 390(1), 113–124 (2008).
[Crossref] [PubMed]

Hermann, C.

P. Bertrand, C. Hermann, G. Lampel, J. Peretti, and V. I. Safarov, “General analytical treatment of optics in layered structures: Application to magneto-optics,” Phys. Rev. B 64(23), 235421 (2001).
[Crossref]

Homola, J.

J. Homola, “Surface plasmon resonance sensors for detection of chemical and biological species,” Chem. Rev. 108(2), 462–493 (2008).
[Crossref] [PubMed]

Hsieh, T.-F.

H.-T. Huang, P.-J. Chen, T.-R. Ger, Y.-J. Chi, C.-W. Huang, K.-T. Liao, J.-Y. Lai, J.-Y. Chen, W.-Y. Peng, Q. Zhang, T.-F. Hsieh, W.-J. Sheu, and Z.-H. Wei, “Magneto-optical Kerr effect enhanced by surface plasmon resonance and its application on biological detection,” IEEE Trans. Magn. 50(1), 1001604 (2014).
[Crossref]

Huang, C.-W.

H.-T. Huang, P.-J. Chen, T.-R. Ger, Y.-J. Chi, C.-W. Huang, K.-T. Liao, J.-Y. Lai, J.-Y. Chen, W.-Y. Peng, Q. Zhang, T.-F. Hsieh, W.-J. Sheu, and Z.-H. Wei, “Magneto-optical Kerr effect enhanced by surface plasmon resonance and its application on biological detection,” IEEE Trans. Magn. 50(1), 1001604 (2014).
[Crossref]

Huang, H.-T.

H.-T. Huang, P.-J. Chen, T.-R. Ger, Y.-J. Chi, C.-W. Huang, K.-T. Liao, J.-Y. Lai, J.-Y. Chen, W.-Y. Peng, Q. Zhang, T.-F. Hsieh, W.-J. Sheu, and Z.-H. Wei, “Magneto-optical Kerr effect enhanced by surface plasmon resonance and its application on biological detection,” IEEE Trans. Magn. 50(1), 1001604 (2014).
[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(3), 1237–1240 (2011).
[Crossref] [PubMed]

Hui, P. M.

P. M. Hui and D. Stroud, “Theory of Faraday rotation by dilute suspensions of small particles,” Appl. Phys. Lett. 50(15), 950–952 (1987).
[Crossref]

Inoue, M.

H. Uchida, Y. Mizutani, Y. Nakai, A. A. Fedyanin, and M. Inoue, “Garnet composite films with Au particles fabricated by repetitive formation for enhancement of Faraday effect,” J. Phys. D Appl. Phys. 44(6), 064014 (2011).
[Crossref]

H. Uchida, Y. Masuda, R. Fujikawa, A. V. Baryshev, and M. Inoue, “Large enhancement of Faraday rotation by localized surface plasmon resonance in Au nanoparticles embedded in Bi:YIG film,” J. Magn. Magn. Mater. 321(7), 843–845 (2009).
[Crossref]

Jalas, D.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is — and what is not — an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

Joannopoulos, J. D.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is — and what is not — an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

Kalish, A. N.

V. I. Belotelov, D. A. Bykov, L. L. Doskolovich, A. N. Kalish, and A. K. Zvezdin, “Giant transversal Kerr effect in magneto-plasmonic heterostructures: The scattering-matrix method,” Sov. Phys. JETP 110(5), 816–824 (2010).
[Crossref]

Käll, M.

J. B. González-Díaz, A. García-Martín, J. M. García-Martín, A. Cebollada, G. Armelles, B. Sepúlveda, Y. Alaverdyan, and M. Käll, “Plasmonic Au/Co/Au Nanosandwiches with Enhanced Magneto-Optical Activity,” Small 4(2), 202–205 (2008).
[Crossref] [PubMed]

Kelley, E. M.

H. J. Williams, R. C. Sherwood, F. G. Foster, and E. M. Kelley, “Magnetic Writing on Thin Films of MnBi,” J. Appl. Phys. 28(10), 1181–1184 (1957).
[Crossref]

Kreilkamp, L. E.

L. E. Kreilkamp, V. I. Belotelov, J. Y. Chin, S. Neutzner, D. Dregely, T. Wehlus, I. A. Akimov, M. Bayer, B. Stritzker, and H. Giessen, “Waveguide-plasmon polaritons enhance transverse magneto-optical Kerr effect,” Phys. Rev. X 3, 041019 (2013).

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(15), 153402 (2007).
[Crossref]

Lai, J.-Y.

H.-T. Huang, P.-J. Chen, T.-R. Ger, Y.-J. Chi, C.-W. Huang, K.-T. Liao, J.-Y. Lai, J.-Y. Chen, W.-Y. Peng, Q. Zhang, T.-F. Hsieh, W.-J. Sheu, and Z.-H. Wei, “Magneto-optical Kerr effect enhanced by surface plasmon resonance and its application on biological detection,” IEEE Trans. Magn. 50(1), 1001604 (2014).
[Crossref]

Lampel, G.

P. Bertrand, C. Hermann, G. Lampel, J. Peretti, and V. I. Safarov, “General analytical treatment of optics in layered structures: Application to magneto-optics,” Phys. Rev. B 64(23), 235421 (2001).
[Crossref]

Lechuga, L. M.

Liao, K.-T.

