Abstract

The evolution of ultrashort pulses in semiconductor laser amplifiers is modeled, including the effects of gain dispersion, slow and fast carrier dynamics, and self-phase modulation, which includes an instantaneous response (n2). The temporal and spectral evolution of 2-ps and 500-fs pulses differ considerably. This is due mainly to saturation caused by the fast (heating) dynamics and to the phase modulation by n2.

© 1992 Optical Society of America

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  1. G. P. Agrawal, N. A. Olsson, IEEE J. Quantum Electron. 25, 2297 (1989).
  2. N. A. Olsson, G. P. Agrawal, Appl. Phys. Lett. 55, 13 (1989).
  3. G. P. Agrawal, N. A. Olsson, Opt. Lett. 14, 500 (1989).
  4. K. L. Hall, J. Mark, E. P. Ippen, G. Eisenstein, Appl. Phys. Lett. 56, 1740 (1990).
  5. Y. Lai, K. L. Hall, E. P. Ippen, G. Eisenstein, IEEE Photon. Technol. Lett. 2, 711 (1990).
  6. P. J. Delfyett, Y. Silberberg, G. A. Alphonse, Appl. Phys. Lett. 59, 10 (1991).
  7. C. T. Hultgren, E. P. Ippen, Appl. Phys. Lett. 59, 635 (1991).
  8. A. Uskov, J. Mørk, J. Mark, IEEE Photon. Technol. Lett. 4, 443 (1992).
  9. A. Dienes, L. Carr, M. Y. Hong, IEEE J. Quantum Electron. 27, 1214 (1991).
  10. G. P. Agrawal, IEEE J. Quantum Electron. 27, 1843 (1991).
  11. K. Vahala, L. C. Chiu, S. Margalit, A. Yariv, Appl. Phys. Lett. 42, 631 (1983).

1992 (1)

A. Uskov, J. Mørk, J. Mark, IEEE Photon. Technol. Lett. 4, 443 (1992).

1991 (4)

A. Dienes, L. Carr, M. Y. Hong, IEEE J. Quantum Electron. 27, 1214 (1991).

G. P. Agrawal, IEEE J. Quantum Electron. 27, 1843 (1991).

P. J. Delfyett, Y. Silberberg, G. A. Alphonse, Appl. Phys. Lett. 59, 10 (1991).

C. T. Hultgren, E. P. Ippen, Appl. Phys. Lett. 59, 635 (1991).

1990 (2)

K. L. Hall, J. Mark, E. P. Ippen, G. Eisenstein, Appl. Phys. Lett. 56, 1740 (1990).

Y. Lai, K. L. Hall, E. P. Ippen, G. Eisenstein, IEEE Photon. Technol. Lett. 2, 711 (1990).

1989 (3)

G. P. Agrawal, N. A. Olsson, IEEE J. Quantum Electron. 25, 2297 (1989).

N. A. Olsson, G. P. Agrawal, Appl. Phys. Lett. 55, 13 (1989).

G. P. Agrawal, N. A. Olsson, Opt. Lett. 14, 500 (1989).

1983 (1)

K. Vahala, L. C. Chiu, S. Margalit, A. Yariv, Appl. Phys. Lett. 42, 631 (1983).

Agrawal, G. P.

G. P. Agrawal, IEEE J. Quantum Electron. 27, 1843 (1991).

G. P. Agrawal, N. A. Olsson, IEEE J. Quantum Electron. 25, 2297 (1989).

N. A. Olsson, G. P. Agrawal, Appl. Phys. Lett. 55, 13 (1989).

G. P. Agrawal, N. A. Olsson, Opt. Lett. 14, 500 (1989).

Alphonse, G. A.

P. J. Delfyett, Y. Silberberg, G. A. Alphonse, Appl. Phys. Lett. 59, 10 (1991).

Carr, L.

A. Dienes, L. Carr, M. Y. Hong, IEEE J. Quantum Electron. 27, 1214 (1991).

Chiu, L. C.

