Abstract

It is shown theoretically that the Faraday rotation becomes anomalously large and exhibits extraordinary behavior near the frequencies of the extraordinary optical transmittance through optically thick perforated metal film with holes filled with a magneto-optically active material. This phenomenon is explained as result of strong confinement of the evanescent electromagnetic field within magnetic material, which occurs due to excitation of the coupled plasmon-polaritons on the opposite surfaces of the film.

© 2007 Optical Society of America

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  1. T. W. Ebbssen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
    [CrossRef]
  2. J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Mimicking Surface Plasmons with structured surfaces," Science 305, 847-848 (2004).
    [CrossRef] [PubMed]
  3. V. I. Belotelov, L. L. Doskolovich, and A. K. Zvezdin, "Extraordinary magneto-optical effects and transmission through Metal-Dielectric Plasmonic Systems," Phys. Rev. Lett. 98, 077401-077404 (2007).
    [CrossRef] [PubMed]
  4. Y. M. Strelniker and D. J. Bergman, "Optical transmission through metal films with a subwavelength hole array in the presence of a magnetic field," Phys. Rev. B 59, R12763-R12766 (1999).
    [CrossRef]
  5. L. E. Helseth, "Tunable plasma response of a metal/ferromagnetic composite material," Phys. Rev. B 72, 033409-033411 (2005).
    [CrossRef]
  6. Z. Wang and S. Fan, "Optical circulators in two-dimensional magneto-optical photonic crystals," Opt. Lett. 30, 1989-1991 (2005).
    [CrossRef] [PubMed]
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    [CrossRef]
  9. M. Inoue, R. Fujikawa, A. Baryshev, A. Khanikaev, P. B. Lim, H. Uchida, O. Aktsipetrov, A. Fedyanin, T. Murzina, and A. Granovsky, "Magnetophotonic crystals," J. Phys. D: Appl. Phys. 39, R151-R161 (2006).
    [CrossRef]
  10. A. A. Fedyanin, O. Aktsipetrov, D. Kobayashi, K. Nishimura, H. Uchida and M. Inoue, "Enhanced Faraday and nonlinear magneto-optical Kerr effects in magnetophotonic crystals," J. Magn. Magn. Mater. 282, 256-259 (2004).
    [CrossRef]
  11. M. Inoue, K. I. Arai, T. Fujii, M. Abe, "Magneto-optical properties of one-dimensional photonic crystals composed of magnetic and dielectric layers," J. Appl. Phys. 83, 6768-6770 (1998).
    [CrossRef]
  12. A. B. Khanikaev, A. V. Baryshev, M. Inoue, A. B. Granovsky, and A. P. Vinogradov, "Two-dimensional magnetophotonic crystal: Exactly solvable model," Phys. Rev. B 72, 035123-035131 (2005).
    [CrossRef]
  13. L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, "Theory of extraordinary optical transmission through subwavelength hole arrays," Phys. Rev. Lett. 86, 1114-1117 (2001).
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2007

V. I. Belotelov, L. L. Doskolovich, and A. K. Zvezdin, "Extraordinary magneto-optical effects and transmission through Metal-Dielectric Plasmonic Systems," Phys. Rev. Lett. 98, 077401-077404 (2007).
[CrossRef] [PubMed]

2006

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

2005

A. B. Khanikaev, A. V. Baryshev, M. Inoue, A. B. Granovsky, and A. P. Vinogradov, "Two-dimensional magnetophotonic crystal: Exactly solvable model," Phys. Rev. B 72, 035123-035131 (2005).
[CrossRef]

L. E. Helseth, "Tunable plasma response of a metal/ferromagnetic composite material," Phys. Rev. B 72, 033409-033411 (2005).
[CrossRef]

Z. Wang and S. Fan, "Optical circulators in two-dimensional magneto-optical photonic crystals," Opt. Lett. 30, 1989-1991 (2005).
[CrossRef] [PubMed]

2004

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Mimicking Surface Plasmons with structured surfaces," Science 305, 847-848 (2004).
[CrossRef] [PubMed]

A. A. Fedyanin, O. Aktsipetrov, D. Kobayashi, K. Nishimura, H. Uchida and M. Inoue, "Enhanced Faraday and nonlinear magneto-optical Kerr effects in magnetophotonic crystals," J. Magn. Magn. Mater. 282, 256-259 (2004).
[CrossRef]

