Abstract

Nonlinear magneto-plasmonics (NMP) describes systems where nonlinear optics, magnetics and plasmonics are all involved. In such systems, nonlinear magneto-optical Kerr effect (nonlinear MOKE) plays an important role as a characterization method, and Surface Plasmons (SPs) work as catalyst to induce many new effects. Magnetization-induced second-harmonic generation (MSHG) is the major nonlinear magneto-optical process involved. The new effects include enhanced MSHG, controlled and enhanced magnetic contrast, etc. Nanostructures such as thin films, nanoparticles, nanogratings, and nanoarrays are critical for the excitation of SPs, which makes NMP an interdisciplinary research field in nanoscience and nanotechnology. In this review article, we organize recent work in this field into two categories: surface plasmon polaritons (SPPs) representing propagating surface plasmons, and localized surface plasmons (LSPs), also called particle plasmons. We review the structures, experiments, findings, and the applications of NMP from various groups.

© 2015 Optical Society of America

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References

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  60. V. K. Valev, N. Smisdom, A. V. Silhanek, B. De Clercq, W. Gillijns, M. Ameloot, V. V. Moshchalkov, and T. Verbiest, “Plasmonic Ratchet Wheels: Switching Circular Dichroism by Arranging Chiral Nanostructures,” Nano Lett. 9(11), 3945–3948 (2009).
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    [Crossref]

2015 (2)

I. Razdolski, S. Parchenko, A. Stupakiewicz, S. Semin, A. Stognij, A. Maziewski, A. Kirilyuk, and T. Rasing, “Second-harmonic generation from a magnetic buried interface enhanced by an interplay of surface plasma resonances,” ACS Photonics 2(1), 20–26 (2015).
[Crossref]

V. L. Krutyanskiy, A. L. Chekhov, V. A. Ketsko, A. I. Stognij, and T. V. Murzina, “Giant nonlinear magneto-optical response of magnetoplasmonic crystals,” Phys. Rev. B 91(12), 121411 (2015).
[Crossref]

2014 (2)

2013 (5)

Y. Fan, K. J. Smith, G. Lüpke, A. T. Hanbicki, R. Goswami, C. H. Li, H. B. Zhao, and B. T. Jonker, “Exchange bias of the interface spin system at the Fe/MgO interface,” Nat. Nanotechnol. 8(6), 438–444 (2013).
[Crossref] [PubMed]

G. Armelles, A. Cebollada, A. Garcia-Martin, and M. U. Gonzalez, “Magnetoplasmonics: Combining Magnetic and Plasmonic Functionalities,” Adv. Opt. Mater. 1(1), 10–35 (2013).
[Crossref]

V. I. Belotelov, L. E. Kreilkamp, I. A. Akimov, A. N. Kalish, D. A. Bykov, S. Kasture, V. J. Yallapragada, A. Venu Gopal, A. M. Grishin, S. I. Khartsev, M. Nur-E-Alam, M. Vasiliev, L. L. Doskolovich, D. R. Yakovlev, K. Alameh, A. K. Zvezdin, and M. Bayer, “Plasmon-mediated magneto-optical transparency,” Nat. Commun. 4, 2128 (2013).
[Crossref] [PubMed]

I. Razdolski, D. G. Gheorghe, E. Melander, B. Hjorvarsson, P. Patoka, A. V. Kimel, A. Kirilyuk, E. T. Papaioannou, and T. Rasing, “Nonlocal nonlinear magneto-optical response of a magnetoplasmonic crystal,” Phys. Rev. B 88(7), 075436 (2013).
[Crossref]

W. Zheng, A. T. Hanbicki, B. T. Jonker, and G. Lüpke, “Surface Plasmon-enhanced Transverse Magnetic Second-Harmonic Generation,” Opt. Express 21(23), 28842–28848 (2013).
[Crossref] [PubMed]

2012 (2)

2011 (4)

M. I. Stockman, “Nanoplasmonics: past, present, and glimpse into future,” Opt. Express 19(22), 22029–22106 (2011).
[PubMed]

E. Petryayeva and U. J. Krull, “Localized surface plasmon resonance: Nanostructures, bioassays and biosensing - A review,” Anal. Chim. Acta 706(1), 8–24 (2011).
[Crossref] [PubMed]

A. V. Kosobukin, “On the theory of near-field magneto-optical microscopy via plasmonic modes of nanowire,” Tech. Phys. Lett. 37(4), 387–390 (2011).
[Crossref]

V. K. Valev, A. V. Silhanek, W. Gillijns, Y. Jeyaram, H. Paddubrouskaya, A. Volodin, C. G. Biris, N. C. Panoiu, B. De Clercq, M. Ameloot, O. A. Aktsipetrov, V. V. Moshchalkov, and T. Verbiest, “Plasmons reveal the direction of magnetization in nickel nanostructures,” ACS Nano 5(1), 91–96 (2011).
[Crossref] [PubMed]

2010 (6)

V. K. Valev, A. V. Silhanek, N. Verellen, W. Gillijns, P. Van Dorpe, O. A. Aktsipetrov, G. A. E. Vandenbosch, V. V. Moshchalkov, and T. Verbiest, “Asymmetric Optical Second-Harmonic Generation from Chiral G-Shaped Gold Nanostructures,” Phys. Rev. Lett. 104(12), 127401 (2010).
[Crossref] [PubMed]

J. Pistora, M. Lesnak, and O. Vlasin, “Surface plasmon resonance sensor with Magneto-Optical thin film,” Acta Electrotechnica et Informatica 10, 19–21 (2010).

D. Regatos, D. Farina, A. Calle, A. Cebollada, B. Sepulveda, G. Armelles, and L. M. Lechuga, “Au/Fe/Au multilayer transducers for magneto-optic surface plasmon resonance sensing,” J. Appl. Phys. 108(5), 054502 (2010).
[Crossref]

V. V. Temnov, G. Armelles, U. Woggon, D. Guzatov, A. Cebollada, A. Garcia-Martin, J. Garcia-Martin, T. Thomays, A. Leitenstorfers, and R. Bratschitschs, “Active magneto-plasmonics in hybrid metal–ferromagnet structures,” Nat. Photonics 4(2), 107–111 (2010).
[Crossref]

A. Berrier, R. Ulbricht, M. Bonn, and J. G. Rivas, “Ultrafast active control of Localized surface plasmon resonances in silicon bowtie antennas,” Opt. Express 18(22), 23226–23235 (2010).
[Crossref] [PubMed]

J. Renger, R. Quidant, N. van Hulst, and L. Novotny, “Surface-enhanced nonlinear four-wave mixing,” Phys. Rev. Lett. 104(4), 046803 (2010).
[Crossref] [PubMed]

2009 (4)

B. Sepúlveda, P. C. Angelome, L. M. Lechuga, and L. M. Liz-Marzan, “LSRP-based nanobiosensors,” Nano Today 4(3), 244–251 (2009).
[Crossref]

V. K. Valev, N. Smisdom, A. V. Silhanek, B. De Clercq, W. Gillijns, M. Ameloot, V. V. Moshchalkov, and T. Verbiest, “Plasmonic Ratchet Wheels: Switching Circular Dichroism by Arranging Chiral Nanostructures,” Nano Lett. 9(11), 3945–3948 (2009).
[Crossref] [PubMed]

S. Zhang, Y. S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative Refractive Index in Chiral Metamaterials,” Phys. Rev. Lett. 102(2), 023901 (2009).
[Crossref] [PubMed]

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with Negative Index Due to Chirality,” Phys. Rev. B 79(3), 035407 (2009).
[Crossref]

2008 (2)

Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal,” Phys. Rev. Lett. 100(2), 023902 (2008).
[Crossref] [PubMed]

S. Palomba and L. Novotny, “Nonlinear excitation of surface plasmon polaritons by four-wave mixing,” Phys. Rev. Lett. 101(5), 056802 (2008).
[Crossref] [PubMed]

2007 (3)

D. Pacifici, H. J. Lezec, and H. A. Atwater, “All-optical modulation by plasmonic excitation of CdSe quantum dots,” Nat. Photonics 1(7), 402–406 (2007).
[Crossref]

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70(1), 1–87 (2007).
[Crossref]

V. K. Valev, A. Kirilyuk, F. Dalla Longa, J. T. Kohlhepp, B. Koopmans, and Th. Rasing, “Observation of periodic oscillations in magnetization-induced second harmonic generation at the Mn/Co interface,” Phys. Rev. B 75(1), 012401 (2007).
[Crossref]

2006 (2)

2005 (3)

2004 (3)

J. B. Pendry, “A Chiral Route to Negative Refraction,” Science 306(5700), 1353–1355 (2004).
[Crossref] [PubMed]

A. V. Krasavin, K. F. MacDonald, N. I. Zheludev, and A. V. Zayats, “High-contrast modulation of light with light by control of surface plasmon polariton wave coupling,” Appl. Phys. Lett. 85(16), 3369–3371 (2004).
[Crossref]

