Abstract

Diffracted magneto-optical (MO) effects are numerically investigated for one-dimensional lossy gyrotropic gratings in the zeroth and the first orders for the polar magnetization by utilizing the rigorous coupled-wave approach implemented as an Airy-like internal-reflection series. The simulated Kerr spectra agree well with the experimental ones. The dependence of the MO Kerr enhancement on the grating depth in the first-order diffraction, compared with that in the zeroth one, is illustrated, and the diffracted MO Faraday effect is theoretically investigated as well. Such a MO enhancement through the gyrotropic gratings is superior to the conventional MO devices and magneto-photonic crystals. The potential applications are also suggested.

© 2008 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  4. M. J. Steel, M. Levy, and R. M. Osgood, "Large magnetooptical Kerr rotation with high reflectivity from photonic bandgap structures with defects," J. Lightwave Technol. 18, 1289-1296 (2000).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  23. G. Neuber, P. Rauer, J. Kunze, T. Korn, C. Pels, G. Meier, U. Merkt, J. Backstrom, and M. Rubhausen, "Temperature-dependent spectral generalized magneto-optical ellipsometry," Appl. Phys. Lett. 83, 4509-4511 (2003).
    [CrossRef]
  24. P. Hones, M. Diserens, and F. Levy, "Characterization of sputter-deposited chromium oxide thin films," Surf. Coat. Technol. 120, 277-283 (1999).
    [CrossRef]
  25. D. F. Edwards, "Silicon (Si)" in Handbook of Optical Constants of Solids, edited by E. D. Palik (Academic, New York, 1998); H. R. Philipp, "Silicon Dioxide (SiO2) (Glass)," ibid.
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    [CrossRef]

2006 (7)

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]

S. Fan, M. F. Yanik, Z. Wang, S. Sandhu, and M. L. Povinelli, "Advances in theory of photonic crystals," J. Lightwave Technol. 24, 4493-4501 (2006).
[CrossRef]

K. Watanabe, "Study of the differential theory of lamellar gratings made of highly conducting materials," J. Opt. Soc. Am. A 23, 69-72 (2006).
[CrossRef]

A. Westphalen, A. Schumann, A. Remhof, H. Zabel, T. Last, and U. Kunze, "Magnetization reversal of equilateral Fe triangles," Phys. Rev. B 74, 104417 (2006).
[CrossRef]

J. B. Kim, G. J. Lee, Y. P. Lee, J. Y. Rhee, K. W. Kim, and C. S. Yoon, "One-dimensional magnetic grating structure made easy," Appl. Phys. Lett. 89, 151111 (2006).
[CrossRef]

F. Jonsson and C. Flytzanis, "Nonlinear magneto-optical Bragg gratings," Phys. Rev. Lett. 96, 063902 (2006).
[CrossRef] [PubMed]

R. Antos, J. Postora, J. Mistrik, T. Yamaguchi, S. Yamaguchi, M. Horie, S. Visnovsky, and Y. Otani, "Convergence properties of critical dimension measurements by spectroscopic ellipsometry on gratings made of various materials," J. Appl. Phys. 100, 054906 (2006).
[CrossRef]

2005 (2)

R. Antos, J. Mistik, T. Yamaguchi, S. Visnovsky, S. O. Demokritov, and B. Hillebrands, "Evidence of native oxides on the capping and substrate of Permalloy gratings by magneto-optical spectroscopy in the zeroth- and first-diffraction orders," Appl. Phys. Lett. 86, 231101 (2005).
[CrossRef]

R. Antos, J. Mistrik, T. Yamaguchi, S. Visnovsky, S. O. Demokritov, and B. Hillebrands, "Evaluation of the quality of Permalloy gratings by diffracted magneto-optical spectroscopy," Opt. Express 13, 4651-4656 (2005).
[CrossRef] [PubMed]

2004 (1)

M. Grimsditch and P. Vavassori, "The diffracted magneto-optical Kerr effect: what does it tell you?" J. Phys.: Condens. Matter 16, R275-R294 (2004).

