Abstract

We present a detailed theoretical investigation of claddingpumped Raman fiber amplification in an unexplored parameter space of high conversion efficiency (> 60%) and high brightness enhancement (> 1000). Fibers with large clad-to-core diameter ratios can provide a promising means for Raman-based brightness enhancement of diode pump sources. Unfortunately, the diameter ratio cannot be extended indefinitely since the intensity generated in the core can greatly exceed that in the cladding long before the pump is fully depleted. If left uncontrolled, this leads to the generation of parasitic second-order Stokes wavelengths in the core, limiting the conversion efficiency and as we will show, clamping the achievable brightness enhancement. Using a coupled-wave formalism, we present the upper limit on brightness enhancement as a function of diameter ratio for conventionally guided fibers. We further present strategies for overcoming this limit based upon depressed well core designs. We consider two configurations: (1) pulsed cladding-pumped Raman fiber amplifier (CPRFA) and (2) cw cladding-pumped Raman fiber laser (CPRFL).

© 2010 Optical Society of America

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References

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  1. C. A. Codemard, J. K. Sahu, and J. Nilsson, “Cladding pumped Raman fiber amplifier for high-gain, high energy single-stage amplification,” in Optical Fiber Communications Technical Digest (Institute of Electrical and Electronics Engineers, 2005).
  2. C. A. Codemard, P. Dupriez, Y. Jeong, J. K. Sahu, M. Ibsen, and J. Nilsson, “High-power continuous-wave cladding-pumped Raman fiber laser,” Opt. Lett. 31, 2290–2292 (2006).
    [CrossRef] [PubMed]
  3. C. A. Codemard, J. K. Sahu, and J. Nilsson, “High-brightness, pulsed, cladding-pumped Raman fiber source at 1660 nm,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2007).
  4. A. K. Sridharan, J. E. Heebner, M. J. Messerly, J. W. Dawson, R. J. Beach, and C. P. J. Barty, “Brightness enhancement in a high-peak-power cladding-pumped Raman fiber amplifier,” Opt. Lett. 34, 2234–2236 (2009).
    [CrossRef] [PubMed]
  5. C. Headley, and G. P. Agrawal, Raman Amplification in Fiber Optical Communication Systems (Academic Press, Amsterdam, 2004).
  6. J. W. Dawson, M. J. Messerly, R. J. Beach, M. Y. Shverdin, E. A. Stappaerts, A. K. Sridharan, P. H. Pax, J. E. Heebner, C. W. Siders, and C. P. J. Barty, “Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power,” Opt. Express 16, 13240–13266 (2008).
    [CrossRef] [PubMed]
  7. A. K. Sridharan, P. H. Pax, M. J. Messerly, and J. W. Dawson, “High-gain photonic crystal fiber regenerative amplifier,” Opt. Lett. 34, 608–610 (2009).
    [CrossRef] [PubMed]
  8. Y Ernori and S. Namiki, “100nm bandwidth flat gain Raman amplifiers pumped and gain-equalized by 12-wavelength-channel WDM high power laser diodes,” OFC, PD19 (1999).
  9. G. P. Agrawal, Nonlinear Fiber optics 3rd ed. San Diego, CA (Academic Press, Amsterdam, 2001).
  10. J. Ji, C. A. Codemard, M. Ibsen, J. K. Sahu, and J. Nilsson, “Analysis of the conversion to the first stokes in cladding-pumped fiber raman amplifiers,” IEEE J. Sel. Top. Quantum Electron. 15, 129–139 (2009).
    [CrossRef]
  11. R. G. Smith, “Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and Brillouin scattering,” Appl. Opt. 11, 2489–2494 (1972).
    [CrossRef] [PubMed]
  12. J. Kim, P. Dupriez, C. Codemard, J. Nilsson, and J. K. Sahu, “Suppression of stimulated Raman scattering in a high power Yb-doped fiber amplifier using a W-type core with fundamental mode cut-off,” Opt. Express 14, 5103–5113 (2006).
    [CrossRef] [PubMed]
  13. J. A. Yeung, and A. Yariv, “Theory of cw Raman oscillation in optical fibers,” J. Opt. Soc. Am. 69, 803–807 (1979).
    [CrossRef]
  14. G. L. Keaton, M. A. Arbore, and T. J. Kane, “Optical wavelength filtering apparatus with depressed index claddings,” US patent 6,563,995 (2001).
  15. J. S. Kim, C. Codemard, Y. Jeong, J. Nilsson, and J. K. Sahu, “High Power Continuous-Wave Yb-Doped Fiber Laser with True Single-Mode Output Using W-Type Structure,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2006).
  16. M. D. Feit, and J. A. Fleck, “Computation of mode properties in optical fiber waveguides by a propagating beam method,” Appl. Opt. 19, 1154–1164 (1980).
    [CrossRef] [PubMed]
  17. M. Heiblum, and J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” J. Quantum Electron. 11, 75–83 (1975).
    [CrossRef]
  18. D. Marcuse, “Field deformation and loss caused by curvature of optical fibers,” J. Opt. Soc. Am. 66, 311–320 (1976).
    [CrossRef]