M. I. Stockman, D. J. Bergman, C. Anceau, S. Brasselet, and J. Zyss, “Enhanced second-harmonic generation by metal surfaces with nanoscale roughness: nanoscale dephasing, depolarization, and correlations,” Phys. Rev. Lett. 92(5), 057402 (2004).
[Crossref] [PubMed]

2003 (2)

S. I. Bozhevolnyi, J. Beermann, and V. Coello, “Direct observation of localized second-harmonic enhancement in random metal nanostructures,” Phys. Rev. Lett. 90(19), 197403 (2003).
[Crossref] [PubMed]

C. Anceau, S. Brasselet, J. Zyss, and P. Gadenne, “Local second-harmonic generation enhancement on gold nanostructures probed by two-photon microscopy,” Opt. Lett. 28(9), 713–715 (2003).
[Crossref] [PubMed]

2002 (2)

D. M. Newman, M. L. Wears, R. J. Matelon, and D. Mchugh, “Non-linear optics and magneto-optics on nano-structured interfaces,” Appl. Phys. B 74(7-8), 719–722 (2002).
[Crossref]

D. M. Newman, M. L. Wears, and R. J. Matelon, “Plasmon enhanced magneto-optic behaviour in the linear and non-linear optical fields,” J. Magn. Magn. Mater. 242-245, 980–983 (2002).
[Crossref]

2001 (3)

K. Sato, A. Kodama, M. Miyamoto, A. V. Petukhov, K. Takanashi, S. Mitani, H. Fujimori, A. Kirilyuk, and T. Rasing, “Anisotropic magnetization-induced second harmonic generation in Fe/Au superlattices,” Phys. Rev. B 64(18), 184427 (2001).
[Crossref]

T. V. Murzina, T. V. Misuryaev, A. F. Kravets, J. Gudde, D. Schuhmacher, G. Marowsky, A. A. Nikulin, and O. A. Aktsipetrov, “Nonlinear magneto-optical Kerr effect and plasmon-asisted SHG in magnetic nanomaterials exhibiting giant magnetoresistance,” Surf. Sci. 482–485, 1101–1106 (2001).

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(23), 235422 (2001).
[Crossref]

2000 (2)

G. Tessier and P. Beauvillain, “Non linear optics and magneto-optics in ultrathin metallic films,” Appl. Surf. Sci. 164(1-4), 175–185 (2000).
[Crossref]

A. Kirilyuk, G. M. H. Knippels, A. F. G. Meer, S. Renard, Th. Rasing, I. R. Heskamp, and J. C. Lodder, “Observation of strong magnetic effects in visible-infrared sum frequency generation from magnetic structures,” Phys. Rev. B 62(2), 783–786 (2000).
[Crossref]

1999 (1)

G. Tessier, C. Malouin, P. Georges, A. Brun, D. Renard, V. V. Pavlov, P. Meyer, J. Ferre, and P. Beauvillain, “Magnetization-induced second-harmonic generation enhanced by surface plasmons in ultrathin Au/Co/Au metallic films,” Appl. Phys. B 68(3), 545–548 (1999).
[Crossref]

1996 (1)

1995 (2)

R. P. Cowburn, S. J. Gray, J. Ferre, J. A. C. Bland, and J. Miltat, “Magnetic switching and in-plane uniaxial anisotropy in ultrathin Ag/Fe/Ag(100) epitaxial films,” Appl. Phys. Lett. 78, 7210 (1995).

C. Daboo, R. J. Hicken, E. Gu, M. Gester, S. J. Gray, D. E. P. Eley, E. Ahmad, J. A. Bland, R. Ploessl, and J. N. Chapman, “Anisotropy and orientational dependence of magnetization reversal processes in epitaxial ferromagnetic thin films,” Phys. Rev. B Condens. Matter 51(22), 15964–15973 (1995).
[Crossref] [PubMed]

1994 (4)

E. Schwarzberg, G. Berkovic, and G. Marowsky, “Nonlinear interferometry and phase measurements for surface second-harmonic generation in a dispersive geometry,” Appl. Phys., A Mater. Sci. Process. 59(6), 631–637 (1994).
[Crossref]

M. Fiebig, D. Fröhlich, B. B. Krichevtsov, and R. V. Pisarev, “Second harmonic generation and magnetic-dipole-electric-dipole interference in antiferromagnetic Cr2O3,” Phys. Rev. Lett. 73(15), 2127–2130 (1994).
[Crossref] [PubMed]

C. Daboo, R. J. Hicken, D. E. P. Eley, M. Gester, S. J. Gray, A. J. R. Ives, and J. A. C. Bland, “Magnetization reversal processes in epitaxial Fe/GaAs(001) films,” Appl. Phys. Lett. 75, 5586 (1994).

V. I. Safarov, V. A. Kosobukin, C. Hermann, G. Lampel, J. Peretti, and C. Marlière, “Magneto-optical effects enhanced by surface plasmons in metallic multilayer films,” Phys. Rev. Lett. 73(26), 3584–3587 (1994).
[Crossref] [PubMed]

1974 (1)

H. J. Simon, D. E. Mitchell, and J. G. Watson, “Optical second-harmonic generation with surface plasmons in silver films,” Phys. Rev. Lett. 33(26), 1531–1534 (1974).
[Crossref]

1973 (1)

R. F. Pearson, “Application of magneto-optic effects in magnetic materials,” Contemp. Phys. 14(3), 201–211 (1973).
[Crossref]

1965 (1)

R. K. Chang, J. Ducuing, and N. Bloembergen, “Relative phase measurement between fundamental and second-harmonic light,” Phys. Rev. Lett. 15(1), 6–8 (1965).
[Crossref]

Ahmad, E.

C. Daboo, R. J. Hicken, E. Gu, M. Gester, S. J. Gray, D. E. P. Eley, E. Ahmad, J. A. Bland, R. Ploessl, and J. N. Chapman, “Anisotropy and orientational dependence of magnetization reversal processes in epitaxial ferromagnetic thin films,” Phys. Rev. B Condens. Matter 51(22), 15964–15973 (1995).
[Crossref] [PubMed]

Akimov, I. A.

V. I. Belotelov, L. E. Kreilkamp, I. A. Akimov, A. N. Kalish, D. A. Bykov, S. Kasture, V. J. Yallapragada, A. Venu Gopal, A. M. Grishin, S. I. Khartsev, M. Nur-E-Alam, M. Vasiliev, L. L. Doskolovich, D. R. Yakovlev, K. Alameh, A. K. Zvezdin, and M. Bayer, “Plasmon-mediated magneto-optical transparency,” Nat. Commun. 4, 2128 (2013).
[Crossref] [PubMed]

Aktsipetrov, O.

Aktsipetrov, O. A.

T. V. Murzina, I. A. Kolmychek, J. Wouters, T. Verbiest, and O. A. Aktsipetrov, “Plasmon-assisted enhancement of third-order nonlinear optical effects in core(shell) nanoparticles,” J. Opt. Soc. Am. B 29(1), 138–143 (2012).
[Crossref]

V. K. Valev, A. V. Silhanek, W. Gillijns, Y. Jeyaram, H. Paddubrouskaya, A. Volodin, C. G. Biris, N. C. Panoiu, B. De Clercq, M. Ameloot, O. A. Aktsipetrov, V. V. Moshchalkov, and T. Verbiest, “Plasmons reveal the direction of magnetization in nickel nanostructures,” ACS Nano 5(1), 91–96 (2011).
[Crossref] [PubMed]

V. K. Valev, A. V. Silhanek, N. Verellen, W. Gillijns, P. Van Dorpe, O. A. Aktsipetrov, G. A. E. Vandenbosch, V. V. Moshchalkov, and T. Verbiest, “Asymmetric Optical Second-Harmonic Generation from Chiral G-Shaped Gold Nanostructures,” Phys. Rev. Lett. 104(12), 127401 (2010).
[Crossref] [PubMed]

E. M. Kim, S. S. Elovikov, T. V. Murzina, A. A. Nikulin, O. A. Aktsipetrov, M. A. Bader, and G. Marowsky, “Surface-enhanced optical third-harmonic generation in Ag island films,” Phys. Rev. Lett. 95(22), 227402 (2005).
[Crossref] [PubMed]

T. V. Murzina, T. V. Misuryaev, A. F. Kravets, J. Gudde, D. Schuhmacher, G. Marowsky, A. A. Nikulin, and O. A. Aktsipetrov, “Nonlinear magneto-optical Kerr effect and plasmon-asisted SHG in magnetic nanomaterials exhibiting giant magnetoresistance,” Surf. Sci. 482–485, 1101–1106 (2001).

Alameh, K.

V. I. Belotelov, L. E. Kreilkamp, I. A. Akimov, A. N. Kalish, D. A. Bykov, S. Kasture, V. J. Yallapragada, A. Venu Gopal, A. M. Grishin, S. I. Khartsev, M. Nur-E-Alam, M. Vasiliev, L. L. Doskolovich, D. R. Yakovlev, K. Alameh, A. K. Zvezdin, and M. Bayer, “Plasmon-mediated magneto-optical transparency,” Nat. Commun. 4, 2128 (2013).
[Crossref] [PubMed]

Ameloot, M.

