Abstract

Efficient modelling of the magneto–optic effects of transition metals such as nickel, cobalt and iron is a topic of growing interest within the nano–optics community. In this paper, we present a general discussion of appropriate material models for the linear dielectric properties for such metals, provide parameter fits and formulate the anisotropic response in terms of auxiliary differential equations suitable for time–domain simulations. We validate both our material models and their implementation by comparing numerical results obtained with the Discontinuous Galerkin time–domain (DGTD) method to analytical results and previously published experimental data.

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  1. E. Th. Papaioannou, V. Kapaklis, E. Melander, B. Hjörvarsson, S. D. Pappas, P. Patoka, M. Giersig, P. Fumagalli, A. García–Martín, G. Ctistis, “Surface plasmons and magneto–optic activity in hexagonal Ni anti–dot arrays,” Opt. Express 19, 23867–23877 (2011).
    [CrossRef] [PubMed]
  2. E. Melander, E. Östman, J. Keller, J. Schmidt, E. Th. Papaioannou, V. Kapaklis, U. B. Arnalds, B. Caballero, A. García–Martín, J. C. Cuevas, B. Hjörvarsson, “Influence of the magnetic field on the plasmonic properties of transparent Ni anti-dot arrays,” Appl. Phys. Lett. 101, 063107 (2012).
    [CrossRef]
  3. V. V. Temnov, G. Armelles, U. Woggon, D. Guzatov, A. Cebollada, A. Garcia–Martin, J.–M. García–Martín, T. Thomay, A. Leitenstorfer, R. Bratschitsch, “Active magneto-plasmonics in hybrid metal-ferromagnet structures,” Nat. Phot. 4, 107–111 (2010).
    [CrossRef]
  4. A. García–Martín, G. Armelles, S. Pereira, “Light transport in photonic crystals composed of magneto–optically active materials,” Phys. Rev. B 71, 205116 (2005).
    [CrossRef]
  5. K. Busch, M. König, J. Niegemann, “Discontinuous Galerkin methods in nanophotonics,” Laser & Photon. Rev. 5, 773–809 (2011).
  6. M. Y. Koledintseva, K. N. Rozanov, A. Orlandi, J. L. Drewniak, “Extraction of Lorentzian and Debye parameters of dielectric and magnetic dispersive materials for FDTD modeling,” J. Electr. Eng.–Slovak 53, 97–100 (2002).
  7. V. Korenman, J. L. Murray, R. E. Prange, “Local-band theory of itinerant ferromagnetism. I. Fermi-liquid theory,” Phys. Rev. B 16, 4032–4047 (1977).
    [CrossRef]
  8. P. R. Berman, “Optical Faraday rotation,” Am. J. Phys. 78, 270–276 (2009).
    [CrossRef]
  9. M. König, K. Busch, J. Niegemann, “The Discontinuous Galerkin time–domain method for Maxwells equations with anisotropic materials,” Phot. Nano. Fund. Appl. 8, 303–309 (2010).
    [CrossRef]
  10. J. Alvarez, L. D. Angulo, A. R. Bretones, S. G. Garcia, “3–D Discontinuous Galerkin time–domain method for anisotropic materials,” IEEE Antenn. Wireless Propag. Lett. 11, 1182 (2012).
    [CrossRef]
  11. J. E. Sipe, V. C. Y. So, M. Fukui, G. I. Stegeman, “Analysis of second–harmonic generation at metal surfaces,” Phys. Rev. B 21, 4389–4402 (1980).
    [CrossRef]
  12. R. E. Wyatt, Quantum Dynamics with Trajectories (Springer, 2005).
  13. P. B. Johnson, R. W. Christy, “Optical constants of transition metals: Ti, V, Cr, Mn, Fe, Co, Ni, and Pd,” Phys. Rev. B 9, 5056–5070 (1974).
    [CrossRef]
  14. Š. Višňovský, V. Pařízek, M. Nývlt, P. Kielar, V. Prosser, R. Krishnan, “Magneto–optical Kerr spectra of nickel,” J. Magn. Magn. Mater. 127, 135–139 (1993).
    [CrossRef]
  15. Š. Višňovský, “Magneto–optical Ellipsometry,” Czech. J. Phys. B 36, 625–650 (1986).
    [CrossRef]

2012

E. Melander, E. Östman, J. Keller, J. Schmidt, E. Th. Papaioannou, V. Kapaklis, U. B. Arnalds, B. Caballero, A. García–Martín, J. C. Cuevas, B. Hjörvarsson, “Influence of the magnetic field on the plasmonic properties of transparent Ni anti-dot arrays,” Appl. Phys. Lett. 101, 063107 (2012).
[CrossRef]

