Abstract

A 980-nm pump-induced nonlinear refractive-index (n2) change in erbium-doped (20-m) and ytterbium-doped (20-m) fibers has been measured at 1064nm by time-delayed photorefractive beam coupling in a copropagating and counterpropagating geometry. It was found that n2 decreases at the wavelength of the probe beam when the pump beam is present. We present a semiclassical theory based on a four-state system that accounts for the pump-induced change of n2. Both theoretical and experimental results show that a significant index change, of the order of 10%, can be obtained for cw pump powers as small as 10mW.

© 2005 Optical Society of America

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  1. R. A. Betts, T. Tjugiarto, Y. L. Xue, and P. L. Chu, IEEE J. Quantum Electron. 27, 908 (1991).
    [CrossRef]
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    [CrossRef]
  4. E. Desurvire, Erbium-Doped Fiber Amplifiers: Principles and Application (Wiley, New York, 1994).
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    [CrossRef] [PubMed]
  6. R. H. Pantell, M. J. F. Digonnet, R. W. Sadowski, and H. J. Shaw, J. Lightwave Technol. 11, 1416 (1993).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  9. M. J. F. Digonnet, R. W. Sadowski, H. J. Shaw, and R. H. Pantell, J. Lightwave Technol. 15, 299 (1997).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  16. Y. H. Kim, B. H. Lee, Y. Chung, U. C. Paek, and W. T. Han, Opt. Lett. 27, 580 (2002). This Letter references our conference paper,[11] indicating our preliminary results on the decrease in the fiber nonlinearity in the presence of a pump beam.
    [CrossRef]

2003 (1)

2002 (1)

1998 (1)

1997 (1)

M. J. F. Digonnet, R. W. Sadowski, H. J. Shaw, and R. H. Pantell, J. Lightwave Technol. 15, 299 (1997).
[CrossRef]

1996 (1)

J. W. Arkwright, P. Elango, T. W. Whitbread, and G. R. Atkins, IEEE Photonics Technol. Lett. 8, 408 (1996).
[CrossRef]

1994 (1)

R. H. Pantell and M. J. F. Digonnet, J. Lightwave Technol. 12, 149 (1994).
[CrossRef]

1993 (2)

Y. L. Xue, P. L. Chu, and W. Zhang, J. Opt. Soc. Am. B 10, 1840 (1993).
[CrossRef]

R. H. Pantell, M. J. F. Digonnet, R. W. Sadowski, and H. J. Shaw, J. Lightwave Technol. 11, 1416 (1993).
[CrossRef]

1992 (3)

1991 (2)

R. A. Betts, T. Tjugiarto, Y. L. Xue, and P. L. Chu, IEEE J. Quantum Electron. 27, 908 (1991).
[CrossRef]

S. C. Fleming and T. J. Whitley, Electron. Lett. 27, 1959 (1991).
[CrossRef]

Arkwright, J. W.

J. W. Arkwright, P. Elango, G. R. Atkins, and T. W. Whitbread, J. Lightwave Technol. 16, 798 (1998).
[CrossRef]

J. W. Arkwright, P. Elango, T. W. Whitbread, and G. R. Atkins, IEEE Photonics Technol. Lett. 8, 408 (1996).
[CrossRef]

Atkins, G. R.

J. W. Arkwright, P. Elango, G. R. Atkins, and T. W. Whitbread, J. Lightwave Technol. 16, 798 (1998).
[CrossRef]

J. W. Arkwright, P. Elango, T. W. Whitbread, and G. R. Atkins, IEEE Photonics Technol. Lett. 8, 408 (1996).
[CrossRef]

Betts, R. A.

R. A. Betts, T. Tjugiarto, Y. L. Xue, and P. L. Chu, IEEE J. Quantum Electron. 27, 908 (1991).
[CrossRef]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, Boston, Mass., 1992).

Chu, P. L.

Chung, Y.

Desurvire, E.

E. Desurvire, IEEE Photonics Technol. Lett. 4, 711 (1992).
[CrossRef]

E. Desurvire, Erbium-Doped Fiber Amplifiers: Principles and Application (Wiley, New York, 1994).

Digonnet, M. J. F.

M. J. F. Digonnet, R. W. Sadowski, H. J. Shaw, and R. H. Pantell, J. Lightwave Technol. 15, 299 (1997).
[CrossRef]

R. H. Pantell and M. J. F. Digonnet, J. Lightwave Technol. 12, 149 (1994).
[CrossRef]

R. H. Pantell, M. J. F. Digonnet, R. W. Sadowski, and H. J. Shaw, J. Lightwave Technol. 11, 1416 (1993).
[CrossRef]

R. H. Pantell, R. W. Sadowski, M. J. F. Digonnet, and H. J. Shaw, Opt. Lett. 17, 1026 (1992).
[CrossRef] [PubMed]

Elango, P.