2009 (3)

2008 (1)

2006 (2)

1980 (1)

1979 (1)

1976 (1)

1975 (1)

M. Heiblum, and J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” J. Quantum Electron. 11, 75–83 (1975).
[CrossRef]

1972 (1)

Barty, C. P. J.

Beach, R. J.

Codemard, C.

Codemard, C. A.

J. Ji, C. A. Codemard, M. Ibsen, J. K. Sahu, and J. Nilsson, “Analysis of the conversion to the first stokes in cladding-pumped fiber raman amplifiers,” IEEE J. Sel. Top. Quantum Electron. 15, 129–139 (2009).
[CrossRef]

C. A. Codemard, P. Dupriez, Y. Jeong, J. K. Sahu, M. Ibsen, and J. Nilsson, “High-power continuous-wave cladding-pumped Raman fiber laser,” Opt. Lett. 31, 2290–2292 (2006).
[CrossRef] [PubMed]

Dawson, J. W.

Dupriez, P.

Feit, M. D.

Fleck, J. A.

Harris, J. H.

M. Heiblum, and J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” J. Quantum Electron. 11, 75–83 (1975).
[CrossRef]

Heebner, J. E.

Heiblum, M.

M. Heiblum, and J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” J. Quantum Electron. 11, 75–83 (1975).
[CrossRef]

Ibsen, M.

J. Ji, C. A. Codemard, M. Ibsen, J. K. Sahu, and J. Nilsson, “Analysis of the conversion to the first stokes in cladding-pumped fiber raman amplifiers,” IEEE J. Sel. Top. Quantum Electron. 15, 129–139 (2009).
[CrossRef]

C. A. Codemard, P. Dupriez, Y. Jeong, J. K. Sahu, M. Ibsen, and J. Nilsson, “High-power continuous-wave cladding-pumped Raman fiber laser,” Opt. Lett. 31, 2290–2292 (2006).
[CrossRef] [PubMed]

Jeong, Y.

Ji, J.

J. Ji, C. A. Codemard, M. Ibsen, J. K. Sahu, and J. Nilsson, “Analysis of the conversion to the first stokes in cladding-pumped fiber raman amplifiers,” IEEE J. Sel. Top. Quantum Electron. 15, 129–139 (2009).
[CrossRef]

Kim, J.

Marcuse, D.

Messerly, M. J.

Nilsson, J.

Pax, P. H.

Sahu, J. K.

Shverdin, M. Y.

Siders, C. W.

Smith, R. G.

Sridharan, A. K.

Stappaerts, E. A.

Yariv, A.

Yeung, J. A.

Appl. Opt. (2)

IEEE J. Sel. Top. Quantum Electron. (1)

J. Ji, C. A. Codemard, M. Ibsen, J. K. Sahu, and J. Nilsson, “Analysis of the conversion to the first stokes in cladding-pumped fiber raman amplifiers,” IEEE J. Sel. Top. Quantum Electron. 15, 129–139 (2009).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Quantum Electron. (1)

M. Heiblum, and J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” J. Quantum Electron. 11, 75–83 (1975).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Other (7)

C. Headley, and G. P. Agrawal, Raman Amplification in Fiber Optical Communication Systems (Academic Press, Amsterdam, 2004).

