Abstract

We report a new, to the best of our knowledge, method for detection of dynamic population gratings in Er-doped fibers with saturable absorption that is based on observation of the transient fluorescence resulting from fast displacement of the recording interference pattern. The signal appears due to essentially different relaxation times of the fluorescence in bright and dark fringes of the light pattern. The experimental results obtained at the recording wavelength λ=1492nm in a single-mode fiber with 5600ppm Er demonstrate good agreement with the theoretical model based on a saturable two-level system. Unlike conventional diffraction-based techniques, the proposed method results in the local grating amplitude value and can be used for characterization of the grating amplitude spatial profile. It can also be suitable for characterization of the grating formation processes in other bulk and thin-film media with saturable absorption.

© 2007 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  6. R. Paschotta, J. Nilsson, L. Reekie, A. C. Trooper, and D. C. Hanna, "Single-frequency ytterbium-doped fiber laser stabilized by spatial hole burning," Opt. Lett. 22, 41-43 (1997).
    [CrossRef]
  7. M. D. Feuer, "Length and power dependence of self-adjusting optical fiber filters," IEEE Photon. Technol. Lett. 10, 1587-1589 (1998).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  12. S. Stepanov, E. Hernández, and M. Plata, "Two-wave mixing of orthogonally polarized waves via anisotropic dynamic gratings in erbium-doped optical fiber," J. Opt. Soc. Am. B 22, 1161-1167 (2005).
    [CrossRef]
  13. S. Stepanov and E. Hernández, "Observation of spatial migration of excitation in Er-doped optical fiber by means of a population grating technique," Opt. Lett. 30, 1926-1928 (2005).
    [CrossRef] [PubMed]
  14. S. Stepanov and C. Nuñez Santiago, "Intensity dependence of the transient two-wave mixing by population grating in Er-doped fiber," Opt. Commun. 264, 105-115 (2006).
    [CrossRef]
  15. S. Stepanov and E. Hernández Hernández, "Phase contribution to dynamic gratings recorded in Er-doped fiber with saturable absorption," Opt. Commun. 271, 91-95 (2007).
    [CrossRef]

2007 (1)

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

2006 (2)

2005 (3)

2004 (1)

1999 (1)

1998 (1)

M. D. Feuer, "Length and power dependence of self-adjusting optical fiber filters," IEEE Photon. Technol. Lett. 10, 1587-1589 (1998).
[CrossRef]

1997 (1)

R. Paschotta, J. Nilsson, L. Reekie, A. C. Trooper, and D. C. Hanna, "Single-frequency ytterbium-doped fiber laser stabilized by spatial hole burning," Opt. Lett. 22, 41-43 (1997).
[CrossRef]

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 (1)

1992 (1)

Andrés, M. V.

Yu. O. Barmenkov, A. V. Kir'yanov, and M. V. Andrés, "Dynamic Bragg gratings induced in erbium-doped fiber at phase-modulated beams' coupling," IEEE J. Quantum Electron. 41, 1176-1180 (2005).
[CrossRef]

Barmenkov, Yu. O.

Yu. O. Barmenkov, A. V. Kir'yanov, and M. V. Andrés, "Dynamic Bragg gratings induced in erbium-doped fiber at phase-modulated beams' coupling," IEEE J. Quantum Electron. 41, 1176-1180 (2005).
[CrossRef]

Becker, P. C.

P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers: Fundamentals and Technology (Academic, 1999), Chap. 4.

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.

Dolfi, D.

Feuer, M. D.

M. D. Feuer, "Length and power dependence of self-adjusting optical fiber filters," IEEE Photon. Technol. Lett. 10, 1587-1589 (1998).
[CrossRef]

Fischer, B.

Frey, R.

Frisken, S.

Hanna, D. C.

R. Paschotta, J. Nilsson, L. Reekie, A. C. Trooper, and D. C. Hanna, "Single-frequency ytterbium-doped fiber laser stabilized by spatial hole burning," Opt. Lett. 22, 41-43 (1997).
[CrossRef]

Havstad, S. A.

Hernández, E.

Hernández Hernández, E.

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

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]

Huignard, J.-P.

Kir'yanov, A. V.

Yu. O. Barmenkov, A. V. Kir'yanov, and M. V. Andrés, "Dynamic Bragg gratings induced in erbium-doped fiber at phase-modulated beams' coupling," IEEE J. Quantum Electron. 41, 1176-1180 (2005).
[CrossRef]

Nilsson, J.

R. Paschotta, J. Nilsson, L. Reekie, A. C. Trooper, and D. C. Hanna, "Single-frequency ytterbium-doped fiber laser stabilized by spatial hole burning," Opt. Lett. 22, 41-43 (1997).
[CrossRef]

Norcia-Molin, S.

Nuñez Santiago, C.

S. Stepanov and C. Nuñez Santiago, "Intensity dependence of the transient two-wave mixing by population grating in Er-doped fiber," Opt. Commun. 264, 105-115 (2006).
[CrossRef]

Olsson, N. A.

P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers: Fundamentals and Technology (Academic, 1999), Chap. 4.

Paschotta, R.

R. Paschotta, J. Nilsson, L. Reekie, A. C. Trooper, and D. C. Hanna, "Single-frequency ytterbium-doped fiber laser stabilized by spatial hole burning," Opt. Lett. 22, 41-43 (1997).
[CrossRef]

Plata, M.

Reekie, L.

R. Paschotta, J. Nilsson, L. Reekie, A. C. Trooper, and D. C. Hanna, "Single-frequency ytterbium-doped fiber laser stabilized by spatial hole burning," Opt. Lett. 22, 41-43 (1997).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, 1986).

