Abstract

We present an experimental and theoretical analysis of four-wave mixing in nanosecond pulsed amplifiers based on double-clad ytterbium-doped fibers. This process leads to saturation of the amplified pulse energy at 1064 nm and to distortion of the spectral and temporal profiles. These behaviours are well described by a simple model considering both Raman and four-wave-mixing contributions. The role of seed laser polarization in birefringent fibers is also presented. These results point out the critical parameters and possible tradeoffs for optimization.

©2007 Optical Society of America

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    [Crossref]
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    [Crossref]
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  27. J.-P. Fève, “Phase-matching and mitigation of four-wave mixing in fibers with positive gain,” Opt. Express 15, 577–582 (2007).
    [Crossref] [PubMed]
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  29. Complete calculation of modal propagation shows waveguide contribution to phase mismatch is less than 3%, so that the single-mode approximation is justified.
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    [Crossref]
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    [Crossref]
  34. S. Sinha, C. Langrock, M. Digonnet, M. Fejer, and R. Byer, “Efficient yellow-light generation by frequency doubling a narrow-linewidth 1150 nm ytterbium fiber oscillator,” Opt. Lett. 31, 347–349 (2006).
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    [Crossref]

2007 (2)

G. R. Hadley, R. L. Farrow, and A. V. Smith, “Three-dimensional time-dependent modeling of high-power fiber amplifiers,” Proc. SPIE 6453, 64531B (2007) in press.
[Crossref]

J.-P. Fève, “Phase-matching and mitigation of four-wave mixing in fibers with positive gain,” Opt. Express 15, 577–582 (2007).
[Crossref] [PubMed]

2006 (6)

P. Wang, L. Cooper, J. Sahu, and W. Clarkson, “Efficient single-mode operation of a cladding-pumped ytterbium-doped helical-core fiber amplifier,” Opt. Lett. 31, 226–228 (2006).
[Crossref] [PubMed]

S. Sinha, C. Langrock, M. Digonnet, M. Fejer, and R. Byer, “Efficient yellow-light generation by frequency doubling a narrow-linewidth 1150 nm ytterbium fiber oscillator,” Opt. Lett. 31, 347–349 (2006).
[Crossref] [PubMed]

P. E. Schrader, R. L. Farrow, D. A. V. Kliner, J.-P. Fève, and N. Landru, “High power fiber amplifier with tunable repetition rate, fixed pulse duration, and multiple output wavelengths,” Opt. Express 14, 11528–11537 (2006).
[Crossref] [PubMed]

R. L. Farrow, D. A. V. Kliner, P. E. Schrader, A. A. Hoops, S. W. Moore, G. R. Hadley, and R. L. Schmitt, “High-peak-power (>1.2MW) pulsed fiber amplifier,” Proc. SPIE 6102, 61020L (2006).
[Crossref]

W. Torruellas, Y. Chen, B. McIntosh, J. Faroni, K. Tankala, S. Webster, D. Hagan, and M. Soileau, “High peak power Yb doped fiber amplifiers,” Proc. SPIE 6102, 61020N (2006).
[Crossref]

M. Hotoleanu, M. Söderlund, D. Kliner, J. Koplow, S. Tammela, and V. Philipov, “Higher-order modes suppression in large mode area active fibers by controlling the radial distribution of the rare earth dopant,” Proc. SPIE 6102, 61021T (2006).
[Crossref]

2005 (3)

2004 (3)

2003 (1)

2002 (4)

F. Di Teodoro, J. P. Koplow, S. W. Moore, and D. A. V. Kliner, “Diffraction-limited, 300-kW peak-power pulses from a coiled multimode fiber amplifier,” Opt. Lett. 27, 518–520 (2002).
[Crossref]

J.-P. Fève and B. Boulanger, “Suppression of quadratic cascading in four-photon interactions using periodically poled media,” Phys. Rev. A 65, 063814 1–l6 (2002).
[Crossref]

J.-P. Fève, B. Boulanger, and J. Douady, “Specific properties of cubic optical parametric interactions compared to quadratic interactions,” Phys. Rev. A 66, 063817 1–11 (2002).
[Crossref]

