Abstract

The ultimate spectrum-narrowing and side-mode suppression due to the presence of a saturable absorber in an external cavity of a fiber Bragg grating semiconductor laser is numerically simulated. The proposed algorithm describes an effect of absorption bleaching in a saturable absorber using earlier measurements and shows the evolution of a dynamic grating in the laser cavity. The simulations confirm for the first time an empirical theory of spectral line narrowing in a laser with an intra-cavity saturable absorber.

© 2006 Optical Society of America

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  1. W. H. Loh, R. I. Laming, M. N. Zervas, M. C Farries, and U. Koren, "Single frequency erbium fiber external cavity semiconductor laser," Appl. Phys. Lett. 66,3422-3424 (1995).
    [CrossRef]
  2. F. N. Timofeev and R. Kashyap, "High-power, ultra-stable, single-frequency operation of a long, doped-fiber external-cavity, grating-semiconductor laser," Opt. Express 11, 515-520 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-6-515
    [CrossRef] [PubMed]
  3. R. Liu, I. Kostko, K. Wu, and R. Kashyap, "Optical generation of microwave signal by doped fiber external cavity semiconductor laser for radio-over-fiber transmission," in Photonic Applications in Nonlinear Optics, Nanophotonics, and Microwave Photonics, R. A. Morandotti, H. E. Ruda, J. Yao, eds, Proc. SPIE 5971, 59711W (2005).
    [CrossRef]
  4. R. N. Liu, I. A. Kostko, R. Kashyap, K. Wu, and P. Kiiveri, "Inband-pumped, broadband bleaching of absorption and refractive index changes in erbium doped fiber," Opt. Commun. 255, 65-71 (2005).
    [CrossRef]
  5. I. A. Kostko and R. Kashyap, "Modeling of self-organized coherence-collapsed and enhanced regime semiconductor fibre grating reflector lasers," in Photonic Applications in Telecommunications, Sensors, Software, and Lasers, J. C. Armitage, R. A. Lessard, G. A. Lampropoulos, eds, Proc. SPIE 5579, 367-374 (2004).
    [CrossRef]
  6. C. R. Giles and E. Desurvire, "Modeling erbium-doped fiber amplifiers," J. Lightwave Technol. 9, 271-283 (1991).
    [CrossRef]
  7. R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium-doped fiber amplifiers," IEEE J. Quantum Electron. 33,1049-1056 (1997)
    [CrossRef]
  8. C. Barnard, P. Myslinski, J. Chrostowski, M. Kavehrad, "Analytical model for rare-earth-doped fiber amplifiers and lasers," IEEE J. Quantum Electron. 30, 1817-1830 (1994).
    [CrossRef]
  9. A. W. T. Wu and A. J. Lowery, "Efficient multiwavelength dynamic model for erbium-doped fiber amplifier," IEEE J. Quantum Electron. 34, 1325-1331 (1998).
    [CrossRef]
  10. A. J. Lowery, "Dynamic modelling of distributed-feedback lasers using scattering matrices," Electron. Lett. 25, 1307-1308 (1989).
    [CrossRef]
  11. M. Frigo and S. G. Johnson, "The design and implementation of FFTW3," inProceedings of IEEE, Special Issue on Program Generation, Optimization, and Platform Adaptation, 93, 216-231 (2005).

2005 (2)

R. N. Liu, I. A. Kostko, R. Kashyap, K. Wu, and P. Kiiveri, "Inband-pumped, broadband bleaching of absorption and refractive index changes in erbium doped fiber," Opt. Commun. 255, 65-71 (2005).
[CrossRef]

M. Frigo and S. G. Johnson, "The design and implementation of FFTW3," inProceedings of IEEE, Special Issue on Program Generation, Optimization, and Platform Adaptation, 93, 216-231 (2005).

