Abstract

An analysis is presented, based on a rigorous solution of the propagation equations, of an array of saturable fiber amplifiers with scatter in length that is subject to global feedback. Passively phase-locked states exhibiting multistability due to resonant or Kerr nonlinearity are predicted in respectively low and high regimes of optical feedback.

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  1. T. Y. Fan, IEEE J. Sel. Top. Quantum Electron. 11, 567 (2005).
    [CrossRef]
  2. J. R. Leger, Proc. SPIE 6102, XVII (2006).
  3. C. X. Yu, S. J. Augst, S. M. Redmond, K. C. Goldizen, D. V. Murphy, A. Sanchez, and T. Y. Fan, Opt. Lett. 36, 2686 (2011).
    [CrossRef]
  4. W. Chang, T. Wu, H. G. Winful, and A. Galvanauskas, Opt. Express 18, 9634 (2010).
    [CrossRef]
  5. C. J. Corcoran and K. A. Pasch, IEEE J. Quantum Electron. 43, 437 (2007).
    [CrossRef]
  6. F. S. Felber and J. H. Marburger, Appl. Phys. Lett. 28, 731 (1976).
    [CrossRef]
  7. C. J. Corcoran and F. Durville, IEEE J. Quantum Electron. 15, 294 (2009).
    [CrossRef]
  8. C. H. Henry, IEEE J. Quantum Electron. 18, 259 (1982).
    [CrossRef]
  9. D. V. Vysotsky, N. N. Elkin, and A. P. Napartovich, Quantum Electron. 40, 861 (2010).
    [CrossRef]
  10. A. P. Napartovich, N. N. Elkin, and D. V. Vysotsky, Proc. SPIE 7914, 791428 (2011).
  11. H.-S. Chiang, J. R. Leger, J. Nilsson, and J. Sahu, Opt. Lett. 38, 4104 (2013).
  12. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).
  13. Y. S. Kivshar and M. L. Quiroga-Teixeiro, Opt. Lett. 18, 980 (1993).
    [CrossRef]
  14. C. J. Corcoran, F. Durville, and W. Ray, IEEE J. Quantum Electron. 47, 1043 (2011).
    [CrossRef]

2013

2011

C. J. Corcoran, F. Durville, and W. Ray, IEEE J. Quantum Electron. 47, 1043 (2011).
[CrossRef]

C. X. Yu, S. J. Augst, S. M. Redmond, K. C. Goldizen, D. V. Murphy, A. Sanchez, and T. Y. Fan, Opt. Lett. 36, 2686 (2011).
[CrossRef]

A. P. Napartovich, N. N. Elkin, and D. V. Vysotsky, Proc. SPIE 7914, 791428 (2011).

2010

D. V. Vysotsky, N. N. Elkin, and A. P. Napartovich, Quantum Electron. 40, 861 (2010).
[CrossRef]

W. Chang, T. Wu, H. G. Winful, and A. Galvanauskas, Opt. Express 18, 9634 (2010).
[CrossRef]

2009

C. J. Corcoran and F. Durville, IEEE J. Quantum Electron. 15, 294 (2009).
[CrossRef]

2007

C. J. Corcoran and K. A. Pasch, IEEE J. Quantum Electron. 43, 437 (2007).
[CrossRef]

2006

J. R. Leger, Proc. SPIE 6102, XVII (2006).

2005

T. Y. Fan, IEEE J. Sel. Top. Quantum Electron. 11, 567 (2005).
[CrossRef]

1993

1982

C. H. Henry, IEEE J. Quantum Electron. 18, 259 (1982).
[CrossRef]

1976

F. S. Felber and J. H. Marburger, Appl. Phys. Lett. 28, 731 (1976).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).

Augst, S. J.

Chang, W.

Chiang, H.-S.

Corcoran, C. J.

C. J. Corcoran, F. Durville, and W. Ray, IEEE J. Quantum Electron. 47, 1043 (2011).
[CrossRef]

C. J. Corcoran and F. Durville, IEEE J. Quantum Electron. 15, 294 (2009).
[CrossRef]

C. J. Corcoran and K. A. Pasch, IEEE J. Quantum Electron. 43, 437 (2007).
[CrossRef]

Durville, F.

C. J. Corcoran, F. Durville, and W. Ray, IEEE J. Quantum Electron. 47, 1043 (2011).
[CrossRef]

C. J. Corcoran and F. Durville, IEEE J. Quantum Electron. 15, 294 (2009).
[CrossRef]

Elkin, N. N.

A. P. Napartovich, N. N. Elkin, and D. V. Vysotsky, Proc. SPIE 7914, 791428 (2011).

D. V. Vysotsky, N. N. Elkin, and A. P. Napartovich, Quantum Electron. 40, 861 (2010).
[CrossRef]

Fan, T. Y.