S. Coen, D. A. Wardle, and J. D. Harvey, “Observation of non-phase-matched parametric amplification in resonant nonlinear optics,” Phys. Rev. Lett. 89, 273901 (2002)
[Crossref]

2001 (1)

P. Tchofo, E. Sève, G. Millot, T. Sylvestre, H. Maillote, and E. Lantz, “Raman-assisted three-wave-mixing of non-phase-matched waves in optical fibres: application to wide range frequency conversion,” Opt. Commun. 192, 107–121 (2001)
[Crossref]

2000 (1)

1999 (1)

1998 (4)

1995 (1)

1992 (1)

1991 (1)

1989 (1)

1981 (2)

Agrawal, G.

G. Agrawal, Nonlinear Fiber Optics, 3rd ed., Optics and Photonics Series (Academic, San Diego, Calif., (2001).

Biancalana, F.

Birks, T.

Bösch, M.

Boulanger, B.

J.-P. Fève and B. Boulanger, “Suppression of quadratic cascading in four-photon interactions using periodically poled media,” Phys. Rev. A 65, 063814 1–l6 (2002).
[Crossref]

J.-P. Fève, B. Boulanger, and J. Douady, “Specific properties of cubic optical parametric interactions compared to quadratic interactions,” Phys. Rev. A 66, 063817 1–11 (2002).
[Crossref]

Broderick, N.

Broeng, J.

Brooks, C.

Byer, R.

Caplen, J.

Cappellini, G.

Chang, Y.

Chankatoti, R.

Chee, J.

Chen, Y.

W. Torruellas, Y. Chen, B. McIntosh, J. Faroni, K. Tankala, S. Webster, D. Hagan, and M. Soileau, “High peak power Yb doped fiber amplifiers,” Proc. SPIE 6102, 61020N (2006).
[Crossref]

Cheng, M. Y.

Clarkson, W.

Coen, S.

S. Coen, D. A. Wardle, and J. D. Harvey, “Observation of non-phase-matched parametric amplification in resonant nonlinear optics,” Phys. Rev. Lett. 89, 273901 (2002)
[Crossref]

Cooper, L.

Daniel, J.

Di Teodoro, F.

Digonnet, M.

Dong, L.

Douady, J.

J.-P. Fève, B. Boulanger, and J. Douady, “Specific properties of cubic optical parametric interactions compared to quadratic interactions,” Phys. Rev. A 66, 063817 1–11 (2002).
[Crossref]

Dougherty, D. J.

Faroni, J.

W. Torruellas, Y. Chen, B. McIntosh, J. Faroni, K. Tankala, S. Webster, D. Hagan, and M. Soileau, “High peak power Yb doped fiber amplifiers,” Proc. SPIE 6102, 61020N (2006).
[Crossref]

Farrow, R. L.

G. R. Hadley, R. L. Farrow, and A. V. Smith, “Three-dimensional time-dependent modeling of high-power fiber amplifiers,” Proc. SPIE 6453, 64531B (2007) in press.
[Crossref]

R. L. Farrow, D. A. V. Kliner, P. E. Schrader, A. A. Hoops, S. W. Moore, G. R. Hadley, and R. L. Schmitt, “High-peak-power (>1.2MW) pulsed fiber amplifier,” Proc. SPIE 6102, 61020L (2006).
[Crossref]

P. E. Schrader, R. L. Farrow, D. A. V. Kliner, J.-P. Fève, and N. Landru, “High power fiber amplifier with tunable repetition rate, fixed pulse duration, and multiple output wavelengths,” Opt. Express 14, 11528–11537 (2006).
[Crossref] [PubMed]

Fejer, M.

Ferman, M.

Fève, J.-P.

