Abstract

This paper presents a simulation technique developed to concurrently model the pump and laser power evolution in a cladding pumped rare-earth doped fiber. The simulation technique uses a series of scaling factors to dramatically decrease simulation run-times, while maintaining accuracy. This approach differs from previous methods in that it can simulate arbitrary pump cladding shapes. The results of the simulation are validated using a decagon-shaped cladding pumped, ytterbium doped fiber. Good correlation is found between the simulated and experimental pump evolution and conversion efficiency.

© 2003 Optical Society of America

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  1. E. Snitzer, H. Po, F. Hakimi, R. Tumminelli, and B.C. McCollum, “Double-clad offset core Nd fiber laser,”in Proc. Of Optical Fiber Sensors’88, pp. PD5, (1988).
  2. A. White and S. Grubb, Optical Fiber Telecommunications IIIB, (Academic Press, 1997), Chap. 7.
  3. H. Po, E. Snitzer, R. Tumminelli, L. Zenteno, F. Hakimi, N.M. Cho, and T. Haw, “Double-clad high brightness Nd fiber laser pumped by GaAlAs phased array,” in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 1989). Pp. PD7
  4. M. Muendel, “Optical fiber structure for efficient use of pump power,” US Patent # 5,533,563, 1996.
  5. D. DiGiovanni, “Method of making a cladding pumped fiber structure,” US Patent # 5,873,923, 1999.
  6. M. Muendel, “Optimal inner cladding shapes for double-clad fiber lasers,” in Conference on Lasers and Electro-Optics, Technical Digest, (Optical Society of America, Washington DC, 1996), pp. 209.
  7. L. Qiao and J. Wang, “A modified ray-optic method for arbitrary dielectric waveguides,” IEEE J. Quantum Electron.,  28, 2721–2727, (1992).
    [Crossref]
  8. M. Feit and J. Fleck, “Light propagation in graded index optical fibers” Appl. Opt.,  17, 3990–3998, (1978).
    [Crossref] [PubMed]
  9. D. Kouznetsov and J. Moloney, “Efficiency of pump absorption in double-clad fiber amplifiers. II. Broken circular symmetry,” J. Opt. Soc. Am. B.,  19, 1259–1263, (2002).
    [Crossref]
  10. D. Kouznetsov and J. Moloney, “Efficiency of pump absorption in double-clad fiber amplifiers. III. Calculation of modes,” J. Opt. Soc. Am. B.,  19, 1304–1309, (2002).
    [Crossref]
  11. L. Thylen, E. Wright, G. Stegeman, C. Seaton, and J. Moloney, “Beam propagation method analysis of a nonlinear directional coupler,” Optics Lett.,  11, 739–741, (1986).
    [Crossref]
  12. A. Liu and K. Ueda, “The absorption characteristics of circular, offset, and rectangular double-clad fibers,” Optics Comm.,  132, 511–518, (1996).
    [Crossref]
  13. B. Kerrinckx, P. Even, and D. Pureur, “New theoretical model of ytterbium-doped double-clad fiber for laser application,” in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 2001). Pp. TuI3-1.
  14. A. Siegman, Lasers. (University Science Books, 1986), Chap. 3, 7.
  15. H. Pask, J Archambault, D. Hanna, L. Reekie, P.St.J. Russell, J. Townsend, and A. Tropper, “Operation of cladding pumped Yb3+-doped silica fibre lasers in the 1 µm region,” Electron. Lett.,  30, 863–864, (1994).
    [Crossref]

2002 (2)

D. Kouznetsov and J. Moloney, “Efficiency of pump absorption in double-clad fiber amplifiers. II. Broken circular symmetry,” J. Opt. Soc. Am. B.,  19, 1259–1263, (2002).
[Crossref]

D. Kouznetsov and J. Moloney, “Efficiency of pump absorption in double-clad fiber amplifiers. III. Calculation of modes,” J. Opt. Soc. Am. B.,  19, 1304–1309, (2002).
[Crossref]

1996 (1)

A. Liu and K. Ueda, “The absorption characteristics of circular, offset, and rectangular double-clad fibers,” Optics Comm.,  132, 511–518, (1996).
[Crossref]

1994 (1)

H. Pask, J Archambault, D. Hanna, L. Reekie, P.St.J. Russell, J. Townsend, and A. Tropper, “Operation of cladding pumped Yb3+-doped silica fibre lasers in the 1 µm region,” Electron. Lett.,  30, 863–864, (1994).
[Crossref]

1992 (1)

L. Qiao and J. Wang, “A modified ray-optic method for arbitrary dielectric waveguides,” IEEE J. Quantum Electron.,  28, 2721–2727, (1992).
[Crossref]

1986 (1)

L. Thylen, E. Wright, G. Stegeman, C. Seaton, and J. Moloney, “Beam propagation method analysis of a nonlinear directional coupler,” Optics Lett.,  11, 739–741, (1986).
[Crossref]

1978 (1)

Archambault, J

H. Pask, J Archambault, D. Hanna, L. Reekie, P.St.J. Russell, J. Townsend, and A. Tropper, “Operation of cladding pumped Yb3+-doped silica fibre lasers in the 1 µm region,” Electron. Lett.,  30, 863–864, (1994).
[Crossref]

Cho, N.M.