2001

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, "Theory of extraordinary optical transmission through subwavelength hole arrays," Phys. Rev. Lett. 86, 1114-1117 (2001).
[CrossRef] [PubMed]

1999

Y. M. Strelniker and D. J. Bergman, "Optical transmission through metal films with a subwavelength hole array in the presence of a magnetic field," Phys. Rev. B 59, R12763-R12766 (1999).
[CrossRef]

1998

T. W. Ebbssen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

M. Inoue, K. I. Arai, T. Fujii, M. Abe, "Magneto-optical properties of one-dimensional photonic crystals composed of magnetic and dielectric layers," J. Appl. Phys. 83, 6768-6770 (1998).
[CrossRef]

1995

V. Gasparian, M. Ortuno, J. Ruiz, and E. Cuevas, "Faraday Rotation and Complex-Valued Traversal Time for Classical Light Waves," Phys. Rev. Lett. 75, 2312-2315 (1995).
[CrossRef] [PubMed]

1994

1989

K. Ando, "Nonreciprocal devices for integrated optics," Proc. SPIE 1126, 58-65 (1989).

1987

P. M. Hui and D. Stroud, "Theory of Faraday rotation by dilute suspensions of small particles," Appl. Phys. Lett. 50, 950-952 (1987).
[CrossRef]

1964

Abe, M.

M. Inoue, K. I. Arai, T. Fujii, M. Abe, "Magneto-optical properties of one-dimensional photonic crystals composed of magnetic and dielectric layers," J. Appl. Phys. 83, 6768-6770 (1998).
[CrossRef]

Aktsipetrov, O.

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

A. A. Fedyanin, O. Aktsipetrov, D. Kobayashi, K. Nishimura, H. Uchida and M. Inoue, "Enhanced Faraday and nonlinear magneto-optical Kerr effects in magnetophotonic crystals," J. Magn. Magn. Mater. 282, 256-259 (2004).
[CrossRef]

Ando, K.

K. Ando, "Nonreciprocal devices for integrated optics," Proc. SPIE 1126, 58-65 (1989).

Arai, K. I.

M. Inoue, K. I. Arai, T. Fujii, M. Abe, "Magneto-optical properties of one-dimensional photonic crystals composed of magnetic and dielectric layers," J. Appl. Phys. 83, 6768-6770 (1998).
[CrossRef]

Baryshev, A.

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

Baryshev, A. V.

A. B. Khanikaev, A. V. Baryshev, M. Inoue, A. B. Granovsky, and A. P. Vinogradov, "Two-dimensional magnetophotonic crystal: Exactly solvable model," Phys. Rev. B 72, 035123-035131 (2005).
[CrossRef]

Belotelov, V. I.

V. I. Belotelov, L. L. Doskolovich, and A. K. Zvezdin, "Extraordinary magneto-optical effects and transmission through Metal-Dielectric Plasmonic Systems," Phys. Rev. Lett. 98, 077401-077404 (2007).
[CrossRef] [PubMed]

Bergman, D. J.

Y. M. Strelniker and D. J. Bergman, "Optical transmission through metal films with a subwavelength hole array in the presence of a magnetic field," Phys. Rev. B 59, R12763-R12766 (1999).
[CrossRef]

Cuevas, E.

V. Gasparian, M. Ortuno, J. Ruiz, and E. Cuevas, "Faraday Rotation and Complex-Valued Traversal Time for Classical Light Waves," Phys. Rev. Lett. 75, 2312-2315 (1995).
[CrossRef] [PubMed]

Doskolovich, L. L.

V. I. Belotelov, L. L. Doskolovich, and A. K. Zvezdin, "Extraordinary magneto-optical effects and transmission through Metal-Dielectric Plasmonic Systems," Phys. Rev. Lett. 98, 077401-077404 (2007).
[CrossRef] [PubMed]

Ebbesen, T. W.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, "Theory of extraordinary optical transmission through subwavelength hole arrays," Phys. Rev. Lett. 86, 1114-1117 (2001).
[CrossRef] [PubMed]

Ebbssen, T. W.

T. W. Ebbssen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Fan, S.

Fedyanin, A.

