Abstract

We propose an optical circulator formed of a magneto-optical cavity in a 2D photonic crystal. With spatially engineered magnetic domain structures, the cavity can be designed to support a pair of counterrotating states at different frequencies. By coupling the cavity to three waveguides, and by proper matching of the frequency split of the cavity modes with the coupling strength between the cavity and the waveguide, ideal three-port circulators with complete isolation and transmission can be created. We present a guideline for domain design needed to maximize the modal coupling and the operational bandwidth for any given magneto-optical constant.

© 2005 Optical Society of America

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  1. R. Wolfe, R. A. Lieberman, V. J. Fratello, R. E. Scotti, and N. Kopylov, Appl. Phys. Lett. 56, 426 (1990).
    [CrossRef]
  2. M. Levy, I. Ilic, R. Scarmozzino, R. M. Osgood, R. Wolfe, C. J. Gutierrez, and G. A. Prinz, IEEE Photon. Technol. Lett. 5, 198 (1993).
    [CrossRef]
  3. M. Levy, IEEE J. Sel. Top. Quantum Electron. 8, 1300 (2002).
    [CrossRef]
  4. M. Inoue, K. Arai, T. Fujii, and M. Abe, J. Appl. Phys. 83, 6768 (1998).
    [CrossRef]
  5. M. J. Steel, M. Levy, and R. M. Osgood, IEEE Photon. Technol. Lett. 12, 1171 (2000).
    [CrossRef]
  6. Y. Ikezawa, K. Nishimura, H. Uchida, and M. Inoue, J. Magn. Magn. Mater. 272/276, 1690 (2004).
    [CrossRef]
  7. S. K. Mondal and B. J. H. Stadler, IEEE Photon. Technol. Lett. 17, 127 (2005).
    [CrossRef]
  8. Z. Wang and S. Fan, “Magneto-optical defects in two-dimensional photonic crystals,” Appl. Phys. B (to be published).
  9. Y. Xu, Y. Li, R. K. Lee, and A. Yariv, Phys. Rev. E 62, 7389 (2000).
    [CrossRef]
  10. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, Phys. Rev. Lett. 80, 960 (1998).
    [CrossRef]
  11. A. P. Zhao, J. Juntunen, and A. V. Raisanen, IEEE Trans. Microwave Theory Tech. 47, 1142 (1999).
    [CrossRef]
  12. N. Adachi, V. P. Denysenkov, S. I. Khartsev, A. M. Grishin, and T. Okuda, J. Appl. Phys. 88, 2734 (2000).
    [CrossRef]
  13. M. Huang and S. Y. Zhang, Appl. Phys. A 74, 177 (2002).
    [CrossRef]

2005 (1)

S. K. Mondal and B. J. H. Stadler, IEEE Photon. Technol. Lett. 17, 127 (2005).
[CrossRef]

2004 (1)

Y. Ikezawa, K. Nishimura, H. Uchida, and M. Inoue, J. Magn. Magn. Mater. 272/276, 1690 (2004).
[CrossRef]

2002 (2)

M. Levy, IEEE J. Sel. Top. Quantum Electron. 8, 1300 (2002).
[CrossRef]

M. Huang and S. Y. Zhang, Appl. Phys. A 74, 177 (2002).
[CrossRef]

2000 (3)

N. Adachi, V. P. Denysenkov, S. I. Khartsev, A. M. Grishin, and T. Okuda, J. Appl. Phys. 88, 2734 (2000).
[CrossRef]

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

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, Phys. Rev. E 62, 7389 (2000).
[CrossRef]

1999 (1)

A. P. Zhao, J. Juntunen, and A. V. Raisanen, IEEE Trans. Microwave Theory Tech. 47, 1142 (1999).
[CrossRef]

1998 (2)

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, Phys. Rev. Lett. 80, 960 (1998).
[CrossRef]

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

1993 (1)

M. Levy, I. Ilic, R. Scarmozzino, R. M. Osgood, R. Wolfe, C. J. Gutierrez, and G. A. Prinz, IEEE Photon. Technol. Lett. 5, 198 (1993).
[CrossRef]

1990 (1)

R. Wolfe, R. A. Lieberman, V. J. Fratello, R. E. Scotti, and N. Kopylov, Appl. Phys. Lett. 56, 426 (1990).
[CrossRef]

Abe, M.