H.-T. Huang, P.-J. Chen, T.-R. Ger, Y.-J. Chi, C.-W. Huang, K.-T. Liao, J.-Y. Lai, J.-Y. Chen, W.-Y. Peng, Q. Zhang, T.-F. Hsieh, W.-J. Sheu, and Z.-H. Wei, “Magneto-optical Kerr effect enhanced by surface plasmon resonance and its application on biological detection,” IEEE Trans. Magn. 50(1), 1001604 (2014).
[Crossref]

Liedberg, B.

C. Nylander, B. Liedberg, and T. Lind, “Gas detection by means of surface plasmon resonance,” Sens. Actuators 3, 79–88 (1982).
[Crossref]

Lind, T.

C. Nylander, B. Liedberg, and T. Lind, “Gas detection by means of surface plasmon resonance,” Sens. Actuators 3, 79–88 (1982).
[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(3), 1237–1240 (2011).
[Crossref] [PubMed]

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(15), 153402 (2007).
[Crossref]

Luo, X.

S. Zhang, S. Tang, J. Gao, X. Luo, W. Xia, and Y. Du, “Theoretical calculation of magneto-optical properties in cobalt nanotube array with hexagonal symmetry,” Solid State Commun. 170, 19–23 (2013).
[Crossref]

Masuda, Y.

H. Uchida, Y. Masuda, R. Fujikawa, A. V. Baryshev, and M. Inoue, “Large enhancement of Faraday rotation by localized surface plasmon resonance in Au nanoparticles embedded in Bi:YIG film,” J. Magn. Magn. Mater. 321(7), 843–845 (2009).
[Crossref]

Mattheis, R.

K. Hering, D. Cialla, K. Ackermann, T. Dörfer, R. Möller, H. Schneidewind, R. Mattheis, W. Fritzsche, P. Rösch, and J. Popp, “SERS: a versatile tool in chemical and biochemical diagnostics,” Anal. Bioanal. Chem. 390(1), 113–124 (2008).
[Crossref] [PubMed]

McQuillan, A. J.

M. Fleischmann, P. J. Hendra, and A. J. McQuillan, “Raman spectra of pyridine adsorbed at a silver electrode,” Chem. Phys. Lett. 26(2), 163–166 (1974).
[Crossref]

Melloni, A.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is — and what is not — an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

Meneses-Rodríguez, D.

D. Meneses-Rodríguez, E. Ferreiro-Vila, P. Prieto, J. Anguita, M. U. González, J. M. García-Martín, A. Cebollada, A. García-Martín, and G. Armelles, “Probing the Electromagnetic Field Distribution within a Metallic Nanodisk,” Small 7(23), 3317–3323 (2011).
[Crossref] [PubMed]

Mizumoto, T.

Y. Shoji, Y. Shirato, and T. Mizumoto, “Silicon Mach–Zehnder interferometer optical isolator having 8 nm bandwidth for over 20 dB isolation,” Jpn. J. Appl. Phys. 53(2), 022202 (2014).
[Crossref]

Y. Sobu, Y. Shoji, K. Sakurai, and T. Mizumoto, “GaInAsP/InP MZI waveguide optical isolator integrated with spot size converter,” Opt. Express 21(13), 15373–15381 (2013).
[Crossref] [PubMed]

Mizutani, Y.

H. Uchida, Y. Mizutani, Y. Nakai, A. A. Fedyanin, and M. Inoue, “Garnet composite films with Au particles fabricated by repetitive formation for enhancement of Faraday effect,” J. Phys. D Appl. Phys. 44(6), 064014 (2011).
[Crossref]

Möller, R.

K. Hering, D. Cialla, K. Ackermann, T. Dörfer, R. Möller, H. Schneidewind, R. Mattheis, W. Fritzsche, P. Rösch, and J. Popp, “SERS: a versatile tool in chemical and biochemical diagnostics,” Anal. Bioanal. Chem. 390(1), 113–124 (2008).
[Crossref] [PubMed]

Montero-Moreno, J. M.

G. Armelles, A. Cebollada, A. García-Martín, J. M. Montero-Moreno, M. Waleczek, and K. Nielsch, “Magneto-optical Properties of Core-Shell Magneto-plasmonic Au-CoxFe3 - xO4 Nanowires,” Langmuir 28(24), 9127–9130 (2012).
[Crossref] [PubMed]

Nakai, Y.

H. Uchida, Y. Mizutani, Y. Nakai, A. A. Fedyanin, and M. Inoue, “Garnet composite films with Au particles fabricated by repetitive formation for enhancement of Faraday effect,” J. Phys. D Appl. Phys. 44(6), 064014 (2011).
[Crossref]

Nakano, Y.

H. Shimizu and Y. Nakano, “Fabrication and characterization of an InGaAsP/InP active waveguide optical isolator with 14.7 dB/mm TE mode nonreciprocal attenuation,” J. Lightwave Technol. 24(1), 38–43 (2006).
[Crossref]

H. Shimizu and Y. Nakano, “First Demonstration of TE Mode Nonreciprocal Propagation in an InGaAsP/InP Active Waveguide for an Integratable Optical Isolator,” Jpn. J. Appl. Phys. 43(12A12A), L1561–L1563 (2004).
[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(18), 2643–2647 (2007).
[Crossref]

Neutzner, S.