V. K. Valev, A. V. Silhanek, W. Gillijns, Y. Jeyaram, H. Paddubrouskaya, A. Volodin, C. G. Biris, N. C. Panoiu, B. De Clercq, M. Ameloot, O. A. Aktsipetrov, V. V. Moshchalkov, and T. Verbiest, “Plasmons reveal the direction of magnetization in nickel nanostructures,” ACS Nano 5(1), 91–96 (2011).
[Crossref] [PubMed]

V. K. Valev, N. Smisdom, A. V. Silhanek, B. De Clercq, W. Gillijns, M. Ameloot, V. V. Moshchalkov, and T. Verbiest, “Plasmonic Ratchet Wheels: Switching Circular Dichroism by Arranging Chiral Nanostructures,” Nano Lett. 9(11), 3945–3948 (2009).
[Crossref] [PubMed]

Anceau, C.

M. I. Stockman, D. J. Bergman, C. Anceau, S. Brasselet, and J. Zyss, “Enhanced second-harmonic generation by metal surfaces with nanoscale roughness: nanoscale dephasing, depolarization, and correlations,” Phys. Rev. Lett. 92(5), 057402 (2004).
[Crossref] [PubMed]

C. Anceau, S. Brasselet, J. Zyss, and P. Gadenne, “Local second-harmonic generation enhancement on gold nanostructures probed by two-photon microscopy,” Opt. Lett. 28(9), 713–715 (2003).
[Crossref] [PubMed]

Angelome, P. C.

B. Sepúlveda, P. C. Angelome, L. M. Lechuga, and L. M. Liz-Marzan, “LSRP-based nanobiosensors,” Nano Today 4(3), 244–251 (2009).
[Crossref]

Armelles, G.

G. Armelles, A. Cebollada, A. Garcia-Martin, and M. U. Gonzalez, “Magnetoplasmonics: Combining Magnetic and Plasmonic Functionalities,” Adv. Opt. Mater. 1(1), 10–35 (2013).
[Crossref]

D. Regatos, D. Farina, A. Calle, A. Cebollada, B. Sepulveda, G. Armelles, and L. M. Lechuga, “Au/Fe/Au multilayer transducers for magneto-optic surface plasmon resonance sensing,” J. Appl. Phys. 108(5), 054502 (2010).
[Crossref]

V. V. Temnov, G. Armelles, U. Woggon, D. Guzatov, A. Cebollada, A. Garcia-Martin, J. Garcia-Martin, T. Thomays, A. Leitenstorfers, and R. Bratschitschs, “Active magneto-plasmonics in hybrid metal–ferromagnet structures,” Nat. Photonics 4(2), 107–111 (2010).
[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]

B. Sepulveda, L. M. Lechuga, and G. Armelles, “Magnetooptic effects in surface-plasmon-plaritons slab waveguides,” J. Lightwave Technol. 24(2), 945–955 (2006).
[Crossref]

Atwater, H. A.

D. Pacifici, H. J. Lezec, and H. A. Atwater, “All-optical modulation by plasmonic excitation of CdSe quantum dots,” Nat. Photonics 1(7), 402–406 (2007).
[Crossref]

Bader, M. A.

E. M. Kim, S. S. Elovikov, T. V. Murzina, A. A. Nikulin, O. A. Aktsipetrov, M. A. Bader, and G. Marowsky, “Surface-enhanced optical third-harmonic generation in Ag island films,” Phys. Rev. Lett. 95(22), 227402 (2005).
[Crossref] [PubMed]

Bayer, M.

V. I. Belotelov, L. E. Kreilkamp, I. A. Akimov, A. N. Kalish, D. A. Bykov, S. Kasture, V. J. Yallapragada, A. Venu Gopal, A. M. Grishin, S. I. Khartsev, M. Nur-E-Alam, M. Vasiliev, L. L. Doskolovich, D. R. Yakovlev, K. Alameh, A. K. Zvezdin, and M. Bayer, “Plasmon-mediated magneto-optical transparency,” Nat. Commun. 4, 2128 (2013).
[Crossref] [PubMed]

Beauvillain, P.

G. Tessier and P. Beauvillain, “Non linear optics and magneto-optics in ultrathin metallic films,” Appl. Surf. Sci. 164(1-4), 175–185 (2000).
[Crossref]

G. Tessier, C. Malouin, P. Georges, A. Brun, D. Renard, V. V. Pavlov, P. Meyer, J. Ferre, and P. Beauvillain, “Magnetization-induced second-harmonic generation enhanced by surface plasmons in ultrathin Au/Co/Au metallic films,” Appl. Phys. B 68(3), 545–548 (1999).
[Crossref]

Beermann, J.

S. I. Bozhevolnyi, J. Beermann, and V. Coello, “Direct observation of localized second-harmonic enhancement in random metal nanostructures,” Phys. Rev. Lett. 90(19), 197403 (2003).
[Crossref] [PubMed]

Belotelov, V. I.

V. I. Belotelov, L. E. Kreilkamp, I. A. Akimov, A. N. Kalish, D. A. Bykov, S. Kasture, V. J. Yallapragada, A. Venu Gopal, A. M. Grishin, S. I. Khartsev, M. Nur-E-Alam, M. Vasiliev, L. L. Doskolovich, D. R. Yakovlev, K. Alameh, A. K. Zvezdin, and M. Bayer, “Plasmon-mediated magneto-optical transparency,” Nat. Commun. 4, 2128 (2013).
[Crossref] [PubMed]

Bergman, D. J.

M. I. Stockman, D. J. Bergman, C. Anceau, S. Brasselet, and J. Zyss, “Enhanced second-harmonic generation by metal surfaces with nanoscale roughness: nanoscale dephasing, depolarization, and correlations,” Phys. Rev. Lett. 92(5), 057402 (2004).
[Crossref] [PubMed]

Berkovic, G.

E. Schwarzberg, G. Berkovic, and G. Marowsky, “Nonlinear interferometry and phase measurements for surface second-harmonic generation in a dispersive geometry,” Appl. Phys., A Mater. Sci. Process. 59(6), 631–637 (1994).
[Crossref]

Berrier, A.

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(23), 235422 (2001).
[Crossref]

Biris, C. G.

V. K. Valev, A. V. Silhanek, W. Gillijns, Y. Jeyaram, H. Paddubrouskaya, A. Volodin, C. G. Biris, N. C. Panoiu, B. De Clercq, M. Ameloot, O. A. Aktsipetrov, V. V. Moshchalkov, and T. Verbiest, “Plasmons reveal the direction of magnetization in nickel nanostructures,” ACS Nano 5(1), 91–96 (2011).
[Crossref] [PubMed]

Bland, J. A.

C. Daboo, R. J. Hicken, E. Gu, M. Gester, S. J. Gray, D. E. P. Eley, E. Ahmad, J. A. Bland, R. Ploessl, and J. N. Chapman, “Anisotropy and orientational dependence of magnetization reversal processes in epitaxial ferromagnetic thin films,” Phys. Rev. B Condens. Matter 51(22), 15964–15973 (1995).
[Crossref] [PubMed]

Bland, J. A. C.

R. P. Cowburn, S. J. Gray, J. Ferre, J. A. C. Bland, and J. Miltat, “Magnetic switching and in-plane uniaxial anisotropy in ultrathin Ag/Fe/Ag(100) epitaxial films,” Appl. Phys. Lett. 78, 7210 (1995).

C. Daboo, R. J. Hicken, D. E. P. Eley, M. Gester, S. J. Gray, A. J. R. Ives, and J. A. C. Bland, “Magnetization reversal processes in epitaxial Fe/GaAs(001) films,” Appl. Phys. Lett. 75, 5586 (1994).

Bloembergen, N.

R. K. Chang, J. Ducuing, and N. Bloembergen, “Relative phase measurement between fundamental and second-harmonic light,” Phys. Rev. Lett. 15(1), 6–8 (1965).
[Crossref]

Bonn, M.

Bozhevolnyi, S. I.

S. I. Bozhevolnyi, J. Beermann, and V. Coello, “Direct observation of localized second-harmonic enhancement in random metal nanostructures,” Phys. Rev. Lett. 90(19), 197403 (2003).
[Crossref] [PubMed]

Brasselet, S.

M. I. Stockman, D. J. Bergman, C. Anceau, S. Brasselet, and J. Zyss, “Enhanced second-harmonic generation by metal surfaces with nanoscale roughness: nanoscale dephasing, depolarization, and correlations,” Phys. Rev. Lett. 92(5), 057402 (2004).
[Crossref] [PubMed]

C. Anceau, S. Brasselet, J. Zyss, and P. Gadenne, “Local second-harmonic generation enhancement on gold nanostructures probed by two-photon microscopy,” Opt. Lett. 28(9), 713–715 (2003).
[Crossref] [PubMed]

Bratschitschs, R.

V. V. Temnov, G. Armelles, U. Woggon, D. Guzatov, A. Cebollada, A. Garcia-Martin, J. Garcia-Martin, T. Thomays, A. Leitenstorfers, and R. Bratschitschs, “Active magneto-plasmonics in hybrid metal–ferromagnet structures,” Nat. Photonics 4(2), 107–111 (2010).
[Crossref]

Brun, A.

