Abstract

The efficiency of the dynamic population gratings recorded in highly doped erbium fibers has been studied. We find that the grating response increases with optical density, although the presence of erbium ion pairs in fibers with ion density of the order of 6.3×1025m3 degrades the grating efficiency. The experimental results have been reproduced including inhomogeneous upconversion processes in the nonlinear coupled-wave equations.

© 2011 Optical Society of America

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References

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  1. S. Frisken, “Transient Bragg reflection gratings in erbium-doped fiber amplifiers,” Opt. Lett. 17, 1776–1778 (1992).
    [CrossRef] [PubMed]
  2. B. Fischer, J. L. Zyskind, J. W. Sulhoff, and D. J. DiGiovanni, “Nonlinear wave mixing and induced gratings in erbium-doped fiber amplifiers,” Opt. Lett. 18, 2108–2110 (1993).
    [CrossRef] [PubMed]
  3. M. Horowitz, R. Daisy, B. Fischer, and J. Zyskind, “Narrow-linewidth, single-mode erbium-doped fibre laser with intracavity wave mixing in saturable absorber,” Electron. Lett. 30, 648–649 (1994).
    [CrossRef]
  4. S. A. Havstad, B. Fischer, A. E. Willner, and M. G. Wickham, “Loop-mirror filters based on saturable-gain or -absorber gratings,” Opt. Lett. 24, 1466–1468 (1999).
    [CrossRef]
  5. S. Stepanov, E. Hernández, and M. Plata, “Two-wave mixing by means of dynamic Bragg gratings recorded by saturation of absorption in erbium-doped fibers,” Opt. Lett. 29, 1327–1329(2004).
    [CrossRef] [PubMed]
  6. S. Stepanov, “Dynamic population gratings in rare-earth-doped optical fibres,” J. Phys. D 41, 224002 (2008).
    [CrossRef]
  7. S. Stepanov and E. Hernández, “Observation of spatial migration of excitation in Er-doped optical fibers by means of a population grating technique,” Opt. Lett. 30, 1926–1928 (2005).
    [CrossRef] [PubMed]
  8. S. Stepanov and E. Hernández, “Phase contribution to dynamic gratings recorded in Er-doped fiber with saturable absorption,” Opt. Commun. 271, 91–95 (2007).
    [CrossRef]
  9. S. Stepanov, E. Hernández, and M. Plata, “Two-wave mixing of orthogonally polarized waves via anisotropic population gratings in erbium-doped optical fiber,” J. Opt. Soc. Am. B 22, 1161–1166 (2005).
    [CrossRef]
  10. D. García Casillas and S. Stepanov, “Sub-milliwatt sub-millisecond recording of population gratings in ytterbium-doped optical fibers at 976 nm,” Opt. Commun. 284, 2202–2205(2011).
    [CrossRef]
  11. S. Stepanov and M. Plata, “Slow and fast light via two-wave mixing in erbium-doped fibers with saturable absorption,” Phys. Rev. A 80, 053830 (2009).
    [CrossRef]
  12. L. F. Shampine, M. W. Reichelt, and J. Kierzenka, “Solving boundary value problems for ordinary differential equations in MATLAB with BVP4C,” http://www.mathworks.com/bvp_tutorial.
  13. F. Sanchez, P. L. Boudec, P.-L. Francois, and G. Stephan, “Effects of ion pairs on the dynamics of erbium-doped fiber lasers,” Phys. Rev. A 48, 2220–2229 (1993).
    [CrossRef] [PubMed]
  14. J. L. Wagener, P. F. Wysocki, M. J. F. Digonnet, H. J. Shaw, and D. J. DiGiovanni, “Effects of concentration and clusters in erbium-doped fiber lasers,” Opt. Lett. 18, 2014–2016 (1993).
    [CrossRef] [PubMed]
  15. P. F. Wysocki, J. L. Wagener, M. J. F. Digonnet, and H. J. Shaw, “Evidence and modelling of paired ions and other loss mechanisms in erbium-doped silica fibers,” Proc. SPIE 1789, 66–79(1993).
    [CrossRef]
  16. J. Li, K. Duan, Y. Wang, W. Zhao, J. Zhu, Y. Guo, and X. Lin, “Modeling and effects of ion pairs in high-concentration erbium-doped fiber lasers,” J. Mod. Opt. 55, 447–458 (2008).
    [CrossRef]
  17. O. G. Calderón, S. Melle, F. Arrieta-Yáñez, M. A. Antón, and F. Carreño, “Effect of ion pairs in fast-light bandwidth in high concentration erbium-doped fibers,” J. Opt. Soc. Am. B 25, C55–C60 (2008).
    [CrossRef]