H. Po, E. Snitzer, R. Tumminelli, L. Zenteno, F. Hakimi, N.M. Cho, and T. Haw, “Double-clad high brightness Nd fiber laser pumped by GaAlAs phased array,” in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 1989). Pp. PD7

DiGiovanni, D.

D. DiGiovanni, “Method of making a cladding pumped fiber structure,” US Patent # 5,873,923, 1999.

Even, P.

B. Kerrinckx, P. Even, and D. Pureur, “New theoretical model of ytterbium-doped double-clad fiber for laser application,” in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 2001). Pp. TuI3-1.

Feit, M.

Fleck, J.

Grubb, S.

A. White and S. Grubb, Optical Fiber Telecommunications IIIB, (Academic Press, 1997), Chap. 7.

Hakimi, F.

E. Snitzer, H. Po, F. Hakimi, R. Tumminelli, and B.C. McCollum, “Double-clad offset core Nd fiber laser,”in Proc. Of Optical Fiber Sensors’88, pp. PD5, (1988).

H. Po, E. Snitzer, R. Tumminelli, L. Zenteno, F. Hakimi, N.M. Cho, and T. Haw, “Double-clad high brightness Nd fiber laser pumped by GaAlAs phased array,” in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 1989). Pp. PD7

Hanna, D.

H. Pask, J Archambault, D. Hanna, L. Reekie, P.St.J. Russell, J. Townsend, and A. Tropper, “Operation of cladding pumped Yb3+-doped silica fibre lasers in the 1 µm region,” Electron. Lett.,  30, 863–864, (1994).
[Crossref]

Haw, T.

H. Po, E. Snitzer, R. Tumminelli, L. Zenteno, F. Hakimi, N.M. Cho, and T. Haw, “Double-clad high brightness Nd fiber laser pumped by GaAlAs phased array,” in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 1989). Pp. PD7

Kerrinckx, B.

B. Kerrinckx, P. Even, and D. Pureur, “New theoretical model of ytterbium-doped double-clad fiber for laser application,” in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 2001). Pp. TuI3-1.

Kouznetsov, D.

D. Kouznetsov and J. Moloney, “Efficiency of pump absorption in double-clad fiber amplifiers. II. Broken circular symmetry,” J. Opt. Soc. Am. B.,  19, 1259–1263, (2002).
[Crossref]

D. Kouznetsov and J. Moloney, “Efficiency of pump absorption in double-clad fiber amplifiers. III. Calculation of modes,” J. Opt. Soc. Am. B.,  19, 1304–1309, (2002).
[Crossref]

Liu, A.

A. Liu and K. Ueda, “The absorption characteristics of circular, offset, and rectangular double-clad fibers,” Optics Comm.,  132, 511–518, (1996).
[Crossref]

McCollum, B.C.

E. Snitzer, H. Po, F. Hakimi, R. Tumminelli, and B.C. McCollum, “Double-clad offset core Nd fiber laser,”in Proc. Of Optical Fiber Sensors’88, pp. PD5, (1988).

Moloney, J.

D. Kouznetsov and J. Moloney, “Efficiency of pump absorption in double-clad fiber amplifiers. III. Calculation of modes,” J. Opt. Soc. Am. B.,  19, 1304–1309, (2002).
[Crossref]

D. Kouznetsov and J. Moloney, “Efficiency of pump absorption in double-clad fiber amplifiers. II. Broken circular symmetry,” J. Opt. Soc. Am. B.,  19, 1259–1263, (2002).
[Crossref]

L. Thylen, E. Wright, G. Stegeman, C. Seaton, and J. Moloney, “Beam propagation method analysis of a nonlinear directional coupler,” Optics Lett.,  11, 739–741, (1986).
[Crossref]

Muendel, M.

M. Muendel, “Optical fiber structure for efficient use of pump power,” US Patent # 5,533,563, 1996.

M. Muendel, “Optimal inner cladding shapes for double-clad fiber lasers,” in Conference on Lasers and Electro-Optics, Technical Digest, (Optical Society of America, Washington DC, 1996), pp. 209.

Pask, H.

H. Pask, J Archambault, D. Hanna, L. Reekie, P.St.J. Russell, J. Townsend, and A. Tropper, “Operation of cladding pumped Yb3+-doped silica fibre lasers in the 1 µm region,” Electron. Lett.,  30, 863–864, (1994).
[Crossref]

Po, H.