L. E. Kreilkamp, V. I. Belotelov, J. Y. Chin, S. Neutzner, D. Dregely, T. Wehlus, I. A. Akimov, M. Bayer, B. Stritzker, and H. Giessen, “Waveguide-plasmon polaritons enhance transverse magneto-optical Kerr effect,” Phys. Rev. X 3, 041019 (2013).

Nielsch, K.

G. Armelles, A. Cebollada, A. García-Martín, J. M. Montero-Moreno, M. Waleczek, and K. Nielsch, “Magneto-optical Properties of Core-Shell Magneto-plasmonic Au-CoxFe3 - xO4 Nanowires,” Langmuir 28(24), 9127–9130 (2012).
[Crossref] [PubMed]

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(18), 2643–2647 (2007).
[Crossref]

Nylander, C.

C. Nylander, B. Liedberg, and T. Lind, “Gas detection by means of surface plasmon resonance,” Sens. Actuators 3, 79–88 (1982).
[Crossref]

Oskuei, M. A.

S. M. Hamidi, M. A. Oskuei, S. Sadeghi, and M. M. Tehranchi, “Enhanced polar magneto-optical Kerr rotation in cobalt thin film incorporating Ag nanoparticles,” J. Supercond. Novel Magn. 27(3), 867–870 (2014).
[Crossref]

Peng, W.-Y.

H.-T. Huang, P.-J. Chen, T.-R. Ger, Y.-J. Chi, C.-W. Huang, K.-T. Liao, J.-Y. Lai, J.-Y. Chen, W.-Y. Peng, Q. Zhang, T.-F. Hsieh, W.-J. Sheu, and Z.-H. Wei, “Magneto-optical Kerr effect enhanced by surface plasmon resonance and its application on biological detection,” IEEE Trans. Magn. 50(1), 1001604 (2014).
[Crossref]

Peretti, J.

P. Bertrand, C. Hermann, G. Lampel, J. Peretti, and V. I. Safarov, “General analytical treatment of optics in layered structures: Application to magneto-optics,” Phys. Rev. B 64(23), 235421 (2001).
[Crossref]

Petrov, A.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is — and what is not — an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

Popovic, M.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is — and what is not — an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

Popp, J.

K. Hering, D. Cialla, K. Ackermann, T. Dörfer, R. Möller, H. Schneidewind, R. Mattheis, W. Fritzsche, P. Rösch, and J. Popp, “SERS: a versatile tool in chemical and biochemical diagnostics,” Anal. Bioanal. Chem. 390(1), 113–124 (2008).
[Crossref] [PubMed]

Prieto, P.

D. Meneses-Rodríguez, E. Ferreiro-Vila, P. Prieto, J. Anguita, M. U. González, J. M. García-Martín, A. Cebollada, A. García-Martín, and G. Armelles, “Probing the Electromagnetic Field Distribution within a Metallic Nanodisk,” Small 7(23), 3317–3323 (2011).
[Crossref] [PubMed]

Regatos, D.

Renner, H.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is — and what is not — an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

Rösch, P.

K. Hering, D. Cialla, K. Ackermann, T. Dörfer, R. Möller, H. Schneidewind, R. Mattheis, W. Fritzsche, P. Rösch, and J. Popp, “SERS: a versatile tool in chemical and biochemical diagnostics,” Anal. Bioanal. Chem. 390(1), 113–124 (2008).
[Crossref] [PubMed]

Rumpf, R. C.

R. C. Rumpf, “Improved formulation of scattering matrices for semi-analytical methods that is consistent with convention,” Prog. Electromagn. Res. B 35, 241–261 (2011).
[Crossref]

Sadeghi, S.

S. M. Hamidi, M. A. Oskuei, S. Sadeghi, and M. M. Tehranchi, “Enhanced polar magneto-optical Kerr rotation in cobalt thin film incorporating Ag nanoparticles,” J. Supercond. Novel Magn. 27(3), 867–870 (2014).
[Crossref]

Safarov, V. I.

P. Bertrand, C. Hermann, G. Lampel, J. Peretti, and V. I. Safarov, “General analytical treatment of optics in layered structures: Application to magneto-optics,” Phys. Rev. B 64(23), 235421 (2001).
[Crossref]

Saito, H.

V. Zayets, H. Saito, S. Yuasa, and K. Ando, “Enhancement of the transverse non-reciprocal magneto-optical effect,” J. Appl. Phys. 111(2), 023103 (2012).
[Crossref]

V. Zayets, H. Saito, K. Ando, and S. Yuasa, “Optical isolator utilizing surface plasmons,” Materials (Basel) 5(5), 857–871 (2012).
[Crossref]

Sakurai, K.

Schneidewind, H.

K. Hering, D. Cialla, K. Ackermann, T. Dörfer, R. Möller, H. Schneidewind, R. Mattheis, W. Fritzsche, P. Rösch, and J. Popp, “SERS: a versatile tool in chemical and biochemical diagnostics,” Anal. Bioanal. Chem. 390(1), 113–124 (2008).
[Crossref] [PubMed]

Sepúlveda, B.

Sherwood, R. C.

H. J. Williams, R. C. Sherwood, F. G. Foster, and E. M. Kelley, “Magnetic Writing on Thin Films of MnBi,” J. Appl. Phys. 28(10), 1181–1184 (1957).
[Crossref]

Sheu, W.-J.