2003 (4)

A. Figotin and I. Vitebskiy, "Electromagnetic unidirectionality in magnetic photonic crystals," Phys. Rev. B 67, 165210 (2003).
[CrossRef]

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, and Th. Rasing, "Magnetic photonic crystals," J. Phys. D: Appl. Phys. 36, R277-R287 (2003).
[CrossRef]

H. Kato, T. Matsushita, A. Takayama, M. Egawa, K. Nishimura, and M. Inoue, "Theoretical analysis of optical and magneto-optical properties of one-dimensional magnetophotonic crystals," J. Appl. Phys. 93, 3906-3911 (2003).
[CrossRef]

G. Neuber, P. Rauer, J. Kunze, T. Korn, C. Pels, G. Meier, U. Merkt, J. Backstrom, and M. Rubhausen, "Temperature-dependent spectral generalized magneto-optical ellipsometry," Appl. Phys. Lett. 83, 4509-4511 (2003).
[CrossRef]

2000 (4)

E. Takeda, N. Todoroki, Y. Kitamoto, M. Abe, M. Inoue, T. Fujii, and K. Arai, "Faraday effect enhancement in Co-ferrite layer incorporated into one-dimensional photonic crystal working as a Fabry-Pérot resonator," J. Appl. Phys. 87, 6782-6784 (2000).
[CrossRef]

M. J. Steel, M. Levy, and R. M. Osgood, "High transmission enhanced Faraday rotation in one-dimensional photonic crystals with defects," IEEE Photon. Technol. Lett. 12, 1171-1173 (2000).
[CrossRef]

M. J. Steel, M. Levy, and R. M. Osgood, "Large magnetooptical Kerr rotation with high reflectivity from photonic bandgap structures with defects," J. Lightwave Technol. 18, 1289-1296 (2000).
[CrossRef]

M. J. Steel, M. Levy, and R. M. Osgood, "Photonic bandgaps with defects and the enhancement of Faraday rotation," J. Lightwave Technol. 18, 1297-1308 (2000).
[CrossRef]

1999 (3)

M. Inoue, K. Arai, T. Fujii, and M. Abe, "One-dimensional magnetophotonic crystals," J. Appl. Phys. 85, 5768-5770 (1999).
[CrossRef]

P. Hones, M. Diserens, and F. Levy, "Characterization of sputter-deposited chromium oxide thin films," Surf. Coat. Technol. 120, 277-283 (1999).
[CrossRef]

I. Abdulhalim, "Analytic propagation matrix method for linear optics of arbitrary biaxial layered media," J. Opt. A: Pure Appl. Opt. 1, 646-653 (1999).
[CrossRef]

1996 (1)

1981 (1)

Appl. Phys. Lett. (3)

J. B. Kim, G. J. Lee, Y. P. Lee, J. Y. Rhee, K. W. Kim, and C. S. Yoon, "One-dimensional magnetic grating structure made easy," Appl. Phys. Lett. 89, 151111 (2006).
[CrossRef]

R. Antos, J. Mistik, T. Yamaguchi, S. Visnovsky, S. O. Demokritov, and B. Hillebrands, "Evidence of native oxides on the capping and substrate of Permalloy gratings by magneto-optical spectroscopy in the zeroth- and first-diffraction orders," Appl. Phys. Lett. 86, 231101 (2005).
[CrossRef]

G. Neuber, P. Rauer, J. Kunze, T. Korn, C. Pels, G. Meier, U. Merkt, J. Backstrom, and M. Rubhausen, "Temperature-dependent spectral generalized magneto-optical ellipsometry," Appl. Phys. Lett. 83, 4509-4511 (2003).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

M. J. Steel, M. Levy, and R. M. Osgood, "High transmission enhanced Faraday rotation in one-dimensional photonic crystals with defects," IEEE Photon. Technol. Lett. 12, 1171-1173 (2000).
[CrossRef]

J. Appl. Phys. (4)

R. Antos, J. Postora, J. Mistrik, T. Yamaguchi, S. Yamaguchi, M. Horie, S. Visnovsky, and Y. Otani, "Convergence properties of critical dimension measurements by spectroscopic ellipsometry on gratings made of various materials," J. Appl. Phys. 100, 054906 (2006).
[CrossRef]

H. Kato, T. Matsushita, A. Takayama, M. Egawa, K. Nishimura, and M. Inoue, "Theoretical analysis of optical and magneto-optical properties of one-dimensional magnetophotonic crystals," J. Appl. Phys. 93, 3906-3911 (2003).
[CrossRef]

M. Inoue, K. Arai, T. Fujii, and M. Abe, "One-dimensional magnetophotonic crystals," J. Appl. Phys. 85, 5768-5770 (1999).
[CrossRef]

E. Takeda, N. Todoroki, Y. Kitamoto, M. Abe, M. Inoue, T. Fujii, and K. Arai, "Faraday effect enhancement in Co-ferrite layer incorporated into one-dimensional photonic crystal working as a Fabry-Pérot resonator," J. Appl. Phys. 87, 6782-6784 (2000).
[CrossRef]

J. Lightwave Technol. (3)

J. Opt. A: Pure Appl. Opt. (1)

I. Abdulhalim, "Analytic propagation matrix method for linear optics of arbitrary biaxial layered media," J. Opt. A: Pure Appl. Opt. 1, 646-653 (1999).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

J. Phys. D: Appl. Phys. (2)

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, and Th. Rasing, "Magnetic photonic crystals," J. Phys. D: Appl. Phys. 36, R277-R287 (2003).
[CrossRef]

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

J. Phys.: Condens. Matter (1)

M. Grimsditch and P. Vavassori, "The diffracted magneto-optical Kerr effect: what does it tell you?" J. Phys.: Condens. Matter 16, R275-R294 (2004).