K. Vahala, L. C. Chiu, S. Margalit, A. Yariv, Appl. Phys. Lett. 42, 631 (1983).

Delfyett, P. J.

P. J. Delfyett, Y. Silberberg, G. A. Alphonse, Appl. Phys. Lett. 59, 10 (1991).

Dienes, A.

A. Dienes, L. Carr, M. Y. Hong, IEEE J. Quantum Electron. 27, 1214 (1991).

Eisenstein, G.

K. L. Hall, J. Mark, E. P. Ippen, G. Eisenstein, Appl. Phys. Lett. 56, 1740 (1990).

Y. Lai, K. L. Hall, E. P. Ippen, G. Eisenstein, IEEE Photon. Technol. Lett. 2, 711 (1990).

Hall, K. L.

Y. Lai, K. L. Hall, E. P. Ippen, G. Eisenstein, IEEE Photon. Technol. Lett. 2, 711 (1990).

K. L. Hall, J. Mark, E. P. Ippen, G. Eisenstein, Appl. Phys. Lett. 56, 1740 (1990).

Hong, M. Y.

A. Dienes, L. Carr, M. Y. Hong, IEEE J. Quantum Electron. 27, 1214 (1991).

Hultgren, C. T.

C. T. Hultgren, E. P. Ippen, Appl. Phys. Lett. 59, 635 (1991).

Ippen, E. P.

C. T. Hultgren, E. P. Ippen, Appl. Phys. Lett. 59, 635 (1991).

Y. Lai, K. L. Hall, E. P. Ippen, G. Eisenstein, IEEE Photon. Technol. Lett. 2, 711 (1990).

K. L. Hall, J. Mark, E. P. Ippen, G. Eisenstein, Appl. Phys. Lett. 56, 1740 (1990).

Lai, Y.

Y. Lai, K. L. Hall, E. P. Ippen, G. Eisenstein, IEEE Photon. Technol. Lett. 2, 711 (1990).

Margalit, S.

K. Vahala, L. C. Chiu, S. Margalit, A. Yariv, Appl. Phys. Lett. 42, 631 (1983).

Mark, J.

A. Uskov, J. Mørk, J. Mark, IEEE Photon. Technol. Lett. 4, 443 (1992).

K. L. Hall, J. Mark, E. P. Ippen, G. Eisenstein, Appl. Phys. Lett. 56, 1740 (1990).

Mørk, J.

A. Uskov, J. Mørk, J. Mark, IEEE Photon. Technol. Lett. 4, 443 (1992).

Olsson, N. A.

G. P. Agrawal, N. A. Olsson, IEEE J. Quantum Electron. 25, 2297 (1989).

N. A. Olsson, G. P. Agrawal, Appl. Phys. Lett. 55, 13 (1989).

G. P. Agrawal, N. A. Olsson, Opt. Lett. 14, 500 (1989).

Silberberg, Y.

P. J. Delfyett, Y. Silberberg, G. A. Alphonse, Appl. Phys. Lett. 59, 10 (1991).

Uskov, A.

A. Uskov, J. Mørk, J. Mark, IEEE Photon. Technol. Lett. 4, 443 (1992).

Vahala, K.

K. Vahala, L. C. Chiu, S. Margalit, A. Yariv, Appl. Phys. Lett. 42, 631 (1983).

Yariv, A.

K. Vahala, L. C. Chiu, S. Margalit, A. Yariv, Appl. Phys. Lett. 42, 631 (1983).

Appl. Phys. Lett. (5)

N. A. Olsson, G. P. Agrawal, Appl. Phys. Lett. 55, 13 (1989).

K. L. Hall, J. Mark, E. P. Ippen, G. Eisenstein, Appl. Phys. Lett. 56, 1740 (1990).

P. J. Delfyett, Y. Silberberg, G. A. Alphonse, Appl. Phys. Lett. 59, 10 (1991).

C. T. Hultgren, E. P. Ippen, Appl. Phys. Lett. 59, 635 (1991).

K. Vahala, L. C. Chiu, S. Margalit, A. Yariv, Appl. Phys. Lett. 42, 631 (1983).

IEEE J. Quantum Electron. (3)