J.-P. Fève, “Phase-matching and mitigation of four-wave mixing in fibers with positive gain,” Opt. Express 15, 577–582 (2007).
[Crossref] [PubMed]

P. E. Schrader, R. L. Farrow, D. A. V. Kliner, J.-P. Fève, and N. Landru, “High power fiber amplifier with tunable repetition rate, fixed pulse duration, and multiple output wavelengths,” Opt. Express 14, 11528–11537 (2006).
[Crossref] [PubMed]

J.-P. Fève, B. Boulanger, and J. Douady, “Specific properties of cubic optical parametric interactions compared to quadratic interactions,” Phys. Rev. A 66, 063817 1–11 (2002).
[Crossref]

J.-P. Fève and B. Boulanger, “Suppression of quadratic cascading in four-photon interactions using periodically poled media,” Phys. Rev. A 65, 063814 1–l6 (2002).
[Crossref]

Galvanauskas, A.

Gatchell, P.

Goldberg, L.

H?, N.

Hadley, G. R.

G. R. Hadley, R. L. Farrow, and A. V. Smith, “Three-dimensional time-dependent modeling of high-power fiber amplifiers,” Proc. SPIE 6453, 64531B (2007) in press.
[Crossref]

R. L. Farrow, D. A. V. Kliner, P. E. Schrader, A. A. Hoops, S. W. Moore, G. R. Hadley, and R. L. Schmitt, “High-peak-power (>1.2MW) pulsed fiber amplifier,” Proc. SPIE 6102, 61020L (2006).
[Crossref]

Hagan, D.

W. Torruellas, Y. Chen, B. McIntosh, J. Faroni, K. Tankala, S. Webster, D. Hagan, and M. Soileau, “High peak power Yb doped fiber amplifiers,” Proc. SPIE 6102, 61020N (2006).
[Crossref]

Harvey, J. D.

S. Coen, D. A. Wardle, and J. D. Harvey, “Observation of non-phase-matched parametric amplification in resonant nonlinear optics,” Phys. Rev. Lett. 89, 273901 (2002)
[Crossref]

Haus, H. A.

Hoops, A. A.

R. L. Farrow, D. A. V. Kliner, P. E. Schrader, A. A. Hoops, S. W. Moore, G. R. Hadley, and R. L. Schmitt, “High-peak-power (>1.2MW) pulsed fiber amplifier,” Proc. SPIE 6102, 61020L (2006).
[Crossref]

Hotoleanu, M.

M. Hotoleanu, M. Söderlund, D. Kliner, J. Koplow, S. Tammela, and V. Philipov, “Higher-order modes suppression in large mode area active fibers by controlling the radial distribution of the rare earth dopant,” Proc. SPIE 6102, 61021T (2006).
[Crossref]

Ippen, E. P.

Jakobsen, C.

Joly, N.

Kärtner, F. X.

Kliner, D.

M. Hotoleanu, M. Söderlund, D. Kliner, J. Koplow, S. Tammela, and V. Philipov, “Higher-order modes suppression in large mode area active fibers by controlling the radial distribution of the rare earth dopant,” Proc. SPIE 6102, 61021T (2006).
[Crossref]

Kliner, D. A. V.

Knight, J.

Koplow, J.

M. Hotoleanu, M. Söderlund, D. Kliner, J. Koplow, S. Tammela, and V. Philipov, “Higher-order modes suppression in large mode area active fibers by controlling the radial distribution of the rare earth dopant,” Proc. SPIE 6102, 61021T (2006).
[Crossref]

Koplow, J. P.

Landru, N.

Langrock, C.

Lantz, E.

P. Tchofo, E. Sève, G. Millot, T. Sylvestre, H. Maillote, and E. Lantz, “Raman-assisted three-wave-mixing of non-phase-matched waves in optical fibres: application to wide range frequency conversion,” Opt. Commun. 192, 107–121 (2001)
[Crossref]

T. Sylvestre, H. Maillotte, E. Lantz, and P. Tchofo Dinda, “Raman-assisted parametric frequency conversion in a normally dispersive single-mode fiber,” Opt. Lett. 24, 1561–1563 (1999).
[Crossref]

Liem, A.

Limpert, J.

Lin, C.

Liu, J.

Maillote, H.

P. Tchofo, E. Sève, G. Millot, T. Sylvestre, H. Maillote, and E. Lantz, “Raman-assisted three-wave-mixing of non-phase-matched waves in optical fibres: application to wide range frequency conversion,” Opt. Commun. 192, 107–121 (2001)
[Crossref]

Maillotte, H.