2011 (1)

D. García Casillas and S. Stepanov, “Sub-milliwatt sub-millisecond recording of population gratings in ytterbium-doped optical fibers at 976 nm,” Opt. Commun. 284, 2202–2205(2011).
[CrossRef]

2009 (1)

S. Stepanov and M. Plata, “Slow and fast light via two-wave mixing in erbium-doped fibers with saturable absorption,” Phys. Rev. A 80, 053830 (2009).
[CrossRef]

2008 (3)

S. Stepanov, “Dynamic population gratings in rare-earth-doped optical fibres,” J. Phys. D 41, 224002 (2008).
[CrossRef]

J. Li, K. Duan, Y. Wang, W. Zhao, J. Zhu, Y. Guo, and X. Lin, “Modeling and effects of ion pairs in high-concentration erbium-doped fiber lasers,” J. Mod. Opt. 55, 447–458 (2008).
[CrossRef]

O. G. Calderón, S. Melle, F. Arrieta-Yáñez, M. A. Antón, and F. Carreño, “Effect of ion pairs in fast-light bandwidth in high concentration erbium-doped fibers,” J. Opt. Soc. Am. B 25, C55–C60 (2008).
[CrossRef]

2007 (1)

S. Stepanov and E. Hernández, “Phase contribution to dynamic gratings recorded in Er-doped fiber with saturable absorption,” Opt. Commun. 271, 91–95 (2007).
[CrossRef]

2005 (2)

2004 (1)

1999 (1)

1994 (1)

M. Horowitz, R. Daisy, B. Fischer, and J. Zyskind, “Narrow-linewidth, single-mode erbium-doped fibre laser with intracavity wave mixing in saturable absorber,” Electron. Lett. 30, 648–649 (1994).
[CrossRef]

1993 (4)

J. L. Wagener, P. F. Wysocki, M. J. F. Digonnet, H. J. Shaw, and D. J. DiGiovanni, “Effects of concentration and clusters in erbium-doped fiber lasers,” Opt. Lett. 18, 2014–2016 (1993).
[CrossRef] [PubMed]

B. Fischer, J. L. Zyskind, J. W. Sulhoff, and D. J. DiGiovanni, “Nonlinear wave mixing and induced gratings in erbium-doped fiber amplifiers,” Opt. Lett. 18, 2108–2110 (1993).
[CrossRef] [PubMed]

F. Sanchez, P. L. Boudec, P.-L. Francois, and G. Stephan, “Effects of ion pairs on the dynamics of erbium-doped fiber lasers,” Phys. Rev. A 48, 2220–2229 (1993).
[CrossRef] [PubMed]

P. F. Wysocki, J. L. Wagener, M. J. F. Digonnet, and H. J. Shaw, “Evidence and modelling of paired ions and other loss mechanisms in erbium-doped silica fibers,” Proc. SPIE 1789, 66–79(1993).
[CrossRef]

1992 (1)

Antón, M. A.

Arrieta-Yáñez, F.

Boudec, P. L.