J. W. Arkwright, P. Elango, G. R. Atkins, and T. W. Whitbread, J. Lightwave Technol. 16, 798 (1998).
[CrossRef]

J. W. Arkwright, P. Elango, T. W. Whitbread, and G. R. Atkins, IEEE Photonics Technol. Lett. 8, 408 (1996).
[CrossRef]

Fleming, S. C.

S. C. Fleming and T. J. Whitley, Electron. Lett. 27, 1959 (1991).
[CrossRef]

Garcia, H.

H. Garcia, A. M. Johnson, F. A. Oguama, and S. Trivedi, Opt. Lett. 28, 1796 (2003).
[CrossRef] [PubMed]

H. Garcia, A. M. Johnson, and S. Trivedi, in Conference on Lasers and Electro-Optics (CLEO), Vol. 73 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), paper CWJ2.

Han, W. T.

Johnson, A. M.

H. Garcia, A. M. Johnson, F. A. Oguama, and S. Trivedi, Opt. Lett. 28, 1796 (2003).
[CrossRef] [PubMed]

H. Garcia, A. M. Johnson, and S. Trivedi, in Conference on Lasers and Electro-Optics (CLEO), Vol. 73 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), paper CWJ2.

Kim, Y. H.

Lee, B. H.

Oguama, F. A.

Paek, U. C.

Pantell, R. H.

M. J. F. Digonnet, R. W. Sadowski, H. J. Shaw, and R. H. Pantell, J. Lightwave Technol. 15, 299 (1997).
[CrossRef]

R. H. Pantell and M. J. F. Digonnet, J. Lightwave Technol. 12, 149 (1994).
[CrossRef]

R. H. Pantell, M. J. F. Digonnet, R. W. Sadowski, and H. J. Shaw, J. Lightwave Technol. 11, 1416 (1993).
[CrossRef]

R. H. Pantell, R. W. Sadowski, M. J. F. Digonnet, and H. J. Shaw, Opt. Lett. 17, 1026 (1992).
[CrossRef] [PubMed]

Sadowski, R. W.

M. J. F. Digonnet, R. W. Sadowski, H. J. Shaw, and R. H. Pantell, J. Lightwave Technol. 15, 299 (1997).
[CrossRef]

R. H. Pantell, M. J. F. Digonnet, R. W. Sadowski, and H. J. Shaw, J. Lightwave Technol. 11, 1416 (1993).
[CrossRef]

R. H. Pantell, R. W. Sadowski, M. J. F. Digonnet, and H. J. Shaw, Opt. Lett. 17, 1026 (1992).
[CrossRef] [PubMed]

Shaw, H. J.

M. J. F. Digonnet, R. W. Sadowski, H. J. Shaw, and R. H. Pantell, J. Lightwave Technol. 15, 299 (1997).
[CrossRef]

R. H. Pantell, M. J. F. Digonnet, R. W. Sadowski, and H. J. Shaw, J. Lightwave Technol. 11, 1416 (1993).
[CrossRef]

R. H. Pantell, R. W. Sadowski, M. J. F. Digonnet, and H. J. Shaw, Opt. Lett. 17, 1026 (1992).
[CrossRef] [PubMed]

Tjugiarto, T.

R. A. Betts, T. Tjugiarto, Y. L. Xue, and P. L. Chu, IEEE J. Quantum Electron. 27, 908 (1991).
[CrossRef]

Trivedi, S.

H. Garcia, A. M. Johnson, F. A. Oguama, and S. Trivedi, Opt. Lett. 28, 1796 (2003).
[CrossRef] [PubMed]

H. Garcia, A. M. Johnson, and S. Trivedi, in Conference on Lasers and Electro-Optics (CLEO), Vol. 73 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), paper CWJ2.

Whitbread, T. W.

J. W. Arkwright, P. Elango, G. R. Atkins, and T. W. Whitbread, J. Lightwave Technol. 16, 798 (1998).
[CrossRef]

J. W. Arkwright, P. Elango, T. W. Whitbread, and G. R. Atkins, IEEE Photonics Technol. Lett. 8, 408 (1996).
[CrossRef]

Whitley, T. J.

S. C. Fleming and T. J. Whitley, Electron. Lett. 27, 1959 (1991).
[CrossRef]

Wu, B.