Mamidipudi, P.

McIntosh, B.

W. Torruellas, Y. Chen, B. McIntosh, J. Faroni, K. Tankala, S. Webster, D. Hagan, and M. Soileau, “High peak power Yb doped fiber amplifiers,” Proc. SPIE 6102, 61020N (2006).
[Crossref]

Ménard, J. M.

Milam, D.

Millot, G.

S. Pitois, A. Sauter, and G. Millot, “Simultaneous achievement of polarization attraction and Raman amplification in isotropic optical fibers,” Opt. Lett. 29, 599–601 (2004).
[Crossref] [PubMed]

P. Tchofo, E. Sève, G. Millot, T. Sylvestre, H. Maillote, and E. Lantz, “Raman-assisted three-wave-mixing of non-phase-matched waves in optical fibres: application to wide range frequency conversion,” Opt. Commun. 192, 107–121 (2001)
[Crossref]

S. Trillo, G. Millot, E. Sève, and S. Wabnitz, “Failure of phase-matching concept in large-signal parametric frequency conversion,” Appl. Phys. Lett. 72, 150–152 (1998).
[Crossref]

P. Tchofo Dinda, G. Millot, and S. Wabnitz, “Polarization switching and suppression of stimulated Raman scattering in birefringent optical fibers,” J. Opt. Soc. Am. B 15, 1433–1441 (1998).
[Crossref]

Moore, S. W.

R. L. Farrow, D. A. V. Kliner, P. E. Schrader, A. A. Hoops, S. W. Moore, G. R. Hadley, and R. L. Schmitt, “High-peak-power (>1.2MW) pulsed fiber amplifier,” Proc. SPIE 6102, 61020L (2006).
[Crossref]

F. Di Teodoro, J. P. Koplow, S. W. Moore, and D. A. V. Kliner, “Diffraction-limited, 300-kW peak-power pulses from a coiled multimode fiber amplifier,” Opt. Lett. 27, 518–520 (2002).
[Crossref]

Nolte, S.

Offerhaus, H.

Paré, C.

Pearson, A.

Petersson, A.

Philipov, V.

M. Hotoleanu, M. Söderlund, D. Kliner, J. Koplow, S. Tammela, and V. Philipov, “Higher-order modes suppression in large mode area active fibers by controlling the radial distribution of the rare earth dopant,” Proc. SPIE 6102, 61021T (2006).
[Crossref]

Pitois, S.

Proulx, A.

Reed, W.

Reich, M.

Richardson, D.

Russell, P.

Sahu, J.

Sammuk, R.

Sauter, A.

Schmitt, R. L.

R. L. Farrow, D. A. V. Kliner, P. E. Schrader, A. A. Hoops, S. W. Moore, G. R. Hadley, and R. L. Schmitt, “High-peak-power (>1.2MW) pulsed fiber amplifier,” Proc. SPIE 6102, 61020L (2006).
[Crossref]

Schrader, P. E.

R. L. Farrow, D. A. V. Kliner, P. E. Schrader, A. A. Hoops, S. W. Moore, G. R. Hadley, and R. L. Schmitt, “High-peak-power (>1.2MW) pulsed fiber amplifier,” Proc. SPIE 6102, 61020L (2006).
[Crossref]

P. E. Schrader, R. L. Farrow, D. A. V. Kliner, J.-P. Fève, and N. Landru, “High power fiber amplifier with tunable repetition rate, fixed pulse duration, and multiple output wavelengths,” Opt. Express 14, 11528–11537 (2006).
[Crossref] [PubMed]

Schreiber, T.

Sève, E.

P. Tchofo, E. Sève, G. Millot, T. Sylvestre, H. Maillote, and E. Lantz, “Raman-assisted three-wave-mixing of non-phase-matched waves in optical fibres: application to wide range frequency conversion,” Opt. Commun. 192, 107–121 (2001)
[Crossref]

S. Trillo, G. Millot, E. Sève, and S. Wabnitz, “Failure of phase-matching concept in large-signal parametric frequency conversion,” Appl. Phys. Lett. 72, 150–152 (1998).
[Crossref]

Shang, H.