2003 (1)

1998 (1)

A. W. T. Wu and A. J. Lowery, "Efficient multiwavelength dynamic model for erbium-doped fiber amplifier," IEEE J. Quantum Electron. 34, 1325-1331 (1998).
[CrossRef]

1997 (1)

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium-doped fiber amplifiers," IEEE J. Quantum Electron. 33,1049-1056 (1997)
[CrossRef]

1995 (1)

W. H. Loh, R. I. Laming, M. N. Zervas, M. C Farries, and U. Koren, "Single frequency erbium fiber external cavity semiconductor laser," Appl. Phys. Lett. 66,3422-3424 (1995).
[CrossRef]

1994 (1)

C. Barnard, P. Myslinski, J. Chrostowski, M. Kavehrad, "Analytical model for rare-earth-doped fiber amplifiers and lasers," IEEE J. Quantum Electron. 30, 1817-1830 (1994).
[CrossRef]

1991 (1)

C. R. Giles and E. Desurvire, "Modeling erbium-doped fiber amplifiers," J. Lightwave Technol. 9, 271-283 (1991).
[CrossRef]

1989 (1)

A. J. Lowery, "Dynamic modelling of distributed-feedback lasers using scattering matrices," Electron. Lett. 25, 1307-1308 (1989).
[CrossRef]

Barnard, C.

C. Barnard, P. Myslinski, J. Chrostowski, M. Kavehrad, "Analytical model for rare-earth-doped fiber amplifiers and lasers," IEEE J. Quantum Electron. 30, 1817-1830 (1994).
[CrossRef]

Chrostowski, J.

C. Barnard, P. Myslinski, J. Chrostowski, M. Kavehrad, "Analytical model for rare-earth-doped fiber amplifiers and lasers," IEEE J. Quantum Electron. 30, 1817-1830 (1994).
[CrossRef]

Desurvire, E.

C. R. Giles and E. Desurvire, "Modeling erbium-doped fiber amplifiers," J. Lightwave Technol. 9, 271-283 (1991).
[CrossRef]

Farries, M. C

W. H. Loh, R. I. Laming, M. N. Zervas, M. C Farries, and U. Koren, "Single frequency erbium fiber external cavity semiconductor laser," Appl. Phys. Lett. 66,3422-3424 (1995).
[CrossRef]

Frigo, M.

M. Frigo and S. G. Johnson, "The design and implementation of FFTW3," inProceedings of IEEE, Special Issue on Program Generation, Optimization, and Platform Adaptation, 93, 216-231 (2005).

Giles, C. R.

C. R. Giles and E. Desurvire, "Modeling erbium-doped fiber amplifiers," J. Lightwave Technol. 9, 271-283 (1991).
[CrossRef]

Hanna, D. C.

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium-doped fiber amplifiers," IEEE J. Quantum Electron. 33,1049-1056 (1997)
[CrossRef]

Johnson, S. G.

M. Frigo and S. G. Johnson, "The design and implementation of FFTW3," inProceedings of IEEE, Special Issue on Program Generation, Optimization, and Platform Adaptation, 93, 216-231 (2005).

Kashyap, R.

R. N. Liu, I. A. Kostko, R. Kashyap, K. Wu, and P. Kiiveri, "Inband-pumped, broadband bleaching of absorption and refractive index changes in erbium doped fiber," Opt. Commun. 255, 65-71 (2005).
[CrossRef]

F. N. Timofeev and R. Kashyap, "High-power, ultra-stable, single-frequency operation of a long, doped-fiber external-cavity, grating-semiconductor laser," Opt. Express 11, 515-520 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-6-515
[CrossRef] [PubMed]

Kavehrad, M.

C. Barnard, P. Myslinski, J. Chrostowski, M. Kavehrad, "Analytical model for rare-earth-doped fiber amplifiers and lasers," IEEE J. Quantum Electron. 30, 1817-1830 (1994).
[CrossRef]

Kiiveri, P.

R. N. Liu, I. A. Kostko, R. Kashyap, K. Wu, and P. Kiiveri, "Inband-pumped, broadband bleaching of absorption and refractive index changes in erbium doped fiber," Opt. Commun. 255, 65-71 (2005).
[CrossRef]

Koren, U.

