Abstract

We propose an approach for the design of resonant cavities employed in magnetophotonic crystal (MPC) circulators and isolators. Starting from the analysis of a model circularly symmetric cavity, we show how to obtain a significant splitting of the eigenfrequencies of the two counterrotating cavity modes without introducing subdomains magnetized in opposite directions. Using the multiple-scattering method extended to handle uniaxial gyrotropic materials, we demonstrate numerically an MPC circulator working in a uniform external magnetic field.

© 2010 Optical Society of America

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  1. A. Figotin and I. Vitebskiy, Phys. Rev. B 67, 165210 (2003).
    [CrossRef]
  2. I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, and T. Rasing, J. Phys. D 36, R277 (2003).
    [CrossRef]
  3. M. Inoue, R. Fujikawa, A. Baryshev, A. Khanikaev, P. B. Lim, H. Uchida, O. Aktsipetrov, A. Fedyanin, T. Murzina, and A. Granovsky, J. Phys. D 39, R151 (2006).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  6. H. Takeda and S. John, Phys. Rev. A 78, 023804 (2008).
    [CrossRef]
  7. Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, Phys. Rev. Lett. 100, 013905 (2008).
    [CrossRef] [PubMed]
  8. Z. Wang and S. Fan, Opt. Lett. 30, 1989 (2005).
    [CrossRef] [PubMed]
  9. Z. Wang and S. Fan, Appl. Phys. B 81, 369 (2005).
    [CrossRef]
  10. Z. Wang and S. Fan, Photonics Nanostruct. Fundam. Appl. 4, 132 (2006).
    [CrossRef]
  11. M. Vanwolleghem, X. Checoury, W. Śmigaj, B. Gralak, L. Magdenko, K. Postava, B. Dagens, P. Beauvillain, and J.-M. Lourtioz, Phys. Rev. B 80, 121102(R) (2009).
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    [CrossRef]
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  15. Faraday rotation of 10 deg/μm has been measured at λ=620 nm in BIG thin films , so a few deg/μm, or g~0.05-0.1, seem accessible in the infrared range. Moderate SEMF (<0.5 T) suffices for BIG saturation .
  16. B. Vertruyen, R. Cloots, J. S. Abell, T. J. Jackson, R. C. da Silva, E. Popova, and N. Keller, Phys. Rev. B 78, 094429 (2008).
    [CrossRef]
  17. N. Adachi, V. P. Denysenkov, S. I. Khartsev, A. M. Grishin, and T. Okuda, J. Appl. Phys. 88, 2734 (2000).
    [CrossRef]

2009 (1)

M. Vanwolleghem, X. Checoury, W. Śmigaj, B. Gralak, L. Magdenko, K. Postava, B. Dagens, P. Beauvillain, and J.-M. Lourtioz, Phys. Rev. B 80, 121102(R) (2009).
[CrossRef]

2008 (3)

B. Vertruyen, R. Cloots, J. S. Abell, T. J. Jackson, R. C. da Silva, E. Popova, and N. Keller, Phys. Rev. B 78, 094429 (2008).
[CrossRef]

H. Takeda and S. John, Phys. Rev. A 78, 023804 (2008).
[CrossRef]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, Phys. Rev. Lett. 100, 013905 (2008).
[CrossRef] [PubMed]

2007 (2)

2006 (2)

Z. Wang and S. Fan, Photonics Nanostruct. Fundam. Appl. 4, 132 (2006).
[CrossRef]

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

2005 (3)

2003 (2)

A. Figotin and I. Vitebskiy, Phys. Rev. B 67, 165210 (2003).
[CrossRef]

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, and T. Rasing, J. Phys. D 36, R277 (2003).
[CrossRef]

2000 (1)

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

1994 (1)

Abell, J. S.

B. Vertruyen, R. Cloots, J. S. Abell, T. J. Jackson, R. C. da Silva, E. Popova, and N. Keller, Phys. Rev. B 78, 094429 (2008).
[CrossRef]

Adachi, N.

N. Adachi, V. P. Denysenkov, S. I. Khartsev, A. M. Grishin, and T. Okuda, J. Appl. Phys. 88, 2734 (2000).
[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, J. Phys. D 39, R151 (2006).
[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, J. Phys. D 39, R151 (2006).
[CrossRef]

Beauvillain, P.

M. Vanwolleghem, X. Checoury, W. Śmigaj, B. Gralak, L. Magdenko, K. Postava, B. Dagens, P. Beauvillain, and J.-M. Lourtioz, Phys. Rev. B 80, 121102(R) (2009).
[CrossRef]

Checoury, X.

M. Vanwolleghem, X. Checoury, W. Śmigaj, B. Gralak, L. Magdenko, K. Postava, B. Dagens, P. Beauvillain, and J.-M. Lourtioz, Phys. Rev. B 80, 121102(R) (2009).
[CrossRef]

Chong, Y. D.

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, Phys. Rev. Lett. 100, 013905 (2008).
[CrossRef] [PubMed]

Cloots, R.

