Abstract

We study the magneto-optic (MO) Faraday rotation in a two-dimensional square-lattice photonic crystal with a central MO defect layer in the optical wavelength range. We show that when a TM plane wave is incident upon a photonic crystal, an enhancement of Faraday rotation takes place in a region where a resonance peak appears in the photonic bandgap. In this region the mode conversion is high.

© 2005 Optical Society of America

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References

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  1. M. Inoue, T. Fujii, K. Arai, and M. Abe, J. Appl. Phys. 83, 6768 (1998).
    [CrossRef]
  2. M. Steel, M. Levy, and R. Osgood, IEEE Photonics Technol. Lett. 12, 1171 (2000).
    [CrossRef]
  3. S. Kahl and A. Grishin, Appl. Phys. Lett. 84, 438 (2004).
    [CrossRef]
  4. M. Levy, H. C. Yang, M. J. Steel, and J. Fujita, J. Lightwave Technol. 19, 1964 (2001).
    [CrossRef]
  5. K. Sakoda, Phys. Rev. B 52, 8992 (1995).
    [CrossRef]
  6. A. A. Jalali and A. T. Friberg, “Faraday rotation in two-dimensional magneto-optic photonic crystal,” Opt. Commun. (to be published).
  7. S. Kahl and A. Grishin, J. Magn. Magn. Mater. 271, 200 (2004).
  8. G. F. Dionne and G. A. Allen, J. Appl. Phys. 73, 6127 (1993).
    [CrossRef]
  9. S. Visnovsky, K. Postava, and T. Yamaguchi, Czech. J. Phys. 51, 917 (2001).
    [CrossRef]
  10. H. Takeda and K. Yoshino, Phys. Rev. E 68, 046602 (2003).
    [CrossRef]

2004 (2)

S. Kahl and A. Grishin, Appl. Phys. Lett. 84, 438 (2004).
[CrossRef]

S. Kahl and A. Grishin, J. Magn. Magn. Mater. 271, 200 (2004).

2003 (1)

H. Takeda and K. Yoshino, Phys. Rev. E 68, 046602 (2003).
[CrossRef]

2001 (2)

S. Visnovsky, K. Postava, and T. Yamaguchi, Czech. J. Phys. 51, 917 (2001).
[CrossRef]

M. Levy, H. C. Yang, M. J. Steel, and J. Fujita, J. Lightwave Technol. 19, 1964 (2001).
[CrossRef]

2000 (1)

M. Steel, M. Levy, and R. Osgood, IEEE Photonics Technol. Lett. 12, 1171 (2000).
[CrossRef]

1998 (1)

M. Inoue, T. Fujii, K. Arai, and M. Abe, J. Appl. Phys. 83, 6768 (1998).
[CrossRef]

1995 (1)

K. Sakoda, Phys. Rev. B 52, 8992 (1995).
[CrossRef]

1993 (1)

G. F. Dionne and G. A. Allen, J. Appl. Phys. 73, 6127 (1993).
[CrossRef]

Abe, M.

M. Inoue, T. Fujii, K. Arai, and M. Abe, J. Appl. Phys. 83, 6768 (1998).
[CrossRef]

Allen, G. A.

G. F. Dionne and G. A. Allen, J. Appl. Phys. 73, 6127 (1993).
[CrossRef]

Arai, K.

M. Inoue, T. Fujii, K. Arai, and M. Abe, J. Appl. Phys. 83, 6768 (1998).
[CrossRef]

Dionne, G. F.

G. F. Dionne and G. A. Allen, J. Appl. Phys. 73, 6127 (1993).
[CrossRef]

Friberg, A. T.

A. A. Jalali and A. T. Friberg, “Faraday rotation in two-dimensional magneto-optic photonic crystal,” Opt. Commun. (to be published).

Fujii, T.

M. Inoue, T. Fujii, K. Arai, and M. Abe, J. Appl. Phys. 83, 6768 (1998).
[CrossRef]

Fujita, J.

Grishin, A.

S. Kahl and A. Grishin, Appl. Phys. Lett. 84, 438 (2004).
[CrossRef]

S. Kahl and A. Grishin, J. Magn. Magn. Mater. 271, 200 (2004).

Inoue, M.

M. Inoue, T. Fujii, K. Arai, and M. Abe, J. Appl. Phys. 83, 6768 (1998).
[CrossRef]

Jalali, A. A.

A. A. Jalali and A. T. Friberg, “Faraday rotation in two-dimensional magneto-optic photonic crystal,” Opt. Commun. (to be published).

Kahl, S.

S. Kahl and A. Grishin, J. Magn. Magn. Mater. 271, 200 (2004).

S. Kahl and A. Grishin, Appl. Phys. Lett. 84, 438 (2004).
[CrossRef]

Levy, M.

M. Levy, H. C. Yang, M. J. Steel, and J. Fujita, J. Lightwave Technol. 19, 1964 (2001).
[CrossRef]

M. Steel, M. Levy, and R. Osgood, IEEE Photonics Technol. Lett. 12, 1171 (2000).
[CrossRef]

Osgood, R.