W. H. Loh, R. I. Laming, M. N. Zervas, M. C Farries, and U. Koren, "Single frequency erbium fiber external cavity semiconductor laser," Appl. Phys. Lett. 66,3422-3424 (1995).
[CrossRef]

Kostko, I. A.

R. N. Liu, I. A. Kostko, R. Kashyap, K. Wu, and P. Kiiveri, "Inband-pumped, broadband bleaching of absorption and refractive index changes in erbium doped fiber," Opt. Commun. 255, 65-71 (2005).
[CrossRef]

Laming, R. I.

W. H. Loh, R. I. Laming, M. N. Zervas, M. C Farries, and U. Koren, "Single frequency erbium fiber external cavity semiconductor laser," Appl. Phys. Lett. 66,3422-3424 (1995).
[CrossRef]

Liu, R. N.

R. N. Liu, I. A. Kostko, R. Kashyap, K. Wu, and P. Kiiveri, "Inband-pumped, broadband bleaching of absorption and refractive index changes in erbium doped fiber," Opt. Commun. 255, 65-71 (2005).
[CrossRef]

Loh, W. H.

W. H. Loh, R. I. Laming, M. N. Zervas, M. C Farries, and U. Koren, "Single frequency erbium fiber external cavity semiconductor laser," Appl. Phys. Lett. 66,3422-3424 (1995).
[CrossRef]

Lowery, A. J.

A. W. T. Wu and A. J. Lowery, "Efficient multiwavelength dynamic model for erbium-doped fiber amplifier," IEEE J. Quantum Electron. 34, 1325-1331 (1998).
[CrossRef]

A. J. Lowery, "Dynamic modelling of distributed-feedback lasers using scattering matrices," Electron. Lett. 25, 1307-1308 (1989).
[CrossRef]

Myslinski, P.

C. Barnard, P. Myslinski, J. Chrostowski, M. Kavehrad, "Analytical model for rare-earth-doped fiber amplifiers and lasers," IEEE J. Quantum Electron. 30, 1817-1830 (1994).
[CrossRef]

Nilsson, J.

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium-doped fiber amplifiers," IEEE J. Quantum Electron. 33,1049-1056 (1997)
[CrossRef]

Paschotta, R.

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium-doped fiber amplifiers," IEEE J. Quantum Electron. 33,1049-1056 (1997)
[CrossRef]

Timofeev, F. N.

Tropper, A. C.

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium-doped fiber amplifiers," IEEE J. Quantum Electron. 33,1049-1056 (1997)
[CrossRef]

Wu, A. W. T.

A. W. T. Wu and A. J. Lowery, "Efficient multiwavelength dynamic model for erbium-doped fiber amplifier," IEEE J. Quantum Electron. 34, 1325-1331 (1998).
[CrossRef]

Wu, K.

R. N. Liu, I. A. Kostko, R. Kashyap, K. Wu, and P. Kiiveri, "Inband-pumped, broadband bleaching of absorption and refractive index changes in erbium doped fiber," Opt. Commun. 255, 65-71 (2005).
[CrossRef]

Zervas, M. N.

W. H. Loh, R. I. Laming, M. N. Zervas, M. C Farries, and U. Koren, "Single frequency erbium fiber external cavity semiconductor laser," Appl. Phys. Lett. 66,3422-3424 (1995).
[CrossRef]

Appl. Phys. Lett. (1)

W. H. Loh, R. I. Laming, M. N. Zervas, M. C Farries, and U. Koren, "Single frequency erbium fiber external cavity semiconductor laser," Appl. Phys. Lett. 66,3422-3424 (1995).
[CrossRef]

Electron. Lett. (1)

A. J. Lowery, "Dynamic modelling of distributed-feedback lasers using scattering matrices," Electron. Lett. 25, 1307-1308 (1989).
[CrossRef]

IEEE J. Quantum Electron. (3)

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium-doped fiber amplifiers," IEEE J. Quantum Electron. 33,1049-1056 (1997)
[CrossRef]

