Abstract

Optical bistability is reported in InPGaInAsP equilateral-triangle-resonator (ETR) microlasers, which are fabricated by planar technology. For a 30μm side ETR microlaser with a 2-μm-wide output waveguide connected to one of the vertices of the ETR, hysteresis loops are observed for the output power versus the injection current from 215to235K. The laser output spectra are measured in the upper and lower states of the hysteresis loop, which show strong mode competition among transverse modes. The hysteresis loops are demonstrated by two-mode rate equations with asymmetric cross gain saturation and different output efficiencies.

© 2009 Optical Society of America

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  1. M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y.-S. Oei, H. Binsma, G.-D. Khoe, and M. K. Smit, Nature 432, 206 (2004).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  5. M. Ueno and R. Lang, J. Appl. Phys. 58, 1689 (1985).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [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]
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    [CrossRef]
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    [CrossRef]

2009 (1)

Y. D. Yang, Y. Z. Huang, K. J. Che, S. J. Wang, Y. H. Hu, and Y. Du, IEEE J. Sel. Top. Quantum Electron. 15, 879 (2009).
[CrossRef]

2008 (4)

Y. Z. Huang, Y. D. Yang, S. J. Wang, K. J. Che, and W. Zhao, Proc. SPIE 7135, 713506 (2008).
[CrossRef]

G. Yuan, Z. Wang, B. Li, M. I. Memon, and S. Yu, IEEE J. Sel. Top. Quantum Electron. 14, 903 (2008).
[CrossRef]

A. Valle, M. Gómez-Molina, and L. Pesquera, IEEE J. Sel. Top. Quantum Electron. 14, 895 (2008).
[CrossRef]

A. Hurtado, I. D. Henning, and M. J. Adams, IEEE J. Sel. Top. Quantum Electron. 14, 911 (2008).
[CrossRef]

2007 (2)

S. V. Zhukovsky, D. N. Chigrin, A. V. Lavrinenko, and J. Kroha, Phys. Rev. Lett. 99, 073902 (2007).
[CrossRef] [PubMed]

Y. Z. Huang, Y. H. Hu, Q. Chen, S. J. Wang, Y. Du, and Z. C. Fan, IEEE Photon. Technol. Lett. 19, 963 (2007).
[CrossRef]

2006 (2)

S. Ishii, A. Nakagawa, and T. Baba, IEEE J. Sel. Top. Quantum Electron. 12, 71 (2006).
[CrossRef]

Y. Z. Huang, Q. Chen, W. H. Guo, Q. Y. Lu, and L. J. Yu, IEEE J. Sel. Top. Quantum Electron. 12, 59 (2006).
[CrossRef]

2005 (1)

2004 (1)

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y.-S. Oei, H. Binsma, G.-D. Khoe, and M. K. Smit, Nature 432, 206 (2004).
[CrossRef] [PubMed]

2002 (1)

M. Sorel, P. J. R. Laybourn, G. Giuliani, and S. Donati, Appl. Phys. Lett. 80, 3051 (2002).
[CrossRef]

2000 (1)

M. F. Booth, A. Schremer, and J. M. Ballantyne, Appl. Phys. Lett. 76, 1095 (2000).
[CrossRef]

1997 (1)

H. Kawaguchi, IEEE J. Sel. Top. Quantum Electron. 3, 1254 (1997).
[CrossRef]

1991 (1)

G. R. Gray and R. Roy, J. Opt. Soc. Am. B 8, 631 (1991).
[CrossRef]

1985 (1)

M. Ueno and R. Lang, J. Appl. Phys. 58, 1689 (1985).
[CrossRef]

1984 (2)

G. P. Agrawal and N. K. Dutta, J. Appl. Phys. 56, 664 (1984).
[CrossRef]

H. Kawaguchi, Appl. Phys. Lett. 45, 1264 (1984).
[CrossRef]

1964 (1)

G. J. Lasher, Solid-State Electron. 7, 707 (1964).
[CrossRef]

Adams, M. J.

A. Hurtado, I. D. Henning, and M. J. Adams, IEEE J. Sel. Top. Quantum Electron. 14, 911 (2008).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal and N. K. Dutta, J. Appl. Phys. 56, 664 (1984).
[CrossRef]

Baba, T.

