Abstract

We derive an expression describing pre-compensation of pulse-distortion due to saturation effects in short pulse laser-amplifiers. The analytical solution determines the optimum input pulse-shape required to obtain any arbitrary target pulse-shape at the output of the saturated laser-amplifier. The relation is experimentally verified using an all-fiber amplifier chain that is seeded by a directly modulated laser-diode. The method will prove useful in applications of high power, high energy laser-amplifier systems that need particular pulse-shapes to be efficient, e.g. micromachining and scientific laser-matter-interactions.

© 2008 Optical Society of America

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  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]
  2. L. M. Frantz and J. S. Nodvik, "Theory of Pulse Propagation in a Laser Amplifier," J. Appl. Phys. 34, 2346-2349 (1963).
    [CrossRef]
  3. Y. Wang, H. Po, "Dynamic Characteristics of Double-Clad Fiber Amplifiers for High-Power Pulse Amplification," J. Lightwave Technol. 21, 2262- (2003).
    [CrossRef]
  4. W. Williams, C. Orth, R. Sacks, J. Lawson, K. Jancaitis, J. Trenholme, S. Haney, J. Auerbach, M. Henesian, and P. Renard,"NIF Design Optimization," in Inertial Confinement Fusion Annual Report, (Lawrence Livermore National Laboratory, 1996) p. 184.
  5. M. Shaw, W. Williams, R. House, and C. Haynam, "Laser Performance Operations Model (LPOM)," in Inertial Confinement Fusion Semiannual Report (Lawrence Livermore National Laboratory, 2004).
  6. W. Shaikh, I. O. Musgrave, A. S. Bhamra, and C. Hernandez-Gomez, "Development of an amplified variable shaped long pulse system for Vulcan," in Central Laser Facility Annual Report (CCLRC Rutherford Appleton Laboratory, 2005/2006) p. 199.
  7. K. T. Vu, A. Malinowski, D. J. Richardson, F. Ghiringhelli, L. M. B. Hickey, and M. N. Zervas, "Adaptive pulse shape control in a diode-seeded nanosecond fiber MOPA system," Opt. Express 14, 10996-11001 (2006).
    [CrossRef] [PubMed]
  8. W. H. Lowdermilk and J. E. Murray, "The multipass amplifier: Theory and numerical analysis," J. Appl. Phys. 51, 2436-2444 (1980).
    [CrossRef]
  9. W. Koechner, Solid-State Laser Engineering, 5th ed., (Springer, 1999).
  10. A. E. Siegman, Lasers, (University Science Books, 1986).
  11. D. E. McCumber, "Einstein Relations Connecting Broadband Emission and Absorption Spectra," Phys. Rev. 136, A954-A957 (1964).
    [CrossRef]
  12. J. Ehlert, H. Stiel, and K. Teucher, "A numerical solver for rate equations and photon transport equations in nonlinear laser spectroscopy," Comput. Phys. Commun. 124, 330-339 (2000).
    [CrossRef]
  13. J. W. Thomas, Numerical Partial Differential Equations: Finite Difference Methods, (Springer, 1995).
  14. Liekki Application Designer, http://www.liekki.fi.
  15. M.-J. Li, X. Chen, J. Wang, S. Gray, A. Liu, J. A. Demeritt, A. B. Ruffin, A. M. Cowley, D. T. Walton, and L. A. Zenteno, "Al/Ge co-doped large mode area fiber with high SBS threshold," Opt. Express 15, 8290-8299 (2007).
    [CrossRef] [PubMed]

2007 (1)

2006 (1)

2000 (1)

J. Ehlert, H. Stiel, and K. Teucher, "A numerical solver for rate equations and photon transport equations in nonlinear laser spectroscopy," Comput. Phys. Commun. 124, 330-339 (2000).
[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]

1980 (1)

W. H. Lowdermilk and J. E. Murray, "The multipass amplifier: Theory and numerical analysis," J. Appl. Phys. 51, 2436-2444 (1980).
[CrossRef]

1964 (1)

D. E. McCumber, "Einstein Relations Connecting Broadband Emission and Absorption Spectra," Phys. Rev. 136, A954-A957 (1964).
[CrossRef]

1963 (1)

L. M. Frantz and J. S. Nodvik, "Theory of Pulse Propagation in a Laser Amplifier," J. Appl. Phys. 34, 2346-2349 (1963).
[CrossRef]

Chen, X.