G. Tessier, C. Malouin, P. Georges, A. Brun, D. Renard, V. V. Pavlov, P. Meyer, J. Ferre, and P. Beauvillain, “Magnetization-induced second-harmonic generation enhanced by surface plasmons in ultrathin Au/Co/Au metallic films,” Appl. Phys. B 68(3), 545–548 (1999).
[Crossref]

Bykov, D. A.

V. I. Belotelov, L. E. Kreilkamp, I. A. Akimov, A. N. Kalish, D. A. Bykov, S. Kasture, V. J. Yallapragada, A. Venu Gopal, A. M. Grishin, S. I. Khartsev, M. Nur-E-Alam, M. Vasiliev, L. L. Doskolovich, D. R. Yakovlev, K. Alameh, A. K. Zvezdin, and M. Bayer, “Plasmon-mediated magneto-optical transparency,” Nat. Commun. 4, 2128 (2013).
[Crossref] [PubMed]

Calle, A.

D. Regatos, D. Farina, A. Calle, A. Cebollada, B. Sepulveda, G. Armelles, and L. M. Lechuga, “Au/Fe/Au multilayer transducers for magneto-optic surface plasmon resonance sensing,” J. Appl. Phys. 108(5), 054502 (2010).
[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]

Cebollada, A.

G. Armelles, A. Cebollada, A. Garcia-Martin, and M. U. Gonzalez, “Magnetoplasmonics: Combining Magnetic and Plasmonic Functionalities,” Adv. Opt. Mater. 1(1), 10–35 (2013).
[Crossref]

D. Regatos, D. Farina, A. Calle, A. Cebollada, B. Sepulveda, G. Armelles, and L. M. Lechuga, “Au/Fe/Au multilayer transducers for magneto-optic surface plasmon resonance sensing,” J. Appl. Phys. 108(5), 054502 (2010).
[Crossref]

V. V. Temnov, G. Armelles, U. Woggon, D. Guzatov, A. Cebollada, A. Garcia-Martin, J. Garcia-Martin, T. Thomays, A. Leitenstorfers, and R. Bratschitschs, “Active magneto-plasmonics in hybrid metal–ferromagnet structures,” Nat. Photonics 4(2), 107–111 (2010).
[Crossref]

Chang, R. K.

R. K. Chang, J. Ducuing, and N. Bloembergen, “Relative phase measurement between fundamental and second-harmonic light,” Phys. Rev. Lett. 15(1), 6–8 (1965).
[Crossref]

Chapman, J. N.

C. Daboo, R. J. Hicken, E. Gu, M. Gester, S. J. Gray, D. E. P. Eley, E. Ahmad, J. A. Bland, R. Ploessl, and J. N. Chapman, “Anisotropy and orientational dependence of magnetization reversal processes in epitaxial ferromagnetic thin films,” Phys. Rev. B Condens. Matter 51(22), 15964–15973 (1995).
[Crossref] [PubMed]

Chekhov, A. L.

V. L. Krutyanskiy, A. L. Chekhov, V. A. Ketsko, A. I. Stognij, and T. V. Murzina, “Giant nonlinear magneto-optical response of magnetoplasmonic crystals,” Phys. Rev. B 91(12), 121411 (2015).
[Crossref]

A. L. Chekhov, V. L. Krutyanskiy, A. N. Shaimanov, A. I. Stognij, and T. V. Murzina, “Wide tunability of magnetoplasmonic crystals due to excitation of multiple waveguide and plasmon modes,” Opt. Express 22(15), 17762–17768 (2014).
[Crossref] [PubMed]

Chulkov, E. V.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70(1), 1–87 (2007).
[Crossref]

Coello, V.

S. I. Bozhevolnyi, J. Beermann, and V. Coello, “Direct observation of localized second-harmonic enhancement in random metal nanostructures,” Phys. Rev. Lett. 90(19), 197403 (2003).
[Crossref] [PubMed]

Cowburn, R. P.

R. P. Cowburn, S. J. Gray, J. Ferre, J. A. C. Bland, and J. Miltat, “Magnetic switching and in-plane uniaxial anisotropy in ultrathin Ag/Fe/Ag(100) epitaxial films,” Appl. Phys. Lett. 78, 7210 (1995).

Daboo, C.

C. Daboo, R. J. Hicken, E. Gu, M. Gester, S. J. Gray, D. E. P. Eley, E. Ahmad, J. A. Bland, R. Ploessl, and J. N. Chapman, “Anisotropy and orientational dependence of magnetization reversal processes in epitaxial ferromagnetic thin films,” Phys. Rev. B Condens. Matter 51(22), 15964–15973 (1995).
[Crossref] [PubMed]

C. Daboo, R. J. Hicken, D. E. P. Eley, M. Gester, S. J. Gray, A. J. R. Ives, and J. A. C. Bland, “Magnetization reversal processes in epitaxial Fe/GaAs(001) films,” Appl. Phys. Lett. 75, 5586 (1994).

Dalla Longa, F.

V. K. Valev, A. Kirilyuk, F. Dalla Longa, J. T. Kohlhepp, B. Koopmans, and Th. Rasing, “Observation of periodic oscillations in magnetization-induced second harmonic generation at the Mn/Co interface,” Phys. Rev. B 75(1), 012401 (2007).
[Crossref]

De Clercq, B.

V. K. Valev, A. V. Silhanek, W. Gillijns, Y. Jeyaram, H. Paddubrouskaya, A. Volodin, C. G. Biris, N. C. Panoiu, B. De Clercq, M. Ameloot, O. A. Aktsipetrov, V. V. Moshchalkov, and T. Verbiest, “Plasmons reveal the direction of magnetization in nickel nanostructures,” ACS Nano 5(1), 91–96 (2011).
[Crossref] [PubMed]

V. K. Valev, N. Smisdom, A. V. Silhanek, B. De Clercq, W. Gillijns, M. Ameloot, V. V. Moshchalkov, and T. Verbiest, “Plasmonic Ratchet Wheels: Switching Circular Dichroism by Arranging Chiral Nanostructures,” Nano Lett. 9(11), 3945–3948 (2009).
[Crossref] [PubMed]

Dolgova, T. V.

Dong, J.

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with Negative Index Due to Chirality,” Phys. Rev. B 79(3), 035407 (2009).
[Crossref]

Doskolovich, L. L.

V. I. Belotelov, L. E. Kreilkamp, I. A. Akimov, A. N. Kalish, D. A. Bykov, S. Kasture, V. J. Yallapragada, A. Venu Gopal, A. M. Grishin, S. I. Khartsev, M. Nur-E-Alam, M. Vasiliev, L. L. Doskolovich, D. R. Yakovlev, K. Alameh, A. K. Zvezdin, and M. Bayer, “Plasmon-mediated magneto-optical transparency,” Nat. Commun. 4, 2128 (2013).
[Crossref] [PubMed]

Ducuing, J.

R. K. Chang, J. Ducuing, and N. Bloembergen, “Relative phase measurement between fundamental and second-harmonic light,” Phys. Rev. Lett. 15(1), 6–8 (1965).
[Crossref]

Echenique, P. M.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70(1), 1–87 (2007).
[Crossref]

Eley, D. E. P.

C. Daboo, R. J. Hicken, E. Gu, M. Gester, S. J. Gray, D. E. P. Eley, E. Ahmad, J. A. Bland, R. Ploessl, and J. N. Chapman, “Anisotropy and orientational dependence of magnetization reversal processes in epitaxial ferromagnetic thin films,” Phys. Rev. B Condens. Matter 51(22), 15964–15973 (1995).
[Crossref] [PubMed]

C. Daboo, R. J. Hicken, D. E. P. Eley, M. Gester, S. J. Gray, A. J. R. Ives, and J. A. C. Bland, “Magnetization reversal processes in epitaxial Fe/GaAs(001) films,” Appl. Phys. Lett. 75, 5586 (1994).

Elovikov, S. S.

E. M. Kim, S. S. Elovikov, T. V. Murzina, A. A. Nikulin, O. A. Aktsipetrov, M. A. Bader, and G. Marowsky, “Surface-enhanced optical third-harmonic generation in Ag island films,” Phys. Rev. Lett. 95(22), 227402 (2005).
[Crossref] [PubMed]

Fan, S.

Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal,” Phys. Rev. Lett. 100(2), 023902 (2008).
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Y. Fan, K. J. Smith, G. Lüpke, A. T. Hanbicki, R. Goswami, C. H. Li, H. B. Zhao, and B. T. Jonker, “Exchange bias of the interface spin system at the Fe/MgO interface,” Nat. Nanotechnol. 8(6), 438–444 (2013).
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D. Regatos, D. Farina, A. Calle, A. Cebollada, B. Sepulveda, G. Armelles, and L. M. Lechuga, “Au/Fe/Au multilayer transducers for magneto-optic surface plasmon resonance sensing,” J. Appl. Phys. 108(5), 054502 (2010).
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E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with Negative Index Due to Chirality,” Phys. Rev. B 79(3), 035407 (2009).
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Ferre, J.