M. Steel, M. Levy, and R. Osgood, IEEE Photonics Technol. Lett. 12, 1171 (2000).
[CrossRef]

Postava, K.

S. Visnovsky, K. Postava, and T. Yamaguchi, Czech. J. Phys. 51, 917 (2001).
[CrossRef]

Sakoda, K.

K. Sakoda, Phys. Rev. B 52, 8992 (1995).
[CrossRef]

Steel, M.

M. Steel, M. Levy, and R. Osgood, IEEE Photonics Technol. Lett. 12, 1171 (2000).
[CrossRef]

Steel, M. J.

Takeda, H.

H. Takeda and K. Yoshino, Phys. Rev. E 68, 046602 (2003).
[CrossRef]

Visnovsky, S.

S. Visnovsky, K. Postava, and T. Yamaguchi, Czech. J. Phys. 51, 917 (2001).
[CrossRef]

Yamaguchi, T.

S. Visnovsky, K. Postava, and T. Yamaguchi, Czech. J. Phys. 51, 917 (2001).
[CrossRef]

Yang, H. C.

Yoshino, K.

H. Takeda and K. Yoshino, Phys. Rev. E 68, 046602 (2003).
[CrossRef]

Appl. Phys. Lett. (1)

S. Kahl and A. Grishin, Appl. Phys. Lett. 84, 438 (2004).
[CrossRef]

Czech. J. Phys. (1)

S. Visnovsky, K. Postava, and T. Yamaguchi, Czech. J. Phys. 51, 917 (2001).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

M. Steel, M. Levy, and R. Osgood, IEEE Photonics Technol. Lett. 12, 1171 (2000).
[CrossRef]

J. Appl. Phys. (2)

M. Inoue, T. Fujii, K. Arai, and M. Abe, J. Appl. Phys. 83, 6768 (1998).
[CrossRef]

G. F. Dionne and G. A. Allen, J. Appl. Phys. 73, 6127 (1993).
[CrossRef]

J. Lightwave Technol. (1)

J. Magn. Magn. Mater. (1)

S. Kahl and A. Grishin, J. Magn. Magn. Mater. 271, 200 (2004).

Phys. Rev. B (1)

K. Sakoda, Phys. Rev. B 52, 8992 (1995).
[CrossRef]

Phys. Rev. E (1)

H. Takeda and K. Yoshino, Phys. Rev. E 68, 046602 (2003).
[CrossRef]

Other (1)

A. A. Jalali and A. T. Friberg, “Faraday rotation in two-dimensional magneto-optic photonic crystal,” Opt. Commun. (to be published).

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram of an isotropic 2D square-lattice PC with a central defect of width 3 a . The crystal and the defect, which consists of MO material, extend indefinitely in the y direction. A plane wave is incident from the left onto the structure. The lattice constant is a, and the radius of each rod is r. The distance between the PC’s surface and the first layer of circular rods is d = a 2 .

Fig. 2
Fig. 2

TM-mode transmittance computed for a 2D square-lattice PC with air holes (a) with an isotropic material of dielectric constant ϵ b = 4.75 as background and (b) with a centered isotropic defect of width 3 a and dielectric constant ϵ = ϵ b .

Fig. 3
Fig. 3

Transmittance of TM (solid curve) and TE (dotted curve) modes with an incident TM-polarized light for a 2D PC with a MO BIG layer defect.

Fig. 4
Fig. 4

FR of a TM-polarized incident light on passage through a PC with a MO BIG layer defect. FR is calculated for the zeroth-order output waves.

Equations (9)

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ϵ ̃ = [ ϵ 1 i ϵ 2 0 i ϵ 2 ϵ 1 0 0 0 ϵ 3 ] ,
E x I ( y , z ) = E 0 x exp [ i ( k I y 0 y + k I z 0 z ) ] + n R n exp [ i ( k y n y + k r z n z ) ] ,
H x I ( y , z ) = n S n exp [ i ( k y n y + k r z n z ) ] ,
E x III ( y , z ) = n T n exp { i [ k y n y + k t z n ( z L ) ] } ,
H x III ( y , z ) = n Q n exp { i [ k y n y + k t z n ( z L ) ] } ,
k r y n = k t y n = k y n = k I y 0 + 2 π n a , n = 0 , ± 1 , ± 2 , ± 3 , ... ,
k r z n = { [ ( k I 0 ) 2 ( k y n ) 2 ] 1 2 k I 0 k y n i [ ( k y n ) 2 ( k I 0 ) 2 ] 1 2 k I 0 < k y n } ,
k t z n = { [ ( k III 0 ) 2 ( k y n ) 2 ] 1 2 k III 0 k y n i [ ( k y n ) 2 ( k III 0 ) 2 ] 1 2 k III 0 < k y n } .
tan 2 θ F = 2 R ( E y { 0 } E x { 0 } ) 1 E y { 0 } E x { 0 } 2 ,

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