Simpson, J. R.

P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers: Fundamentals and Technology (Academic, 1999), Chap. 4.

Stepanov, S.

Sulhoff, J. W.

Tonda-Goldstein, S.

Trooper, A. C.

R. Paschotta, J. Nilsson, L. Reekie, A. C. Trooper, and D. C. Hanna, "Single-frequency ytterbium-doped fiber laser stabilized by spatial hole burning," Opt. Lett. 22, 41-43 (1997).
[CrossRef]

Wickham, M. G.

Willner, A. E.

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]

IEEE J. Quantum Electron. (1)

Yu. O. Barmenkov, A. V. Kir'yanov, and M. V. Andrés, "Dynamic Bragg gratings induced in erbium-doped fiber at phase-modulated beams' coupling," IEEE J. Quantum Electron. 41, 1176-1180 (2005).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

M. D. Feuer, "Length and power dependence of self-adjusting optical fiber filters," IEEE Photon. Technol. Lett. 10, 1587-1589 (1998).
[CrossRef]

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

Opt. Commun. (2)

S. Stepanov and C. Nuñez Santiago, "Intensity dependence of the transient two-wave mixing by population grating in Er-doped fiber," Opt. Commun. 264, 105-115 (2006).
[CrossRef]

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

Opt. Lett. (7)

Other (2)

A. E. Siegman, Lasers (University Science Books, 1986).

P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers: Fundamentals and Technology (Academic, 1999), Chap. 4.

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Figures (7)

Fig. 1
Fig. 1

Schematic of experimental setup (EDF, Er-doped fiber; EOM, electro-optic modulator; PD, photodiode; PC1 and PC2, polarization controllers; VA, variable attenuator). Inset shows typical fluorescence signal that appears in reply to rectangular phase modulation.

Fig. 2
Fig. 2

(a) Normalized profiles of transient fluorescence signal experimentally observed for different total input laser powers P 0 (in milliwatts: 0.3 (curve a), 0.6 (curve b), 1.2 (curve c), 1.8 (curve d), and 2.4 (curve e) (equal input powers of the recording waves, U = U π = 3.8 V p p ). Inset shows dependence of transient fluorescence amplitude on modulation voltage U [solid curve presents approximating curve sin 2 ( π U 2 U π ) , calculated for U π = 3.8 V p p ]. (b) Theoretical approximations for normalized transient fluorescence signal evaluated for sinusoidal interference pattern with different average transmitted light power P 0 P s a t = 0.5 (curve a), 1 (curve b), 2 (curve c), 4 (curve d), and 8 (curve e) ( m = 1 ) , and for light pattern approximated by rectangular profile (curve f) ( P 0 P s a t = 2 , reduced by a factor of 2).

Fig. 3
Fig. 3

(a) Theoretical curves of normalized transient fluorescence response evaluated for P 0 P s a t = 2 and for different contrasts of the sinusoidal interference pattern m : 1 (curve a), 0.8 (curve b), 0.6 (curve c), and 0.4 (curve d). (b) Theoretical dependences of maximum signal amplitudes as functions of the recording pattern contrast calculated for P 0 P s a t = 3 , 1, and 0.3 (shown by dashed, solid, and dotted line curves, respectively). Experimental points were obtained at P 0 = 2.0 mW , U = U π = 3.8 V p p .

Fig. 4
Fig. 4

(a) Solid curves show experimental profiles of transient fluorescence signals observed at m : 1 (curve a), 0.8 (curve b), 0.6 (curve c), and 0.4 (curve d) ( P 0 = 2.0 mW , U = U π = 3.8 V p p ). Dashed curves present theoretical curves calculated for the above-mentioned experimental values of m multiplied by 0.75 ( P s a t = 0.65 mW , τ 0 = 10 ms ). (b) Same experimental signal profiles as those presented in (a) approximated by multiplying by a factor of 0.4 theoretical curves calculated for initial pattern contrast values used in the experiment.

Fig. 5
Fig. 5

Spectral dependence of the normalized transient fluorescence peak amplitude ( P 0 = 0.3 mW , U = 3.8 V p p ).

Fig. 6
Fig. 6

Experimental dependence of normalized transient fluorescence peak amplitude as a function of angle θ between linear input polarizations of the recording waves ( P 0 = 2.3 mW , U = U π = 3.8 V p p ). Solid curve presents the approximating theoretical curve calculated using Eq. (1) for P 0 P s a t = 3 and m cos ( θ ) , and the dashed curve presents the simplified approximation by [ cos ( θ ) ] 2 .

Fig. 7
Fig. 7

Longitudinal profiles of transient fluorescence signal amplitude obtained in the case of the laser source with high ( ) and low ( ) coherence ( λ = 1549 nm , P 0 = 0.6 mW , U = 3.8 V p p , P s a t = 0.5 mW ). Inset shows schematic of configuration used in measurements.

Equations (4)

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P t r ( t ) P s t = 0 2 π K d x [ N 2 i ( x ) N 2 f ( x ) ] exp [ t τ f ( x ) ] 0 2 π K d x N 2 f ( x ) .
N 2 i ( x ) = N 0 2 ( P 0 P s a t ) ( 1 + m cos K x ) 1 + ( P 0 P s a t ) ( 1 + m cos K x ) ,
N 2 f ( x ) = N 0 2 ( P 0 P s a t ) ( 1 m cos K x ) 1 + ( P 0 P s a t ) ( 1 m cos K x ) ,
τ f ( x ) = τ 0 1 + ( P 0 P s a t ) ( 1 m cos K x ) ,

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