J. Alvarez, L. D. Angulo, A. R. Bretones, S. G. Garcia, “3–D Discontinuous Galerkin time–domain method for anisotropic materials,” IEEE Antenn. Wireless Propag. Lett. 11, 1182 (2012).
[CrossRef]

2011

2010

V. V. Temnov, G. Armelles, U. Woggon, D. Guzatov, A. Cebollada, A. Garcia–Martin, J.–M. García–Martín, T. Thomay, A. Leitenstorfer, R. Bratschitsch, “Active magneto-plasmonics in hybrid metal-ferromagnet structures,” Nat. Phot. 4, 107–111 (2010).
[CrossRef]

M. König, K. Busch, J. Niegemann, “The Discontinuous Galerkin time–domain method for Maxwells equations with anisotropic materials,” Phot. Nano. Fund. Appl. 8, 303–309 (2010).
[CrossRef]

2009

P. R. Berman, “Optical Faraday rotation,” Am. J. Phys. 78, 270–276 (2009).
[CrossRef]

2005

A. García–Martín, G. Armelles, S. Pereira, “Light transport in photonic crystals composed of magneto–optically active materials,” Phys. Rev. B 71, 205116 (2005).
[CrossRef]

2002

M. Y. Koledintseva, K. N. Rozanov, A. Orlandi, J. L. Drewniak, “Extraction of Lorentzian and Debye parameters of dielectric and magnetic dispersive materials for FDTD modeling,” J. Electr. Eng.–Slovak 53, 97–100 (2002).

1993

Š. Višňovský, V. Pařízek, M. Nývlt, P. Kielar, V. Prosser, R. Krishnan, “Magneto–optical Kerr spectra of nickel,” J. Magn. Magn. Mater. 127, 135–139 (1993).
[CrossRef]

1986

Š. Višňovský, “Magneto–optical Ellipsometry,” Czech. J. Phys. B 36, 625–650 (1986).
[CrossRef]

1980

J. E. Sipe, V. C. Y. So, M. Fukui, G. I. Stegeman, “Analysis of second–harmonic generation at metal surfaces,” Phys. Rev. B 21, 4389–4402 (1980).
[CrossRef]

1977

V. Korenman, J. L. Murray, R. E. Prange, “Local-band theory of itinerant ferromagnetism. I. Fermi-liquid theory,” Phys. Rev. B 16, 4032–4047 (1977).
[CrossRef]

1974

P. B. Johnson, R. W. Christy, “Optical constants of transition metals: Ti, V, Cr, Mn, Fe, Co, Ni, and Pd,” Phys. Rev. B 9, 5056–5070 (1974).
[CrossRef]

Alvarez, J.

J. Alvarez, L. D. Angulo, A. R. Bretones, S. G. Garcia, “3–D Discontinuous Galerkin time–domain method for anisotropic materials,” IEEE Antenn. Wireless Propag. Lett. 11, 1182 (2012).
[CrossRef]

Angulo, L. D.

J. Alvarez, L. D. Angulo, A. R. Bretones, S. G. Garcia, “3–D Discontinuous Galerkin time–domain method for anisotropic materials,” IEEE Antenn. Wireless Propag. Lett. 11, 1182 (2012).
[CrossRef]

Armelles, G.

V. V. Temnov, G. Armelles, U. Woggon, D. Guzatov, A. Cebollada, A. Garcia–Martin, J.–M. García–Martín, T. Thomay, A. Leitenstorfer, R. Bratschitsch, “Active magneto-plasmonics in hybrid metal-ferromagnet structures,” Nat. Phot. 4, 107–111 (2010).
[CrossRef]

A. García–Martín, G. Armelles, S. Pereira, “Light transport in photonic crystals composed of magneto–optically active materials,” Phys. Rev. B 71, 205116 (2005).
[CrossRef]

Arnalds, U. B.

E. Melander, E. Östman, J. Keller, J. Schmidt, E. Th. Papaioannou, V. Kapaklis, U. B. Arnalds, B. Caballero, A. García–Martín, J. C. Cuevas, B. Hjörvarsson, “Influence of the magnetic field on the plasmonic properties of transparent Ni anti-dot arrays,” Appl. Phys. Lett. 101, 063107 (2012).
[CrossRef]

Berman, P. R.

P. R. Berman, “Optical Faraday rotation,” Am. J. Phys. 78, 270–276 (2009).
[CrossRef]

Bratschitsch, R.