E. Snitzer, H. Po, F. Hakimi, R. Tumminelli, and B.C. McCollum, “Double-clad offset core Nd fiber laser,”in Proc. Of Optical Fiber Sensors’88, pp. PD5, (1988).

H. Po, E. Snitzer, R. Tumminelli, L. Zenteno, F. Hakimi, N.M. Cho, and T. Haw, “Double-clad high brightness Nd fiber laser pumped by GaAlAs phased array,” in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 1989). Pp. PD7

Pureur, D.

B. Kerrinckx, P. Even, and D. Pureur, “New theoretical model of ytterbium-doped double-clad fiber for laser application,” in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 2001). Pp. TuI3-1.

Qiao, L.

L. Qiao and J. Wang, “A modified ray-optic method for arbitrary dielectric waveguides,” IEEE J. Quantum Electron.,  28, 2721–2727, (1992).
[Crossref]

Reekie, L.

H. Pask, J Archambault, D. Hanna, L. Reekie, P.St.J. Russell, J. Townsend, and A. Tropper, “Operation of cladding pumped Yb3+-doped silica fibre lasers in the 1 µm region,” Electron. Lett.,  30, 863–864, (1994).
[Crossref]

Russell, P.St.J.

H. Pask, J Archambault, D. Hanna, L. Reekie, P.St.J. Russell, J. Townsend, and A. Tropper, “Operation of cladding pumped Yb3+-doped silica fibre lasers in the 1 µm region,” Electron. Lett.,  30, 863–864, (1994).
[Crossref]

Seaton, C.

L. Thylen, E. Wright, G. Stegeman, C. Seaton, and J. Moloney, “Beam propagation method analysis of a nonlinear directional coupler,” Optics Lett.,  11, 739–741, (1986).
[Crossref]

Siegman, A.

A. Siegman, Lasers. (University Science Books, 1986), Chap. 3, 7.

Snitzer, E.

H. Po, E. Snitzer, R. Tumminelli, L. Zenteno, F. Hakimi, N.M. Cho, and T. Haw, “Double-clad high brightness Nd fiber laser pumped by GaAlAs phased array,” in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 1989). Pp. PD7

E. Snitzer, H. Po, F. Hakimi, R. Tumminelli, and B.C. McCollum, “Double-clad offset core Nd fiber laser,”in Proc. Of Optical Fiber Sensors’88, pp. PD5, (1988).

Stegeman, G.

L. Thylen, E. Wright, G. Stegeman, C. Seaton, and J. Moloney, “Beam propagation method analysis of a nonlinear directional coupler,” Optics Lett.,  11, 739–741, (1986).
[Crossref]

Thylen, L.

L. Thylen, E. Wright, G. Stegeman, C. Seaton, and J. Moloney, “Beam propagation method analysis of a nonlinear directional coupler,” Optics Lett.,  11, 739–741, (1986).
[Crossref]

Townsend, J.

H. Pask, J Archambault, D. Hanna, L. Reekie, P.St.J. Russell, J. Townsend, and A. Tropper, “Operation of cladding pumped Yb3+-doped silica fibre lasers in the 1 µm region,” Electron. Lett.,  30, 863–864, (1994).
[Crossref]

Tropper, A.

H. Pask, J Archambault, D. Hanna, L. Reekie, P.St.J. Russell, J. Townsend, and A. Tropper, “Operation of cladding pumped Yb3+-doped silica fibre lasers in the 1 µm region,” Electron. Lett.,  30, 863–864, (1994).
[Crossref]

Tumminelli, R.

E. Snitzer, H. Po, F. Hakimi, R. Tumminelli, and B.C. McCollum, “Double-clad offset core Nd fiber laser,”in Proc. Of Optical Fiber Sensors’88, pp. PD5, (1988).

H. Po, E. Snitzer, R. Tumminelli, L. Zenteno, F. Hakimi, N.M. Cho, and T. Haw, “Double-clad high brightness Nd fiber laser pumped by GaAlAs phased array,” in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 1989). Pp. PD7

Ueda, K.

A. Liu and K. Ueda, “The absorption characteristics of circular, offset, and rectangular double-clad fibers,” Optics Comm.,  132, 511–518, (1996).
[Crossref]

Wang, J.

L. Qiao and J. Wang, “A modified ray-optic method for arbitrary dielectric waveguides,” IEEE J. Quantum Electron.,  28, 2721–2727, (1992).
[Crossref]

White, A.

A. White and S. Grubb, Optical Fiber Telecommunications IIIB, (Academic Press, 1997), Chap. 7.

Wright, E.

L. Thylen, E. Wright, G. Stegeman, C. Seaton, and J. Moloney, “Beam propagation method analysis of a nonlinear directional coupler,” Optics Lett.,  11, 739–741, (1986).
[Crossref]

Zenteno, L.

