Abstract

We explain an observed spontaneous transition to the high-brightness, in-phase array state of a seven-core ytterbium-doped fiber laser array [IEEE Photonics Technol. Lett. 13, 439 (2001)]. The responsible mechanism is nonlinear refraction, and either in-phase or antiphase array modes can be selected by control of pump intensity. The phenomenon appears to be robust and scalable.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. C. Cook and T. Y. Fan, in Advanced Solid State Lasers, M. Fejer, H. Injeyan, and U. Keller, eds., Vol. 26 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1999), p. 163.
  2. P. Glas, A. Schirmacher, H. Schönnagel, and M. Naumann, IEEE J. Quantum Electron. 31, 1619 (1995).
    [CrossRef]
  3. P. Glas, M. Naumann, A. Schirmacher, and Th. Pertsch, Opt. Commun. 151, 187 (1998).
    [CrossRef]
  4. L. Kapon, J. Katz, and A. Yariv, Opt. Lett. 10, 125 (1984).
    [CrossRef]
  5. P. K. Cheo, A. Liu, and G. G. King, IEEE Photon. Technol. Lett. 13, 439 (2001).
    [CrossRef]
  6. M. Wrage, P. Glas, D. Fischer, M. Leitner, N. N. Elkin, D. V. Vyosoysky, A. P. Napartovich, and V. N. Troshchieva, Opt. Commun. 205, 367 (2002).
    [CrossRef]
  7. A. Hardy and W. Streifer, J. Lightwave Technol. 4, 90 (1986).
    [CrossRef]
  8. S. M. Jensen, IEEE J. Quantum Electron. QE-18, 1580 (1982).
    [CrossRef]
  9. H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, IEEE J. Sel. Top. Quantum Electron. 1, 2 (1995).
    [CrossRef]
  10. C. H. Henry, R. A. Logan, and K. A. Bertness, J. Appl. Phys. 52, 4457 (1981).
    [CrossRef]
  11. F. Patel, “Solid-state rare-earth doped media for applications in waveguide lasers,” Ph.D. dissertation (University of California, Davis, Davis, Calif., 2000).
  12. K. Vahala, L. C. Chiu, S. Margalit, and A. Yariv, Appl. Phys. Lett. 42, 631 (1983).
    [CrossRef]
  13. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).
  14. M. Wrage, P. Glas, M. Leitner, T. Sandrock, N. N. Elkin, A. P. Napartovich, and A. G. Sukharev, Opt. Commun. 175, 97 (2000).
    [CrossRef]
  15. A. E. Siegman, in Diode Pumped Solid State Lasers: Applications and Issues, M. W. Dowley, ed., Vol. 17 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 184–199.
  16. D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988).
    [CrossRef] [PubMed]
  17. W. Królikowski, U. Trutschel, M. Cronin-Golomb, and C. Schmidt-Hattenberger, Opt. Lett. 19, 320 (1994).
    [CrossRef]
  18. A. V. Buryak and N. N. Akhmediev, IEEE J. Quantum Electron. 31, 682 (1995).
    [CrossRef]
  19. H. Haken, Advanced Synergetics (Springer-Verlag, Berlin, 1983).

2002 (1)

M. Wrage, P. Glas, D. Fischer, M. Leitner, N. N. Elkin, D. V. Vyosoysky, A. P. Napartovich, and V. N. Troshchieva, Opt. Commun. 205, 367 (2002).
[CrossRef]

2001 (1)

P. K. Cheo, A. Liu, and G. G. King, IEEE Photon. Technol. Lett. 13, 439 (2001).
[CrossRef]

2000 (1)

M. Wrage, P. Glas, M. Leitner, T. Sandrock, N. N. Elkin, A. P. Napartovich, and A. G. Sukharev, Opt. Commun. 175, 97 (2000).
[CrossRef]

1998 (1)

P. Glas, M. Naumann, A. Schirmacher, and Th. Pertsch, Opt. Commun. 151, 187 (1998).
[CrossRef]

1995 (3)

P. Glas, A. Schirmacher, H. Schönnagel, and M. Naumann, IEEE J. Quantum Electron. 31, 1619 (1995).
[CrossRef]

H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, IEEE J. Sel. Top. Quantum Electron. 1, 2 (1995).
[CrossRef]

A. V. Buryak and N. N. Akhmediev, IEEE J. Quantum Electron. 31, 682 (1995).
[CrossRef]

1994 (1)

1988 (1)

1986 (1)

A. Hardy and W. Streifer, J. Lightwave Technol. 4, 90 (1986).
[CrossRef]

1984 (1)

1983 (1)

K. Vahala, L. C. Chiu, S. Margalit, and A. Yariv, Appl. Phys. Lett. 42, 631 (1983).
[CrossRef]

1982 (1)

S. M. Jensen, IEEE J. Quantum Electron. QE-18, 1580 (1982).
[CrossRef]

1981 (1)

C. H. Henry, R. A. Logan, and K. A. Bertness, J. Appl. Phys. 52, 4457 (1981).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).