F. Sanchez, P. L. Boudec, P.-L. Francois, and G. Stephan, “Effects of ion pairs on the dynamics of erbium-doped fiber lasers,” Phys. Rev. A 48, 2220–2229 (1993).
[CrossRef] [PubMed]

Calderón, O. G.

Carreño, F.

Daisy, R.

M. Horowitz, R. Daisy, B. Fischer, and J. Zyskind, “Narrow-linewidth, single-mode erbium-doped fibre laser with intracavity wave mixing in saturable absorber,” Electron. Lett. 30, 648–649 (1994).
[CrossRef]

DiGiovanni, D. J.

Digonnet, M. J. F.

J. L. Wagener, P. F. Wysocki, M. J. F. Digonnet, H. J. Shaw, and D. J. DiGiovanni, “Effects of concentration and clusters in erbium-doped fiber lasers,” Opt. Lett. 18, 2014–2016 (1993).
[CrossRef] [PubMed]

P. F. Wysocki, J. L. Wagener, M. J. F. Digonnet, and H. J. Shaw, “Evidence and modelling of paired ions and other loss mechanisms in erbium-doped silica fibers,” Proc. SPIE 1789, 66–79(1993).
[CrossRef]

Duan, K.

J. Li, K. Duan, Y. Wang, W. Zhao, J. Zhu, Y. Guo, and X. Lin, “Modeling and effects of ion pairs in high-concentration erbium-doped fiber lasers,” J. Mod. Opt. 55, 447–458 (2008).
[CrossRef]

Fischer, B.

Francois, P.-L.

F. Sanchez, P. L. Boudec, P.-L. Francois, and G. Stephan, “Effects of ion pairs on the dynamics of erbium-doped fiber lasers,” Phys. Rev. A 48, 2220–2229 (1993).
[CrossRef] [PubMed]

Frisken, S.

García Casillas, D.

D. García Casillas and S. Stepanov, “Sub-milliwatt sub-millisecond recording of population gratings in ytterbium-doped optical fibers at 976 nm,” Opt. Commun. 284, 2202–2205(2011).
[CrossRef]

Guo, Y.

J. Li, K. Duan, Y. Wang, W. Zhao, J. Zhu, Y. Guo, and X. Lin, “Modeling and effects of ion pairs in high-concentration erbium-doped fiber lasers,” J. Mod. Opt. 55, 447–458 (2008).
[CrossRef]

Havstad, S. A.

Hernández, E.

Horowitz, M.

M. Horowitz, R. Daisy, B. Fischer, and J. Zyskind, “Narrow-linewidth, single-mode erbium-doped fibre laser with intracavity wave mixing in saturable absorber,” Electron. Lett. 30, 648–649 (1994).
[CrossRef]

Kierzenka, J.

L. F. Shampine, M. W. Reichelt, and J. Kierzenka, “Solving boundary value problems for ordinary differential equations in MATLAB with BVP4C,” http://www.mathworks.com/bvp_tutorial.

Li, J.

J. Li, K. Duan, Y. Wang, W. Zhao, J. Zhu, Y. Guo, and X. Lin, “Modeling and effects of ion pairs in high-concentration erbium-doped fiber lasers,” J. Mod. Opt. 55, 447–458 (2008).
[CrossRef]

Lin, X.

J. Li, K. Duan, Y. Wang, W. Zhao, J. Zhu, Y. Guo, and X. Lin, “Modeling and effects of ion pairs in high-concentration erbium-doped fiber lasers,” J. Mod. Opt. 55, 447–458 (2008).
[CrossRef]

Melle, S.

Plata, M.

Reichelt, M. W.

L. F. Shampine, M. W. Reichelt, and J. Kierzenka, “Solving boundary value problems for ordinary differential equations in MATLAB with BVP4C,” http://www.mathworks.com/bvp_tutorial.

Sanchez, F.

F. Sanchez, P. L. Boudec, P.-L. Francois, and G. Stephan, “Effects of ion pairs on the dynamics of erbium-doped fiber lasers,” Phys. Rev. A 48, 2220–2229 (1993).
[CrossRef] [PubMed]

Shampine, L. F.