B. Vertruyen, R. Cloots, J. S. Abell, T. J. Jackson, R. C. da Silva, E. Popova, and N. Keller, Phys. Rev. B 78, 094429 (2008).
[CrossRef]

da Silva, R. C.

B. Vertruyen, R. Cloots, J. S. Abell, T. J. Jackson, R. C. da Silva, E. Popova, and N. Keller, Phys. Rev. B 78, 094429 (2008).
[CrossRef]

Dadoenkova, N. N.

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, and T. Rasing, J. Phys. D 36, R277 (2003).
[CrossRef]

Dagens, B.

M. Vanwolleghem, X. Checoury, W. Śmigaj, B. Gralak, L. Magdenko, K. Postava, B. Dagens, P. Beauvillain, and J.-M. Lourtioz, Phys. Rev. B 80, 121102(R) (2009).
[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.

Z. Wang and S. Fan, Photonics Nanostruct. Fundam. Appl. 4, 132 (2006).
[CrossRef]

Z. Wang and S. Fan, Appl. Phys. B 81, 369 (2005).
[CrossRef]

Z. Wang and S. Fan, Opt. Lett. 30, 1989 (2005).
[CrossRef] [PubMed]

Fedyanin, A.

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

Felbacq, D.

Figotin, A.

A. Figotin and I. Vitebskiy, Phys. Rev. B 67, 165210 (2003).
[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, J. Phys. D 39, R151 (2006).
[CrossRef]

Gralak, B.

M. Vanwolleghem, X. Checoury, W. Śmigaj, B. Gralak, L. Magdenko, K. Postava, B. Dagens, P. Beauvillain, and J.-M. Lourtioz, Phys. Rev. B 80, 121102(R) (2009).
[CrossRef]

W. Śmigaj and B. Gralak, http://arxiv.org/abs/0909.2591 (2009).

Granovsky, A.

M. Inoue, R. Fujikawa, A. Baryshev, A. Khanikaev, P. B. Lim, H. Uchida, O. Aktsipetrov, A. Fedyanin, T. Murzina, and A. Granovsky, J. Phys. D 39, R151 (2006).
[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]

Inoue, M.

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

Jackson, T. J.

B. Vertruyen, R. Cloots, J. S. Abell, T. J. Jackson, R. C. da Silva, E. Popova, and N. Keller, Phys. Rev. B 78, 094429 (2008).
[CrossRef]

Joannopoulos, J. D.

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, Phys. Rev. Lett. 100, 013905 (2008).
[CrossRef] [PubMed]

John, S.

H. Takeda and S. John, Phys. Rev. A 78, 023804 (2008).
[CrossRef]

Kakihara, K.

Keller, N.

B. Vertruyen, R. Cloots, J. S. Abell, T. J. Jackson, R. C. da Silva, E. Popova, and N. Keller, Phys. Rev. B 78, 094429 (2008).
[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, J. Phys. D 39, R151 (2006).
[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]

Kono, N.

Koshiba, M.

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, J. Phys. D 39, R151 (2006).
[CrossRef]

Lourtioz, J.-M.

M. Vanwolleghem, X. Checoury, W. Śmigaj, B. Gralak, L. Magdenko, K. Postava, B. Dagens, P. Beauvillain, and J.-M. Lourtioz, Phys. Rev. B 80, 121102(R) (2009).
[CrossRef]

Lyubchanskii, I. L.

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, and T. Rasing, J. Phys. D 36, R277 (2003).
[CrossRef]

Lyubchanskii, M. I.

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, and T. Rasing, J. Phys. D 36, R277 (2003).
[CrossRef]

Magdenko, L.

M. Vanwolleghem, X. Checoury, W. Śmigaj, B. Gralak, L. Magdenko, K. Postava, B. Dagens, P. Beauvillain, and J.-M. Lourtioz, Phys. Rev. B 80, 121102(R) (2009).
[CrossRef]

Maystre, D.

Murzina, T.

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

Okuda, T.

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

Popova, E.

B. Vertruyen, R. Cloots, J. S. Abell, T. J. Jackson, R. C. da Silva, E. Popova, and N. Keller, Phys. Rev. B 78, 094429 (2008).
[CrossRef]

Postava, K.

M. Vanwolleghem, X. Checoury, W. Śmigaj, B. Gralak, L. Magdenko, K. Postava, B. Dagens, P. Beauvillain, and J.-M. Lourtioz, Phys. Rev. B 80, 121102(R) (2009).
[CrossRef]

Rasing, T.

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, and T. Rasing, J. Phys. D 36, R277 (2003).
[CrossRef]

Saitoh, K.

Scheuer, J.

Shapovalov, E. A.

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, and T. Rasing, J. Phys. D 36, R277 (2003).
[CrossRef]

Smigaj, W.

M. Vanwolleghem, X. Checoury, W. Śmigaj, B. Gralak, L. Magdenko, K. Postava, B. Dagens, P. Beauvillain, and J.-M. Lourtioz, Phys. Rev. B 80, 121102(R) (2009).
[CrossRef]

W. Śmigaj and B. Gralak, http://arxiv.org/abs/0909.2591 (2009).

Soljacic, M.