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

Adachi, N.

N. Adachi, V. P. Denysenkov, S. I. Khartsev, A. M. Grishin, and T. Okuda, J. Appl. Phys. 88, 2734 (2000).
[CrossRef]

Arai, K.

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

Denysenkov, V. P.

N. Adachi, V. P. Denysenkov, S. I. Khartsev, A. M. Grishin, and T. Okuda, J. Appl. Phys. 88, 2734 (2000).
[CrossRef]

Fan, S.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, Phys. Rev. Lett. 80, 960 (1998).
[CrossRef]

Z. Wang and S. Fan, “Magneto-optical defects in two-dimensional photonic crystals,” Appl. Phys. B (to be published).

Fratello, V. J.

R. Wolfe, R. A. Lieberman, V. J. Fratello, R. E. Scotti, and N. Kopylov, Appl. Phys. Lett. 56, 426 (1990).
[CrossRef]

Fujii, T.

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

Grishin, A. M.

N. Adachi, V. P. Denysenkov, S. I. Khartsev, A. M. Grishin, and T. Okuda, J. Appl. Phys. 88, 2734 (2000).
[CrossRef]

Gutierrez, C. J.

M. Levy, I. Ilic, R. Scarmozzino, R. M. Osgood, R. Wolfe, C. J. Gutierrez, and G. A. Prinz, IEEE Photon. Technol. Lett. 5, 198 (1993).
[CrossRef]

Haus, H. A.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, Phys. Rev. Lett. 80, 960 (1998).
[CrossRef]

Huang, M.

M. Huang and S. Y. Zhang, Appl. Phys. A 74, 177 (2002).
[CrossRef]

Ikezawa, Y.

Y. Ikezawa, K. Nishimura, H. Uchida, and M. Inoue, J. Magn. Magn. Mater. 272/276, 1690 (2004).
[CrossRef]

Ilic, I.

M. Levy, I. Ilic, R. Scarmozzino, R. M. Osgood, R. Wolfe, C. J. Gutierrez, and G. A. Prinz, IEEE Photon. Technol. Lett. 5, 198 (1993).
[CrossRef]

Inoue, M.

Y. Ikezawa, K. Nishimura, H. Uchida, and M. Inoue, J. Magn. Magn. Mater. 272/276, 1690 (2004).
[CrossRef]

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

Joannopoulos, J. D.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, Phys. Rev. Lett. 80, 960 (1998).
[CrossRef]

Juntunen, J.

A. P. Zhao, J. Juntunen, and A. V. Raisanen, IEEE Trans. Microwave Theory Tech. 47, 1142 (1999).
[CrossRef]

Khartsev, S. I.

N. Adachi, V. P. Denysenkov, S. I. Khartsev, A. M. Grishin, and T. Okuda, J. Appl. Phys. 88, 2734 (2000).
[CrossRef]

Kopylov, N.

R. Wolfe, R. A. Lieberman, V. J. Fratello, R. E. Scotti, and N. Kopylov, Appl. Phys. Lett. 56, 426 (1990).
[CrossRef]

Lee, R. K.

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, Phys. Rev. E 62, 7389 (2000).
[CrossRef]

Levy, M.

M. Levy, IEEE J. Sel. Top. Quantum Electron. 8, 1300 (2002).
[CrossRef]

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

M. Levy, I. Ilic, R. Scarmozzino, R. M. Osgood, R. Wolfe, C. J. Gutierrez, and G. A. Prinz, IEEE Photon. Technol. Lett. 5, 198 (1993).
[CrossRef]

Li, Y.

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, Phys. Rev. E 62, 7389 (2000).
[CrossRef]

Lieberman, R. A.