L. F. Shampine, M. W. Reichelt, and J. Kierzenka, “Solving boundary value problems for ordinary differential equations in MATLAB with BVP4C,” http://www.mathworks.com/bvp_tutorial.

Shaw, H. J.

J. L. Wagener, P. F. Wysocki, M. J. F. Digonnet, H. J. Shaw, and D. J. DiGiovanni, “Effects of concentration and clusters in erbium-doped fiber lasers,” Opt. Lett. 18, 2014–2016 (1993).
[CrossRef] [PubMed]

P. F. Wysocki, J. L. Wagener, M. J. F. Digonnet, and H. J. Shaw, “Evidence and modelling of paired ions and other loss mechanisms in erbium-doped silica fibers,” Proc. SPIE 1789, 66–79(1993).
[CrossRef]

Stepanov, S.

D. García Casillas and S. Stepanov, “Sub-milliwatt sub-millisecond recording of population gratings in ytterbium-doped optical fibers at 976 nm,” Opt. Commun. 284, 2202–2205(2011).
[CrossRef]

S. Stepanov and M. Plata, “Slow and fast light via two-wave mixing in erbium-doped fibers with saturable absorption,” Phys. Rev. A 80, 053830 (2009).
[CrossRef]

S. Stepanov, “Dynamic population gratings in rare-earth-doped optical fibres,” J. Phys. D 41, 224002 (2008).
[CrossRef]

S. Stepanov and E. Hernández, “Phase contribution to dynamic gratings recorded in Er-doped fiber with saturable absorption,” Opt. Commun. 271, 91–95 (2007).
[CrossRef]

S. Stepanov, E. Hernández, and M. Plata, “Two-wave mixing of orthogonally polarized waves via anisotropic population gratings in erbium-doped optical fiber,” J. Opt. Soc. Am. B 22, 1161–1166 (2005).
[CrossRef]

S. Stepanov and E. Hernández, “Observation of spatial migration of excitation in Er-doped optical fibers by means of a population grating technique,” Opt. Lett. 30, 1926–1928 (2005).
[CrossRef] [PubMed]

S. Stepanov, E. Hernández, and M. Plata, “Two-wave mixing by means of dynamic Bragg gratings recorded by saturation of absorption in erbium-doped fibers,” Opt. Lett. 29, 1327–1329(2004).
[CrossRef] [PubMed]

Stephan, G.

F. Sanchez, P. L. Boudec, P.-L. Francois, and G. Stephan, “Effects of ion pairs on the dynamics of erbium-doped fiber lasers,” Phys. Rev. A 48, 2220–2229 (1993).
[CrossRef] [PubMed]

Sulhoff, J. W.

Wagener, J. L.

J. L. Wagener, P. F. Wysocki, M. J. F. Digonnet, H. J. Shaw, and D. J. DiGiovanni, “Effects of concentration and clusters in erbium-doped fiber lasers,” Opt. Lett. 18, 2014–2016 (1993).
[CrossRef] [PubMed]

P. F. Wysocki, J. L. Wagener, M. J. F. Digonnet, and H. J. Shaw, “Evidence and modelling of paired ions and other loss mechanisms in erbium-doped silica fibers,” Proc. SPIE 1789, 66–79(1993).
[CrossRef]

Wang, Y.

J. Li, K. Duan, Y. Wang, W. Zhao, J. Zhu, Y. Guo, and X. Lin, “Modeling and effects of ion pairs in high-concentration erbium-doped fiber lasers,” J. Mod. Opt. 55, 447–458 (2008).
[CrossRef]

Wickham, M. G.

Willner, A. E.

Wysocki, P. F.