G. L. Keaton, M. A. Arbore, and T. J. Kane, “Optical wavelength filtering apparatus with depressed index claddings,” US patent 6,563,995 (2001).

J. S. Kim, C. Codemard, Y. Jeong, J. Nilsson, and J. K. Sahu, “High Power Continuous-Wave Yb-Doped Fiber Laser with True Single-Mode Output Using W-Type Structure,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2006).

C. A. Codemard, J. K. Sahu, and J. Nilsson, “Cladding pumped Raman fiber amplifier for high-gain, high energy single-stage amplification,” in Optical Fiber Communications Technical Digest (Institute of Electrical and Electronics Engineers, 2005).

C. A. Codemard, J. K. Sahu, and J. Nilsson, “High-brightness, pulsed, cladding-pumped Raman fiber source at 1660 nm,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2007).

Y Ernori and S. Namiki, “100nm bandwidth flat gain Raman amplifiers pumped and gain-equalized by 12-wavelength-channel WDM high power laser diodes,” OFC, PD19 (1999).

G. P. Agrawal, Nonlinear Fiber optics 3rd ed. San Diego, CA (Academic Press, Amsterdam, 2001).

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Figures (10)

Fig. 1.
Fig. 1.

Simulation of a pulsed cladding-pumped Raman fiber amplifier. Single-pass evolution of pump, first-order Stokes and higher-order Stokes powers vs propagation length.Here, at a clad-to-core diameter ratio of 125:20, and NA ratio of 0.45:0.07, the conversion efficiency is limited to about 30% before the first-order Stokes power in the core is rapidly dissipated into second-order Stokes. Apart from the quantum defect losses incurred at each conversion responsible for the downward step in the total power, the system is assumed to be lossless. Because the pump is no longer stimulated by the presence of signal power, its power remains unconverted and clamped.

Fig. 2.
Fig. 2.

Conversion efficiency and brightness enhancement achievable for an NA ratio of 0.45:0.07 as a function of clad-to-core diameter ratio. Due to incomplete pump depletion when the threshold for second-order Stokes is reached in the core, the conversion efficiency is increasingly limited as the clad-to-core diameter ratio is increased. The result of numerical simulations (solid) is compared against an approximate analytic expression given in Eq. (14) This in turn clamps the achievable brightness enhancement to the expression given in Eq. (16). Assumed parameters include a peak pump power of 50kW, injected signal of 10 W, second-order Stokes seed 50 dB below the injected signal, and a core diameter of 20 µm.

Fig. 3.
Fig. 3.

Conversion efficiency and brightness enhancement achievable for an NA ratio of 0.45:0.07 as a function of clad-to-core diameter ratio with loss at the second-order Stokes wavelength. Increased loss raises the second-order Stokes threshold enabling quantumdefect-limited conversion efficiency for losses above 10 dB/m.

Fig. 4.
Fig. 4.

Contour plot of the expected conversion efficiency of a cw cladding-pumped Raman fiber laser when limited by signal dissipation into passive losses and second-order Stokes conversion. The contours are plotted vs. losses on the first and second Stokes orders. Parameters assumed include a 100 W cw pump, 100 m fiber length, clad-to-core diameter ratio of 80:12 µm. Loss at the pump wavelengths is 5.2 dB/km.

Fig. 5.
Fig. 5.

Depressed well core design enabling low loss (1 dB/km) at the first-order Stokes signal wavelength and high loss (1 dB/m) at the second-order Stokes parasitic wavelength. The index profile and unbent mode intensity profiles are plotted on linear scales. The inserts show a 400 µm × 400 µm grid displaying the 475 mm diameter bent mode intensity profiles on decibel scales where each contour represents a 10 dB falloff.

Fig. 6.
Fig. 6.