R. Wolfe, R. A. Lieberman, V. J. Fratello, R. E. Scotti, and N. Kopylov, Appl. Phys. Lett. 56, 426 (1990).
[CrossRef]

Mondal, S. K.

S. K. Mondal and B. J. H. Stadler, IEEE Photon. Technol. Lett. 17, 127 (2005).
[CrossRef]

Nishimura, K.

Y. Ikezawa, K. Nishimura, H. Uchida, and M. Inoue, J. Magn. Magn. Mater. 272/276, 1690 (2004).
[CrossRef]

Okuda, T.

N. Adachi, V. P. Denysenkov, S. I. Khartsev, A. M. Grishin, and T. Okuda, J. Appl. Phys. 88, 2734 (2000).
[CrossRef]

Osgood, R. M.

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

M. Levy, I. Ilic, R. Scarmozzino, R. M. Osgood, R. Wolfe, C. J. Gutierrez, and G. A. Prinz, IEEE Photon. Technol. Lett. 5, 198 (1993).
[CrossRef]

Prinz, G. A.

M. Levy, I. Ilic, R. Scarmozzino, R. M. Osgood, R. Wolfe, C. J. Gutierrez, and G. A. Prinz, IEEE Photon. Technol. Lett. 5, 198 (1993).
[CrossRef]

Raisanen, A. V.

A. P. Zhao, J. Juntunen, and A. V. Raisanen, IEEE Trans. Microwave Theory Tech. 47, 1142 (1999).
[CrossRef]

Scarmozzino, R.

M. Levy, I. Ilic, R. Scarmozzino, R. M. Osgood, R. Wolfe, C. J. Gutierrez, and G. A. Prinz, IEEE Photon. Technol. Lett. 5, 198 (1993).
[CrossRef]

Scotti, R. E.

R. Wolfe, R. A. Lieberman, V. J. Fratello, R. E. Scotti, and N. Kopylov, Appl. Phys. Lett. 56, 426 (1990).
[CrossRef]

Stadler, B. J. H.

S. K. Mondal and B. J. H. Stadler, IEEE Photon. Technol. Lett. 17, 127 (2005).
[CrossRef]

Steel, M. J.

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

Uchida, H.

Y. Ikezawa, K. Nishimura, H. Uchida, and M. Inoue, J. Magn. Magn. Mater. 272/276, 1690 (2004).
[CrossRef]

Villeneuve, P. R.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, Phys. Rev. Lett. 80, 960 (1998).
[CrossRef]

Wang, Z.

Z. Wang and S. Fan, “Magneto-optical defects in two-dimensional photonic crystals,” Appl. Phys. B (to be published).

Wolfe, R.

M. Levy, I. Ilic, R. Scarmozzino, R. M. Osgood, R. Wolfe, C. J. Gutierrez, and G. A. Prinz, IEEE Photon. Technol. Lett. 5, 198 (1993).
[CrossRef]

R. Wolfe, R. A. Lieberman, V. J. Fratello, R. E. Scotti, and N. Kopylov, Appl. Phys. Lett. 56, 426 (1990).
[CrossRef]

Xu, Y.

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, Phys. Rev. E 62, 7389 (2000).
[CrossRef]

Yariv, A.

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, Phys. Rev. E 62, 7389 (2000).
[CrossRef]

Zhang, S. Y.

M. Huang and S. Y. Zhang, Appl. Phys. A 74, 177 (2002).
[CrossRef]

Zhao, A. P.