V. V. Temnov, G. Armelles, U. Woggon, D. Guzatov, A. Cebollada, A. Garcia–Martin, J.–M. García–Martín, T. Thomay, A. Leitenstorfer, R. Bratschitsch, “Active magneto-plasmonics in hybrid metal-ferromagnet structures,” Nat. Phot. 4, 107–111 (2010).
[CrossRef]

Bretones, A. R.

J. Alvarez, L. D. Angulo, A. R. Bretones, S. G. Garcia, “3–D Discontinuous Galerkin time–domain method for anisotropic materials,” IEEE Antenn. Wireless Propag. Lett. 11, 1182 (2012).
[CrossRef]

Busch, K.

K. Busch, M. König, J. Niegemann, “Discontinuous Galerkin methods in nanophotonics,” Laser & Photon. Rev. 5, 773–809 (2011).

M. König, K. Busch, J. Niegemann, “The Discontinuous Galerkin time–domain method for Maxwells equations with anisotropic materials,” Phot. Nano. Fund. Appl. 8, 303–309 (2010).
[CrossRef]

Caballero, B.

E. Melander, E. Östman, J. Keller, J. Schmidt, E. Th. Papaioannou, V. Kapaklis, U. B. Arnalds, B. Caballero, A. García–Martín, J. C. Cuevas, B. Hjörvarsson, “Influence of the magnetic field on the plasmonic properties of transparent Ni anti-dot arrays,” Appl. Phys. Lett. 101, 063107 (2012).
[CrossRef]

Cebollada, A.

V. V. Temnov, G. Armelles, U. Woggon, D. Guzatov, A. Cebollada, A. Garcia–Martin, J.–M. García–Martín, T. Thomay, A. Leitenstorfer, R. Bratschitsch, “Active magneto-plasmonics in hybrid metal-ferromagnet structures,” Nat. Phot. 4, 107–111 (2010).
[CrossRef]

Christy, R. W.

P. B. Johnson, R. W. Christy, “Optical constants of transition metals: Ti, V, Cr, Mn, Fe, Co, Ni, and Pd,” Phys. Rev. B 9, 5056–5070 (1974).
[CrossRef]

Ctistis, G.

Cuevas, J. C.

E. Melander, E. Östman, J. Keller, J. Schmidt, E. Th. Papaioannou, V. Kapaklis, U. B. Arnalds, B. Caballero, A. García–Martín, J. C. Cuevas, B. Hjörvarsson, “Influence of the magnetic field on the plasmonic properties of transparent Ni anti-dot arrays,” Appl. Phys. Lett. 101, 063107 (2012).
[CrossRef]

Drewniak, J. L.

M. Y. Koledintseva, K. N. Rozanov, A. Orlandi, J. L. Drewniak, “Extraction of Lorentzian and Debye parameters of dielectric and magnetic dispersive materials for FDTD modeling,” J. Electr. Eng.–Slovak 53, 97–100 (2002).

Fukui, M.

J. E. Sipe, V. C. Y. So, M. Fukui, G. I. Stegeman, “Analysis of second–harmonic generation at metal surfaces,” Phys. Rev. B 21, 4389–4402 (1980).
[CrossRef]

Fumagalli, P.

Garcia, S. G.

J. Alvarez, L. D. Angulo, A. R. Bretones, S. G. Garcia, “3–D Discontinuous Galerkin time–domain method for anisotropic materials,” IEEE Antenn. Wireless Propag. Lett. 11, 1182 (2012).
[CrossRef]

Garcia–Martin, A.

V. V. Temnov, G. Armelles, U. Woggon, D. Guzatov, A. Cebollada, A. Garcia–Martin, J.–M. García–Martín, T. Thomay, A. Leitenstorfer, R. Bratschitsch, “Active magneto-plasmonics in hybrid metal-ferromagnet structures,” Nat. Phot. 4, 107–111 (2010).
[CrossRef]

García–Martín, A.

E. Melander, E. Östman, J. Keller, J. Schmidt, E. Th. Papaioannou, V. Kapaklis, U. B. Arnalds, B. Caballero, A. García–Martín, J. C. Cuevas, B. Hjörvarsson, “Influence of the magnetic field on the plasmonic properties of transparent Ni anti-dot arrays,” Appl. Phys. Lett. 101, 063107 (2012).
[CrossRef]

E. Th. Papaioannou, V. Kapaklis, E. Melander, B. Hjörvarsson, S. D. Pappas, P. Patoka, M. Giersig, P. Fumagalli, A. García–Martín, G. Ctistis, “Surface plasmons and magneto–optic activity in hexagonal Ni anti–dot arrays,” Opt. Express 19, 23867–23877 (2011).
[CrossRef] [PubMed]

A. García–Martín, G. Armelles, S. Pereira, “Light transport in photonic crystals composed of magneto–optically active materials,” Phys. Rev. B 71, 205116 (2005).
[CrossRef]

García–Martín, J.–M.