Xue, Y. L.

Y. L. Xue, P. L. Chu, and W. Zhang, J. Opt. Soc. Am. B 10, 1840 (1993).
[CrossRef]

R. A. Betts, T. Tjugiarto, Y. L. Xue, and P. L. Chu, IEEE J. Quantum Electron. 27, 908 (1991).
[CrossRef]

Zhang, W.

Electron. Lett. (1)

S. C. Fleming and T. J. Whitley, Electron. Lett. 27, 1959 (1991).
[CrossRef]

IEEE J. Quantum Electron. (1)

R. A. Betts, T. Tjugiarto, Y. L. Xue, and P. L. Chu, IEEE J. Quantum Electron. 27, 908 (1991).
[CrossRef]

IEEE Photonics Technol. Lett. (2)

J. W. Arkwright, P. Elango, T. W. Whitbread, and G. R. Atkins, IEEE Photonics Technol. Lett. 8, 408 (1996).
[CrossRef]

E. Desurvire, IEEE Photonics Technol. Lett. 4, 711 (1992).
[CrossRef]

J. Lightwave Technol. (4)

R. H. Pantell, M. J. F. Digonnet, R. W. Sadowski, and H. J. Shaw, J. Lightwave Technol. 11, 1416 (1993).
[CrossRef]

J. W. Arkwright, P. Elango, G. R. Atkins, and T. W. Whitbread, J. Lightwave Technol. 16, 798 (1998).
[CrossRef]

M. J. F. Digonnet, R. W. Sadowski, H. J. Shaw, and R. H. Pantell, J. Lightwave Technol. 15, 299 (1997).
[CrossRef]

R. H. Pantell and M. J. F. Digonnet, J. Lightwave Technol. 12, 149 (1994).
[CrossRef]

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

Opt. Lett. (4)

Other (3)

E. Desurvire, Erbium-Doped Fiber Amplifiers: Principles and Application (Wiley, New York, 1994).

H. Garcia, A. M. Johnson, and S. Trivedi, in Conference on Lasers and Electro-Optics (CLEO), Vol. 73 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), paper CWJ2.

R. W. Boyd, Nonlinear Optics (Academic, Boston, Mass., 1992).

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Figures (4)

Fig. 1
Fig. 1

Typical energy-level diagram for a four-level system used for analysis of the erbium and ytterbium elements.

Fig. 2
Fig. 2

Experimental setup for measuring the pump-induced change in a nonlinear refractive index by use of a photorefractive beam-coupling arrangement ( 1064 - nm laser pulse width, τ p 52 ps at a 100 - MHz repetition rate).

Fig. 3
Fig. 3

Experimental IGA traces with the pump laser on and off for erbium-doped fiber.

Fig. 4
Fig. 4

Effective nonlinear refractive-index change (normalized) versus pump power: (a) erbium-doped fiber ( α = 4.22 dB m , P p th = 0.8 mW ) and (b) ytterbium-doped fiber ( α p = 270 dB m , α s = 1 dB m , P s sat = 1 mW , P p th = 0.1 mW ) .

Equations (9)

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

W 12 τ = 1 1 + η I s I s sat , W 21 τ = η 1 + η I s I s sat ,
R τ = I p I p th , R τ 1 = I pr I pr th ,
I i sat , th = ω i ( σ i peak 1 + δ i ) τ i ,
δ i = 2 ( ω i ω i 1 ) Δ ω i 1 , σ i peak = λ i 2 2 π n 2 τ i Δ ω i 1 ,
i = 2 , 3 , 4 , j = p , pr , s ,
χ s ( ω s ) = n N c σ s peak ω s ( δ + i ) 1 + δ 2 ( I p I p th 1 ) ( I s I s sat + 1 ) ( I p I p th + I pr I pr th + 1 ) ,
χ s ( 3 ) ( ω s ) = n 2 ε o N c 2 σ s peak ω s I s sat δ ( δ 2 + 1 ) ( I p I p th ) 1 ( I p I pr th + I pr I p th ) + 1 .
χ s ( 3 ) ( ω s ) = n 2 ε o N c 2 σ s peak ω s I ¯ s sat δ ( δ 2 + 1 ) 1 ( I p I p th ) [ ( I p I p th ) + 1 ] 2 ,
χ pr ( 3 ) ( ω pr ) = n 2 ε o N c 2 σ pr peak ω p I ¯ pr sat δ pr ( δ pr 2 + 1 ) 2 + ( I p I p th ) [ ( I p I p th ) + 1 ] 2 .

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