A. P. Zhao, J. Juntunen, and A. V. Raisanen, IEEE Trans. Microwave Theory Tech. 47, 1142 (1999).
[CrossRef]

Appl. Phys. A (1)

M. Huang and S. Y. Zhang, Appl. Phys. A 74, 177 (2002).
[CrossRef]

Appl. Phys. Lett. (1)

R. Wolfe, R. A. Lieberman, V. J. Fratello, R. E. Scotti, and N. Kopylov, Appl. Phys. Lett. 56, 426 (1990).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

M. Levy, IEEE J. Sel. Top. Quantum Electron. 8, 1300 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

M. Levy, I. Ilic, R. Scarmozzino, R. M. Osgood, R. Wolfe, C. J. Gutierrez, and G. A. Prinz, IEEE Photon. Technol. Lett. 5, 198 (1993).
[CrossRef]

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

S. K. Mondal and B. J. H. Stadler, IEEE Photon. Technol. Lett. 17, 127 (2005).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

A. P. Zhao, J. Juntunen, and A. V. Raisanen, IEEE Trans. Microwave Theory Tech. 47, 1142 (1999).
[CrossRef]

J. Appl. Phys. (2)

N. Adachi, V. P. Denysenkov, S. I. Khartsev, A. M. Grishin, and T. Okuda, J. Appl. Phys. 88, 2734 (2000).
[CrossRef]

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

J. Magn. Magn. Mater. (1)

Y. Ikezawa, K. Nishimura, H. Uchida, and M. Inoue, J. Magn. Magn. Mater. 272/276, 1690 (2004).
[CrossRef]

Phys. Rev. E (1)

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, Phys. Rev. E 62, 7389 (2000).
[CrossRef]

Phys. Rev. Lett. (1)

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, Phys. Rev. Lett. 80, 960 (1998).
[CrossRef]

Other (1)

Z. Wang and S. Fan, “Magneto-optical defects in two-dimensional photonic crystals,” Appl. Phys. B (to be published).

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Figures (4)

Fig. 1
Fig. 1

Schematic of a three-port Y-junction circulator. The straight arrows indicate the incoming and outgoing waves. The curved arrows represent the two counterrotating modes in the resonator.

Fig. 2
Fig. 2

Blue and red, large positive and negative values, respectively. (a) and (b) Hz fields for the two doubly degenerate cavity modes in a point defect formed by a missing airhole in a photonic crystal. The crystal consists of a triangular lattice of airholes with a radius of 0.35 a , introduced into a dielectric of ε = 6.25 . A mirror plane of the crystal is marked with a dashed line in each panel. (c) Spatial distribution of the cross product between the E fields of the two modes shown in (a) and (b).

Fig. 3
Fig. 3

Inset, transmission spectra at the output and isolated ports of a three-port junction circulator. The circulator is constructed as a point defect coupled to three waveguides. Circles, airholes in BIG. The light and dark gray areas represent the magnetic domains with opposite out-of-plane magnetization directions. The FDTD spectra (circles) agree well with the coupled-mode theory analysis (solid curves).

Fig. 4
Fig. 4

Out-of-plane H field patterns of the three-port junction circulator shown in Fig. 3 when excited at ω = 0.3468 ( c a ) . Red and blue represent large positive and negative values, respectively. (a) Non-MO cavity ( ε i = 0 ) excited at the input port; (b) MO cavity with ε a = 0.02463 , excited at the input port; (c) MO cavity excited at the output port.

Equations (9)

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

T 1 2 = 2 3 [ exp ( i 4 π 3 ) 1 + i ( ω ω + ) γ + + exp ( i 2 π 3 ) 1 + i ( ω ω ) γ ] 2 ,
T 1 3 = 2 3 [ exp ( i 2 π 3 ) 1 + i ( ω ω + ) γ + + exp ( i 4 π 3 ) 1 + i ( ω ω ) γ ] 2 ,
ω + = ω 0 + γ + 3 , ω = ω 0 γ 3 ,
ε = [ ε i ε a 0 i ε a ε 0 0 0 ε ] ,
Θ = [ 0 i ε 1 × i μ 0 1 × 0 ]
Θ 0 = [ 0 i ε 1 × u μ 0 1 × 0 ] ,
V = [ 0 i ( ε 1 I ε 1 ) × 0 0 ] .
V α β = i 2 ω α ω β ε a z ̂ ( E α * × E β ) d V ,
( ω e V e o V e o ω e )

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