V. V. Temnov, G. Armelles, U. Woggon, D. Guzatov, A. Cebollada, A. Garcia–Martin, J.–M. García–Martín, T. Thomay, A. Leitenstorfer, R. Bratschitsch, “Active magneto-plasmonics in hybrid metal-ferromagnet structures,” Nat. Phot. 4, 107–111 (2010).
[CrossRef]

Giersig, M.

Guzatov, D.

V. V. Temnov, G. Armelles, U. Woggon, D. Guzatov, A. Cebollada, A. Garcia–Martin, J.–M. García–Martín, T. Thomay, A. Leitenstorfer, R. Bratschitsch, “Active magneto-plasmonics in hybrid metal-ferromagnet structures,” Nat. Phot. 4, 107–111 (2010).
[CrossRef]

Hjörvarsson, B.

E. Melander, E. Östman, J. Keller, J. Schmidt, E. Th. Papaioannou, V. Kapaklis, U. B. Arnalds, B. Caballero, A. García–Martín, J. C. Cuevas, B. Hjörvarsson, “Influence of the magnetic field on the plasmonic properties of transparent Ni anti-dot arrays,” Appl. Phys. Lett. 101, 063107 (2012).
[CrossRef]

E. Th. Papaioannou, V. Kapaklis, E. Melander, B. Hjörvarsson, S. D. Pappas, P. Patoka, M. Giersig, P. Fumagalli, A. García–Martín, G. Ctistis, “Surface plasmons and magneto–optic activity in hexagonal Ni anti–dot arrays,” Opt. Express 19, 23867–23877 (2011).
[CrossRef] [PubMed]

Johnson, P. B.

P. B. Johnson, R. W. Christy, “Optical constants of transition metals: Ti, V, Cr, Mn, Fe, Co, Ni, and Pd,” Phys. Rev. B 9, 5056–5070 (1974).
[CrossRef]

Kapaklis, V.

E. Melander, E. Östman, J. Keller, J. Schmidt, E. Th. Papaioannou, V. Kapaklis, U. B. Arnalds, B. Caballero, A. García–Martín, J. C. Cuevas, B. Hjörvarsson, “Influence of the magnetic field on the plasmonic properties of transparent Ni anti-dot arrays,” Appl. Phys. Lett. 101, 063107 (2012).
[CrossRef]

E. Th. Papaioannou, V. Kapaklis, E. Melander, B. Hjörvarsson, S. D. Pappas, P. Patoka, M. Giersig, P. Fumagalli, A. García–Martín, G. Ctistis, “Surface plasmons and magneto–optic activity in hexagonal Ni anti–dot arrays,” Opt. Express 19, 23867–23877 (2011).
[CrossRef] [PubMed]

Keller, J.

E. Melander, E. Östman, J. Keller, J. Schmidt, E. Th. Papaioannou, V. Kapaklis, U. B. Arnalds, B. Caballero, A. García–Martín, J. C. Cuevas, B. Hjörvarsson, “Influence of the magnetic field on the plasmonic properties of transparent Ni anti-dot arrays,” Appl. Phys. Lett. 101, 063107 (2012).
[CrossRef]

Kielar, P.

Š. Višňovský, V. Pařízek, M. Nývlt, P. Kielar, V. Prosser, R. Krishnan, “Magneto–optical Kerr spectra of nickel,” J. Magn. Magn. Mater. 127, 135–139 (1993).
[CrossRef]

Koledintseva, M. Y.

M. Y. Koledintseva, K. N. Rozanov, A. Orlandi, J. L. Drewniak, “Extraction of Lorentzian and Debye parameters of dielectric and magnetic dispersive materials for FDTD modeling,” J. Electr. Eng.–Slovak 53, 97–100 (2002).

König, M.

K. Busch, M. König, J. Niegemann, “Discontinuous Galerkin methods in nanophotonics,” Laser & Photon. Rev. 5, 773–809 (2011).

M. König, K. Busch, J. Niegemann, “The Discontinuous Galerkin time–domain method for Maxwells equations with anisotropic materials,” Phot. Nano. Fund. Appl. 8, 303–309 (2010).
[CrossRef]

Korenman, V.