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, Phys. Rev. Lett. 100, 013905 (2008).
[CrossRef] [PubMed]

Takeda, H.

H. Takeda and S. John, Phys. Rev. A 78, 023804 (2008).
[CrossRef]

Tayeb, G.

Uchida, H.

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

Vanwolleghem, M.

M. Vanwolleghem, X. Checoury, W. Śmigaj, B. Gralak, L. Magdenko, K. Postava, B. Dagens, P. Beauvillain, and J.-M. Lourtioz, Phys. Rev. B 80, 121102(R) (2009).
[CrossRef]

Vertruyen, B.

B. Vertruyen, R. Cloots, J. S. Abell, T. J. Jackson, R. C. da Silva, E. Popova, and N. Keller, Phys. Rev. B 78, 094429 (2008).
[CrossRef]

Vitebskiy, I.

A. Figotin and I. Vitebskiy, Phys. Rev. B 67, 165210 (2003).
[CrossRef]

Wang, Z.

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, Phys. Rev. Lett. 100, 013905 (2008).
[CrossRef] [PubMed]

Z. Wang and S. Fan, Photonics Nanostruct. Fundam. Appl. 4, 132 (2006).
[CrossRef]

Z. Wang and S. Fan, Appl. Phys. B 81, 369 (2005).
[CrossRef]

Z. Wang and S. Fan, Opt. Lett. 30, 1989 (2005).
[CrossRef] [PubMed]

Appl. Phys. B (1)

Z. Wang and S. Fan, Appl. Phys. B 81, 369 (2005).
[CrossRef]

J. Appl. Phys. (1)

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

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

J. Phys. D (2)

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, and T. Rasing, J. Phys. D 36, R277 (2003).
[CrossRef]

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

Opt. Express (2)

Opt. Lett. (1)

Photonics Nanostruct. Fundam. Appl. (1)

Z. Wang and S. Fan, Photonics Nanostruct. Fundam. Appl. 4, 132 (2006).
[CrossRef]

Phys. Rev. A (1)

H. Takeda and S. John, Phys. Rev. A 78, 023804 (2008).
[CrossRef]

Phys. Rev. B (3)

M. Vanwolleghem, X. Checoury, W. Śmigaj, B. Gralak, L. Magdenko, K. Postava, B. Dagens, P. Beauvillain, and J.-M. Lourtioz, Phys. Rev. B 80, 121102(R) (2009).
[CrossRef]

A. Figotin and I. Vitebskiy, Phys. Rev. B 67, 165210 (2003).
[CrossRef]

B. Vertruyen, R. Cloots, J. S. Abell, T. J. Jackson, R. C. da Silva, E. Popova, and N. Keller, Phys. Rev. B 78, 094429 (2008).
[CrossRef]

Phys. Rev. Lett. (1)

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, Phys. Rev. Lett. 100, 013905 (2008).
[CrossRef] [PubMed]

Other (2)

W. Śmigaj and B. Gralak, http://arxiv.org/abs/0909.2591 (2009).

Faraday rotation of 10 deg/μm has been measured at λ=620 nm in BIG thin films , so a few deg/μm, or g~0.05-0.1, seem accessible in the infrared range. Moderate SEMF (<0.5 T) suffices for BIG saturation .

Supplementary Material (1)

» Media 1: CSV (15 KB)     

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Figures (4)

Fig. 1
Fig. 1

Radial dependence of H z of the dipolar eigenmodes of the circular cavity shown in the inset. Regions filled with BIG are shaded in gray (red online).

Fig. 2
Fig. 2

(a) Direct insertion of the circular cavity into the MPC. (b) Result after adjustment of hole positions.

Fig. 3
Fig. 3

(a), (b) Magnetic field H z of the degenerate eigenmodes of the cavity from Fig. 2b. (c) Distribution of g ( E e * × E o ) z ̂ . All plots show the real parts of the respective quantities normalized to the interval [ 1 , 1 ] ; with the chosen global phase of eigenmode fields, the imaginary parts are negligible.

Fig. 4
Fig. 4

(a) Magnitude of the magnetic field excited by a point source of frequency ω = 0.3124 ( 2 π c a ) placed near the inlet of waveguide W 1 of the circulator. Positions and sizes of all holes are given in Media 1. (b) Transmission and isolation spectra. T i ( i = 2 , 3 ) denotes the Poynting flux through segment L i . To minimize the influence of backreflections on transmission, waveguide terminations have been adjusted to ensure very low reflection losses near the resonant frequency of the cavity.

Equations (3)

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

V = i 2 ω g ( r ) z ̂ [ E e * ( r ) × E o ( r ) ] d r ϵ ( r ) | E o ( r ) | 2 d r ϵ ( r ) | E e ( r ) | 2 d r
( E e * × E o ) ( r , ϕ ) = l R ( r ) R ( r ) ω 2 r ϵ ( r ) 2 z ̂ , R d R d r ,
V = i ω l 0 ϵ 2 ( r ) g ( r ) R ( r ) R ( r ) d r 0 ϵ 1 ( r ) { l 2 r 1 [ R ( r ) ] 2 + r [ R ( r ) ] 2 } d r .

Metrics