Abstract

We propose a model for designing and analyzing rare-earth-doped distributed-feedback (DFB) lasers. The effects of pump depletion and cross-gain saturation are included and shown to be significant for high-efficiency lasers. Our simulations show good agreement with experimental data from an ytterbium-doped fiber laser. We also give some design guidelines for DFB fiber lasers.

© 1996 Optical Society of America

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References

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  1. H. Kogelnik, C. V. Shank, J. Appl. Phys. 43, 2327 (1972).
    [CrossRef]
  2. H. A. Haus, Appl. Opt. 14, 2650 (1975).
    [CrossRef] [PubMed]
  3. P. Szczepanski, D. Sikorski, W. Wolinski, IEEE J. Quantum Electron. 25, 871 (1989).
    [CrossRef]
  4. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  5. A. Asseh, H. Storoy, J. T. Kringlebotn, W. Margulis, B. Sahlgren, S. Sandgren, R. Stubbe, G. Edwall, Electron. Lett. 31, 969 (1995).
    [CrossRef]
  6. M. Yamada, K. Sakuda, Appl. Opt. 26, 3474 (1987).
    [CrossRef] [PubMed]
  7. J.-L. Archambault, L. Reekie, P. St, J. Russel, Electron. Lett. 29, 453 (1993).
    [CrossRef]

1995

A. Asseh, H. Storoy, J. T. Kringlebotn, W. Margulis, B. Sahlgren, S. Sandgren, R. Stubbe, G. Edwall, Electron. Lett. 31, 969 (1995).
[CrossRef]

1993

J.-L. Archambault, L. Reekie, P. St, J. Russel, Electron. Lett. 29, 453 (1993).
[CrossRef]

1989

P. Szczepanski, D. Sikorski, W. Wolinski, IEEE J. Quantum Electron. 25, 871 (1989).
[CrossRef]

1987

1975

1972

H. Kogelnik, C. V. Shank, J. Appl. Phys. 43, 2327 (1972).
[CrossRef]

Archambault, J.-L.

J.-L. Archambault, L. Reekie, P. St, J. Russel, Electron. Lett. 29, 453 (1993).
[CrossRef]

Asseh, A.

A. Asseh, H. Storoy, J. T. Kringlebotn, W. Margulis, B. Sahlgren, S. Sandgren, R. Stubbe, G. Edwall, Electron. Lett. 31, 969 (1995).
[CrossRef]

Edwall, G.

A. Asseh, H. Storoy, J. T. Kringlebotn, W. Margulis, B. Sahlgren, S. Sandgren, R. Stubbe, G. Edwall, Electron. Lett. 31, 969 (1995).
[CrossRef]

Haus, H. A.

Kogelnik, H.

H. Kogelnik, C. V. Shank, J. Appl. Phys. 43, 2327 (1972).
[CrossRef]

Kringlebotn, J. T.

A. Asseh, H. Storoy, J. T. Kringlebotn, W. Margulis, B. Sahlgren, S. Sandgren, R. Stubbe, G. Edwall, Electron. Lett. 31, 969 (1995).
[CrossRef]

Margulis, W.

A. Asseh, H. Storoy, J. T. Kringlebotn, W. Margulis, B. Sahlgren, S. Sandgren, R. Stubbe, G. Edwall, Electron. Lett. 31, 969 (1995).
[CrossRef]

Reekie, L.

J.-L. Archambault, L. Reekie, P. St, J. Russel, Electron. Lett. 29, 453 (1993).
[CrossRef]

Russel, J.

J.-L. Archambault, L. Reekie, P. St, J. Russel, Electron. Lett. 29, 453 (1993).
[CrossRef]

Sahlgren, B.

A. Asseh, H. Storoy, J. T. Kringlebotn, W. Margulis, B. Sahlgren, S. Sandgren, R. Stubbe, G. Edwall, Electron. Lett. 31, 969 (1995).
[CrossRef]

Sakuda, K.

Sandgren, S.

A. Asseh, H. Storoy, J. T. Kringlebotn, W. Margulis, B. Sahlgren, S. Sandgren, R. Stubbe, G. Edwall, Electron. Lett. 31, 969 (1995).
[CrossRef]

Shank, C. V.