J. L. Wagener, P. F. Wysocki, M. J. F. Digonnet, H. J. Shaw, and D. J. DiGiovanni, “Effects of concentration and clusters in erbium-doped fiber lasers,” Opt. Lett. 18, 2014–2016 (1993).
[CrossRef] [PubMed]

P. F. Wysocki, J. L. Wagener, M. J. F. Digonnet, and H. J. Shaw, “Evidence and modelling of paired ions and other loss mechanisms in erbium-doped silica fibers,” Proc. SPIE 1789, 66–79(1993).
[CrossRef]

Zhao, W.

J. Li, K. Duan, Y. Wang, W. Zhao, J. Zhu, Y. Guo, and X. Lin, “Modeling and effects of ion pairs in high-concentration erbium-doped fiber lasers,” J. Mod. Opt. 55, 447–458 (2008).
[CrossRef]

Zhu, J.

J. Li, K. Duan, Y. Wang, W. Zhao, J. Zhu, Y. Guo, and X. Lin, “Modeling and effects of ion pairs in high-concentration erbium-doped fiber lasers,” J. Mod. Opt. 55, 447–458 (2008).
[CrossRef]

Zyskind, J.

M. Horowitz, R. Daisy, B. Fischer, and J. Zyskind, “Narrow-linewidth, single-mode erbium-doped fibre laser with intracavity wave mixing in saturable absorber,” Electron. Lett. 30, 648–649 (1994).
[CrossRef]

Zyskind, J. L.

Electron. Lett. (1)

M. Horowitz, R. Daisy, B. Fischer, and J. Zyskind, “Narrow-linewidth, single-mode erbium-doped fibre laser with intracavity wave mixing in saturable absorber,” Electron. Lett. 30, 648–649 (1994).
[CrossRef]

J. Mod. Opt. (1)

J. Li, K. Duan, Y. Wang, W. Zhao, J. Zhu, Y. Guo, and X. Lin, “Modeling and effects of ion pairs in high-concentration erbium-doped fiber lasers,” J. Mod. Opt. 55, 447–458 (2008).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Phys. D (1)

S. Stepanov, “Dynamic population gratings in rare-earth-doped optical fibres,” J. Phys. D 41, 224002 (2008).
[CrossRef]

Opt. Commun. (2)

S. Stepanov and E. Hernández, “Phase contribution to dynamic gratings recorded in Er-doped fiber with saturable absorption,” Opt. Commun. 271, 91–95 (2007).
[CrossRef]

D. García Casillas and S. Stepanov, “Sub-milliwatt sub-millisecond recording of population gratings in ytterbium-doped optical fibers at 976 nm,” Opt. Commun. 284, 2202–2205(2011).
[CrossRef]

Opt. Lett. (6)

Phys. Rev. A (2)

F. Sanchez, P. L. Boudec, P.-L. Francois, and G. Stephan, “Effects of ion pairs on the dynamics of erbium-doped fiber lasers,” Phys. Rev. A 48, 2220–2229 (1993).
[CrossRef] [PubMed]

S. Stepanov and M. Plata, “Slow and fast light via two-wave mixing in erbium-doped fibers with saturable absorption,” Phys. Rev. A 80, 053830 (2009).
[CrossRef]

Proc. SPIE (1)

P. F. Wysocki, J. L. Wagener, M. J. F. Digonnet, and H. J. Shaw, “Evidence and modelling of paired ions and other loss mechanisms in erbium-doped silica fibers,” Proc. SPIE 1789, 66–79(1993).
[CrossRef]

Other (1)

L. F. Shampine, M. W. Reichelt, and J. Kierzenka, “Solving boundary value problems for ordinary differential equations in MATLAB with BVP4C,” http://www.mathworks.com/bvp_tutorial.