V. Korenman, J. L. Murray, R. E. Prange, “Local-band theory of itinerant ferromagnetism. I. Fermi-liquid theory,” Phys. Rev. B 16, 4032–4047 (1977).
[CrossRef]

Krishnan, R.

Š. Višňovský, V. Pařízek, M. Nývlt, P. Kielar, V. Prosser, R. Krishnan, “Magneto–optical Kerr spectra of nickel,” J. Magn. Magn. Mater. 127, 135–139 (1993).
[CrossRef]

Leitenstorfer, A.

V. V. Temnov, G. Armelles, U. Woggon, D. Guzatov, A. Cebollada, A. Garcia–Martin, J.–M. García–Martín, T. Thomay, A. Leitenstorfer, R. Bratschitsch, “Active magneto-plasmonics in hybrid metal-ferromagnet structures,” Nat. Phot. 4, 107–111 (2010).
[CrossRef]

Melander, E.

E. Melander, E. Östman, J. Keller, J. Schmidt, E. Th. Papaioannou, V. Kapaklis, U. B. Arnalds, B. Caballero, A. García–Martín, J. C. Cuevas, B. Hjörvarsson, “Influence of the magnetic field on the plasmonic properties of transparent Ni anti-dot arrays,” Appl. Phys. Lett. 101, 063107 (2012).
[CrossRef]

E. Th. Papaioannou, V. Kapaklis, E. Melander, B. Hjörvarsson, S. D. Pappas, P. Patoka, M. Giersig, P. Fumagalli, A. García–Martín, G. Ctistis, “Surface plasmons and magneto–optic activity in hexagonal Ni anti–dot arrays,” Opt. Express 19, 23867–23877 (2011).
[CrossRef] [PubMed]

Murray, J. L.

V. Korenman, J. L. Murray, R. E. Prange, “Local-band theory of itinerant ferromagnetism. I. Fermi-liquid theory,” Phys. Rev. B 16, 4032–4047 (1977).
[CrossRef]

Niegemann, J.

K. Busch, M. König, J. Niegemann, “Discontinuous Galerkin methods in nanophotonics,” Laser & Photon. Rev. 5, 773–809 (2011).

M. König, K. Busch, J. Niegemann, “The Discontinuous Galerkin time–domain method for Maxwells equations with anisotropic materials,” Phot. Nano. Fund. Appl. 8, 303–309 (2010).
[CrossRef]

Nývlt, M.

Š. Višňovský, V. Pařízek, M. Nývlt, P. Kielar, V. Prosser, R. Krishnan, “Magneto–optical Kerr spectra of nickel,” J. Magn. Magn. Mater. 127, 135–139 (1993).
[CrossRef]

Orlandi, A.

M. Y. Koledintseva, K. N. Rozanov, A. Orlandi, J. L. Drewniak, “Extraction of Lorentzian and Debye parameters of dielectric and magnetic dispersive materials for FDTD modeling,” J. Electr. Eng.–Slovak 53, 97–100 (2002).

Östman, E.

E. Melander, E. Östman, J. Keller, J. Schmidt, E. Th. Papaioannou, V. Kapaklis, U. B. Arnalds, B. Caballero, A. García–Martín, J. C. Cuevas, B. Hjörvarsson, “Influence of the magnetic field on the plasmonic properties of transparent Ni anti-dot arrays,” Appl. Phys. Lett. 101, 063107 (2012).
[CrossRef]

Papaioannou, E. Th.

E. Melander, E. Östman, J. Keller, J. Schmidt, E. Th. Papaioannou, V. Kapaklis, U. B. Arnalds, B. Caballero, A. García–Martín, J. C. Cuevas, B. Hjörvarsson, “Influence of the magnetic field on the plasmonic properties of transparent Ni anti-dot arrays,” Appl. Phys. Lett. 101, 063107 (2012).
[CrossRef]

E. Th. Papaioannou, V. Kapaklis, E. Melander, B. Hjörvarsson, S. D. Pappas, P. Patoka, M. Giersig, P. Fumagalli, A. García–Martín, G. Ctistis, “Surface plasmons and magneto–optic activity in hexagonal Ni anti–dot arrays,” Opt. Express 19, 23867–23877 (2011).
[CrossRef] [PubMed]

Pappas, S. D.

Parízek, V.