H. Kogelnik, C. V. Shank, J. Appl. Phys. 43, 2327 (1972).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

Sikorski, D.

P. Szczepanski, D. Sikorski, W. Wolinski, IEEE J. Quantum Electron. 25, 871 (1989).
[CrossRef]

St, P.

J.-L. Archambault, L. Reekie, P. St, J. Russel, Electron. Lett. 29, 453 (1993).
[CrossRef]

Storoy, H.

A. Asseh, H. Storoy, J. T. Kringlebotn, W. Margulis, B. Sahlgren, S. Sandgren, R. Stubbe, G. Edwall, Electron. Lett. 31, 969 (1995).
[CrossRef]

Stubbe, R.

A. Asseh, H. Storoy, J. T. Kringlebotn, W. Margulis, B. Sahlgren, S. Sandgren, R. Stubbe, G. Edwall, Electron. Lett. 31, 969 (1995).
[CrossRef]

Szczepanski, P.

P. Szczepanski, D. Sikorski, W. Wolinski, IEEE J. Quantum Electron. 25, 871 (1989).
[CrossRef]

Wolinski, W.

P. Szczepanski, D. Sikorski, W. Wolinski, IEEE J. Quantum Electron. 25, 871 (1989).
[CrossRef]

Yamada, M.

Appl. Opt.

Electron. Lett.

J.-L. Archambault, L. Reekie, P. St, J. Russel, Electron. Lett. 29, 453 (1993).
[CrossRef]

A. Asseh, H. Storoy, J. T. Kringlebotn, W. Margulis, B. Sahlgren, S. Sandgren, R. Stubbe, G. Edwall, Electron. Lett. 31, 969 (1995).
[CrossRef]

IEEE J. Quantum Electron.

P. Szczepanski, D. Sikorski, W. Wolinski, IEEE J. Quantum Electron. 25, 871 (1989).
[CrossRef]

J. Appl. Phys.

H. Kogelnik, C. V. Shank, J. Appl. Phys. 43, 2327 (1972).
[CrossRef]

Other

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

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Figures (3)

Fig. 1
Fig. 1

Solid line, calculated output power; triangles, measured output power; dashed line, calculated transmitted pump power; squares, measured transmitted pump power.

Fig. 2
Fig. 2

Slope efficiency as a function of gain g0. Solid curve, our model; dashed line, cross-gain saturation and pump depletion neglected.

Fig. 3
Fig. 3

Slope efficiency as a function of gain g0 for different cavity lengths L.

Equations (8)

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N 2 t = N 1 t = N 2 T 1 + [ σ a ( ω s ) S s ω s A 2 + σ a ( ω p ) S p ω p P p ] N 1 [ σ e ( ω s ) S s ω s A 2 + σ e ( ω p ) S p ω p P p ] N 2 .
g = g 0 1 + ω p ω s g 0 α 0 P p A + exp ( i k z ) + A exp ( i k z ) 2 ,
g 0 = N 0 S i S s σ e ( ω s ) σ a ( ω p ) σ e ( ω p ) σ a ( ω s ) σ a ( ω p ) + σ e ( ω p )
α 0 = N 0 S i S p σ e ( ω s ) σ a ( ω p ) σ e ( ω p ) σ a ( ω s ) σ a ( ω s ) + σ e ( ω s ) .
d A + d z + i δ A + = i κ c A exp [ 2 i ϕ ( z ) ] + g + 2 A + ,
d A d z i δ A = i κ c A + exp [ 2 i ϕ ( z ) ] g 2 A ,
g ± = g 0 D ± + C 2 B 2 C 2 B 2 ( C + C 2 B 2 ) , B = 2 ω p ω s g 0 α 0 P p A + A , C = 1 + ω p ω s g 0 α 0 P p ( A + 2 + A 2 ) , D ± = 1 + ω p ω s g 0 α 0 P p ( A ± 2 A 2 ) ;
d P p d z ( α L + α 0 α 0 C 2 B 2 ) P p ,

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