Akhmediev, N. N.

A. V. Buryak and N. N. Akhmediev, IEEE J. Quantum Electron. 31, 682 (1995).
[CrossRef]

Barber, P. R.

H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, IEEE J. Sel. Top. Quantum Electron. 1, 2 (1995).
[CrossRef]

Bertness, K. A.

C. H. Henry, R. A. Logan, and K. A. Bertness, J. Appl. Phys. 52, 4457 (1981).
[CrossRef]

Buryak, A. V.

A. V. Buryak and N. N. Akhmediev, IEEE J. Quantum Electron. 31, 682 (1995).
[CrossRef]

Carman, R. J.

H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, IEEE J. Sel. Top. Quantum Electron. 1, 2 (1995).
[CrossRef]

Cheo, P. K.

P. K. Cheo, A. Liu, and G. G. King, IEEE Photon. Technol. Lett. 13, 439 (2001).
[CrossRef]

Chiu, L. C.

K. Vahala, L. C. Chiu, S. Margalit, and A. Yariv, Appl. Phys. Lett. 42, 631 (1983).
[CrossRef]

Christodoulides, D. N.

Cook, C. C.

C. C. Cook and T. Y. Fan, in Advanced Solid State Lasers, M. Fejer, H. Injeyan, and U. Keller, eds., Vol. 26 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1999), p. 163.

Cronin-Golomb, M.

Dawes, J. M.

H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, IEEE J. Sel. Top. Quantum Electron. 1, 2 (1995).
[CrossRef]

Elkin, N. N.

M. Wrage, P. Glas, D. Fischer, M. Leitner, N. N. Elkin, D. V. Vyosoysky, A. P. Napartovich, and V. N. Troshchieva, Opt. Commun. 205, 367 (2002).
[CrossRef]

M. Wrage, P. Glas, M. Leitner, T. Sandrock, N. N. Elkin, A. P. Napartovich, and A. G. Sukharev, Opt. Commun. 175, 97 (2000).
[CrossRef]

Fan, T. Y.

C. C. Cook and T. Y. Fan, in Advanced Solid State Lasers, M. Fejer, H. Injeyan, and U. Keller, eds., Vol. 26 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1999), p. 163.

Fischer, D.

M. Wrage, P. Glas, D. Fischer, M. Leitner, N. N. Elkin, D. V. Vyosoysky, A. P. Napartovich, and V. N. Troshchieva, Opt. Commun. 205, 367 (2002).
[CrossRef]

Glas, P.

M. Wrage, P. Glas, D. Fischer, M. Leitner, N. N. Elkin, D. V. Vyosoysky, A. P. Napartovich, and V. N. Troshchieva, Opt. Commun. 205, 367 (2002).
[CrossRef]

M. Wrage, P. Glas, M. Leitner, T. Sandrock, N. N. Elkin, A. P. Napartovich, and A. G. Sukharev, Opt. Commun. 175, 97 (2000).
[CrossRef]

P. Glas, M. Naumann, A. Schirmacher, and Th. Pertsch, Opt. Commun. 151, 187 (1998).
[CrossRef]

P. Glas, A. Schirmacher, H. Schönnagel, and M. Naumann, IEEE J. Quantum Electron. 31, 1619 (1995).
[CrossRef]

Haken, H.

H. Haken, Advanced Synergetics (Springer-Verlag, Berlin, 1983).

Hanna, D. C.

H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, IEEE J. Sel. Top. Quantum Electron. 1, 2 (1995).
[CrossRef]

Hardy, A.

A. Hardy and W. Streifer, J. Lightwave Technol. 4, 90 (1986).
[CrossRef]

Henry, C. H.

C. H. Henry, R. A. Logan, and K. A. Bertness, J. Appl. Phys. 52, 4457 (1981).
[CrossRef]

Jensen, S. M.

S. M. Jensen, IEEE J. Quantum Electron. QE-18, 1580 (1982).
[CrossRef]

Joseph, R. I.

Kapon, L.

Katz, J.

King, G. G.

P. K. Cheo, A. Liu, and G. G. King, IEEE Photon. Technol. Lett. 13, 439 (2001).
[CrossRef]

Królikowski, W.

Leitner, M.