Š. Višňovský, V. Pařízek, M. Nývlt, P. Kielar, V. Prosser, R. Krishnan, “Magneto–optical Kerr spectra of nickel,” J. Magn. Magn. Mater. 127, 135–139 (1993).
[CrossRef]

Patoka, P.

Pereira, S.

A. García–Martín, G. Armelles, S. Pereira, “Light transport in photonic crystals composed of magneto–optically active materials,” Phys. Rev. B 71, 205116 (2005).
[CrossRef]

Prange, R. E.

V. Korenman, J. L. Murray, R. E. Prange, “Local-band theory of itinerant ferromagnetism. I. Fermi-liquid theory,” Phys. Rev. B 16, 4032–4047 (1977).
[CrossRef]

Prosser, V.

Š. Višňovský, V. Pařízek, M. Nývlt, P. Kielar, V. Prosser, R. Krishnan, “Magneto–optical Kerr spectra of nickel,” J. Magn. Magn. Mater. 127, 135–139 (1993).
[CrossRef]

Rozanov, K. N.

M. Y. Koledintseva, K. N. Rozanov, A. Orlandi, J. L. Drewniak, “Extraction of Lorentzian and Debye parameters of dielectric and magnetic dispersive materials for FDTD modeling,” J. Electr. Eng.–Slovak 53, 97–100 (2002).

Schmidt, J.

E. Melander, E. Östman, J. Keller, J. Schmidt, E. Th. Papaioannou, V. Kapaklis, U. B. Arnalds, B. Caballero, A. García–Martín, J. C. Cuevas, B. Hjörvarsson, “Influence of the magnetic field on the plasmonic properties of transparent Ni anti-dot arrays,” Appl. Phys. Lett. 101, 063107 (2012).
[CrossRef]

Sipe, J. E.

J. E. Sipe, V. C. Y. So, M. Fukui, G. I. Stegeman, “Analysis of second–harmonic generation at metal surfaces,” Phys. Rev. B 21, 4389–4402 (1980).
[CrossRef]

So, V. C. Y.

J. E. Sipe, V. C. Y. So, M. Fukui, G. I. Stegeman, “Analysis of second–harmonic generation at metal surfaces,” Phys. Rev. B 21, 4389–4402 (1980).
[CrossRef]

Stegeman, G. I.

J. E. Sipe, V. C. Y. So, M. Fukui, G. I. Stegeman, “Analysis of second–harmonic generation at metal surfaces,” Phys. Rev. B 21, 4389–4402 (1980).
[CrossRef]

Temnov, V. V.

V. V. Temnov, G. Armelles, U. Woggon, D. Guzatov, A. Cebollada, A. Garcia–Martin, J.–M. García–Martín, T. Thomay, A. Leitenstorfer, R. Bratschitsch, “Active magneto-plasmonics in hybrid metal-ferromagnet structures,” Nat. Phot. 4, 107–111 (2010).
[CrossRef]

Thomay, T.

V. V. Temnov, G. Armelles, U. Woggon, D. Guzatov, A. Cebollada, A. Garcia–Martin, J.–M. García–Martín, T. Thomay, A. Leitenstorfer, R. Bratschitsch, “Active magneto-plasmonics in hybrid metal-ferromagnet structures,” Nat. Phot. 4, 107–111 (2010).
[CrossRef]

Višnovský, Š.

Š. Višňovský, V. Pařízek, M. Nývlt, P. Kielar, V. Prosser, R. Krishnan, “Magneto–optical Kerr spectra of nickel,” J. Magn. Magn. Mater. 127, 135–139 (1993).
[CrossRef]

Š. Višňovský, “Magneto–optical Ellipsometry,” Czech. J. Phys. B 36, 625–650 (1986).
[CrossRef]

Woggon, U.

V. V. Temnov, G. Armelles, U. Woggon, D. Guzatov, A. Cebollada, A. Garcia–Martin, J.–M. García–Martín, T. Thomay, A. Leitenstorfer, R. Bratschitsch, “Active magneto-plasmonics in hybrid metal-ferromagnet structures,” Nat. Phot. 4, 107–111 (2010).
[CrossRef]

Wyatt, R. E.

R. E. Wyatt, Quantum Dynamics with Trajectories (Springer, 2005).

Am. J. Phys.

P. R. Berman, “Optical Faraday rotation,” Am. J. Phys. 78, 270–276 (2009).
[CrossRef]

Appl. Phys. Lett.