Cowley, A. M.

Demeritt, J. A.

Ehlert, J.

J. Ehlert, H. Stiel, and K. Teucher, "A numerical solver for rate equations and photon transport equations in nonlinear laser spectroscopy," Comput. Phys. Commun. 124, 330-339 (2000).
[CrossRef]

Frantz, L. M.

L. M. Frantz and J. S. Nodvik, "Theory of Pulse Propagation in a Laser Amplifier," J. Appl. Phys. 34, 2346-2349 (1963).
[CrossRef]

Ghiringhelli, F.

Gray, S.

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]

Hickey, L. M. B.

Li, M.-J.

Liu, A.

Lowdermilk, W. H.

W. H. Lowdermilk and J. E. Murray, "The multipass amplifier: Theory and numerical analysis," J. Appl. Phys. 51, 2436-2444 (1980).
[CrossRef]

Malinowski, A.

McCumber, D. E.

D. E. McCumber, "Einstein Relations Connecting Broadband Emission and Absorption Spectra," Phys. Rev. 136, A954-A957 (1964).
[CrossRef]

Murray, J. E.

W. H. Lowdermilk and J. E. Murray, "The multipass amplifier: Theory and numerical analysis," J. Appl. Phys. 51, 2436-2444 (1980).
[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]

Nodvik, J. S.

L. M. Frantz and J. S. Nodvik, "Theory of Pulse Propagation in a Laser Amplifier," J. Appl. Phys. 34, 2346-2349 (1963).
[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]

Po, H.

Y. Wang, H. Po, "Dynamic Characteristics of Double-Clad Fiber Amplifiers for High-Power Pulse Amplification," J. Lightwave Technol. 21, 2262- (2003).
[CrossRef]

Richardson, D. J.

Ruffin, A. B.

Stiel, H.

J. Ehlert, H. Stiel, and K. Teucher, "A numerical solver for rate equations and photon transport equations in nonlinear laser spectroscopy," Comput. Phys. Commun. 124, 330-339 (2000).
[CrossRef]

Teucher, K.

J. Ehlert, H. Stiel, and K. Teucher, "A numerical solver for rate equations and photon transport equations in nonlinear laser spectroscopy," Comput. Phys. Commun. 124, 330-339 (2000).
[CrossRef]

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]

Vu, K. T.

Walton, D. T.

Wang, J.

Wang, Y.

Y. Wang, H. Po, "Dynamic Characteristics of Double-Clad Fiber Amplifiers for High-Power Pulse Amplification," J. Lightwave Technol. 21, 2262- (2003).
[CrossRef]

Zenteno, L. A.

Zervas, M. N.

Comput. Phys. Commun. (1)

J. Ehlert, H. Stiel, and K. Teucher, "A numerical solver for rate equations and photon transport equations in nonlinear laser spectroscopy," Comput. Phys. Commun. 124, 330-339 (2000).
[CrossRef]

IEEE J Quantum Electron. (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]

J. Appl. Phys. (2)

L. M. Frantz and J. S. Nodvik, "Theory of Pulse Propagation in a Laser Amplifier," J. Appl. Phys. 34, 2346-2349 (1963).
[CrossRef]

W. H. Lowdermilk and J. E. Murray, "The multipass amplifier: Theory and numerical analysis," J. Appl. Phys. 51, 2436-2444 (1980).
[CrossRef]

Opt. Express (2)

Phys. Rev. (1)

D. E. McCumber, "Einstein Relations Connecting Broadband Emission and Absorption Spectra," Phys. Rev. 136, A954-A957 (1964).
[CrossRef]

Other (8)

W. Koechner, Solid-State Laser Engineering, 5th ed., (Springer, 1999).

A. E. Siegman, Lasers, (University Science Books, 1986).

Y. Wang, H. Po, "Dynamic Characteristics of Double-Clad Fiber Amplifiers for High-Power Pulse Amplification," J. Lightwave Technol. 21, 2262- (2003).
[CrossRef]

W. Williams, C. Orth, R. Sacks, J. Lawson, K. Jancaitis, J. Trenholme, S. Haney, J. Auerbach, M. Henesian, and P. Renard,"NIF Design Optimization," in Inertial Confinement Fusion Annual Report, (Lawrence Livermore National Laboratory, 1996) p. 184.