Sinha, S.

Smith, A. V.

G. R. Hadley, R. L. Farrow, and A. V. Smith, “Three-dimensional time-dependent modeling of high-power fiber amplifiers,” Proc. SPIE 6453, 64531B (2007) in press.
[Crossref]

Söderlund, M.

M. Hotoleanu, M. Söderlund, D. Kliner, J. Koplow, S. Tammela, and V. Philipov, “Higher-order modes suppression in large mode area active fibers by controlling the radial distribution of the rare earth dopant,” Proc. SPIE 6102, 61021T (2006).
[Crossref]

Soileau, M.

W. Torruellas, Y. Chen, B. McIntosh, J. Faroni, K. Tankala, S. Webster, D. Hagan, and M. Soileau, “High peak power Yb doped fiber amplifiers,” Proc. SPIE 6102, 61020N (2006).
[Crossref]

Stolen, R.

Sylvestre, T.

P. Tchofo, E. Sève, G. Millot, T. Sylvestre, H. Maillote, and E. Lantz, “Raman-assisted three-wave-mixing of non-phase-matched waves in optical fibres: application to wide range frequency conversion,” Opt. Commun. 192, 107–121 (2001)
[Crossref]

T. Sylvestre, H. Maillotte, E. Lantz, and P. Tchofo Dinda, “Raman-assisted parametric frequency conversion in a normally dispersive single-mode fiber,” Opt. Lett. 24, 1561–1563 (1999).
[Crossref]

Tammela, S.

M. Hotoleanu, M. Söderlund, D. Kliner, J. Koplow, S. Tammela, and V. Philipov, “Higher-order modes suppression in large mode area active fibers by controlling the radial distribution of the rare earth dopant,” Proc. SPIE 6102, 61021T (2006).
[Crossref]

Tankala, K.

W. Torruellas, Y. Chen, B. McIntosh, J. Faroni, K. Tankala, S. Webster, D. Hagan, and M. Soileau, “High peak power Yb doped fiber amplifiers,” Proc. SPIE 6102, 61020N (2006).
[Crossref]

Tchofo, P.

P. Tchofo, E. Sève, G. Millot, T. Sylvestre, H. Maillote, and E. Lantz, “Raman-assisted three-wave-mixing of non-phase-matched waves in optical fibres: application to wide range frequency conversion,” Opt. Commun. 192, 107–121 (2001)
[Crossref]

Tchofo Dinda, P.

Teodoro, F. Di

Torruellas, W.

W. Torruellas, Y. Chen, B. McIntosh, J. Faroni, K. Tankala, S. Webster, D. Hagan, and M. Soileau, “High peak power Yb doped fiber amplifiers,” Proc. SPIE 6102, 61020N (2006).
[Crossref]

Trillo, S.

Tünnermann, A.

Vallée, R.

Wabnitz, S.

Wadsworth, W.

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G. Agrawal, Nonlinear Fiber Optics, 3rd ed., Optics and Photonics Series (Academic, San Diego, Calif., (2001).

Complete calculation of modal propagation shows waveguide contribution to phase mismatch is less than 3%, so that the single-mode approximation is justified.

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Figures (9)

Fig. 1.
Fig. 1.

(a). Output spectrum at four values of E out. (b) Total output energy (integrated over the whole spectrum, open squares), energy transmitted through a band-pass filter at 1064 nm (filled circles) and out-of-band energy (stars) vs. diode pump power coupled into the fiber.

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Fig. 2.
Fig. 2.

Calculated peak powers along the fiber for the pump (λ 1 = 1064 nm, solid) and signal (λ 3 = 1084 nm, dotted) for two values of E out, 313 μJ (blue) and 576 μJ (black).

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Fig. 3.
Fig. 3.

(a). Measured temporal profiles of the amplified pulses at five values of E out. Dashed: unfiltered pulses; solid: transmitted by band-pass filter at 1064 nm; diamonds: reflected from filter. (b). Calculated normalized temporal profiles.