S. Ishii, A. Nakagawa, and T. Baba, IEEE J. Sel. Top. Quantum Electron. 12, 71 (2006).
[CrossRef]

Ballantyne, J. M.

M. F. Booth, A. Schremer, and J. M. Ballantyne, Appl. Phys. Lett. 76, 1095 (2000).
[CrossRef]

Binsma, H.

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y.-S. Oei, H. Binsma, G.-D. Khoe, and M. K. Smit, Nature 432, 206 (2004).
[CrossRef] [PubMed]

Booth, M. F.

M. F. Booth, A. Schremer, and J. M. Ballantyne, Appl. Phys. Lett. 76, 1095 (2000).
[CrossRef]

Che, K. J.

Y. D. Yang, Y. Z. Huang, K. J. Che, S. J. Wang, Y. H. Hu, and Y. Du, IEEE J. Sel. Top. Quantum Electron. 15, 879 (2009).
[CrossRef]

Y. Z. Huang, Y. D. Yang, S. J. Wang, K. J. Che, and W. Zhao, Proc. SPIE 7135, 713506 (2008).
[CrossRef]

Chen, Q.

Y. Z. Huang, Y. H. Hu, Q. Chen, S. J. Wang, Y. Du, and Z. C. Fan, IEEE Photon. Technol. Lett. 19, 963 (2007).
[CrossRef]

Y. Z. Huang, Q. Chen, W. H. Guo, Q. Y. Lu, and L. J. Yu, IEEE J. Sel. Top. Quantum Electron. 12, 59 (2006).
[CrossRef]

Chigrin, D. N.

S. V. Zhukovsky, D. N. Chigrin, A. V. Lavrinenko, and J. Kroha, Phys. Rev. Lett. 99, 073902 (2007).
[CrossRef] [PubMed]

de Vries, T.

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y.-S. Oei, H. Binsma, G.-D. Khoe, and M. K. Smit, Nature 432, 206 (2004).
[CrossRef] [PubMed]

den Besten, J. H.

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y.-S. Oei, H. Binsma, G.-D. Khoe, and M. K. Smit, Nature 432, 206 (2004).
[CrossRef] [PubMed]

Donati, S.

M. Sorel, P. J. R. Laybourn, G. Giuliani, and S. Donati, Appl. Phys. Lett. 80, 3051 (2002).
[CrossRef]

Dorren, H. J. S.

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y.-S. Oei, H. Binsma, G.-D. Khoe, and M. K. Smit, Nature 432, 206 (2004).
[CrossRef] [PubMed]

Du, Y.

Y. D. Yang, Y. Z. Huang, K. J. Che, S. J. Wang, Y. H. Hu, and Y. Du, IEEE J. Sel. Top. Quantum Electron. 15, 879 (2009).
[CrossRef]

Y. Z. Huang, Y. H. Hu, Q. Chen, S. J. Wang, Y. Du, and Z. C. Fan, IEEE Photon. Technol. Lett. 19, 963 (2007).
[CrossRef]

Dutta, N. K.

G. P. Agrawal and N. K. Dutta, J. Appl. Phys. 56, 664 (1984).
[CrossRef]

Fan, Z. C.

Y. Z. Huang, Y. H. Hu, Q. Chen, S. J. Wang, Y. Du, and Z. C. Fan, IEEE Photon. Technol. Lett. 19, 963 (2007).
[CrossRef]

Giuliani, G.

M. Sorel, P. J. R. Laybourn, G. Giuliani, and S. Donati, Appl. Phys. Lett. 80, 3051 (2002).
[CrossRef]

Gómez-Molina, M.

A. Valle, M. Gómez-Molina, and L. Pesquera, IEEE J. Sel. Top. Quantum Electron. 14, 895 (2008).
[CrossRef]

Gray, G. R.

G. R. Gray and R. Roy, J. Opt. Soc. Am. B 8, 631 (1991).
[CrossRef]

Guo, W. H.

Y. Z. Huang, Q. Chen, W. H. Guo, Q. Y. Lu, and L. J. Yu, IEEE J. Sel. Top. Quantum Electron. 12, 59 (2006).
[CrossRef]

Henning, I. D.

A. Hurtado, I. D. Henning, and M. J. Adams, IEEE J. Sel. Top. Quantum Electron. 14, 911 (2008).
[CrossRef]

Hill, M. T.