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

Fedyanin, A. A.

A. A. Fedyanin, O. Aktsipetrov, D. Kobayashi, K. Nishimura, H. Uchida and M. Inoue, "Enhanced Faraday and nonlinear magneto-optical Kerr effects in magnetophotonic crystals," J. Magn. Magn. Mater. 282, 256-259 (2004).
[CrossRef]

Fujii, T.

M. Inoue, K. I. Arai, T. Fujii, M. Abe, "Magneto-optical properties of one-dimensional photonic crystals composed of magnetic and dielectric layers," J. Appl. Phys. 83, 6768-6770 (1998).
[CrossRef]

Fujikawa, R.

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

Garcia-Vidal, F. J.

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Mimicking Surface Plasmons with structured surfaces," Science 305, 847-848 (2004).
[CrossRef] [PubMed]

García-Vidal, F. J.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, "Theory of extraordinary optical transmission through subwavelength hole arrays," Phys. Rev. Lett. 86, 1114-1117 (2001).
[CrossRef] [PubMed]

Gasparian, V.

V. Gasparian, M. Ortuno, J. Ruiz, and E. Cuevas, "Faraday Rotation and Complex-Valued Traversal Time for Classical Light Waves," Phys. Rev. Lett. 75, 2312-2315 (1995).
[CrossRef] [PubMed]

Ghaemi, H. F.

T. W. Ebbssen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Granovsky, A.

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

Granovsky, A. B.

A. B. Khanikaev, A. V. Baryshev, M. Inoue, A. B. Granovsky, and A. P. Vinogradov, "Two-dimensional magnetophotonic crystal: Exactly solvable model," Phys. Rev. B 72, 035123-035131 (2005).
[CrossRef]

Helseth, L. E.

L. E. Helseth, "Tunable plasma response of a metal/ferromagnetic composite material," Phys. Rev. B 72, 033409-033411 (2005).
[CrossRef]

Herriott, D. R.

Hui, P. M.

P. M. Hui and D. Stroud, "Theory of Faraday rotation by dilute suspensions of small particles," Appl. Phys. Lett. 50, 950-952 (1987).
[CrossRef]

Inoue, M.

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

A. B. Khanikaev, A. V. Baryshev, M. Inoue, A. B. Granovsky, and A. P. Vinogradov, "Two-dimensional magnetophotonic crystal: Exactly solvable model," Phys. Rev. B 72, 035123-035131 (2005).
[CrossRef]

A. A. Fedyanin, O. Aktsipetrov, D. Kobayashi, K. Nishimura, H. Uchida and M. Inoue, "Enhanced Faraday and nonlinear magneto-optical Kerr effects in magnetophotonic crystals," J. Magn. Magn. Mater. 282, 256-259 (2004).
[CrossRef]

M. Inoue, K. I. Arai, T. Fujii, M. Abe, "Magneto-optical properties of one-dimensional photonic crystals composed of magnetic and dielectric layers," J. Appl. Phys. 83, 6768-6770 (1998).
[CrossRef]

Khanikaev, A.

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

Khanikaev, A. B.

A. B. Khanikaev, A. V. Baryshev, M. Inoue, A. B. Granovsky, and A. P. Vinogradov, "Two-dimensional magnetophotonic crystal: Exactly solvable model," Phys. Rev. B 72, 035123-035131 (2005).
[CrossRef]

Kobayashi, D.

A. A. Fedyanin, O. Aktsipetrov, D. Kobayashi, K. Nishimura, H. Uchida and M. Inoue, "Enhanced Faraday and nonlinear magneto-optical Kerr effects in magnetophotonic crystals," J. Magn. Magn. Mater. 282, 256-259 (2004).
[CrossRef]

Lezec, H. J.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, "Theory of extraordinary optical transmission through subwavelength hole arrays," Phys. Rev. Lett. 86, 1114-1117 (2001).
[CrossRef] [PubMed]

T. W. Ebbssen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Lim, P. B.

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

Ling, H. Y.

Martin-Moreno, L.

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Mimicking Surface Plasmons with structured surfaces," Science 305, 847-848 (2004).
[CrossRef] [PubMed]

Martín-Moreno, L.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, "Theory of extraordinary optical transmission through subwavelength hole arrays," Phys. Rev. Lett. 86, 1114-1117 (2001).
[CrossRef] [PubMed]

Murzina, T.