Opt. Express (1)

Phys. Rev. B (2)

A. Westphalen, A. Schumann, A. Remhof, H. Zabel, T. Last, and U. Kunze, "Magnetization reversal of equilateral Fe triangles," Phys. Rev. B 74, 104417 (2006).
[CrossRef]

A. Figotin and I. Vitebskiy, "Electromagnetic unidirectionality in magnetic photonic crystals," Phys. Rev. B 67, 165210 (2003).
[CrossRef]

Phys. Rev. Lett. (1)

F. Jonsson and C. Flytzanis, "Nonlinear magneto-optical Bragg gratings," Phys. Rev. Lett. 96, 063902 (2006).
[CrossRef] [PubMed]

Surf. Coat. Technol. (1)

P. Hones, M. Diserens, and F. Levy, "Characterization of sputter-deposited chromium oxide thin films," Surf. Coat. Technol. 120, 277-283 (1999).
[CrossRef]

Other (4)

D. F. Edwards, "Silicon (Si)" in Handbook of Optical Constants of Solids, edited by E. D. Palik (Academic, New York, 1998); H. R. Philipp, "Silicon Dioxide (SiO2) (Glass)," ibid.

E. Hecht, Optics (Addison-Wesley, New York, 1998).

J. B. Kim, G. J. Lee, Y. P. Lee, J. Y. Rhee, and C. S. Yoon, "Enhancement of magneto-optical properties of a magnetic grating," J. Appl. Phys. 101, 09C518 (2007).
[CrossRef]

A. K. Zvezdin and V. A. Kotov, Modern Magnetooptics and Magnetooptical Materials (Institute of Physics Publishing, London, 1997).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

(Color online) Diffracted MO effects from a one-dimensional multilayered gyrotropic grating for the polar magnetization.

Fig. 2.
Fig. 2.

(Color online) Theoretical and experimental Kerr rotation spectra in the 0th (a) and the -1st (b) order diffractions for s-polarized incidence. Incident angle was 7° for the 0th order. For the -1st order diffraction, the angle between incident and reflected beams was fixed to 20°. A truncation order of nmax =10 was sufficient enough for the good convergence.

Fig. 3.
Fig. 3.

Simulated Kerr rotation as a function of grating depth. Incident angle was set to 7° for both (a) the 0th and (b) the -1st orders. The truncation order nmax was 50 because of the increase in the grating depth.

Fig. 4.
Fig. 4.

Magnification M as a function of grating depth.

Fig. 5.
Fig. 5.

Simulated spectra of Faraday rotation in (a) the 0th and (b) the -1st orders. The grating depth was set to 12 nm and the truncation order nmax was equal to 10.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

× E = i H , ˜
× H ˜ = i [ ε ( y ¯ ) ] E ,
q = λ d ,
q n = sin θ i + n q ,
E k ( y ¯ , z ¯ ) = n = + f k , n exp [ i ( q n y ¯ + s z ¯ ) ] ,
H ˜ k ( y _ , z _ ) = n = + g k , n exp [ i ( q n y _ + s z _ ) ] ,
[ ε ( y ) ] = { [ ε w ] , 0 y w , [ ε b ] , w y d ,
[ ε w ] = ( ε x x ε x y 0 ε y x ε y y 0 0 0 ε z z ) .
ε ( y ¯ ) α β = n = + ε α β , n exp ( inq y ¯ ) ,
d 2 d z 2 ( f x f y ) = ( [ ε xx ] q 2 [ ε xy ] ( 1 q [ ε zz ] 1 q ) [ ε yx ] ( 1 q [ ε zz ] 1 q ) [ ε yy ] ) ( f x f y ) ,
d d z ( g y g x ) = ( [ ε xx ] q 2 [ ε xy ] [ ε yx ] [ ε yy ] ) ( f x f y ) ,
q = ( 0 0 0 0 0 q 1 0 0 0 0 0 q 0 0 0 0 0 0 q 1 0 0 0 0 0 ) .
θ K ( n ) = 1 2 tan 1 ( 2 Re ( χ ( n ) ) 1 χ ( n ) 2 ) ,
M = θ Ks ( 1 ) θ Ks ( 0 ) ,
sin θ D = sin θ i + N λ d ,

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