Abstract

It is shown that parametric mixing through χ(3) of two injected laser lines can provide index modulation sufficient for the mode locking of the semiconductor laser. Numerical estimates indicate that picosecond pulses with 100-GHz repetition rates should be possible with a few watts of external laser power.

© 1984 Optical Society of America

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References

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  1. P. T. Ho, L. A. Glasser, E. P. Ippen, H. A. Haus, Appl. Phys. Lett. 33, 241, (1978);H. Yukoyama, H. Ito, H. Inaba, Appl. Phys. Lett. 40, 105 (1982);C. Harder, J. S. Smith, K. Y. Lau, A. Yariv, Appl. Phys. Lett. 42, 773 (1983), and the references therein.
    [CrossRef]
  2. R. A. Elliot, Huang DeXiu, R. K. DeFreez, J. M. Hunt, P. G. Rickman, Appl. Phys. Lett. 42, 1012 (1983).
    [CrossRef]
  3. K. Y. Lau, C. Harder, A. Yariv, Appl. Phys. Lett. 44, 273 (1984).
    [CrossRef]
  4. T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsitz, P. L. Kelley, Phys. Rev. 177, 306 (1969).
    [CrossRef]
  5. H. Haus, Fields and Waves in Optical Electronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).
  6. Background material dispersion in GaAs is estimated to be ≈104 psec nm−1 km−1 [estimated from data ofD. Sell et al., J. Appl. Phys. 45, 2650 (1974)] in contrast to αgT22, which gives ≈105 psec nm−1 km−1. Thus this approximation is expected to be valid.
    [CrossRef]
  7. D. J. Kuizenga, A. E. Siegman, IEEE J. Quantum Electron. QE-6, 694 (1970).
    [CrossRef]
  8. E. T. Whittaker, G. N. Watson, A Course In Modern Analysis (Cambridge U. Press, Cambridge, 1950), Chap. X.
  9. H. C. Casey, M. B. Panish, Heterostructure Lasers Part B (Academic, New York, 1978), Fig.7.9-2.
  10. M. D. Levenson, Introduction to Nonlinear Laser Spectroscopy (Academic, New York, 1982).
  11. C. K. N. Patel, R. E. Slusher, P. A. Fleurey, Phys. Rev. Lett. 17, 1011 (1966).
    [CrossRef]
  12. For a 10-psec pulse approximation (7) is not satisfied, and thus the full cosine modulation should be considered.
  13. Y. J. Chen, G. M. Carter, Appl. Phys. Lett. 41, 307 (1982).
    [CrossRef]
  14. Such as the fundamental lattice resonance at 37.2 μm, which would also permit group-velocity match without guiding [C. J. Johnson, G. H. Sherman, R. Werl, Appl. Opt. 8, 1667 (1969)].
    [CrossRef] [PubMed]
  15. D. S. Chemla, T. C. Daman, D. A. B. Miller, A. C. Gossard, W. WiegmannAppl. Phys. Lett. 42, 864 (1983);D. A. B. Miller, D. S. Chemla, D. J. Eilenberger, P. W. Smith, A. C. Gossard, W. T. Tsang, Appl. Phys. Lett. 41, 679 (1982).
    [CrossRef]
  16. P. A. Wolff, G. A. Pearson, Phys. Rev. Lett. 17, 1015 (1966).
    [CrossRef]

1984 (1)

K. Y. Lau, C. Harder, A. Yariv, Appl. Phys. Lett. 44, 273 (1984).
[CrossRef]

1983 (2)

R. A. Elliot, Huang DeXiu, R. K. DeFreez, J. M. Hunt, P. G. Rickman, Appl. Phys. Lett. 42, 1012 (1983).
[CrossRef]

D. S. Chemla, T. C. Daman, D. A. B. Miller, A. C. Gossard, W. WiegmannAppl. Phys. Lett. 42, 864 (1983);D. A. B. Miller, D. S. Chemla, D. J. Eilenberger, P. W. Smith, A. C. Gossard, W. T. Tsang, Appl. Phys. Lett. 41, 679 (1982).
[CrossRef]

1982 (1)

Y. J. Chen, G. M. Carter, Appl. Phys. Lett. 41, 307 (1982).
[CrossRef]

1978 (1)