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

Nishimura, K.

A. A. Fedyanin, O. Aktsipetrov, D. Kobayashi, K. Nishimura, H. Uchida and M. Inoue, "Enhanced Faraday and nonlinear magneto-optical Kerr effects in magnetophotonic crystals," J. Magn. Magn. Mater. 282, 256-259 (2004).
[CrossRef]

Ortuno, M.

V. Gasparian, M. Ortuno, J. Ruiz, and E. Cuevas, "Faraday Rotation and Complex-Valued Traversal Time for Classical Light Waves," Phys. Rev. Lett. 75, 2312-2315 (1995).
[CrossRef] [PubMed]

Pellerin, K. M.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, "Theory of extraordinary optical transmission through subwavelength hole arrays," Phys. Rev. Lett. 86, 1114-1117 (2001).
[CrossRef] [PubMed]

Pendry, J. B.

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Mimicking Surface Plasmons with structured surfaces," Science 305, 847-848 (2004).
[CrossRef] [PubMed]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, "Theory of extraordinary optical transmission through subwavelength hole arrays," Phys. Rev. Lett. 86, 1114-1117 (2001).
[CrossRef] [PubMed]

Rosenberg, R.

Rubinstein, C. B.

Ruiz, J.

V. Gasparian, M. Ortuno, J. Ruiz, and E. Cuevas, "Faraday Rotation and Complex-Valued Traversal Time for Classical Light Waves," Phys. Rev. Lett. 75, 2312-2315 (1995).
[CrossRef] [PubMed]

Strelniker, Y. M.

Y. M. Strelniker and D. J. Bergman, "Optical transmission through metal films with a subwavelength hole array in the presence of a magnetic field," Phys. Rev. B 59, R12763-R12766 (1999).
[CrossRef]

Stroud, D.

P. M. Hui and D. Stroud, "Theory of Faraday rotation by dilute suspensions of small particles," Appl. Phys. Lett. 50, 950-952 (1987).
[CrossRef]

Thio, T.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, "Theory of extraordinary optical transmission through subwavelength hole arrays," Phys. Rev. Lett. 86, 1114-1117 (2001).
[CrossRef] [PubMed]

T. W. Ebbssen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Uchida, H.

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

A. A. Fedyanin, O. Aktsipetrov, D. Kobayashi, K. Nishimura, H. Uchida and M. Inoue, "Enhanced Faraday and nonlinear magneto-optical Kerr effects in magnetophotonic crystals," J. Magn. Magn. Mater. 282, 256-259 (2004).
[CrossRef]

Vinogradov, A. P.

A. B. Khanikaev, A. V. Baryshev, M. Inoue, A. B. Granovsky, and A. P. Vinogradov, "Two-dimensional magnetophotonic crystal: Exactly solvable model," Phys. Rev. B 72, 035123-035131 (2005).
[CrossRef]

Wang, Z.

Wolff, P. A.

T. W. Ebbssen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Zvezdin, A. K.

V. I. Belotelov, L. L. Doskolovich, and A. K. Zvezdin, "Extraordinary magneto-optical effects and transmission through Metal-Dielectric Plasmonic Systems," Phys. Rev. Lett. 98, 077401-077404 (2007).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. Lett.

P. M. Hui and D. Stroud, "Theory of Faraday rotation by dilute suspensions of small particles," Appl. Phys. Lett. 50, 950-952 (1987).
[CrossRef]

J. Appl. Phys.

M. Inoue, K. I. Arai, T. Fujii, M. Abe, "Magneto-optical properties of one-dimensional photonic crystals composed of magnetic and dielectric layers," J. Appl. Phys. 83, 6768-6770 (1998).
[CrossRef]

J. Magn. Magn. Mater.

A. A. Fedyanin, O. Aktsipetrov, D. Kobayashi, K. Nishimura, H. Uchida and M. Inoue, "Enhanced Faraday and nonlinear magneto-optical Kerr effects in magnetophotonic crystals," J. Magn. Magn. Mater. 282, 256-259 (2004).
[CrossRef]

J. Opt. Soc. Am. A

J. Phys. D: Appl. Phys.

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

Nature

T. W. Ebbssen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Opt. Lett.

Phys. Rev. B

Y. M. Strelniker and D. J. Bergman, "Optical transmission through metal films with a subwavelength hole array in the presence of a magnetic field," Phys. Rev. B 59, R12763-R12766 (1999).
[CrossRef]

L. E. Helseth, "Tunable plasma response of a metal/ferromagnetic composite material," Phys. Rev. B 72, 033409-033411 (2005).
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

Geometrical arrangement of a perforated metal film with magnetic holes. Red arrows show magnetization direction of a magnetic component.