H.-T. Huang, P.-J. Chen, T.-R. Ger, Y.-J. Chi, C.-W. Huang, K.-T. Liao, J.-Y. Lai, J.-Y. Chen, W.-Y. Peng, Q. Zhang, T.-F. Hsieh, W.-J. Sheu, and Z.-H. Wei, “Magneto-optical Kerr effect enhanced by surface plasmon resonance and its application on biological detection,” IEEE Trans. Magn. 50(1), 1001604 (2014).
[Crossref]

Shimizu, H.

H. Shimizu and Y. Nakano, “Fabrication and characterization of an InGaAsP/InP active waveguide optical isolator with 14.7 dB/mm TE mode nonreciprocal attenuation,” J. Lightwave Technol. 24(1), 38–43 (2006).
[Crossref]

H. Shimizu and Y. Nakano, “First Demonstration of TE Mode Nonreciprocal Propagation in an InGaAsP/InP Active Waveguide for an Integratable Optical Isolator,” Jpn. J. Appl. Phys. 43(12A12A), L1561–L1563 (2004).
[Crossref]

Shintaku, T.

T. Shintaku, “Integrated optical isolator based on efficient nonreciprocal radiation mode conversion,” Appl. Phys. Lett. 73(14), 1946–1948 (1998).
[Crossref]

T. Shintaku and T. Uno, “Optical waveguide isolator based on nonreciprocal radiation,” J. Appl. Phys. 76(12), 8155–8159 (1994).
[Crossref]

Shirato, Y.

Y. Shoji, Y. Shirato, and T. Mizumoto, “Silicon Mach–Zehnder interferometer optical isolator having 8 nm bandwidth for over 20 dB isolation,” Jpn. J. Appl. Phys. 53(2), 022202 (2014).
[Crossref]

Shoji, Y.

Y. Shoji, Y. Shirato, and T. Mizumoto, “Silicon Mach–Zehnder interferometer optical isolator having 8 nm bandwidth for over 20 dB isolation,” Jpn. J. Appl. Phys. 53(2), 022202 (2014).
[Crossref]

Y. Sobu, Y. Shoji, K. Sakurai, and T. Mizumoto, “GaInAsP/InP MZI waveguide optical isolator integrated with spot size converter,” Opt. Express 21(13), 15373–15381 (2013).
[Crossref] [PubMed]

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(15), 153402 (2007).
[Crossref]

Smith, D. Y.

Sobu, Y.

Stritzker, B.

L. E. Kreilkamp, V. I. Belotelov, J. Y. Chin, S. Neutzner, D. Dregely, T. Wehlus, I. A. Akimov, M. Bayer, B. Stritzker, and H. Giessen, “Waveguide-plasmon polaritons enhance transverse magneto-optical Kerr effect,” Phys. Rev. X 3, 041019 (2013).

Stroud, D.

P. M. Hui and D. Stroud, “Theory of Faraday rotation by dilute suspensions of small particles,” Appl. Phys. Lett. 50(15), 950–952 (1987).
[Crossref]

Tang, S.

S. Zhang, S. Tang, J. Gao, X. Luo, W. Xia, and Y. Du, “Theoretical calculation of magneto-optical properties in cobalt nanotube array with hexagonal symmetry,” Solid State Commun. 170, 19–23 (2013).
[Crossref]

Tehranchi, M. M.

S. M. Hamidi, M. A. Oskuei, S. Sadeghi, and M. M. Tehranchi, “Enhanced polar magneto-optical Kerr rotation in cobalt thin film incorporating Ag nanoparticles,” J. Supercond. Novel Magn. 27(3), 867–870 (2014).
[Crossref]

Uchida, H.

H. Uchida, Y. Mizutani, Y. Nakai, A. A. Fedyanin, and M. Inoue, “Garnet composite films with Au particles fabricated by repetitive formation for enhancement of Faraday effect,” J. Phys. D Appl. Phys. 44(6), 064014 (2011).
[Crossref]

H. Uchida, Y. Masuda, R. Fujikawa, A. V. Baryshev, and M. Inoue, “Large enhancement of Faraday rotation by localized surface plasmon resonance in Au nanoparticles embedded in Bi:YIG film,” J. Magn. Magn. Mater. 321(7), 843–845 (2009).
[Crossref]

Uno, T.

T. Shintaku and T. Uno, “Optical waveguide isolator based on nonreciprocal radiation,” J. Appl. Phys. 76(12), 8155–8159 (1994).
[Crossref]

Vanwolleghem, M.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is — and what is not — an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[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(18), 2643–2647 (2007).
[Crossref]

Waleczek, M.

G. Armelles, A. Cebollada, A. García-Martín, J. M. Montero-Moreno, M. Waleczek, and K. Nielsch, “Magneto-optical Properties of Core-Shell Magneto-plasmonic Au-CoxFe3 - xO4 Nanowires,” Langmuir 28(24), 9127–9130 (2012).
[Crossref] [PubMed]

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(3), 1237–1240 (2011).
[Crossref] [PubMed]

Wehlus, T.

L. E. Kreilkamp, V. I. Belotelov, J. Y. Chin, S. Neutzner, D. Dregely, T. Wehlus, I. A. Akimov, M. Bayer, B. Stritzker, and H. Giessen, “Waveguide-plasmon polaritons enhance transverse magneto-optical Kerr effect,” Phys. Rev. X 3, 041019 (2013).

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(18), 2643–2647 (2007).
[Crossref]

Wei, Z.-H.