Felber, F. S.

F. S. Felber and J. H. Marburger, Appl. Phys. Lett. 28, 731 (1976).
[CrossRef]

Galvanauskas, A.

Goldizen, K. C.

Henry, C. H.

C. H. Henry, IEEE J. Quantum Electron. 18, 259 (1982).
[CrossRef]

Kivshar, Y. S.

Leger, J. R.

Marburger, J. H.

F. S. Felber and J. H. Marburger, Appl. Phys. Lett. 28, 731 (1976).
[CrossRef]

Murphy, D. V.

Napartovich, A. P.

A. P. Napartovich, N. N. Elkin, and D. V. Vysotsky, Proc. SPIE 7914, 791428 (2011).

D. V. Vysotsky, N. N. Elkin, and A. P. Napartovich, Quantum Electron. 40, 861 (2010).
[CrossRef]

Nilsson, J.

Pasch, K. A.

C. J. Corcoran and K. A. Pasch, IEEE J. Quantum Electron. 43, 437 (2007).
[CrossRef]

Quiroga-Teixeiro, M. L.

Ray, W.

C. J. Corcoran, F. Durville, and W. Ray, IEEE J. Quantum Electron. 47, 1043 (2011).
[CrossRef]

Redmond, S. M.

Sahu, J.

Sanchez, A.

Vysotsky, D. V.

A. P. Napartovich, N. N. Elkin, and D. V. Vysotsky, Proc. SPIE 7914, 791428 (2011).

D. V. Vysotsky, N. N. Elkin, and A. P. Napartovich, Quantum Electron. 40, 861 (2010).
[CrossRef]

Winful, H. G.

Wu, T.

Yu, C. X.

Appl. Phys. Lett.

F. S. Felber and J. H. Marburger, Appl. Phys. Lett. 28, 731 (1976).
[CrossRef]

IEEE J. Quantum Electron.

C. J. Corcoran and F. Durville, IEEE J. Quantum Electron. 15, 294 (2009).
[CrossRef]

C. H. Henry, IEEE J. Quantum Electron. 18, 259 (1982).
[CrossRef]

C. J. Corcoran and K. A. Pasch, IEEE J. Quantum Electron. 43, 437 (2007).
[CrossRef]

C. J. Corcoran, F. Durville, and W. Ray, IEEE J. Quantum Electron. 47, 1043 (2011).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

T. Y. Fan, IEEE J. Sel. Top. Quantum Electron. 11, 567 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE

J. R. Leger, Proc. SPIE 6102, XVII (2006).

A. P. Napartovich, N. N. Elkin, and D. V. Vysotsky, Proc. SPIE 7914, 791428 (2011).

Quantum Electron.

D. V. Vysotsky, N. N. Elkin, and A. P. Napartovich, Quantum Electron. 40, 861 (2010).
[CrossRef]

Other

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).

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Figures (3)

Fig. 1.
Fig. 1.

Schematic of a single amplifier.

Fig. 2.
Fig. 2.

Typical form of the function f(g), of which the roots are the solutions for the gain parameters.

Fig. 3.
Fig. 3.

(a) Steady-state solutions of a five-element array plotted in the RocSN plane, where Roc is the output coupler reflectivity and SN is the order parameter (phasing) for 600 values of the input intensity Iin. Two situations are shown: the case when both nonlinearities are present using the given nonzero values marked by ooo and the case with n2=αH=0, marked by ×××. (b) Steady-state solutions in the RocIin plane, where Iin is the incident intensity in W/m2, for normal values for the two nonlinear constants. (c) Steady-state solutions in the RocP plane, where P is the output power, for normal values of the two nonlinear constants. The K-K contribution is not visible, for reasons not yet understood.

Equations (8)

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Ej(z,t)=Fj(z)ei(k0n0zω0t)+Bj(z)ei(k0n0z+ω0t),
Fjz=12γjFj+i(k0n2(IFj+σIBj)+12αHγj)Fj,Bjz=12γjBj+i(k0n2(IBj+σIFj)+12αHγj)Bj,
Tj=(gjexp(iφj)r)/(1rgjexp(iφj)),
fj(g)=1+r2g22rgcosφj(g)(1r2)(g21)γ0LjlngIinjIsat,
φj(g)=2k0n0Lj+αHlng+(1+σ)k0n2Isat(Ljγ01lng)×[1+(γ0Ljlng)(g41+4g2lng)2(g21)2].
G=|N1j=1NTj|2.
S=|Eoutj/|Eoutj||2=|Tj/|Tj||2.
P=(1Roc)j=1N|Tj|2Pinj,

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