P. T. Ho, L. A. Glasser, E. P. Ippen, H. A. Haus, Appl. Phys. Lett. 33, 241, (1978);H. Yukoyama, H. Ito, H. Inaba, Appl. Phys. Lett. 40, 105 (1982);C. Harder, J. S. Smith, K. Y. Lau, A. Yariv, Appl. Phys. Lett. 42, 773 (1983), and the references therein.
[CrossRef]

1974 (1)

Background material dispersion in GaAs is estimated to be ≈104 psec nm−1 km−1 [estimated from data ofD. Sell et al., J. Appl. Phys. 45, 2650 (1974)] in contrast to αgT22, which gives ≈105 psec nm−1 km−1. Thus this approximation is expected to be valid.
[CrossRef]

1970 (1)

D. J. Kuizenga, A. E. Siegman, IEEE J. Quantum Electron. QE-6, 694 (1970).
[CrossRef]

1969 (2)

1966 (2)

C. K. N. Patel, R. E. Slusher, P. A. Fleurey, Phys. Rev. Lett. 17, 1011 (1966).
[CrossRef]

P. A. Wolff, G. A. Pearson, Phys. Rev. Lett. 17, 1015 (1966).
[CrossRef]

Carter, G. M.

Y. J. Chen, G. M. Carter, Appl. Phys. Lett. 41, 307 (1982).
[CrossRef]

Casey, H. C.

H. C. Casey, M. B. Panish, Heterostructure Lasers Part B (Academic, New York, 1978), Fig.7.9-2.

Chemla, D. S.

D. S. Chemla, T. C. Daman, D. A. B. Miller, A. C. Gossard, W. WiegmannAppl. Phys. Lett. 42, 864 (1983);D. A. B. Miller, D. S. Chemla, D. J. Eilenberger, P. W. Smith, A. C. Gossard, W. T. Tsang, Appl. Phys. Lett. 41, 679 (1982).
[CrossRef]

Chen, Y. J.

Y. J. Chen, G. M. Carter, Appl. Phys. Lett. 41, 307 (1982).
[CrossRef]

Daman, T. C.

D. S. Chemla, T. C. Daman, D. A. B. Miller, A. C. Gossard, W. WiegmannAppl. Phys. Lett. 42, 864 (1983);D. A. B. Miller, D. S. Chemla, D. J. Eilenberger, P. W. Smith, A. C. Gossard, W. T. Tsang, Appl. Phys. Lett. 41, 679 (1982).
[CrossRef]

DeFreez, R. K.

R. A. Elliot, Huang DeXiu, R. K. DeFreez, J. M. Hunt, P. G. Rickman, Appl. Phys. Lett. 42, 1012 (1983).
[CrossRef]

DeXiu, Huang

R. A. Elliot, Huang DeXiu, R. K. DeFreez, J. M. Hunt, P. G. Rickman, Appl. Phys. Lett. 42, 1012 (1983).
[CrossRef]

Elliot, R. A.

R. A. Elliot, Huang DeXiu, R. K. DeFreez, J. M. Hunt, P. G. Rickman, Appl. Phys. Lett. 42, 1012 (1983).
[CrossRef]

Fleurey, P. A.

C. K. N. Patel, R. E. Slusher, P. A. Fleurey, Phys. Rev. Lett. 17, 1011 (1966).
[CrossRef]

Glasser, L. A.

P. T. Ho, L. A. Glasser, E. P. Ippen, H. A. Haus, Appl. Phys. Lett. 33, 241, (1978);H. Yukoyama, H. Ito, H. Inaba, Appl. Phys. Lett. 40, 105 (1982);C. Harder, J. S. Smith, K. Y. Lau, A. Yariv, Appl. Phys. Lett. 42, 773 (1983), and the references therein.
[CrossRef]

Gossard, A. C.

D. S. Chemla, T. C. Daman, D. A. B. Miller, A. C. Gossard, W. WiegmannAppl. Phys. Lett. 42, 864 (1983);D. A. B. Miller, D. S. Chemla, D. J. Eilenberger, P. W. Smith, A. C. Gossard, W. T. Tsang, Appl. Phys. Lett. 41, 679 (1982).
[CrossRef]

Gustafson, T. K.

T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsitz, P. L. Kelley, Phys. Rev. 177, 306 (1969).
[CrossRef]

Harder, C.

K. Y. Lau, C. Harder, A. Yariv, Appl. Phys. Lett. 44, 273 (1984).
[CrossRef]

Haus, H.

H. Haus, Fields and Waves in Optical Electronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).

Haus, H. A.