H.-T. Huang, P.-J. Chen, T.-R. Ger, Y.-J. Chi, C.-W. Huang, K.-T. Liao, J.-Y. Lai, J.-Y. Chen, W.-Y. Peng, Q. Zhang, T.-F. Hsieh, W.-J. Sheu, and Z.-H. Wei, “Magneto-optical Kerr effect enhanced by surface plasmon resonance and its application on biological detection,” IEEE Trans. Magn. 50(1), 1001604 (2014).
[Crossref]

Williams, H. J.

H. J. Williams, R. C. Sherwood, F. G. Foster, and E. M. Kelley, “Magnetic Writing on Thin Films of MnBi,” J. Appl. Phys. 28(10), 1181–1184 (1957).
[Crossref]

Xia, W.

S. Zhang, S. Tang, J. Gao, X. Luo, W. Xia, and Y. Du, “Theoretical calculation of magneto-optical properties in cobalt nanotube array with hexagonal symmetry,” Solid State Commun. 170, 19–23 (2013).
[Crossref]

Yu, Z.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is — and what is not — an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

Yuasa, S.

V. Zayets, H. Saito, K. Ando, and S. Yuasa, “Optical isolator utilizing surface plasmons,” Materials (Basel) 5(5), 857–871 (2012).
[Crossref]

V. Zayets, H. Saito, S. Yuasa, and K. Ando, “Enhancement of the transverse non-reciprocal magneto-optical effect,” J. Appl. Phys. 111(2), 023103 (2012).
[Crossref]

Zayets, V.

V. Zayets, H. Saito, S. Yuasa, and K. Ando, “Enhancement of the transverse non-reciprocal magneto-optical effect,” J. Appl. Phys. 111(2), 023103 (2012).
[Crossref]

V. Zayets, H. Saito, K. Ando, and S. Yuasa, “Optical isolator utilizing surface plasmons,” Materials (Basel) 5(5), 857–871 (2012).
[Crossref]

Zhang, Q.

H.-T. Huang, P.-J. Chen, T.-R. Ger, Y.-J. Chi, C.-W. Huang, K.-T. Liao, J.-Y. Lai, J.-Y. Chen, W.-Y. Peng, Q. Zhang, T.-F. Hsieh, W.-J. Sheu, and Z.-H. Wei, “Magneto-optical Kerr effect enhanced by surface plasmon resonance and its application on biological detection,” IEEE Trans. Magn. 50(1), 1001604 (2014).
[Crossref]

Zhang, S.

S. Zhang, S. Tang, J. Gao, X. Luo, W. Xia, and Y. Du, “Theoretical calculation of magneto-optical properties in cobalt nanotube array with hexagonal symmetry,” Solid State Commun. 170, 19–23 (2013).
[Crossref]

Zvezdin, A. K.

V. I. Belotelov, D. A. Bykov, L. L. Doskolovich, A. N. Kalish, and A. K. Zvezdin, “Giant transversal Kerr effect in magneto-plasmonic heterostructures: The scattering-matrix method,” Sov. Phys. JETP 110(5), 816–824 (2010).
[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(18), 2643–2647 (2007).
[Crossref]

Adv. Opt. Mater. (1)

G. Armelles, A. Cebollada, A. García-Martín, and M. U. González, “Magnetoplasmonics: combining magnetic and plasmonic functionalities,” Adv. Opt. Mater. 1(1), 10–35 (2013).
[Crossref]

Anal. Bioanal. Chem. (1)

K. Hering, D. Cialla, K. Ackermann, T. Dörfer, R. Möller, H. Schneidewind, R. Mattheis, W. Fritzsche, P. Rösch, and J. Popp, “SERS: a versatile tool in chemical and biochemical diagnostics,” Anal. Bioanal. Chem. 390(1), 113–124 (2008).
[Crossref] [PubMed]

Appl. Phys. Lett. (2)

P. M. Hui and D. Stroud, “Theory of Faraday rotation by dilute suspensions of small particles,” Appl. Phys. Lett. 50(15), 950–952 (1987).
[Crossref]

T. Shintaku, “Integrated optical isolator based on efficient nonreciprocal radiation mode conversion,” Appl. Phys. Lett. 73(14), 1946–1948 (1998).
[Crossref]

Chem. Phys. Lett. (1)

M. Fleischmann, P. J. Hendra, and A. J. McQuillan, “Raman spectra of pyridine adsorbed at a silver electrode,” Chem. Phys. Lett. 26(2), 163–166 (1974).
[Crossref]

Chem. Rev. (1)

J. Homola, “Surface plasmon resonance sensors for detection of chemical and biological species,” Chem. Rev. 108(2), 462–493 (2008).
[Crossref] [PubMed]

IEEE Trans. Magn. (1)

H.-T. Huang, P.-J. Chen, T.-R. Ger, Y.-J. Chi, C.-W. Huang, K.-T. Liao, J.-Y. Lai, J.-Y. Chen, W.-Y. Peng, Q. Zhang, T.-F. Hsieh, W.-J. Sheu, and Z.-H. Wei, “Magneto-optical Kerr effect enhanced by surface plasmon resonance and its application on biological detection,” IEEE Trans. Magn. 50(1), 1001604 (2014).
[Crossref]