M. Shaw, W. Williams, R. House, and C. Haynam, "Laser Performance Operations Model (LPOM)," in Inertial Confinement Fusion Semiannual Report (Lawrence Livermore National Laboratory, 2004).

W. Shaikh, I. O. Musgrave, A. S. Bhamra, and C. Hernandez-Gomez, "Development of an amplified variable shaped long pulse system for Vulcan," in Central Laser Facility Annual Report (CCLRC Rutherford Appleton Laboratory, 2005/2006) p. 199.

J. W. Thomas, Numerical Partial Differential Equations: Finite Difference Methods, (Springer, 1995).

Liekki Application Designer, http://www.liekki.fi.

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Figures (3)

Fig. 1.
Fig. 1.

(a) Convergence to the steady state; one cycle consists of the pump stage as well as the actual pulse-amplification stage. In the steady state: (b) pump-absorption, (c) and inversion distribution before and after passage of the pulse. The horizontal lines are the upper and lower boundary which are given by σ(p) 12/(σ(p) 12(p) 21) and σ(s) 12/(σ(s) 12(s) 21), respectively. (d) signal growth along the fiber.

Fig. 2.
Fig. 2.

(a) Rectangular wave-form generated with the AWG, and the corresponding optical output of the laser-diode; (b) pulse-profiles at the output from the fiber MOPA at various characteristic energies relative to the saturation energy of the amplifier.

Fig. 3.
Fig. 3.

(a) rectangular input pulse, (b) and the corresponding output pulse which is deformed due to saturation. (c) the seed pulse which pre-compensates this deformation to obtain a rectangular target pulse at the output (d). Seed pulse (e) to produce a ‘M’-shaped pulse at the output (f), (g) input to generate a ‘roof’-shaped output (h) of the saturated amplifier.

Equations (13)

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1 c s ϕ s t + ϕ s z = ( σ 21 ( s ) n 2 σ 12 ( s ) ( n 0 n 2 ) ) ϕ s
1 c p ϕ p ± t ± ϕ p ± z = ( σ 21 ( p ) n 2 σ 12 ( p ) ( n 0 n 2 ) ) ϕ p ± η
d n 2 d t = c s ( σ 12 ( s ) ( n 0 n 2 ) σ 21 ( s ) n 2 ) ϕ s + c p ( σ 12 ( p ) ( n 0 n 2 ) σ 21 ( p ) n 2 ) ( ϕ p + + ϕ p ) n 2 τ fl
t ϕ s + c s z ϕ s = c s σ ( s ) ϕ s Δ
t Δ = c s σ ( s ) ϕ s Δ .
ϕ s ( z , t ) = ϕ s , 0 ( t z c s ) 1 [ 1 exp ( σ ( s ) 0 z dz Δ 0 ( z ) ) ] exp ( σ ( s ) c s t z c s dt ϕ s , 0 ( t ) )
Δ ( z , t ) = Δ 0 ( z ) 1 [ 1 exp ( σ ( s ) c s t z c s dt ϕ s , 0 ( t ) ) ] exp ( σ ( s ) 0 z dz Δ 0 ( z ) ) .
I s , z ( T ) = I s , 0 ( T ) 1 [ 1 G 0 1 ( z ) ] exp ( J sat 1 T dt I s , 0 ( t ) )
J ( z ) = J sat ln [ 1 + G 0 ( z ) ( exp ( J 0 J sat ) 1 ) ]
ln G ( z ) = ln [ 1 + exp ( J 0 J sat ) ( G 0 1 ( z ) 1 ) ] .
ln G 0 ( z ) ln G ( z ) = J ( z ) J 0 J sat
0 z dz n 2 , 0 ( z ) 0 z dz n 2 ( z ) = c z c τ + z c dt ϕ s , z ( t ) c 0 τ dt ϕ s , 0 ( t ) .
I s , 0 ( t ) = I s , z ( t ) 1 [ 1 G 0 ( z ) ] exp ( J sat 1 0 t dt I s , z ( t ) ) .

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