G. Tessier, C. Malouin, P. Georges, A. Brun, D. Renard, V. V. Pavlov, P. Meyer, J. Ferre, and P. Beauvillain, “Magnetization-induced second-harmonic generation enhanced by surface plasmons in ultrathin Au/Co/Au metallic films,” Appl. Phys. B 68(3), 545–548 (1999).
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R. P. Cowburn, S. J. Gray, J. Ferre, J. A. C. Bland, and J. Miltat, “Magnetic switching and in-plane uniaxial anisotropy in ultrathin Ag/Fe/Ag(100) epitaxial films,” Appl. Phys. Lett. 78, 7210 (1995).

Fiebig, M.

M. Fiebig, D. Fröhlich, B. B. Krichevtsov, and R. V. Pisarev, “Second harmonic generation and magnetic-dipole-electric-dipole interference in antiferromagnetic Cr2O3,” Phys. Rev. Lett. 73(15), 2127–2130 (1994).
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M. Fiebig, D. Fröhlich, B. B. Krichevtsov, and R. V. Pisarev, “Second harmonic generation and magnetic-dipole-electric-dipole interference in antiferromagnetic Cr2O3,” Phys. Rev. Lett. 73(15), 2127–2130 (1994).
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K. Sato, A. Kodama, M. Miyamoto, A. V. Petukhov, K. Takanashi, S. Mitani, H. Fujimori, A. Kirilyuk, and T. Rasing, “Anisotropic magnetization-induced second harmonic generation in Fe/Au superlattices,” Phys. Rev. B 64(18), 184427 (2001).
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Garcia-Martin, A.

G. Armelles, A. Cebollada, A. Garcia-Martin, and M. U. Gonzalez, “Magnetoplasmonics: Combining Magnetic and Plasmonic Functionalities,” Adv. Opt. Mater. 1(1), 10–35 (2013).
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V. V. Temnov, G. Armelles, U. Woggon, D. Guzatov, A. Cebollada, A. Garcia-Martin, J. Garcia-Martin, T. Thomays, A. Leitenstorfers, and R. Bratschitschs, “Active magneto-plasmonics in hybrid metal–ferromagnet structures,” Nat. Photonics 4(2), 107–111 (2010).
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V. V. Temnov, G. Armelles, U. Woggon, D. Guzatov, A. Cebollada, A. Garcia-Martin, J. Garcia-Martin, T. Thomays, A. Leitenstorfers, and R. Bratschitschs, “Active magneto-plasmonics in hybrid metal–ferromagnet structures,” Nat. Photonics 4(2), 107–111 (2010).
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G. Tessier, C. Malouin, P. Georges, A. Brun, D. Renard, V. V. Pavlov, P. Meyer, J. Ferre, and P. Beauvillain, “Magnetization-induced second-harmonic generation enhanced by surface plasmons in ultrathin Au/Co/Au metallic films,” Appl. Phys. B 68(3), 545–548 (1999).
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C. Daboo, R. J. Hicken, E. Gu, M. Gester, S. J. Gray, D. E. P. Eley, E. Ahmad, J. A. Bland, R. Ploessl, and J. N. Chapman, “Anisotropy and orientational dependence of magnetization reversal processes in epitaxial ferromagnetic thin films,” Phys. Rev. B Condens. Matter 51(22), 15964–15973 (1995).
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C. Daboo, R. J. Hicken, D. E. P. Eley, M. Gester, S. J. Gray, A. J. R. Ives, and J. A. C. Bland, “Magnetization reversal processes in epitaxial Fe/GaAs(001) films,” Appl. Phys. Lett. 75, 5586 (1994).

Gheorghe, D. G.

I. Razdolski, D. G. Gheorghe, E. Melander, B. Hjorvarsson, P. Patoka, A. V. Kimel, A. Kirilyuk, E. T. Papaioannou, and T. Rasing, “Nonlocal nonlinear magneto-optical response of a magnetoplasmonic crystal,” Phys. Rev. B 88(7), 075436 (2013).
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Gillijns, W.

V. K. Valev, A. V. Silhanek, W. Gillijns, Y. Jeyaram, H. Paddubrouskaya, A. Volodin, C. G. Biris, N. C. Panoiu, B. De Clercq, M. Ameloot, O. A. Aktsipetrov, V. V. Moshchalkov, and T. Verbiest, “Plasmons reveal the direction of magnetization in nickel nanostructures,” ACS Nano 5(1), 91–96 (2011).
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V. K. Valev, A. V. Silhanek, N. Verellen, W. Gillijns, P. Van Dorpe, O. A. Aktsipetrov, G. A. E. Vandenbosch, V. V. Moshchalkov, and T. Verbiest, “Asymmetric Optical Second-Harmonic Generation from Chiral G-Shaped Gold Nanostructures,” Phys. Rev. Lett. 104(12), 127401 (2010).
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V. K. Valev, N. Smisdom, A. V. Silhanek, B. De Clercq, W. Gillijns, M. Ameloot, V. V. Moshchalkov, and T. Verbiest, “Plasmonic Ratchet Wheels: Switching Circular Dichroism by Arranging Chiral Nanostructures,” Nano Lett. 9(11), 3945–3948 (2009).
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Gonzalez, M. U.

G. Armelles, A. Cebollada, A. Garcia-Martin, and M. U. Gonzalez, “Magnetoplasmonics: Combining Magnetic and Plasmonic Functionalities,” Adv. Opt. Mater. 1(1), 10–35 (2013).
[Crossref]

Goswami, R.

Y. Fan, K. J. Smith, G. Lüpke, A. T. Hanbicki, R. Goswami, C. H. Li, H. B. Zhao, and B. T. Jonker, “Exchange bias of the interface spin system at the Fe/MgO interface,” Nat. Nanotechnol. 8(6), 438–444 (2013).
[Crossref] [PubMed]

Gray, S. J.

C. Daboo, R. J. Hicken, E. Gu, M. Gester, S. J. Gray, D. E. P. Eley, E. Ahmad, J. A. Bland, R. Ploessl, and J. N. Chapman, “Anisotropy and orientational dependence of magnetization reversal processes in epitaxial ferromagnetic thin films,” Phys. Rev. B Condens. Matter 51(22), 15964–15973 (1995).
[Crossref] [PubMed]

R. P. Cowburn, S. J. Gray, J. Ferre, J. A. C. Bland, and J. Miltat, “Magnetic switching and in-plane uniaxial anisotropy in ultrathin Ag/Fe/Ag(100) epitaxial films,” Appl. Phys. Lett. 78, 7210 (1995).

C. Daboo, R. J. Hicken, D. E. P. Eley, M. Gester, S. J. Gray, A. J. R. Ives, and J. A. C. Bland, “Magnetization reversal processes in epitaxial Fe/GaAs(001) films,” Appl. Phys. Lett. 75, 5586 (1994).

Grishin, A. M.

V. I. Belotelov, L. E. Kreilkamp, I. A. Akimov, A. N. Kalish, D. A. Bykov, S. Kasture, V. J. Yallapragada, A. Venu Gopal, A. M. Grishin, S. I. Khartsev, M. Nur-E-Alam, M. Vasiliev, L. L. Doskolovich, D. R. Yakovlev, K. Alameh, A. K. Zvezdin, and M. Bayer, “Plasmon-mediated magneto-optical transparency,” Nat. Commun. 4, 2128 (2013).
[Crossref] [PubMed]

Gu, E.

C. Daboo, R. J. Hicken, E. Gu, M. Gester, S. J. Gray, D. E. P. Eley, E. Ahmad, J. A. Bland, R. Ploessl, and J. N. Chapman, “Anisotropy and orientational dependence of magnetization reversal processes in epitaxial ferromagnetic thin films,” Phys. Rev. B Condens. Matter 51(22), 15964–15973 (1995).
[Crossref] [PubMed]

Gudde, J.

T. V. Murzina, T. V. Misuryaev, A. F. Kravets, J. Gudde, D. Schuhmacher, G. Marowsky, A. A. Nikulin, and O. A. Aktsipetrov, “Nonlinear magneto-optical Kerr effect and plasmon-asisted SHG in magnetic nanomaterials exhibiting giant magnetoresistance,” Surf. Sci. 482–485, 1101–1106 (2001).

Guzatov, D.

V. V. Temnov, G. Armelles, U. Woggon, D. Guzatov, A. Cebollada, A. Garcia-Martin, J. Garcia-Martin, T. Thomays, A. Leitenstorfers, and R. Bratschitschs, “Active magneto-plasmonics in hybrid metal–ferromagnet structures,” Nat. Photonics 4(2), 107–111 (2010).
[Crossref]

Hanbicki, A. T.