J. Appl. Phys. (3)

H. J. Williams, R. C. Sherwood, F. G. Foster, and E. M. Kelley, “Magnetic Writing on Thin Films of MnBi,” J. Appl. Phys. 28(10), 1181–1184 (1957).
[Crossref]

T. Shintaku and T. Uno, “Optical waveguide isolator based on nonreciprocal radiation,” J. Appl. Phys. 76(12), 8155–8159 (1994).
[Crossref]

V. Zayets, H. Saito, S. Yuasa, and K. Ando, “Enhancement of the transverse non-reciprocal magneto-optical effect,” J. Appl. Phys. 111(2), 023103 (2012).
[Crossref]

J. Lightwave Technol. (1)

J. Magn. Magn. Mater. (1)

H. Uchida, Y. Masuda, R. Fujikawa, A. V. Baryshev, and M. Inoue, “Large enhancement of Faraday rotation by localized surface plasmon resonance in Au nanoparticles embedded in Bi:YIG film,” J. Magn. Magn. Mater. 321(7), 843–845 (2009).
[Crossref]

J. Opt. Soc. Am. (1)

J. Phys. D Appl. Phys. (1)

H. Uchida, Y. Mizutani, Y. Nakai, A. A. Fedyanin, and M. Inoue, “Garnet composite films with Au particles fabricated by repetitive formation for enhancement of Faraday effect,” J. Phys. D Appl. Phys. 44(6), 064014 (2011).
[Crossref]

J. Supercond. Novel Magn. (1)

S. M. Hamidi, M. A. Oskuei, S. Sadeghi, and M. M. Tehranchi, “Enhanced polar magneto-optical Kerr rotation in cobalt thin film incorporating Ag nanoparticles,” J. Supercond. Novel Magn. 27(3), 867–870 (2014).
[Crossref]

Jpn. J. Appl. Phys. (2)

Y. Shoji, Y. Shirato, and T. Mizumoto, “Silicon Mach–Zehnder interferometer optical isolator having 8 nm bandwidth for over 20 dB isolation,” Jpn. J. Appl. Phys. 53(2), 022202 (2014).
[Crossref]

H. Shimizu and Y. Nakano, “First Demonstration of TE Mode Nonreciprocal Propagation in an InGaAsP/InP Active Waveguide for an Integratable Optical Isolator,” Jpn. J. Appl. Phys. 43(12A12A), L1561–L1563 (2004).
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Langmuir (1)

G. Armelles, A. Cebollada, A. García-Martín, J. M. Montero-Moreno, M. Waleczek, and K. Nielsch, “Magneto-optical Properties of Core-Shell Magneto-plasmonic Au-CoxFe3 - xO4 Nanowires,” Langmuir 28(24), 9127–9130 (2012).
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Materials (Basel) (1)

V. Zayets, H. Saito, K. Ando, and S. Yuasa, “Optical isolator utilizing surface plasmons,” Materials (Basel) 5(5), 857–871 (2012).
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Nano Lett. (1)

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(3), 1237–1240 (2011).
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Nat. Photonics (1)

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is — and what is not — an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
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Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. B (3)

B. Caballero, A. García-Martín, and J. C. Cuevas, “Generalized scattering-matrix approach for magneto-optics in periodically patterned multilayer systems,” Phys. Rev. B 85(24), 245103 (2012).
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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(15), 153402 (2007).
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EM Lab - University of Texas at El Paso, “News 2012 | EM Lab,” http://emlab.utep.edu/ee5390cem.htm

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Figures (14)