G. P. Agrawal, N. A. Olsson, IEEE J. Quantum Electron. 25, 2297 (1989).

A. Dienes, L. Carr, M. Y. Hong, IEEE J. Quantum Electron. 27, 1214 (1991).

G. P. Agrawal, IEEE J. Quantum Electron. 27, 1843 (1991).

IEEE Photon. Technol. Lett. (2)

A. Uskov, J. Mørk, J. Mark, IEEE Photon. Technol. Lett. 4, 443 (1992).

Y. Lai, K. L. Hall, E. P. Ippen, G. Eisenstein, IEEE Photon. Technol. Lett. 2, 711 (1990).

Opt. Lett. (1)

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Figures (2)

Fig. 1
Fig. 1

Pulse evolution for 500-fs-long, 0.4-pJ Gaussian input pulses in a 300-μm-long, 27-dB peak linear gain GaAs amplifier (60-μm steps). The photon energy is 1.433 eV; Δg0 = 20.7 cm−1, αN = 5, αT = 2; A1 = 5 ps/cm, B1 = 0.024 ps, A2 = 0.68 ps2/cm, B2 = 0; Ws1 = 5 pJ, Ws2 = 0.2 pJ, τ2 = 1.0 ps, A = 1 μm2, n2 = −4 × 10−12 cm2/W, γfc = γ2p = 0. Inset: calculated gain spectrum of the GaAs laser. Curve (a), N = 2.5 × 1018 cm−3, Tc = 300 K; curve (b), N = 2.5 × 1018 cm−3, Tc = 325 K; curve (c), N = 2.1 × 1018 cm−3, Tc = 300 K.

Fig. 2
Fig. 2

Pulse evolution for 2.0-ps-long, 0.4-pJ Gaussian input pulses for the same amplifier as in Fig. 1. Inset: index change (Δn = ½χR) spectrum of GaAs for the same cases as in Fig. 2.

Equations (8)

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z V = i ω 0 c [ 1 + χ m ( ω ) + χ R ( ω , N , T c ) + i χ I ( ω , N , T c ) ] 1 / 2 V .
( z + 1 υ g t i 2 β 2 2 t 2 ) V ( t , z ) = ω 0 2 c n ̅ { [ χ I ( ω 0 ) i χ R ( ω 0 ) ] ( i χ I ω + χ R ω ) ω 0 t 1 2 ( 2 χ I ω 2 i 2 χ R ω 2 ) ω 0 2 t 2 } V ( t , z ) ,
α N = χ R / N χ I / N = 2 k Δ n N Δ g N , α T = χ R / T c χ I / T c = 2 k Δ n T Δ g T .
g N ( τ ) = g 0 exp [ 1 W s 1 0 τ | V ( s ) | 2 d s ] ,
Δ g T ( τ ) = Δ g 0 W s 2 + u ( s ) exp ( s / τ 2 ) | V ( τ s ) | 2 d s ,
g ( τ ) ω | ω 0 = A 1 + B 1 [ ( g 0 ω 0 ) g ( τ , ω 0 ) ] ,
2 g ( τ ) ω 2 | ω 0 = A 2 + B 2 [ ( g 0 ω 0 ) g ( τ , ω 0 ) ] ,
( z i 2 β 2 2 τ 2 ) V ( t , z ) = [ 1 2 g N ( τ , ω 0 ) ( 1 + i α N ) 1 2 Δ g T ( τ , ω 0 ) ( 1 + i α T ) i 1 2 g ( τ , ω ) ω | ω 0 τ 1 4 2 g ( τ , ω ) ω 2 | ω 0 2 τ 2 γ fc ( γ 2 p + ib 2 | V ( τ , z ) | 2 ] V ( τ , z ) .

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