W. Zheng, A. T. Hanbicki, B. T. Jonker, and G. Lüpke, “Control of magnetic contrast with nonlinear magneto-plasmonics,” Sci. Rep. 4, 6191 (2014).
[Crossref] [PubMed]

Y. Fan, K. J. Smith, G. Lüpke, A. T. Hanbicki, R. Goswami, C. H. Li, H. B. Zhao, and B. T. Jonker, “Exchange bias of the interface spin system at the Fe/MgO interface,” Nat. Nanotechnol. 8(6), 438–444 (2013).
[Crossref] [PubMed]

W. Zheng, A. T. Hanbicki, B. T. Jonker, and G. Lüpke, “Surface Plasmon-enhanced Transverse Magnetic Second-Harmonic Generation,” Opt. Express 21(23), 28842–28848 (2013).
[Crossref] [PubMed]

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(23), 235422 (2001).
[Crossref]

V. I. Safarov, V. A. Kosobukin, C. Hermann, G. Lampel, J. Peretti, and C. Marlière, “Magneto-optical effects enhanced by surface plasmons in metallic multilayer films,” Phys. Rev. Lett. 73(26), 3584–3587 (1994).
[Crossref] [PubMed]

Heskamp, I. R.

A. Kirilyuk, G. M. H. Knippels, A. F. G. Meer, S. Renard, Th. Rasing, I. R. Heskamp, and J. C. Lodder, “Observation of strong magnetic effects in visible-infrared sum frequency generation from magnetic structures,” Phys. Rev. B 62(2), 783–786 (2000).
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Hicken, R. J.

C. Daboo, R. J. Hicken, E. Gu, M. Gester, S. J. Gray, D. E. P. Eley, E. Ahmad, J. A. Bland, R. Ploessl, and J. N. Chapman, “Anisotropy and orientational dependence of magnetization reversal processes in epitaxial ferromagnetic thin films,” Phys. Rev. B Condens. Matter 51(22), 15964–15973 (1995).
[Crossref] [PubMed]

C. Daboo, R. J. Hicken, D. E. P. Eley, M. Gester, S. J. Gray, A. J. R. Ives, and J. A. C. Bland, “Magnetization reversal processes in epitaxial Fe/GaAs(001) films,” Appl. Phys. Lett. 75, 5586 (1994).

Hjorvarsson, B.

I. Razdolski, D. G. Gheorghe, E. Melander, B. Hjorvarsson, P. Patoka, A. V. Kimel, A. Kirilyuk, E. T. Papaioannou, and T. Rasing, “Nonlocal nonlinear magneto-optical response of a magnetoplasmonic crystal,” Phys. Rev. B 88(7), 075436 (2013).
[Crossref]

Inoue, M.

Ivanchenko, M. V.

Ives, A. J. R.

C. Daboo, R. J. Hicken, D. E. P. Eley, M. Gester, S. J. Gray, A. J. R. Ives, and J. A. C. Bland, “Magnetization reversal processes in epitaxial Fe/GaAs(001) films,” Appl. Phys. Lett. 75, 5586 (1994).

Jeyaram, Y.

V. K. Valev, A. V. Silhanek, W. Gillijns, Y. Jeyaram, H. Paddubrouskaya, A. Volodin, C. G. Biris, N. C. Panoiu, B. De Clercq, M. Ameloot, O. A. Aktsipetrov, V. V. Moshchalkov, and T. Verbiest, “Plasmons reveal the direction of magnetization in nickel nanostructures,” ACS Nano 5(1), 91–96 (2011).
[Crossref] [PubMed]

Jonker, B. T.

W. Zheng, A. T. Hanbicki, B. T. Jonker, and G. Lüpke, “Control of magnetic contrast with nonlinear magneto-plasmonics,” Sci. Rep. 4, 6191 (2014).
[Crossref] [PubMed]

Y. Fan, K. J. Smith, G. Lüpke, A. T. Hanbicki, R. Goswami, C. H. Li, H. B. Zhao, and B. T. Jonker, “Exchange bias of the interface spin system at the Fe/MgO interface,” Nat. Nanotechnol. 8(6), 438–444 (2013).
[Crossref] [PubMed]

W. Zheng, A. T. Hanbicki, B. T. Jonker, and G. Lüpke, “Surface Plasmon-enhanced Transverse Magnetic Second-Harmonic Generation,” Opt. Express 21(23), 28842–28848 (2013).
[Crossref] [PubMed]

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V. I. Belotelov, L. E. Kreilkamp, I. A. Akimov, A. N. Kalish, D. A. Bykov, S. Kasture, V. J. Yallapragada, A. Venu Gopal, A. M. Grishin, S. I. Khartsev, M. Nur-E-Alam, M. Vasiliev, L. L. Doskolovich, D. R. Yakovlev, K. Alameh, A. K. Zvezdin, and M. Bayer, “Plasmon-mediated magneto-optical transparency,” Nat. Commun. 4, 2128 (2013).
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Kapra, R. V.

Kasture, S.

V. I. Belotelov, L. E. Kreilkamp, I. A. Akimov, A. N. Kalish, D. A. Bykov, S. Kasture, V. J. Yallapragada, A. Venu Gopal, A. M. Grishin, S. I. Khartsev, M. Nur-E-Alam, M. Vasiliev, L. L. Doskolovich, D. R. Yakovlev, K. Alameh, A. K. Zvezdin, and M. Bayer, “Plasmon-mediated magneto-optical transparency,” Nat. Commun. 4, 2128 (2013).
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M. Kauranen and A. V. Zayats, “Nonlinear Plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
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V. L. Krutyanskiy, A. L. Chekhov, V. A. Ketsko, A. I. Stognij, and T. V. Murzina, “Giant nonlinear magneto-optical response of magnetoplasmonic crystals,” Phys. Rev. B 91(12), 121411 (2015).
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Khartsev, S. I.

V. I. Belotelov, L. E. Kreilkamp, I. A. Akimov, A. N. Kalish, D. A. Bykov, S. Kasture, V. J. Yallapragada, A. Venu Gopal, A. M. Grishin, S. I. Khartsev, M. Nur-E-Alam, M. Vasiliev, L. L. Doskolovich, D. R. Yakovlev, K. Alameh, A. K. Zvezdin, and M. Bayer, “Plasmon-mediated magneto-optical transparency,” Nat. Commun. 4, 2128 (2013).
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Kim, E. M.

O. Aktsipetrov, T. V. Murzina, E. M. Kim, R. V. Kapra, A. A. Fedyanin, M. Inoue, A. F. Kravets, S. V. Kuznetsova, M. V. Ivanchenko, and V. C. Lifshits, “Magnetization-induced second- and third- harmonic generation in magnetic thin films and nanoparticles,” J. Opt. Soc. Am. B 22(1), 138–147 (2005).
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E. M. Kim, S. S. Elovikov, T. V. Murzina, A. A. Nikulin, O. A. Aktsipetrov, M. A. Bader, and G. Marowsky, “Surface-enhanced optical third-harmonic generation in Ag island films,” Phys. Rev. Lett. 95(22), 227402 (2005).
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I. Razdolski, D. G. Gheorghe, E. Melander, B. Hjorvarsson, P. Patoka, A. V. Kimel, A. Kirilyuk, E. T. Papaioannou, and T. Rasing, “Nonlocal nonlinear magneto-optical response of a magnetoplasmonic crystal,” Phys. Rev. B 88(7), 075436 (2013).
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Kirilyuk, A.

I. Razdolski, S. Parchenko, A. Stupakiewicz, S. Semin, A. Stognij, A. Maziewski, A. Kirilyuk, and T. Rasing, “Second-harmonic generation from a magnetic buried interface enhanced by an interplay of surface plasma resonances,” ACS Photonics 2(1), 20–26 (2015).
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I. Razdolski, D. G. Gheorghe, E. Melander, B. Hjorvarsson, P. Patoka, A. V. Kimel, A. Kirilyuk, E. T. Papaioannou, and T. Rasing, “Nonlocal nonlinear magneto-optical response of a magnetoplasmonic crystal,” Phys. Rev. B 88(7), 075436 (2013).
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V. K. Valev, A. Kirilyuk, F. Dalla Longa, J. T. Kohlhepp, B. Koopmans, and Th. Rasing, “Observation of periodic oscillations in magnetization-induced second harmonic generation at the Mn/Co interface,” Phys. Rev. B 75(1), 012401 (2007).
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K. Sato, A. Kodama, M. Miyamoto, A. V. Petukhov, K. Takanashi, S. Mitani, H. Fujimori, A. Kirilyuk, and T. Rasing, “Anisotropic magnetization-induced second harmonic generation in Fe/Au superlattices,” Phys. Rev. B 64(18), 184427 (2001).
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A. Kirilyuk, G. M. H. Knippels, A. F. G. Meer, S. Renard, Th. Rasing, I. R. Heskamp, and J. C. Lodder, “Observation of strong magnetic effects in visible-infrared sum frequency generation from magnetic structures,” Phys. Rev. B 62(2), 783–786 (2000).
[Crossref]

Knippels, G. M. H.

A. Kirilyuk, G. M. H. Knippels, A. F. G. Meer, S. Renard, Th. Rasing, I. R. Heskamp, and J. C. Lodder, “Observation of strong magnetic effects in visible-infrared sum frequency generation from magnetic structures,” Phys. Rev. B 62(2), 783–786 (2000).
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Kodama, A.