P. T. Ho, L. A. Glasser, E. P. Ippen, H. A. Haus, Appl. Phys. Lett. 33, 241, (1978);H. Yukoyama, H. Ito, H. Inaba, Appl. Phys. Lett. 40, 105 (1982);C. Harder, J. S. Smith, K. Y. Lau, A. Yariv, Appl. Phys. Lett. 42, 773 (1983), and the references therein.
[CrossRef]

T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsitz, P. L. Kelley, Phys. Rev. 177, 306 (1969).
[CrossRef]

Ho, P. T.

P. T. Ho, L. A. Glasser, E. P. Ippen, H. A. Haus, Appl. Phys. Lett. 33, 241, (1978);H. Yukoyama, H. Ito, H. Inaba, Appl. Phys. Lett. 40, 105 (1982);C. Harder, J. S. Smith, K. Y. Lau, A. Yariv, Appl. Phys. Lett. 42, 773 (1983), and the references therein.
[CrossRef]

Hunt, J. M.

R. A. Elliot, Huang DeXiu, R. K. DeFreez, J. M. Hunt, P. G. Rickman, Appl. Phys. Lett. 42, 1012 (1983).
[CrossRef]

Ippen, E. P.

P. T. Ho, L. A. Glasser, E. P. Ippen, H. A. Haus, Appl. Phys. Lett. 33, 241, (1978);H. Yukoyama, H. Ito, H. Inaba, Appl. Phys. Lett. 40, 105 (1982);C. Harder, J. S. Smith, K. Y. Lau, A. Yariv, Appl. Phys. Lett. 42, 773 (1983), and the references therein.
[CrossRef]

Johnson, C. J.

Kelley, P. L.

T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsitz, P. L. Kelley, Phys. Rev. 177, 306 (1969).
[CrossRef]

Kuizenga, D. J.

D. J. Kuizenga, A. E. Siegman, IEEE J. Quantum Electron. QE-6, 694 (1970).
[CrossRef]

Lau, K. Y.

K. Y. Lau, C. Harder, A. Yariv, Appl. Phys. Lett. 44, 273 (1984).
[CrossRef]

Levenson, M. D.

M. D. Levenson, Introduction to Nonlinear Laser Spectroscopy (Academic, New York, 1982).

Lifsitz, J. R.

T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsitz, P. L. Kelley, Phys. Rev. 177, 306 (1969).
[CrossRef]

Miller, D. A. B.

D. S. Chemla, T. C. Daman, D. A. B. Miller, A. C. Gossard, W. WiegmannAppl. Phys. Lett. 42, 864 (1983);D. A. B. Miller, D. S. Chemla, D. J. Eilenberger, P. W. Smith, A. C. Gossard, W. T. Tsang, Appl. Phys. Lett. 41, 679 (1982).
[CrossRef]

Panish, M. B.

H. C. Casey, M. B. Panish, Heterostructure Lasers Part B (Academic, New York, 1978), Fig.7.9-2.

Patel, C. K. N.

C. K. N. Patel, R. E. Slusher, P. A. Fleurey, Phys. Rev. Lett. 17, 1011 (1966).
[CrossRef]

Pearson, G. A.

P. A. Wolff, G. A. Pearson, Phys. Rev. Lett. 17, 1015 (1966).
[CrossRef]

Rickman, P. G.

R. A. Elliot, Huang DeXiu, R. K. DeFreez, J. M. Hunt, P. G. Rickman, Appl. Phys. Lett. 42, 1012 (1983).
[CrossRef]

Sell, D.

Background material dispersion in GaAs is estimated to be ≈104 psec nm−1 km−1 [estimated from data ofD. Sell et al., J. Appl. Phys. 45, 2650 (1974)] in contrast to αgT22, which gives ≈105 psec nm−1 km−1. Thus this approximation is expected to be valid.
[CrossRef]

Sherman, G. H.

Siegman, A. E.

D. J. Kuizenga, A. E. Siegman, IEEE J. Quantum Electron. QE-6, 694 (1970).
[CrossRef]

Slusher, R. E.

C. K. N. Patel, R. E. Slusher, P. A. Fleurey, Phys. Rev. Lett. 17, 1011 (1966).
[CrossRef]

Taran, J. P.

T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsitz, P. L. Kelley, Phys. Rev. 177, 306 (1969).
[CrossRef]

Watson, G. N.