C. Barnard, P. Myslinski, J. Chrostowski, M. Kavehrad, "Analytical model for rare-earth-doped fiber amplifiers and lasers," IEEE J. Quantum Electron. 30, 1817-1830 (1994).
[CrossRef]

A. W. T. Wu and A. J. Lowery, "Efficient multiwavelength dynamic model for erbium-doped fiber amplifier," IEEE J. Quantum Electron. 34, 1325-1331 (1998).
[CrossRef]

J. Lightwave Technol. (1)

C. R. Giles and E. Desurvire, "Modeling erbium-doped fiber amplifiers," J. Lightwave Technol. 9, 271-283 (1991).
[CrossRef]

Opt. Commun. (1)

R. N. Liu, I. A. Kostko, R. Kashyap, K. Wu, and P. Kiiveri, "Inband-pumped, broadband bleaching of absorption and refractive index changes in erbium doped fiber," Opt. Commun. 255, 65-71 (2005).
[CrossRef]

Opt. Express (1)

Proceedings of IEEE, Special Issue on Program Generation, Optimization, and Platform Adaptation (1)

M. Frigo and S. G. Johnson, "The design and implementation of FFTW3," inProceedings of IEEE, Special Issue on Program Generation, Optimization, and Platform Adaptation, 93, 216-231 (2005).

Other (2)

R. Liu, I. Kostko, K. Wu, and R. Kashyap, "Optical generation of microwave signal by doped fiber external cavity semiconductor laser for radio-over-fiber transmission," in Photonic Applications in Nonlinear Optics, Nanophotonics, and Microwave Photonics, R. A. Morandotti, H. E. Ruda, J. Yao, eds, Proc. SPIE 5971, 59711W (2005).
[CrossRef]

I. A. Kostko and R. Kashyap, "Modeling of self-organized coherence-collapsed and enhanced regime semiconductor fibre grating reflector lasers," in Photonic Applications in Telecommunications, Sensors, Software, and Lasers, J. C. Armitage, R. A. Lessard, G. A. Lampropoulos, eds, Proc. SPIE 5579, 367-374 (2004).
[CrossRef]

Supplementary Material (1)

» Media 1: MOV (1732 KB)     

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Figures (6)

Fig. 1.
Fig. 1.

Semiconductor laser with saturable absorber in the external cavity.

Fig. 2.
Fig. 2.

The absorption (solid red line) and the coupling of the dynamic grating (dashed blue line) inside the doped fiber as a function of optical power.

Fig. 3.
Fig. 3.

The absorption (red) and the coupling (blue) of the dynamic grating inside the SA, calculated in the model.

Fig. 4.
Fig. 4.

Calculated number of modes in the spectrum inside the cavity (blue stars) and at the output of the laser (red circles). The roman numbers denote the phases of operation (see the text).

Fig. 5.
Fig. 5.

The output spectra of the laser, calculated during simulations: (a) after 15 iterations, before the absorption has reached its minimum and during the growth of the dynamic grating; (b) after 125 iterations when the absorption of the SA is fully bleached.

Fig. 6.
Fig. 6.

(1.8 MB) Movie of the simulated time-domain evolution of the output spectra of the DFECL.

Equations (7)

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α ( P , t ) = α max , P ( t ) P min ;
α ( P , t ) = ( P ( t ) P min ) α max α min P max P min + α max , P min < P ( t ) < P max ;
α ( P , t ) = α min , P ( t ) P max .
Δ n ( ω ) = c π P . V . ω 1 ω 2 Δ α ( ω ' ) ( ω ' ) 2 ω 2 d ω ' ,
κ = 2 Δ n n λ ,
κ ( P , t ) = ( P ( t ) P min ) κ max κ min P max P min + κ min , P min < P ( t ) < P max ,
k + 1 [ A i ( n + 1 ) B i ( n ) ] = [ 1 + η κ ( P , t ) Δ L η κ ( P , t ) Δ L η κ ( P , t ) Δ L 1 η κ ( P , t ) Δ L ] k [ A r ( n ) B r ( n + 1 ) ] ,

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