K. Sato, A. Kodama, M. Miyamoto, A. V. Petukhov, K. Takanashi, S. Mitani, H. Fujimori, A. Kirilyuk, and T. Rasing, “Anisotropic magnetization-induced second harmonic generation in Fe/Au superlattices,” Phys. Rev. B 64(18), 184427 (2001).
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Kohlhepp, J. T.

V. K. Valev, A. Kirilyuk, F. Dalla Longa, J. T. Kohlhepp, B. Koopmans, and Th. Rasing, “Observation of periodic oscillations in magnetization-induced second harmonic generation at the Mn/Co interface,” Phys. Rev. B 75(1), 012401 (2007).
[Crossref]

Kolmychek, I. A.

Koopmans, B.

V. K. Valev, A. Kirilyuk, F. Dalla Longa, J. T. Kohlhepp, B. Koopmans, and Th. Rasing, “Observation of periodic oscillations in magnetization-induced second harmonic generation at the Mn/Co interface,” Phys. Rev. B 75(1), 012401 (2007).
[Crossref]

Koschny, T.

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with Negative Index Due to Chirality,” Phys. Rev. B 79(3), 035407 (2009).
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A. V. Kosobukin, “On the theory of near-field magneto-optical microscopy via plasmonic modes of nanowire,” Tech. Phys. Lett. 37(4), 387–390 (2011).
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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(23), 235422 (2001).
[Crossref]

V. I. Safarov, V. A. Kosobukin, C. Hermann, G. Lampel, J. Peretti, and C. Marlière, “Magneto-optical effects enhanced by surface plasmons in metallic multilayer films,” Phys. Rev. Lett. 73(26), 3584–3587 (1994).
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Krasavin, A. V.

A. V. Krasavin, K. F. MacDonald, N. I. Zheludev, and A. V. Zayats, “High-contrast modulation of light with light by control of surface plasmon polariton wave coupling,” Appl. Phys. Lett. 85(16), 3369–3371 (2004).
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Kravets, A. F.

O. Aktsipetrov, T. V. Murzina, E. M. Kim, R. V. Kapra, A. A. Fedyanin, M. Inoue, A. F. Kravets, S. V. Kuznetsova, M. V. Ivanchenko, and V. C. Lifshits, “Magnetization-induced second- and third- harmonic generation in magnetic thin films and nanoparticles,” J. Opt. Soc. Am. B 22(1), 138–147 (2005).
[Crossref]

T. V. Murzina, T. V. Misuryaev, A. F. Kravets, J. Gudde, D. Schuhmacher, G. Marowsky, A. A. Nikulin, and O. A. Aktsipetrov, “Nonlinear magneto-optical Kerr effect and plasmon-asisted SHG in magnetic nanomaterials exhibiting giant magnetoresistance,” Surf. Sci. 482–485, 1101–1106 (2001).

Kreilkamp, L. E.

V. I. Belotelov, L. E. Kreilkamp, I. A. Akimov, A. N. Kalish, D. A. Bykov, S. Kasture, V. J. Yallapragada, A. Venu Gopal, A. M. Grishin, S. I. Khartsev, M. Nur-E-Alam, M. Vasiliev, L. L. Doskolovich, D. R. Yakovlev, K. Alameh, A. K. Zvezdin, and M. Bayer, “Plasmon-mediated magneto-optical transparency,” Nat. Commun. 4, 2128 (2013).
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Krichevtsov, B. B.

M. Fiebig, D. Fröhlich, B. B. Krichevtsov, and R. V. Pisarev, “Second harmonic generation and magnetic-dipole-electric-dipole interference in antiferromagnetic Cr2O3,” Phys. Rev. Lett. 73(15), 2127–2130 (1994).
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E. Petryayeva and U. J. Krull, “Localized surface plasmon resonance: Nanostructures, bioassays and biosensing - A review,” Anal. Chim. Acta 706(1), 8–24 (2011).
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V. L. Krutyanskiy, A. L. Chekhov, V. A. Ketsko, A. I. Stognij, and T. V. Murzina, “Giant nonlinear magneto-optical response of magnetoplasmonic crystals,” Phys. Rev. B 91(12), 121411 (2015).
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A. L. Chekhov, V. L. Krutyanskiy, A. N. Shaimanov, A. I. Stognij, and T. V. Murzina, “Wide tunability of magnetoplasmonic crystals due to excitation of multiple waveguide and plasmon modes,” Opt. Express 22(15), 17762–17768 (2014).
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Kuznetsova, S. V.

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(23), 235422 (2001).
[Crossref]

V. I. Safarov, V. A. Kosobukin, C. Hermann, G. Lampel, J. Peretti, and C. Marlière, “Magneto-optical effects enhanced by surface plasmons in metallic multilayer films,” Phys. Rev. Lett. 73(26), 3584–3587 (1994).
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Lechuga, L. M.

D. Regatos, D. Farina, A. Calle, A. Cebollada, B. Sepulveda, G. Armelles, and L. M. Lechuga, “Au/Fe/Au multilayer transducers for magneto-optic surface plasmon resonance sensing,” J. Appl. Phys. 108(5), 054502 (2010).
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B. Sepúlveda, P. C. Angelome, L. M. Lechuga, and L. M. Liz-Marzan, “LSRP-based nanobiosensors,” Nano Today 4(3), 244–251 (2009).
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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).
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B. Sepulveda, L. M. Lechuga, and G. Armelles, “Magnetooptic effects in surface-plasmon-plaritons slab waveguides,” J. Lightwave Technol. 24(2), 945–955 (2006).
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Leitenstorfers, A.

V. V. Temnov, G. Armelles, U. Woggon, D. Guzatov, A. Cebollada, A. Garcia-Martin, J. Garcia-Martin, T. Thomays, A. Leitenstorfers, and R. Bratschitschs, “Active magneto-plasmonics in hybrid metal–ferromagnet structures,” Nat. Photonics 4(2), 107–111 (2010).
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V. K. Valev, A. V. Silhanek, W. Gillijns, Y. Jeyaram, H. Paddubrouskaya, A. Volodin, C. G. Biris, N. C. Panoiu, B. De Clercq, M. Ameloot, O. A. Aktsipetrov, V. V. Moshchalkov, and T. Verbiest, “Plasmons reveal the direction of magnetization in nickel nanostructures,” ACS Nano 5(1), 91–96 (2011).
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Acta Electrotechnica et Informatica (1)

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Opt. Lett. (3)

Phys. Rev. B (7)

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(23), 235422 (2001).
[Crossref]

V. K. Valev, A. Kirilyuk, F. Dalla Longa, J. T. Kohlhepp, B. Koopmans, and Th. Rasing, “Observation of periodic oscillations in magnetization-induced second harmonic generation at the Mn/Co interface,” Phys. Rev. B 75(1), 012401 (2007).
[Crossref]

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with Negative Index Due to Chirality,” Phys. Rev. B 79(3), 035407 (2009).
[Crossref]

I. Razdolski, D. G. Gheorghe, E. Melander, B. Hjorvarsson, P. Patoka, A. V. Kimel, A. Kirilyuk, E. T. Papaioannou, and T. Rasing, “Nonlocal nonlinear magneto-optical response of a magnetoplasmonic crystal,” Phys. Rev. B 88(7), 075436 (2013).
[Crossref]

K. Sato, A. Kodama, M. Miyamoto, A. V. Petukhov, K. Takanashi, S. Mitani, H. Fujimori, A. Kirilyuk, and T. Rasing, “Anisotropic magnetization-induced second harmonic generation in Fe/Au superlattices,” Phys. Rev. B 64(18), 184427 (2001).
[Crossref]

A. Kirilyuk, G. M. H. Knippels, A. F. G. Meer, S. Renard, Th. Rasing, I. R. Heskamp, and J. C. Lodder, “Observation of strong magnetic effects in visible-infrared sum frequency generation from magnetic structures,” Phys. Rev. B 62(2), 783–786 (2000).
[Crossref]

V. L. Krutyanskiy, A. L. Chekhov, V. A. Ketsko, A. I. Stognij, and T. V. Murzina, “Giant nonlinear magneto-optical response of magnetoplasmonic crystals,” Phys. Rev. B 91(12), 121411 (2015).
[Crossref]

Phys. Rev. B Condens. Matter (1)

C. Daboo, R. J. Hicken, E. Gu, M. Gester, S. J. Gray, D. E. P. Eley, E. Ahmad, J. A. Bland, R. Ploessl, and J. N. Chapman, “Anisotropy and orientational dependence of magnetization reversal processes in epitaxial ferromagnetic thin films,” Phys. Rev. B Condens. Matter 51(22), 15964–15973 (1995).
[Crossref] [PubMed]

Phys. Rev. Lett. (12)

R. K. Chang, J. Ducuing, and N. Bloembergen, “Relative phase measurement between fundamental and second-harmonic light,” Phys. Rev. Lett. 15(1), 6–8 (1965).
[Crossref]

S. Zhang, Y. S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative Refractive Index in Chiral Metamaterials,” Phys. Rev. Lett. 102(2), 023901 (2009).
[Crossref] [PubMed]