E. Melander, E. Östman, J. Keller, J. Schmidt, E. Th. Papaioannou, V. Kapaklis, U. B. Arnalds, B. Caballero, A. García–Martín, J. C. Cuevas, B. Hjörvarsson, “Influence of the magnetic field on the plasmonic properties of transparent Ni anti-dot arrays,” Appl. Phys. Lett. 101, 063107 (2012).
[CrossRef]

Czech. J. Phys. B

Š. Višňovský, “Magneto–optical Ellipsometry,” Czech. J. Phys. B 36, 625–650 (1986).
[CrossRef]

IEEE Antenn. Wireless Propag. Lett.

J. Alvarez, L. D. Angulo, A. R. Bretones, S. G. Garcia, “3–D Discontinuous Galerkin time–domain method for anisotropic materials,” IEEE Antenn. Wireless Propag. Lett. 11, 1182 (2012).
[CrossRef]

J. Electr. Eng.–Slovak

M. Y. Koledintseva, K. N. Rozanov, A. Orlandi, J. L. Drewniak, “Extraction of Lorentzian and Debye parameters of dielectric and magnetic dispersive materials for FDTD modeling,” J. Electr. Eng.–Slovak 53, 97–100 (2002).

J. Magn. Magn. Mater.

Š. Višňovský, V. Pařízek, M. Nývlt, P. Kielar, V. Prosser, R. Krishnan, “Magneto–optical Kerr spectra of nickel,” J. Magn. Magn. Mater. 127, 135–139 (1993).
[CrossRef]

Laser & Photon. Rev.

K. Busch, M. König, J. Niegemann, “Discontinuous Galerkin methods in nanophotonics,” Laser & Photon. Rev. 5, 773–809 (2011).

Nat. Phot.

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Figures (5)

Fig. 1
Fig. 1

Left panel: The asymptotic behavior of the measured permittivity’s imaginary parts of nickel, cobalt and iron (solid lines) [13] compared to the asymptotic behavior of the Drude model (dashed line, ω−3 scaling) and a curve with ω−1 scaling (dash–dotted).

Fig. 2
Fig. 2

Panels (a) and (b): Literature [13] values for the complex permittivity of nickel and our fit using the retarded Drude model with two additional Lorentz oscillator terms.

Fig. 3
Fig. 3

Panels (a) and (b): Literature [13] values for the complex permittivity of cobalt and our fit using the retarded Drude model with two additional Lorentz oscillator terms.

Fig. 4
Fig. 4

Left panel: Vertical cut through the numerical domain to simulate the reflection spectrum of a nickel half space; the length unit is one nanometer. PEC indicates a perfect electric conductor boundary, PML stands for perfectly matched layers.

Fig. 5
Fig. 5

Left panel: Vertical cut through the numerical domain used to calculate the polar MOKE reported on in [1], Papaioannou et al.. The lateral cross section is a regular hexagon with an edge length of 271.4nm corresponding to a triangular lattice with a lattice constant of 470nm; a cylindrical hole with radius 137.5nm is cut out from the nickel film. The length unit is one nanometer.

Tables (1)

Tables Icon

Table 1 Fit parameters of a retarded Drude model with two additional Lorentz oscillators for nickel, cobalt and iron. The cyclotron frequencies Ω are valid for magnetically saturated nickel films. The fits were performed for different windows of photon energies . The fit errors are upper bounds to the relative error throughout the respective energy windows.

Equations (55)