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Fig. 4.
Fig. 4.

Calculated pulse shapes for five values of E out: 100μJ, 152μJ, 216μJ, 267μJ and 329μJ (increasing along arrow). All parameters are similar to Fig. 3. (a) pump λ 1 = 1064 nm; (b) signal λ 3 = 1115 nm.

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Fig. 5.
Fig. 5.

(a). Calculated normalized peak power spectrum (t = 0) for four values of E out (L = 3.5 m, E seed = 1.5 μJ, Δt = 1 ns FWHM, Δk offset = 3 m-1). (b). Spectral dependence of the Raman gain g R (from [31]) and the phase-mismatch Δk for a pump wavelength of 1064 nm; the value of Δk offset used in the calculations is also shown.

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Fig. 6.
Fig. 6.

Amplified 1064 nm and out-of-band pulse energies vs. total output pulse energy. Points: experimental data from Fig. 1(b); dashed curves: calculated with parameters of Fig. 5.

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Fig.7.
Fig.7.

Total output energy and energy at 1064 nm vs. fiber length for different fiber designs. Calculations assume 21 W of launched diode pump power and λ 3 = 1115nm. Fiber parameters (core diameter in μm/inner-cladding diameter in μm / 976 nm pump-absorption coefficient for light propagating in the core in dB/m): A: 30/250/1200; B: 30/250/500 (corresponding to the fiber employed in the present experiments).

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Fig. 8.
Fig. 8.

(a). Measured values of E out (squares), E 1064 (circles), and the PER (stars) vs. angle of the seed polarization. (b). Measured output spectra for different orientations of the seed polarization.

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Fig.9.
Fig.9.

Calculated normalized peak-power spectra for various polarizations of the seed pulse. Top: output power polarized along the slow axis; center: output power polarized along the fast axis; bottom: total output power. Parameters used in the calculations: L = 3.5 m, Δk offset = 3 m-1, E seed = 1.5 μJ, E out = 175 μJ.

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Tables (1)

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Table 1. Influence of seed polarization on E out and E 1064.

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Equations (3)

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{ ∂ E 1 ∂ z = j γ [ ∣ E 1 ∣ 2 + ( 2 − ρ ) ( ∣ E 3 ∣ 2 + ∣ E 4 ∣ 2 ) ] E 1 − g R 2 A eff ∣ E 3 ∣ 2 E 1 + g 2 E 1 + j γ E 1 * E 3 E 4 e j Δ kz ∂ E 3 ∂ z = j γ [ ∣ E 3 ∣ 2 + ( 2 − ρ ) ( ∣ E 1 ∣ 2 + ∣ E 4 ∣ 2 ) ] E 3 − g R 2 A eff ∣ E 1 ∣ 2 E 3 + j γ E 4 * E 1 E 1 e − j Δ kz ∂ E 4 ∂ z = j γ [ ∣ E 4 ∣ 2 + ( 2 − ρ ) ( ∣ E 1 ∣ 2 + ∣ E 3 ∣ 2 ) ] E 4 + j γ E 3 * E 1 E 1 e − j Δ kz
dE 1 , s dz = j γ [ ∣ E 1 , s ∣ 2 + 2 3 ∣ E 1 , f ∣ 2 + ( 2 − ρ ) ( ∣ E 3 , s ∣ 2 + ∣ E 4 , s ∣ 2 ) + 2 − ρ 3 ( ∣ E 3 , f ∣ 2 + ∣ E 4 , f ∣ 2 ) ] E 1 , s − g R , ∥ 2 A eff ∣ E 3 , s ∣ 2 E 1 , s
− g R , ⊥ 2 A eff ∣ E 3 , f ∣ 2 E 1 , s + g 2 E 1 , s + j γ { E 1 , s * E 3 , s E 4 , s exp ( j Δ k ssss z ) + 1 3 E 1 , s * E 3 , f E 4 , f exp ( j Δ k ssff z ) + 1 3 E 1 , f * E 3 , s E 4 , f exp ( j Δ k sffs z ) + 1 3 E 1 , f * E 3 , s E 4 , f exp ( j Δ k sfsf z ) }

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