V. K. Valev, A. V. Silhanek, N. Verellen, W. Gillijns, P. Van Dorpe, O. A. Aktsipetrov, G. A. E. Vandenbosch, V. V. Moshchalkov, and T. Verbiest, “Asymmetric Optical Second-Harmonic Generation from Chiral G-Shaped Gold Nanostructures,” Phys. Rev. Lett. 104(12), 127401 (2010).
[Crossref] [PubMed]

M. Fiebig, D. Fröhlich, B. B. Krichevtsov, and R. V. Pisarev, “Second harmonic generation and magnetic-dipole-electric-dipole interference in antiferromagnetic Cr2O3,” Phys. Rev. Lett. 73(15), 2127–2130 (1994).
[Crossref] [PubMed]

V. I. Safarov, V. A. Kosobukin, C. Hermann, G. Lampel, J. Peretti, and C. Marlière, “Magneto-optical effects enhanced by surface plasmons in metallic multilayer films,” Phys. Rev. Lett. 73(26), 3584–3587 (1994).
[Crossref] [PubMed]

Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal,” Phys. Rev. Lett. 100(2), 023902 (2008).
[Crossref] [PubMed]

E. M. Kim, S. S. Elovikov, T. V. Murzina, A. A. Nikulin, O. A. Aktsipetrov, M. A. Bader, and G. Marowsky, “Surface-enhanced optical third-harmonic generation in Ag island films,” Phys. Rev. Lett. 95(22), 227402 (2005).
[Crossref] [PubMed]

S. Palomba and L. Novotny, “Nonlinear excitation of surface plasmon polaritons by four-wave mixing,” Phys. Rev. Lett. 101(5), 056802 (2008).
[Crossref] [PubMed]

J. Renger, R. Quidant, N. van Hulst, and L. Novotny, “Surface-enhanced nonlinear four-wave mixing,” Phys. Rev. Lett. 104(4), 046803 (2010).
[Crossref] [PubMed]

M. I. Stockman, D. J. Bergman, C. Anceau, S. Brasselet, and J. Zyss, “Enhanced second-harmonic generation by metal surfaces with nanoscale roughness: nanoscale dephasing, depolarization, and correlations,” Phys. Rev. Lett. 92(5), 057402 (2004).
[Crossref] [PubMed]

H. J. Simon, D. E. Mitchell, and J. G. Watson, “Optical second-harmonic generation with surface plasmons in silver films,” Phys. Rev. Lett. 33(26), 1531–1534 (1974).
[Crossref]

S. I. Bozhevolnyi, J. Beermann, and V. Coello, “Direct observation of localized second-harmonic enhancement in random metal nanostructures,” Phys. Rev. Lett. 90(19), 197403 (2003).
[Crossref] [PubMed]

Rep. Prog. Phys. (1)

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70(1), 1–87 (2007).
[Crossref]

Sci. Rep. (1)

W. Zheng, A. T. Hanbicki, B. T. Jonker, and G. Lüpke, “Control of magnetic contrast with nonlinear magneto-plasmonics,” Sci. Rep. 4, 6191 (2014).
[Crossref] [PubMed]

Science (1)

J. B. Pendry, “A Chiral Route to Negative Refraction,” Science 306(5700), 1353–1355 (2004).
[Crossref] [PubMed]

Surf. Sci. (1)

T. V. Murzina, T. V. Misuryaev, A. F. Kravets, J. Gudde, D. Schuhmacher, G. Marowsky, A. A. Nikulin, and O. A. Aktsipetrov, “Nonlinear magneto-optical Kerr effect and plasmon-asisted SHG in magnetic nanomaterials exhibiting giant magnetoresistance,” Surf. Sci. 482–485, 1101–1106 (2001).

Tech. Phys. Lett. (1)

A. V. Kosobukin, “On the theory of near-field magneto-optical microscopy via plasmonic modes of nanowire,” Tech. Phys. Lett. 37(4), 387–390 (2011).
[Crossref]

Other (5)

A. Kirilyuk and T. Rasing, “Magnetization-induced second harmonic generation,” in Handbook of Magnetism and Advanced Magnetic Materials (John Wiley & Sons, Ltd. 2007, Volume 3: Novel Techniques for Characterizing and Preparing Samples).

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings of Springer Tracts in Modern Physics (Springer-Verlag, 1988, Vol. 111).

M. R. Parker, “The Kerr magneto-optic effect (1876-1976),” Physica BC, 86, 1171–1176 (1977).

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).

R. W. Boyd, Nonlinear Optics 3rd ed (Academic, 2008).

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Figures (9)

Fig. 1
Fig. 1 (a) Kretschmann geometry for SPP excitation in NMP, and (b) coordinate system for MSHG. Red lines represent the fundamental beam, which is normally generated by a Titanium doped Sapphire laser, with a wavelength of around 800 nm. Blue lines represent the double frequency beam with a wavelength of about 400 nm. (adapted from ref. 38)

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Fig. 2
Fig. 2 Longitudinal and transverse magnetic contrasts of MSHG as a function of the incident angle, the signs of magnetic contrast change drastically at about 44°, the open dots are measured values, the curves represent best fits. (adapted from ref. 35)

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Fig. 3
Fig. 3 (a) Enhanced signal strength of transverse MSHG as a function of the incident angle on 10-nm thick Fe thin film sample, and (b) comparison of SPP-enhanced magnetic contrast of MSHG and MOKE. The ATR curve (green) is shown as reference. (adapted from ref. 38)

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Fig. 4
Fig. 4 As a magnetically anisotropic material, crystalline Fe has four magnetization states. With the help of SPs, MSHG technique can read out all four magnetization states with good magnetic contrast, the longitudinal and transverse MSHG can be studied simultaneously. The hysteresis loops on the right reveal the control effect of magnetic contrast with NMP. (adapted from ref. 39)

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Fig. 5
Fig. 5 (a) Au/BTIG/GGG grating structures, (b) at 31° incidence, wavelength dependence of reflectivity and SHG intensity. Vertical dashed lines indicate the spectral positions of SPs at two interfaces, and (c) SHG intensity as a function of wavelength and angle of incidence, point 1 and 2 indicate the conditions where SPs at each interface are excited, respectively, point 3 indicates the condition that SPs are excited at both interfaces. (adapted from ref. 45)

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Fig. 6
Fig. 6 (a) SHG magnetic contrast as a function of incident angle for the reference (empty dots) and perforated (green full dots) films. Black diamonds represent the phase difference between even and odd (refer to Eq. (3) and (4)) magnetic SHG contributions, (b) relative phases of the even (red empty dots) and odd (blue full dots) SHG components. The dashed area represents phase shift introduced by the SPPs. Dotted lines are the result of an interpolation. The vertical line refers to the SP resonant angle. (adapted from ref. 46)

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Fig. 7
Fig. 7 (a) The grating structure is also called magneto -plasmonic crystal, a transmission geometry is used to excite SPP and generate SHG. A dc magnetic field is applied parallel to the stripes to control the light flow, (b) Wavelength dependent transmission and SHG intensity indicate both SPPs and waveguide modes contribute to the SHG. IIa, IIb and IIc indicate the waveguide modes, and III indicate the SPP. (adapted from ref. 51)

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Fig. 8
Fig. 8 (a)(b) MSHG intensity as a function of x. x is the weight of element for CoxAg1-x and (CoFe)x(Al2O3)1-x nano-granular films at the fundamental wavelengths of 1064 nm and 800 nm, (c) MSHG magnetic contrast and magnetoresistance as a function of x for CoxAg1-x. (adapted from ref. 54)

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Fig. 9
Fig. 9 (a)(b)MSHG intensities as a function of azimuthal sample rotation angle show asymmetric secondary peaks, (c)(d) the position of secondary peaks changes with wavelength, while the structure remain same, which excludes the structure anisotropy as the origin of the asymmetry, (e) the position of the secondary peaks remains unaffected with different magnetic field applied, which excludes the magnetic field as the origin, (f) the four-fold symmetric sample and experimental setup. (adapted from ref. 58)

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Tables (1)

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Table 1 Comparison of different NMP structures

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Equations (5)

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P ( ω , 2 ω , ... ) = χ ( 1 ) E ( ω ) + χ ( 2 ) E ( ω ) E ( ω ) + ...
| r p s | ∝ 〈 E p E s 〉 d | ε m o |
χ i j k ( L ) = ( 0 0 0 0 χ x z x e v e n χ x y x o d d χ y x x o d d χ y y y o d d χ y z z o d d χ y z y e v e n 0 0 χ z x x e v e n χ z y y e v e n χ z z z e v e n χ z y z e v e n 0 0 )
χ i j k ( T ) = ( χ x x x o d d χ x y y o d d χ x z z o d d 0 χ x z x e v e n 0 0 0 0 χ y z y e v e n 0 χ y x y o d d χ z x x e v e n χ z y y e v e n χ z z z e v e n 0 χ z x z o d d 0 ) ,
C = I ( 2 ω ) ( + M ) − I ( 2 ω ) ( − M ) I ( 2 ω ) ( + M ) + I ( 2 ω ) ( − M ) ,

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