Fig. 1
Fig. 1 A trilayer structure consisting of double-layer dielectrics and a ferromagnetic metal for nonreciprocal plasmonic propagation. The yellow curve represents the distribution of the SPPs.
Fig. 2
Fig. 2 A schematic diagram of the Al2O3/SiO2/Fe trilayer deposited on a SiO2 substrate. The incident light, defined by orthogonal unit vectors ÂTM and ÂTE, comes from the Al2O3 side with p-polarization (ϕ = 0, CTE = 0) and an arbitrary incident angle, θ. Arrows M indicate the positive magnetization directions of the PMOKE and TMOKE.
Fig. 3
Fig. 3 Reflectance, R, and change in reflectance, ΔR, of the TMOKE as a function of incident angle, θ, at SiO2 thicknesses, t, of (a) 645 nm and (b) 661 nm. Enlarged views depict the reflectance in decibel units. Red, blue, and black curves denote positive, negative, and no magnetization, respectively. The inset in (a) shows the case of s-polarization.
Fig. 4
Fig. 4 SiO2 thickness dependence of (a) maximum ΔR (black) and ΔR/R (green) and (b) minimum reflectance, R, ( + M in red, −M in blue) of the TMOKE. The values of (a) and (b) are obtained at incident angles shown in (c) and (d), respectively.
Fig. 5
Fig. 5 (a) Real part and (b) imaginary part of the effective refractive index, Neff, of the SPPs with the TMOKE as a function of the SiO2 thickness. Red, blue, and black curves denote positive, negative, and no magnetization, respectively.
Fig. 6
Fig. 6 Optical field distribution of TM mode in the Al2O3/SiO2/Fe trilayer waveguide with t = ∞, 1645, 1145, and 645 nm. The curves are normalized at 0 nm.
Fig. 7
Fig. 7 Reflectance, R, and change in reflectance, ΔR, of the PMOKE as a function of incident angle, θ, at t = 652 nm. The enlarged view depicts the reflectance in decibel units. The curve for positive magnetization (red) is perfectly overlapped with that for negative magnetization (blue). The black curve denotes the no magnetization case.
Fig. 8
Fig. 8 The Kerr rotation (red), ϕK, and ellipticity (blue), ηK, at t = 652 nm as a function of the incident angle with positive magnetization, + M. Insets show the polarization normalized by the maximum norm at each angle indicated by arrows.
Fig. 9
Fig. 9 SiO2 thickness dependence of (a) the maximum Kerr rotation, |ϕK| (red), ellipticity, |ηK| (blue), and (b) the minimum reflectance, R (black). The values of (a) and (b) are obtained at incident angles shown in (c) and (d), respectively.
Fig. 10
Fig. 10 Incident angle dependence at t = 645, 652 and 660 nm: (a) The absolute amplitude of the p-polarization, Ep (red), and induced s-polarization, Es (blue). (b) The normalized phase shift of each argument, arg(Ep) (red) and arg(Es)(blue), and phase difference, Δφ (black). (c) The Kerr rotation (red) and ellipticity (blue).
Fig. 11
Fig. 11 Reflectance, R (positive (red), negative (blue) and no (black) magnetizations), and change in reflectance, ΔR (broken curve), of The TMOKE as a function of the incident angle. The thickness of the interface layer is assumed to be (a) tint = 0 nm, (b) 1 nm and (c) 3 nm with the SiO2 layer of t = 661 − tint/2 nm and the Fe layer of 300 − tint/2 nm.
Fig. 12
Fig. 12 The Kerr (a) rotation and (b) ellipticity as a function of the incident angle. The thickness of the interface layer is assumed to be tint = 0, 1, 3 and 5 nm as written beside the curves, and the SiO2 layer is set to t = 652 − tint/2 nm and the Fe layer of 300 − tint/2 nm.
Fig. 13
Fig. 13 Reflectance, R (positive (red), negative (blue) and no (black) magnetizations), and change in reflectance, ΔR (broken curve), of The TMOKE as a function of the incident angle. The deviation angle from p-polarization is assumed to be (a) tint = 0°, (b) 1° and (c) 3° with the SiO2 layer of t = 661 nm.
Fig. 14
Fig. 14 The Kerr (a) rotation and (b) ellipticity as a function of the incident angle. The deviation angle from p-polarization is assumed to be 0° up to 10°.as written beside the curves, and the SiO2 layer is set to t = 652 nm.

Equations (39)