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Figures (6)

Fig. 1
Fig. 1

(a) Experimental setup used to measure transient TWM in high-concentration EDFs. DFB LD, distributed feedback laser diode; LD TEC, laser diode and temperature controller; PS, phase shifter; FG, function generator; PC1 and PC2, polarization controllers; VOA, variable optical attenuator; CIR1 and CIR2, circulators; EDF, erbium-doped fiber; PD, photodetector; OS, oscilloscope. (b) Traces at the oscilloscope showing the backward transmitted signal in response to a square phase modulation with amplitude π introduced in the forward beam.

Fig. 2
Fig. 2

(a) Experimental relative amplitude as a function of input power for fibers with (left) moderate ion density ( 2.7 × 10 25 m 3 ) and (right) high ion density ( 6.3 × 10 25 m 3 ). (b) Power at the maximum relative amplitude and (c) maximum relative amplitude as a function of optical density for fibers with moderate ion density (circles) and with high ion density (squares). Solid curves, simulations with κ = 0 ; dashed curves, simulations with κ = 0.25 .

Fig. 3
Fig. 3

(Left/bottom axes) Experimental fiber fluorescence as a function of input power for two fibers with different optical density (symbols). (Right/top axes) Simulated fiber fluorescence given by Eq. (10) as a function of intensity I / I sat (solid and dashed curves). In the case of the Er80-0.3 fiber, we plotted the results for κ = 0 (solid curves) and for κ = 0.25 (dashed curves).

Fig. 4
Fig. 4

Normalized stationary transmittance for the forward beam as a function of the frequency offset for fiber (a) Er20-1.0 and (b) Er80-0.3: experimental data (symbols), theoretical fit (solid curve). (b) Lorentzian absorption curve showing partial amplitude-grating contribution (dashed curve) and Lorentzian dispersive curve showing phase-grating contribution (dotted curve).

Fig. 5
Fig. 5

Experimental grating formation rate as a function of input power for fibers with (a) moderate ion density ( 2.7 × 10 25 m 3 ) and (b) high ion density ( 6.3 × 10 25 m 3 ).

Fig. 6
Fig. 6

(a) Two-level system for isolated Er ions with concentration N i and (b) three-level system for Er ion pairs with concentration N pr . The total concentration of ions is N T = N i + 2 N pr .

Tables (1)

Tables Icon

Table 1 Fiber Properties a

Equations (13)

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I ( z ) / I sat = I F + I B + 2 I F I B m cos ( K z ) = I 0 ( 1 + 2 I F I B m I 0 cos ( K z ) ) .
α ¯ = α 0 1 + I 0 ,
δ α = α 0 2 m I F I B ( 1 + I 0 ) 2 .
E F z = α ¯ 2 E F + δ α 4 E B ,
E B z = α ¯ 2 E B δ α 4 E F ,
N 2 t = σ a I ω ( N i N 2 ) σ e I ω N 2 1 τ 0 N 2 ,
N 2 , pr t = 2 σ a I ω ( N pr N 2 , pr ) σ e I ω N 2 , pr 1 τ 0 N 2 , pr ,
N 2 = N T ( 1 2 κ ) 2 I / I sat 1 + I / I sat ,
N 2 , pr = N T κ I / I sat 1 + ( 3 / 2 ) I / I sat .
I f L N T 2 [ ( 1 2 κ ) I / I sat 1 + I / I sat + 2 κ I / I sat 1 + ( 3 / 2 ) I / I sat ] .
α = σ a N 1 σ e N 2 + 2 σ a N 1 , pr = α 0 ( 1 2 κ ) 1 + I / I sat + α 0 2 κ [ 1 + ( 1 / 2 ) I / I sat ] 1 + ( 3 / 2 ) I / I sat .
α ¯ = α 0 ( 1 2 κ ) 1 + I 0 + α 0 2 κ ( 1 + 1 2 I 0 ) 1 + 3 2 I 0 ,
δ α = δ α i + δ α pr = α 0 ( 1 2 κ ) 2 m I F I B ( 1 + I 0 ) 2 + α 0 2 κ 2 m I F I B ( 1 + 3 2 I 0 ) 2 .

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