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μ ( ω ) = 1
χ Drude ( ω ) = ω P 2 ω ( ω + i γ D ) ,
σ ( ω ) = i ω χ ( ω ) ,
t j D ( t ) + γ D j D ( t ) = ω P 2 E ( t ) .
t j D ( t ) + γ D j D ( t ) = 0 Z ( s ) E ( t s ) d s .
t j D ( t ) + γ D j D ( t ) = n = 0 ζ ( n ) ( t n E ) ( t ) ,
ζ ( n ) = ( 1 ) n n ! 0 s n Z ( s ) d s
t j D ( t ) + γ D j D ( t ) = ω P 2 ( 1 + τ t ) E ( t ) .
χ rD ( ω ) = ω P 2 ( 1 i ω τ ) ω ( ω + i γ D ) ,
ω P = e 2 n m eff
ω P 2 = [ ω P ] 2 + [ ω P ] 2 ,
τ = ( [ ω P ] 2 τ + [ ω P ] 2 τ ) ω P 2 .
χ Lorentz ( ω ) = Δ ε L ω L 2 ω L 2 i ω γ L ω 2 .
t 2 j + γ t j + ω L 2 j = Δ ε L ω L 2 E + Ω × t j .
Ω = e m B ext
e t n div j = 0 ,
t j + γ j + div [ j v ] e m grad p ( n ) = e m [ e n E μ j × H ] .
e t δ n div j = 0 ,
t j + γ j e m p ( n 0 ) grad δ n = e m [ e n 0 E μ j × H 0 ] ,
t δ n = 0 ,
t j + γ j = n 0 e 2 m E e m j × B ext
= ω P 2 E + Ω × j .
t j D ( t ) + γ D j D ( t ) = ω P 2 ( 1 + τ t ) E ( t ) + Ω × j D ( t ) .
p ( n ) ( i ω ) j ( ω ) ( i ω ) n 1 Ω × j ( ω ) = ζ ( i ω ) E ( ω ) ,
[ p ( n ) ( i ω ) 1 ( i ω ) n 1 ε ̳ Ω ] j ( ω ) = ζ ( i ω ) E ( ω ) ,
χ _ ( ω ) = ζ ( i ω ) i ω [ p ( n ) ( i ω ) 1 ( i ω ) n 1 ε ̳ Ω ] 1 .
χ _ ( ω ) = ζ ( i ω ) i ω ( A 2 + B 2 ) ( A B 0 B A 0 0 0 A 2 + B 2 A )
χ x x ( ω ) = ω 2 + i ω γ ω L 2 ( ω 2 + i ω γ ω L 2 ) 2 ω 2 Ω 2 ,
χ x y ( ω ) = i Δ ε L ω L 2 ω Ω ( ω 2 + i ω γ ω L 2 ) 2 ω 2 Ω 2 .
χ x x ( ω ) = ω + i γ ω [ ( ω + i γ ) 2 Ω 2 ] ,
χ x y ( ω ) = i ω P 2 Ω ω [ ( ω + i γ ) 2 Ω 2 ] .
χ x x ( ω ) = ( ω + i γ ) ( 1 i ω τ ) ω [ ( ω + i γ ) 2 Ω 2 ] ,
χ x y ( ω ) = i ω P 2 Ω ( 1 i ω τ ) ω [ ( ω + i γ ) 2 Ω 2 ] .
t j D = γ D j D ω P 2 E .
t j D = γ D j D + Ω × j D ω P 2 E .
t j L = p L + Δ ε L ω L 2 E ,
t p L = γ L p L ω L 2 j L Δ ε L ω L 2 γ L E .
i ω j L ( ω ) + γ L j L + ω L 2 i ω j L Ω × j L = Δ ε L ω L 2 E .
p ( ω ) = ω L 2 i ω γ L i ω j L ( ω ) ,
i ω j L ( ω ) = p L ( ω ) + Ω × j L ( ω ) + Δ ε L ω L 2 E ( ω ) ,
i ω p L ( ω ) = γ L p L ( ω ) ω L 2 j L ( ω ) γ L Ω × j L ( ω ) Δ ε L ω L 2 γ L E ( ω ) .
t j L ( t ) = p L ( t ) + Δ ε L ω L 2 E ( t ) + Ω × j L ,
t p L ( t ) = γ L p L ( t ) ω L 2 j L ( t ) γ L Ω × j L ( t ) Δ ε L ω L 2 γ L E ( t ) .
χ rD ( ω ) = ω P 2 ( 1 i ω τ ) ω ( ω + i γ D ) .
( 1 + γ D τ 1 τ 1 i ω ) j rD ( ω ) = ω P 2 τ E ( ω ) .
p ( ω ) = j rD ( ω ) τ 1 i ω ,
j rD ( ω ) = ( τ 1 γ D ) p ( ω ) + ω P 2 τ E ( ω ) ,
i ω p ( ω ) = γ D p ( ω ) + ω P 2 τ E ( ω ) .
t p ( t ) = γ D p ( t ) + ω P 2 τ E ( t ) ,
j rD ( t ) = ( τ 1 γ D ) p ( t ) + ω P 2 τ E ( t ) .
t j rD ( t ) + γ D j rD ( t ) Ω × j rD ( t ) = ω P 2 ( 1 + τ t ) E ( t ) .
( 1 + γ D τ 1 Ω × τ 1 i ω ) j rD ( ω ) = ω P 2 τ E ( ω ) .
p ( ω ) = ( γ D τ 1 ) j rD ( ω ) Ω × j rD ( ω ) i ω τ 1 ,
j rD ( t ) = p ( t ) + ω P 2 τ E ( t ) ,
t p ( t ) = γ D p ( t ) + ( 1 τ γ D ) ω P 2 E ( t ) + Ω × j rD ( t ) .

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