Fig. 2.
Fig. 2.

Transmittance and Faraday rotation of: (i) a perforated perfect conductor film with holes filled with Bi:YIG (shown by blue solid lines) and (ii) film of Bi:YIG of the same thickness (shown by green lines with circles). Calculations were performed for following parameters: film thickness of h=350 nm, lattice constant o L=700 nm, holes’ size of a=145 nm, ε 11 = 5.59 + i5.4910-3, and ε 11 = -3.6910-3.

Fig. 3.
Fig. 3.

Transmittance and Faraday rotation spectra vs. the thickness of a perforated perfect conductor film with MO holes. Parameters used for calculations are the same as in Fig. 2.

Fig. 4.
Fig. 4.

Figure of merit vs. the thickness of: (i) homogeneous MO film at wavelength of 705 nm (green line) and (ii) perforated perfect conductor film with MO holes at the left (red line) and right (blue line) resonances, respectively. Parameters used for calculations are the same as in Fig. 2.

Fig. 5.
Fig. 5.

Figure of merit vs. the holes’ size at the left (red line) and right (blue line) resonances, respectively. Parameters used for calculations are the same as in Fig. 2.

Fig. 6.
Fig. 6.

Transmittance and Faraday rotation vs. the absorption in MO holes’ filler. Parameters used for calculations are the same as in Fig. 2.

Equations (19)

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t ̂ if = α , β , γ τ ̂ αf 12 e ̂ α lin ( δ ̂ αβ ρ ̂ αγ 21 e ̂ γ lin ρ ̂ γβ 21 e ̂ β lin ) 1 τ ̂ 12 ,
ρ ̂ αf 21 = ρ αf 21 ( 1 0 0 1 ) , τ ̂ αf 21 = τ αf 21 ( 1 0 0 1 ) and τ ̂ αf 21 = τ αf 21 ( 1 0 0 1 ) ,
ε ̂ = ( ε 11 i ε 12 0 i ε 12 ε 11 0 0 0 ε 33 ) .
[ 2 x 2 + 2 y 2 + ω 2 ε ̂ 0 q m 2 ] E m 0 x y = 0
E = m A m ( z ) E m 0 x y exp ( i q m z iωt ) .
[ + ω 2 ( ε ̂ 0 + Δ ε ̂ ) ] E = 0
d 2 d z 2 A m q m d dz A m
N m d dz A m ( z ) = ω 2 2 i q m l M ml A l ( z ) exp [ i ( q m q l ) ] ,
N m = E m 0 2 dxdy ,
M ml = E m 0 * Δ ε ̂ E l 0 dxdy .
E 10 = i x E 10 π a sin ( πy a ) exp ( iq z z iωt ) ,
E 01 = i y E 01 π a sin ( πx a ) exp ( iq z z iωt ) ,
E = i = 10,01 A i ( z ) E i ,
( A 10 ( z ) A 01 ( z ) ) = ( cos αz sin αz sin αz cos αz ) ( A 10 0 A 01 0 ) ,
α = 4 ω 2 ε 12 ( c 2 π 2 q z )
t ̂ 00 = τ ̂ 12 e ̂ ( δ ̂ ρ ̂ 21 e ̂ ρ ̂ 21 e ̂ ) 1 τ ̂ 12 ,
e ̂ = ( cos αh sin αh sin αh cos αh ) exp ( i q z h ) ,
t ̂ 00 21 t ̂ 00 11 = sin ( αh ) cos ( αh ) ,
t ̂ 00 21 t ̂ 00 11 i [ sinh ( α h ) cosh ( α h ) 1 + ( ρ 21 exp ( i q z h ) ) 2 1 ( ρ 21 exp ( i q z h ) ) 2 ] .

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