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ε r =( n 2 0 γ 0 n 2 0 γ 0 n 2 ),
ε r =( n 2 γ 0 γ n 2 0 0 0 n 2 ).
ΔR=R( M )R( +M ) [ dB ],
ΔR R = R( M )R( +M ) [ % ] ( R( M )+R( +M ) [ % ] ) /2 ,
ϕ ˜ K = r sp r pp
| r sp | E s ( z ) Δ ε M   E p ( z )dz,
'×E= μ r H ˜
'× H ˜ = ε r E
z' ψ=Ωψ
Ω=( i( n x ε 31 ε 33 + n x μ 23 μ 33 ) i n x ( ε 32 ε 33 μ 23 μ 33 ) n x n y ε 33 + μ 21 μ 23 μ 31 μ 33 n x 2 ε 33 + μ 22 μ 23 μ 32 μ 33 i n y ( ε 31 ε 33 μ 13 μ 33 ) i( n y ε 32 ε 33 + n x μ 13 μ 33 ) n y 2 ε 33 μ 11 + μ 13 μ 31 μ 33 n x n y ε 33 μ 21 + μ 23 μ 32 μ 33 ε 21 ε 23 ε 31 ε 33 + n x n y μ 33 ε 22 ε 23 ε 32 ε 33 n x 2 μ 33 i( n y ε 23 ε 33 + n x μ 31 μ 33 ) i n x ( ε 23 ε 33 μ 32 μ 33 ) ε 11 + ε 13 ε 31 ε 33 + n y 2 μ 33 ε 12 + ε 13 ε 32 ε 33 n x n y μ 33 i n y ( ε 13 ε 33 μ 31 μ 33 ) i( n x ε 13 ε 33 + n y μ 32 μ 33 ) )
ψ= [ E x E y H ˜ x H ˜ y ] T
ψ( z )=W e λ z W 1 ψ( 0 )
ψ( z' )= W i e λ i z' c i =( W Ei + W Ei W Hi + W Hi )( e λ i z' 0 0 e λ i z' )( c i + c i ).
( W Ei + W Ei W Hi + W Hi ) 1 ( W Ei1 + W Ei1 W Hi1 + W Hi1 )( c i1 + c i1 ) =( e λ i k 0 L i 0 0 e λ i k 0 L i ) ( W Ei + W Ei W Hi + W Hi ) 1 ( W Ei+1 + W Ei+1 W Hi+1 + W Hi+1 )( c i+1 + c i+1 )
( W Ei + ' W Ei ' W Hi + ' W Hi ' )( c i1 + c i1 )=( e λ i k 0 L i 0 0 e λ i k 0 L i )( W Ei + ' W Ei ' W Hi + ' W Hi ' )( c i+1 + c i+1 )
( W Ei + ' W Ei ' W Hi + ' W Hi ' )= ( W Ei + W Ei W Hi + W Hi ) 1 ( W Ei±1 + W Ei±1 W Hi±1 + W Hi±1 ).
( c i1 c i+1 + )=( S 11 i S 12 i S 21 i S 22 i )( c i1 + c i+1 )
S 11 i = ( A 1 i ) 1 ( ( W Hi ' ) 1 λ i W Hi + ' ( W Ei + ' ) 1 λ i W Ei + ' ( W Hi ' ) 1 W Hi + ' )
S 12 i = ( A 1 i ) 1 ( ( W Hi ' ) 1 λ i W Hi ' ( W Hi ' ) 1 λ i W Hi ' ( W Ei + ' ) 1 W Ei ' )
S 21 i = ( A 2 i ) 1 ( ( W Ei + ' ) 1 λ i W Ei ' ( W Hi ' ) 1 W Hi + '+ ( W Ei + ' ) 1 λ i W Ei + ' )
S 22 i = ( A 2 i ) 1 ( ( W Ei + ' ) 1 W Ei '+ ( W Ei + ' ) 1 λ i W Ei ' ( W Hi ' ) 1 λ i W Hi ' )
A 1 i =I ( W Hi ' ) 1 λ i W Hi + ' ( W Ei + ' ) 1 λ i W Ei '
A 2 i =I ( W Ei + ' ) 1 λ i W Ei ' ( W Hi ' ) 1 λ i W Hi + '
S A S B =( S 11 a + S 12 a ( I S 11 b S 22 a ) 1 S 11 b S 21 a S 12 a ( I S 11 b S 22 a ) 1 S 12 b S 21 b ( I S 22 a S 11 b ) 1 S 21 a S 21 b ( I S 22 a S 11 b ) 1 S 22 a S 12 b + S 22 b )
S A/B =( S 11 a/b S 12 a/b S 21 a/b S 22 a/b ).
( c ref c 1 + )=( S 11 ref S 12 ref S 21 ref S 22 ref )( c inc + c 1 ),
( c ref c trn + )=( S 11 global S 12 global S 21 global S 22 global )( c inc + c trn =0 ).
ψ( 0 )=( W Eref + W Eref W Href + W Href )( c inc + c ref ) ( E x ref ( 0 ) E y ref ( 0 ) H ˜ x ref ( 0 ) H ˜ y ref ( 0 ) )=( W Eref c ref W Href c ref )=( W Eref S 11 global c inc + W Href S 11 global c inc + )
ψ( L total )=( W Etrn + W Etrn W Htrn + W Htrn )( c trn + c trn =0 ) ( E x trn ( L total ) E y trn ( L total ) H ˜ x trn ( L total ) H ˜ y trn ( L total ) )=( W Etrn + c trn + W Htrn + c trn + )=( W Etrn + S 21 global c inc + W Htrn + S 21 global c inc + )
E z ref/trn = i( H ˜ y ref/trn n x + H ˜ x ref/trn n y ) E x ref/trn ε 31 ref/trn E y ref/trn ε 32 ref/trn ε 33 ref/trn H ˜ z ref/trn = i( E y ref/trn n x + E x ref/trn n y ) H ˜ x ref/trn μ 31 ref/trn H ˜ y ref/trn μ 32 ref/trn μ 33 ref/trn
c inc + = ( W Eref + ) 1 ( E x inc ( 0 ) E y inc ( 0 ) ).
R= ( E ref E inc ) 2 .
[ xy ] T = [ ( E xr +i E xi ) e iωt ( E yr +i E yi ) e iωt ] T = [ E xr cos( ωt ) E xi sin( ωt ) E yr cos( ωt ) E yi sin( ωt ) ] T
cos 2 ( ωt )+ sin 2 ( ωt ) = ( E yi 2 + E yr 2 ) x 2 ( E xr E yi E xi E yr ) 2 2 ( E xi E yi + E xr E yr )xy ( E xr E yi E xi E yr ) 2 + ( E xi 2 + E xr 2 ) y 2 ( E xr E yi E xi E yr ) 2 =1
X T QX=1 Q=( E yi 2 + E yr 2 ( E xr E yi E xi E yr ) 2 E xi E yi + E xr E yr ( E xr E yi E xi E yr ) 2 E xi E yi + E xr E yr ( E xr E yi E xi E yr ) 2 E xi 2 + E xr 2 ( E xr E yi E xi E yr ) 2 ) X= [ xy ] T
X ' T BX'=1( X ' T P 1 )Q( PX' )=1 ( PX' ) T Q( PX' )=1 X=PX'
P=( cos( φ K ) sin( φ K ) sin( φ K ) cos( φ K ) )
φ K =arctan[ 2( E ' xi E yi +E ' xr E yr ) E ' xi 2 +E ' xr 2 E yi 2 E yr 2 + 4 ( E ' xr E yi E ' xi E yr ) 2 + ( E yi 2 + E yr 2 +E ' xi 2 +E ' xr 2 ) 2 ]
η K =arctan[ E yi 2 + E yr 2 +E ' xi 2 +E ' xr 2 4 ( E ' xr E yi E ' xi E yr ) 2 + ( E yi 2 + E yr 2 +E ' xi 2 +E ' xr 2 ) 2 E yi 2 + E yr 2 +E ' xi 2 +E ' xr 2 + 4 ( E ' xr E yi E ' xi E yr ) 2 + ( E yi 2 + E yr 2 +E ' xi 2 +E ' xr 2 ) 2 ]

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