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y.-S. Oei, H. Binsma, G.-D. Khoe, and M. K. Smit, Nature 432, 206 (2004).
[CrossRef] [PubMed]

Hu, Y. H.

Y. D. Yang, Y. Z. Huang, K. J. Che, S. J. Wang, Y. H. Hu, and Y. Du, IEEE J. Sel. Top. Quantum Electron. 15, 879 (2009).
[CrossRef]

Y. Z. Huang, Y. H. Hu, Q. Chen, S. J. Wang, Y. Du, and Z. C. Fan, IEEE Photon. Technol. Lett. 19, 963 (2007).
[CrossRef]

Huang, Y. Z.

Y. D. Yang, Y. Z. Huang, K. J. Che, S. J. Wang, Y. H. Hu, and Y. Du, IEEE J. Sel. Top. Quantum Electron. 15, 879 (2009).
[CrossRef]

Y. Z. Huang, Y. D. Yang, S. J. Wang, K. J. Che, and W. Zhao, Proc. SPIE 7135, 713506 (2008).
[CrossRef]

Y. Z. Huang, Y. H. Hu, Q. Chen, S. J. Wang, Y. Du, and Z. C. Fan, IEEE Photon. Technol. Lett. 19, 963 (2007).
[CrossRef]

Y. Z. Huang, Q. Chen, W. H. Guo, Q. Y. Lu, and L. J. Yu, IEEE J. Sel. Top. Quantum Electron. 12, 59 (2006).
[CrossRef]

Hurtado, A.

A. Hurtado, I. D. Henning, and M. J. Adams, IEEE J. Sel. Top. Quantum Electron. 14, 911 (2008).
[CrossRef]

Ishii, S.

S. Ishii, A. Nakagawa, and T. Baba, IEEE J. Sel. Top. Quantum Electron. 12, 71 (2006).
[CrossRef]

Kawaguchi, H.

H. Kawaguchi, IEEE J. Sel. Top. Quantum Electron. 3, 1254 (1997).
[CrossRef]

H. Kawaguchi, Appl. Phys. Lett. 45, 1264 (1984).
[CrossRef]

Khoe, G.-D.

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y.-S. Oei, H. Binsma, G.-D. Khoe, and M. K. Smit, Nature 432, 206 (2004).
[CrossRef] [PubMed]

Kira, G.

Kroha, J.

S. V. Zhukovsky, D. N. Chigrin, A. V. Lavrinenko, and J. Kroha, Phys. Rev. Lett. 99, 073902 (2007).
[CrossRef] [PubMed]

Kuramochi, E.

Lang, R.

M. Ueno and R. Lang, J. Appl. Phys. 58, 1689 (1985).
[CrossRef]

Lasher, G. J.

G. J. Lasher, Solid-State Electron. 7, 707 (1964).
[CrossRef]

Lavrinenko, A. V.

S. V. Zhukovsky, D. N. Chigrin, A. V. Lavrinenko, and J. Kroha, Phys. Rev. Lett. 99, 073902 (2007).
[CrossRef] [PubMed]

Laybourn, P. J. R.

M. Sorel, P. J. R. Laybourn, G. Giuliani, and S. Donati, Appl. Phys. Lett. 80, 3051 (2002).
[CrossRef]

Leijtens, X. J. M.

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y.-S. Oei, H. Binsma, G.-D. Khoe, and M. K. Smit, Nature 432, 206 (2004).
[CrossRef] [PubMed]

Li, B.

G. Yuan, Z. Wang, B. Li, M. I. Memon, and S. Yu, IEEE J. Sel. Top. Quantum Electron. 14, 903 (2008).
[CrossRef]

Lu, Q. Y.

Y. Z. Huang, Q. Chen, W. H. Guo, Q. Y. Lu, and L. J. Yu, IEEE J. Sel. Top. Quantum Electron. 12, 59 (2006).
[CrossRef]

Memon, M. I.

G. Yuan, Z. Wang, B. Li, M. I. Memon, and S. Yu, IEEE J. Sel. Top. Quantum Electron. 14, 903 (2008).
[CrossRef]

Mitsugi, S.

Nakagawa, A.

S. Ishii, A. Nakagawa, and T. Baba, IEEE J. Sel. Top. Quantum Electron. 12, 71 (2006).
[CrossRef]

Notomi, M.