M. Wrage, P. Glas, D. Fischer, M. Leitner, N. N. Elkin, D. V. Vyosoysky, A. P. Napartovich, and V. N. Troshchieva, Opt. Commun. 205, 367 (2002).
[CrossRef]

M. Wrage, P. Glas, M. Leitner, T. Sandrock, N. N. Elkin, A. P. Napartovich, and A. G. Sukharev, Opt. Commun. 175, 97 (2000).
[CrossRef]

Liu, A.

P. K. Cheo, A. Liu, and G. G. King, IEEE Photon. Technol. Lett. 13, 439 (2001).
[CrossRef]

Logan, R. A.

C. H. Henry, R. A. Logan, and K. A. Bertness, J. Appl. Phys. 52, 4457 (1981).
[CrossRef]

Mackechnie, C. J.

H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, IEEE J. Sel. Top. Quantum Electron. 1, 2 (1995).
[CrossRef]

Margalit, S.

K. Vahala, L. C. Chiu, S. Margalit, and A. Yariv, Appl. Phys. Lett. 42, 631 (1983).
[CrossRef]

Napartovich, A. P.

M. Wrage, P. Glas, D. Fischer, M. Leitner, N. N. Elkin, D. V. Vyosoysky, A. P. Napartovich, and V. N. Troshchieva, Opt. Commun. 205, 367 (2002).
[CrossRef]

M. Wrage, P. Glas, M. Leitner, T. Sandrock, N. N. Elkin, A. P. Napartovich, and A. G. Sukharev, Opt. Commun. 175, 97 (2000).
[CrossRef]

Naumann, M.

P. Glas, M. Naumann, A. Schirmacher, and Th. Pertsch, Opt. Commun. 151, 187 (1998).
[CrossRef]

P. Glas, A. Schirmacher, H. Schönnagel, and M. Naumann, IEEE J. Quantum Electron. 31, 1619 (1995).
[CrossRef]

Pask, H. M.

H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, IEEE J. Sel. Top. Quantum Electron. 1, 2 (1995).
[CrossRef]

Patel, F.

F. Patel, “Solid-state rare-earth doped media for applications in waveguide lasers,” Ph.D. dissertation (University of California, Davis, Davis, Calif., 2000).

Pertsch, Th.

P. Glas, M. Naumann, A. Schirmacher, and Th. Pertsch, Opt. Commun. 151, 187 (1998).
[CrossRef]

Sandrock, T.

M. Wrage, P. Glas, M. Leitner, T. Sandrock, N. N. Elkin, A. P. Napartovich, and A. G. Sukharev, Opt. Commun. 175, 97 (2000).
[CrossRef]

Schirmacher, A.

P. Glas, M. Naumann, A. Schirmacher, and Th. Pertsch, Opt. Commun. 151, 187 (1998).
[CrossRef]

P. Glas, A. Schirmacher, H. Schönnagel, and M. Naumann, IEEE J. Quantum Electron. 31, 1619 (1995).
[CrossRef]

Schmidt-Hattenberger, C.

Schönnagel, H.

P. Glas, A. Schirmacher, H. Schönnagel, and M. Naumann, IEEE J. Quantum Electron. 31, 1619 (1995).
[CrossRef]

Siegman, A. E.

A. E. Siegman, in Diode Pumped Solid State Lasers: Applications and Issues, M. W. Dowley, ed., Vol. 17 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 184–199.

Streifer, W.

A. Hardy and W. Streifer, J. Lightwave Technol. 4, 90 (1986).
[CrossRef]

Sukharev, A. G.

M. Wrage, P. Glas, M. Leitner, T. Sandrock, N. N. Elkin, A. P. Napartovich, and A. G. Sukharev, Opt. Commun. 175, 97 (2000).
[CrossRef]

Tropper, A. C.

H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, IEEE J. Sel. Top. Quantum Electron. 1, 2 (1995).
[CrossRef]

Troshchieva, V. N.

M. Wrage, P. Glas, D. Fischer, M. Leitner, N. N. Elkin, D. V. Vyosoysky, A. P. Napartovich, and V. N. Troshchieva, Opt. Commun. 205, 367 (2002).
[CrossRef]

Trutschel, U.

Vahala, K.

K. Vahala, L. C. Chiu, S. Margalit, and A. Yariv, Appl. Phys. Lett. 42, 631 (1983).
[CrossRef]

Vyosoysky, D. V.

M. Wrage, P. Glas, D. Fischer, M. Leitner, N. N. Elkin, D. V. Vyosoysky, A. P. Napartovich, and V. N. Troshchieva, Opt. Commun. 205, 367 (2002).
[CrossRef]

Wrage, M.

M. Wrage, P. Glas, D. Fischer, M. Leitner, N. N. Elkin, D. V. Vyosoysky, A. P. Napartovich, and V. N. Troshchieva, Opt. Commun. 205, 367 (2002).
[CrossRef]

M. Wrage, P. Glas, M. Leitner, T. Sandrock, N. N. Elkin, A. P. Napartovich, and A. G. Sukharev, Opt. Commun. 175, 97 (2000).
[CrossRef]

Yariv, A.