H. Po, E. Snitzer, R. Tumminelli, L. Zenteno, F. Hakimi, N.M. Cho, and T. Haw, “Double-clad high brightness Nd fiber laser pumped by GaAlAs phased array,” in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 1989). Pp. PD7

Appl. Opt. (1)

Electron. Lett. (1)

H. Pask, J Archambault, D. Hanna, L. Reekie, P.St.J. Russell, J. Townsend, and A. Tropper, “Operation of cladding pumped Yb3+-doped silica fibre lasers in the 1 µm region,” Electron. Lett.,  30, 863–864, (1994).
[Crossref]

IEEE J. Quantum Electron. (1)

L. Qiao and J. Wang, “A modified ray-optic method for arbitrary dielectric waveguides,” IEEE J. Quantum Electron.,  28, 2721–2727, (1992).
[Crossref]

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

D. Kouznetsov and J. Moloney, “Efficiency of pump absorption in double-clad fiber amplifiers. II. Broken circular symmetry,” J. Opt. Soc. Am. B.,  19, 1259–1263, (2002).
[Crossref]

D. Kouznetsov and J. Moloney, “Efficiency of pump absorption in double-clad fiber amplifiers. III. Calculation of modes,” J. Opt. Soc. Am. B.,  19, 1304–1309, (2002).
[Crossref]

Optics Comm. (1)

A. Liu and K. Ueda, “The absorption characteristics of circular, offset, and rectangular double-clad fibers,” Optics Comm.,  132, 511–518, (1996).
[Crossref]

Optics Lett. (1)

L. Thylen, E. Wright, G. Stegeman, C. Seaton, and J. Moloney, “Beam propagation method analysis of a nonlinear directional coupler,” Optics Lett.,  11, 739–741, (1986).
[Crossref]

Other (8)

E. Snitzer, H. Po, F. Hakimi, R. Tumminelli, and B.C. McCollum, “Double-clad offset core Nd fiber laser,”in Proc. Of Optical Fiber Sensors’88, pp. PD5, (1988).

A. White and S. Grubb, Optical Fiber Telecommunications IIIB, (Academic Press, 1997), Chap. 7.

H. Po, E. Snitzer, R. Tumminelli, L. Zenteno, F. Hakimi, N.M. Cho, and T. Haw, “Double-clad high brightness Nd fiber laser pumped by GaAlAs phased array,” in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 1989). Pp. PD7

M. Muendel, “Optical fiber structure for efficient use of pump power,” US Patent # 5,533,563, 1996.

D. DiGiovanni, “Method of making a cladding pumped fiber structure,” US Patent # 5,873,923, 1999.

M. Muendel, “Optimal inner cladding shapes for double-clad fiber lasers,” in Conference on Lasers and Electro-Optics, Technical Digest, (Optical Society of America, Washington DC, 1996), pp. 209.

B. Kerrinckx, P. Even, and D. Pureur, “New theoretical model of ytterbium-doped double-clad fiber for laser application,” in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 2001). Pp. TuI3-1.

A. Siegman, Lasers. (University Science Books, 1986), Chap. 3, 7.

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Figures (4)

Fig. 1.
Fig. 1.

Pump and laser (signal) power evolution as a function of length for the simulated decagon-shaped fiber. In this case a pump power of 2 watts was used. The simulation length was 16 cm.

Fig. 2.
Fig. 2.

End micrograph of the experimental decagon-shaped fiber. The diameter of the pump clad is nominally 230 µm. Cleave damage obscures the upper and lower apices.

Fig. 3.
Fig. 3.

Simulated and experimental pump absorption as a function of length for the 230 µm diameter decagonal fiber. The length scale chosen reflects a range of typical device lengths for cladding pumped devices.

Fig. 4.
Fig. 4.

Simulated and experimental conversion efficiency as a function of length for the 230 µm diameter decagonal fiber.

Equations (8)

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E z = j 1 2 k 2 E j μ 0 ω 2 2 k P
P = ε 0 χ at E
χ at ( w ) = j 4 π 2 I 3 g rad , 2 1 Δ w a ( g 2 g 1 N 1 N 2 ) 1 1 + 2 j ( w w a ) Δ w a
χ = 1 4 π 2 λ 3 γ rad 2 1 Δ ω a ( g 2 g 1 N 1 N 2 )
u ( x , y , z ) = j ( z z 0 ) λ u ( x 0 , y 0 , z 0 ) e j k ( x x 0 ) 2 + ( y y 0 ) 2 2 ( z z 0 ) d x 0 d y 0
Δ N = [ N 0 W a + W e + 1 τ 2 + R 13 ] [ g 2 g 1 ( W e + 1 τ 2 ) ( W a + R 13 ) ]
Δ E = j k χ 2 n 2 E in Δ z
α fiber = α core A core A clad

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