Oei, Y.-S.

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y.-S. Oei, H. Binsma, G.-D. Khoe, and M. K. Smit, Nature 432, 206 (2004).
[CrossRef] [PubMed]

Pesquera, L.

A. Valle, M. Gómez-Molina, and L. Pesquera, IEEE J. Sel. Top. Quantum Electron. 14, 895 (2008).
[CrossRef]

Roy, R.

G. R. Gray and R. Roy, J. Opt. Soc. Am. B 8, 631 (1991).
[CrossRef]

Schremer, A.

M. F. Booth, A. Schremer, and J. M. Ballantyne, Appl. Phys. Lett. 76, 1095 (2000).
[CrossRef]

Shinya, A.

Smalbrugge, B.

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y.-S. Oei, H. Binsma, G.-D. Khoe, and M. K. Smit, Nature 432, 206 (2004).
[CrossRef] [PubMed]

Smit, M. K.

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y.-S. Oei, H. Binsma, G.-D. Khoe, and M. K. Smit, Nature 432, 206 (2004).
[CrossRef] [PubMed]

Sorel, M.

M. Sorel, P. J. R. Laybourn, G. Giuliani, and S. Donati, Appl. Phys. Lett. 80, 3051 (2002).
[CrossRef]

Tanabe, T.

Ueno, M.

M. Ueno and R. Lang, J. Appl. Phys. 58, 1689 (1985).
[CrossRef]

Valle, A.

A. Valle, M. Gómez-Molina, and L. Pesquera, IEEE J. Sel. Top. Quantum Electron. 14, 895 (2008).
[CrossRef]

Wang, S. J.

Y. D. Yang, Y. Z. Huang, K. J. Che, S. J. Wang, Y. H. Hu, and Y. Du, IEEE J. Sel. Top. Quantum Electron. 15, 879 (2009).
[CrossRef]

Y. Z. Huang, Y. D. Yang, S. J. Wang, K. J. Che, and W. Zhao, Proc. SPIE 7135, 713506 (2008).
[CrossRef]

Y. Z. Huang, Y. H. Hu, Q. Chen, S. J. Wang, Y. Du, and Z. C. Fan, IEEE Photon. Technol. Lett. 19, 963 (2007).
[CrossRef]

Wang, Z.

G. Yuan, Z. Wang, B. Li, M. I. Memon, and S. Yu, IEEE J. Sel. Top. Quantum Electron. 14, 903 (2008).
[CrossRef]

Yang, Y. D.

Y. D. Yang, Y. Z. Huang, K. J. Che, S. J. Wang, Y. H. Hu, and Y. Du, IEEE J. Sel. Top. Quantum Electron. 15, 879 (2009).
[CrossRef]

Y. Z. Huang, Y. D. Yang, S. J. Wang, K. J. Che, and W. Zhao, Proc. SPIE 7135, 713506 (2008).
[CrossRef]

Yu, L. J.

Y. Z. Huang, Q. Chen, W. H. Guo, Q. Y. Lu, and L. J. Yu, IEEE J. Sel. Top. Quantum Electron. 12, 59 (2006).
[CrossRef]

Yu, S.

G. Yuan, Z. Wang, B. Li, M. I. Memon, and S. Yu, IEEE J. Sel. Top. Quantum Electron. 14, 903 (2008).
[CrossRef]

Yuan, G.

G. Yuan, Z. Wang, B. Li, M. I. Memon, and S. Yu, IEEE J. Sel. Top. Quantum Electron. 14, 903 (2008).
[CrossRef]

Zhao, W.

Y. Z. Huang, Y. D. Yang, S. J. Wang, K. J. Che, and W. Zhao, Proc. SPIE 7135, 713506 (2008).
[CrossRef]

Zhukovsky, S. V.