L. Kapon, J. Katz, and A. Yariv, Opt. Lett. 10, 125 (1984).
[CrossRef]

K. Vahala, L. C. Chiu, S. Margalit, and A. Yariv, Appl. Phys. Lett. 42, 631 (1983).
[CrossRef]

Appl. Phys. Lett. (1)

K. Vahala, L. C. Chiu, S. Margalit, and A. Yariv, Appl. Phys. Lett. 42, 631 (1983).
[CrossRef]

IEEE J. Quantum Electron. (3)

P. Glas, A. Schirmacher, H. Schönnagel, and M. Naumann, IEEE J. Quantum Electron. 31, 1619 (1995).
[CrossRef]

S. M. Jensen, IEEE J. Quantum Electron. QE-18, 1580 (1982).
[CrossRef]

A. V. Buryak and N. N. Akhmediev, IEEE J. Quantum Electron. 31, 682 (1995).
[CrossRef]

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

H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, IEEE J. Sel. Top. Quantum Electron. 1, 2 (1995).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

P. K. Cheo, A. Liu, and G. G. King, IEEE Photon. Technol. Lett. 13, 439 (2001).
[CrossRef]

J. Appl. Phys. (1)

C. H. Henry, R. A. Logan, and K. A. Bertness, J. Appl. Phys. 52, 4457 (1981).
[CrossRef]

J. Lightwave Technol. (1)

A. Hardy and W. Streifer, J. Lightwave Technol. 4, 90 (1986).
[CrossRef]

Opt. Commun. (3)

M. Wrage, P. Glas, M. Leitner, T. Sandrock, N. N. Elkin, A. P. Napartovich, and A. G. Sukharev, Opt. Commun. 175, 97 (2000).
[CrossRef]

M. Wrage, P. Glas, D. Fischer, M. Leitner, N. N. Elkin, D. V. Vyosoysky, A. P. Napartovich, and V. N. Troshchieva, Opt. Commun. 205, 367 (2002).
[CrossRef]

P. Glas, M. Naumann, A. Schirmacher, and Th. Pertsch, Opt. Commun. 151, 187 (1998).
[CrossRef]

Opt. Lett. (3)

OSA Trends in Optics and Photonics Series (1)

C. C. Cook and T. Y. Fan, in Advanced Solid State Lasers, M. Fejer, H. Injeyan, and U. Keller, eds., Vol. 26 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1999), p. 163.

OSA Trends in Optics and Photonics Series (1)

A. E. Siegman, in Diode Pumped Solid State Lasers: Applications and Issues, M. W. Dowley, ed., Vol. 17 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 184–199.

Other (3)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).

F. Patel, “Solid-state rare-earth doped media for applications in waveguide lasers,” Ph.D. dissertation (University of California, Davis, Davis, Calif., 2000).

H. Haken, Advanced Synergetics (Springer-Verlag, Berlin, 1983).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Experimental beam shapes compared with array modes predicted by coupled-mode theory: (a) Observed beam just above threshold, (b) higher-order asynchronous array mode, (c) beam observed at pump power of approximately 5× threshold, (d) lowest order, synchronous array mode.

Fig. 2
Fig. 2

Calculated dependence of nonlinear index on pump intensity for a Yb-doped core at pump wavelength 915 nm and laser wavelength 1079 nm. Yb concentration, N0=7.7×1024 m-3. A, approximate pump intensity at the lower value in Ref. 5; B, the same at the higher value used in Ref. 5; C, critical intensity at which n2=0.

Fig. 3
Fig. 3

Effect of nonlinearity on self-organization of the signal in a seven-core fiber amplifier. Plotted is the array phase fluctuation defined in text. (a) At critical pump intensity (n2=0). (b) Locking into higher-order array modes at low pump power (n2<0). (c) Intermediate pump power (n2<0). (d) Locking into the fundamental (synchronous) array mode when n2>0 at high pump levels.

Fig. 4
Fig. 4

Near and far fields predicted by coupled-mode model applied to a 19-core fiber amplifier at high pump level (n2>0).

Equations (4)

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

Esx,y,z=l=1NAlzelx,y,
dAlzdz=im=1NKlmμ1,μ2,,μNAmz.
dAlzdz=im=1NKlm0Amz+iq=1Nm=1NKlm0nqλs2πigqz-γ+Δn1qz+n2qIsqzAmz,
gqz=N0σaλsIpqz/Ic-1/1+Ipqz/Isatλp+Isqz/Isatλs,

Metrics