Simulation of a cw cladding-pumped Raman fiber laser. Single-pass evolution of pump, self-consistent, multi-pass evolution of the first-order Stokes and single-pass evolution of second-order Stokes powers vs length. Parameters assumed include a 100 W pump, 100 m 80:12 µm fiber, α s1 =1 dB/km, and α s2 =1 dB/m. At these low pump power levels, high reflectivity (88%) is required, the circulating intensity is 8.8 W/µm2, a brightness enhancement of 800 can be achieved, but only 31% conversion is predicted.

Fig. 7.
Fig. 7.

Contour plot of the expected conversion efficiency of a cw cladding-pumped Raman fiber laser when limited by second-order Stokes conversion. The contours are plotted vs.pump power and fiber length. Also shown are the reflectivities required to optimized the oscillator output power. We assume the same clad-to-core diameter ratio seed and pump loss and fix the losses at 1 dB/km and 1 dB/m for the first and second-order Stokes shifted wavelengths respectively.

Fig. 8.
Fig. 8.

Simulation of a cw cladding-pumped Raman fiber laser. Single-pass evolution of pump, self-consistent, multi-pass evolution of the first-order Stokes and single-pass evolution of second-order Stokes powers vs length. Parameters assumed include a 1 kWpump, 350 m 80:12 µm fiber, α s1 =1 dB/km, and α s2 =1 dB/m. At these higher pump power levels, weak reflectivity (2.3%) is required, the circulating intensity is 12 W/µm2, a brightness enhancement of 1600 can be achieved, and 63% conversion is predicted.

Fig. 9.
Fig. 9.

Power input output relationships for 100 m and 350 m cladding-pumped Raman fiber lasers with 88% and 2.3% reflectivities for α s2 = 1,5 dB/m.

Fig. 10.
Fig. 10.

Flowchart useful as a guide to designing cladding-pumped Raman fiber lasers.

Equations (23)

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dP p dz = α p P p g A clad v p v s 1 P s 1 P p
dP s 1 dz = α s 1 P s 1 + g A clad P p P s 1 g A core v s 1 v s 2 P s 2 P s 1
d P s 2 dz = α s 2 P s 2 + g A core P s 1 P s 2
B = η ( π N A clad D clad 2 λ s 1 ) 2
P p ( 0 ) P p ( z pk ) + P s 1 ( z pk )
η pk 1 1 + P p ( z pk ) P s 1 ( z pk )
P s 2 ( z pk ) P s 2 ( 0 ) e gIL eff
g IL eff = g d z I s 1 ( 0 ) e g I p ( z ) z g d z I s 1 ( z p k ) e g I p ( z p k ) ( z z p k )
= I s 1 ( z pk ) I p ( z pk ) [ 1 e gI p ( z pk ) z pk ]
( A clad A core ) ( P s 1 ( z pk ) P p ( z pk ) )
P s 1 ( z pk ) = P p ( z pk ) ( A core A clad ) ln ( P s 2 ( z pk ) P s 2 ( 0 ) )
dP s 1 dz g A clad P p P s 1 g A core P s 2 P s 1 = 0
P s 2 ( z pk ) A core A clad P p ( z pk )
η pk 1 1 + A clad A core ln ( A core A clad P p ( z pk ) P s 2 ( 0 ) )
η 10 ( D clad D core ) 2
B Stokes limited 10 ( π NA clad D core 2 λ s ) 2
dP p dz = α p P p g A clad v p v s 1 ( P s 1 a + P s 1 b ) P p
dP s 1 a dz = α s 1 P s 1 a + g A clad P p P s 1 a g A core v s 1 v s 2 P s 2 P s 1 a
dP s 1 b dz = + α s 1 P s 1 b g A clad P p P s 1 b + g A core v s 1 v s 2 P s 2 P s 1 b
dP s 2 a dz = α s 2 P s 2 a + g A core ( P s 1 a + P s 1 b ) P s 2 a
dP s 2 b dz = + α s 2 P s 2 b g A core ( P s 1 a + P s 1 b ) P s 2 b
α s 2 > gP p A core ( 1 + R ) ( 1 R )
( A clad g ) [ α s 1 ln ( R ) 2 L ]

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