S. V. Zhukovsky, D. N. Chigrin, A. V. Lavrinenko, and J. Kroha, Phys. Rev. Lett. 99, 073902 (2007).
[CrossRef] [PubMed]

Appl. Phys. Lett. (3)

H. Kawaguchi, Appl. Phys. Lett. 45, 1264 (1984).
[CrossRef]

M. F. Booth, A. Schremer, and J. M. Ballantyne, Appl. Phys. Lett. 76, 1095 (2000).
[CrossRef]

M. Sorel, P. J. R. Laybourn, G. Giuliani, and S. Donati, Appl. Phys. Lett. 80, 3051 (2002).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (7)

G. Yuan, Z. Wang, B. Li, M. I. Memon, and S. Yu, IEEE J. Sel. Top. Quantum Electron. 14, 903 (2008).
[CrossRef]

S. Ishii, A. Nakagawa, and T. Baba, IEEE J. Sel. Top. Quantum Electron. 12, 71 (2006).
[CrossRef]

H. Kawaguchi, IEEE J. Sel. Top. Quantum Electron. 3, 1254 (1997).
[CrossRef]

A. Valle, M. Gómez-Molina, and L. Pesquera, IEEE J. Sel. Top. Quantum Electron. 14, 895 (2008).
[CrossRef]

A. Hurtado, I. D. Henning, and M. J. Adams, IEEE J. Sel. Top. Quantum Electron. 14, 911 (2008).
[CrossRef]

Y. D. Yang, Y. Z. Huang, K. J. Che, S. J. Wang, Y. H. Hu, and Y. Du, IEEE J. Sel. Top. Quantum Electron. 15, 879 (2009).
[CrossRef]

Y. Z. Huang, Q. Chen, W. H. Guo, Q. Y. Lu, and L. J. Yu, IEEE J. Sel. Top. Quantum Electron. 12, 59 (2006).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

Y. Z. Huang, Y. H. Hu, Q. Chen, S. J. Wang, Y. Du, and Z. C. Fan, IEEE Photon. Technol. Lett. 19, 963 (2007).
[CrossRef]

J. Appl. Phys. (2)

M. Ueno and R. Lang, J. Appl. Phys. 58, 1689 (1985).
[CrossRef]

G. P. Agrawal and N. K. Dutta, J. Appl. Phys. 56, 664 (1984).
[CrossRef]

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

G. R. Gray and R. Roy, J. Opt. Soc. Am. B 8, 631 (1991).
[CrossRef]

Nature (1)

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y.-S. Oei, H. Binsma, G.-D. Khoe, and M. K. Smit, Nature 432, 206 (2004).
[CrossRef] [PubMed]

Opt. Express (1)

Phys. Rev. Lett. (1)

S. V. Zhukovsky, D. N. Chigrin, A. V. Lavrinenko, and J. Kroha, Phys. Rev. Lett. 99, 073902 (2007).
[CrossRef] [PubMed]

Proc. SPIE (1)

Y. Z. Huang, Y. D. Yang, S. J. Wang, K. J. Che, and W. Zhao, Proc. SPIE 7135, 713506 (2008).
[CrossRef]

Solid-State Electron. (1)

G. J. Lasher, Solid-State Electron. 7, 707 (1964).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Schematic graph of an ETR microlaser. The etched semiconductor ETR is indicated by dashed lines and is covered by an insulating Si O 2 layer (gray band) except at the top of the ETR for current injection (triangle), and the P-electrode.

Fig. 2
Fig. 2

Field patterns of magnetic field component H z for (a) the symmetric and (b) the antisymmetric states of the TE 0,33 mode in a 10 μ m side ETR with a 0.7 - μ m -wide output waveguide, where the field in the output waveguide is magnified five times.

Fig. 3
Fig. 3

Output power versus the increased and decreased cw injection current for an In P Ga In As P ETR laser with 30 μ m side at 200 and 230 K , respectively.

Fig. 4
Fig. 4

Output spectra in the lower and the upper states plotted as dashed and solid curves for the In P Ga In As P ETR laser with 30 μ m side at 220 K and 30 mA .

Fig. 5
Fig. 5

Mode photon densities S 1 and S 2 and the output S versus the normalized pumping rate obtained from the two-mode rate equations with S = 0.7 S 1 + 0.3 S 2 .

Equations (4)

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

d N d t = P A N B N 2 C N 3 v g ( g 1 S 1 + g 2 S 2 ) ,
d S 1 d t = Γ γ B N 2 + v g ( Γ g 1 α 1 ) S 1 ,
d S 2 d t = Γ γ B N 2 + v g ( Γ g 2 α 2 ) S 2 ,
g i = a ( N N 0 ) [ 1 ( λ i λ 0 ) 2 δ 2 ] ( 1 C i , i S i C i , 3 i S 3 i ) .

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