E. T. Whittaker, G. N. Watson, A Course In Modern Analysis (Cambridge U. Press, Cambridge, 1950), Chap. X.

Werl, R.

Whittaker, E. T.

E. T. Whittaker, G. N. Watson, A Course In Modern Analysis (Cambridge U. Press, Cambridge, 1950), Chap. X.

Wiegmann, W.

D. S. Chemla, T. C. Daman, D. A. B. Miller, A. C. Gossard, W. WiegmannAppl. Phys. Lett. 42, 864 (1983);D. A. B. Miller, D. S. Chemla, D. J. Eilenberger, P. W. Smith, A. C. Gossard, W. T. Tsang, Appl. Phys. Lett. 41, 679 (1982).
[CrossRef]

Wolff, P. A.

P. A. Wolff, G. A. Pearson, Phys. Rev. Lett. 17, 1015 (1966).
[CrossRef]

Yariv, A.

K. Y. Lau, C. Harder, A. Yariv, Appl. Phys. Lett. 44, 273 (1984).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (5)

Y. J. Chen, G. M. Carter, Appl. Phys. Lett. 41, 307 (1982).
[CrossRef]

D. S. Chemla, T. C. Daman, D. A. B. Miller, A. C. Gossard, W. WiegmannAppl. Phys. Lett. 42, 864 (1983);D. A. B. Miller, D. S. Chemla, D. J. Eilenberger, P. W. Smith, A. C. Gossard, W. T. Tsang, Appl. Phys. Lett. 41, 679 (1982).
[CrossRef]

P. T. Ho, L. A. Glasser, E. P. Ippen, H. A. Haus, Appl. Phys. Lett. 33, 241, (1978);H. Yukoyama, H. Ito, H. Inaba, Appl. Phys. Lett. 40, 105 (1982);C. Harder, J. S. Smith, K. Y. Lau, A. Yariv, Appl. Phys. Lett. 42, 773 (1983), and the references therein.
[CrossRef]

R. A. Elliot, Huang DeXiu, R. K. DeFreez, J. M. Hunt, P. G. Rickman, Appl. Phys. Lett. 42, 1012 (1983).
[CrossRef]

K. Y. Lau, C. Harder, A. Yariv, Appl. Phys. Lett. 44, 273 (1984).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. J. Kuizenga, A. E. Siegman, IEEE J. Quantum Electron. QE-6, 694 (1970).
[CrossRef]

J. Appl. Phys. (1)

Background material dispersion in GaAs is estimated to be ≈104 psec nm−1 km−1 [estimated from data ofD. Sell et al., J. Appl. Phys. 45, 2650 (1974)] in contrast to αgT22, which gives ≈105 psec nm−1 km−1. Thus this approximation is expected to be valid.
[CrossRef]

Phys. Rev. (1)

T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsitz, P. L. Kelley, Phys. Rev. 177, 306 (1969).
[CrossRef]

Phys. Rev. Lett. (2)

P. A. Wolff, G. A. Pearson, Phys. Rev. Lett. 17, 1015 (1966).
[CrossRef]

C. K. N. Patel, R. E. Slusher, P. A. Fleurey, Phys. Rev. Lett. 17, 1011 (1966).
[CrossRef]

Other (5)

For a 10-psec pulse approximation (7) is not satisfied, and thus the full cosine modulation should be considered.

H. Haus, Fields and Waves in Optical Electronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).

E. T. Whittaker, G. N. Watson, A Course In Modern Analysis (Cambridge U. Press, Cambridge, 1950), Chap. X.

H. C. Casey, M. B. Panish, Heterostructure Lasers Part B (Academic, New York, 1978), Fig.7.9-2.

M. D. Levenson, Introduction to Nonlinear Laser Spectroscopy (Academic, New York, 1982).

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Equations (21)

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{ i [ β ( ω 0 ) k 0 ] + ( z + k 1 t ) } E ( t , z ) = k 2 i 2 E t 2 i 2 k 0 ( ω 0 c ) 2 P NL ( z , t ) 0 .
k 1 = β ω ω 0 , k 2 = ½ 2 β ω 2 ω 0 ,
T 2 F ( r ̅ ) [ β 2 ω 2 c 2 ( r ̅ ) ] F ( r ̅ ) = 0 ,
T 2 F = k T 2 F ,
ω 0 2 c 2 1 2 k 0 P NL ( z , t ) 0 = α m { 1 cos [ ω m t ( β 1 β 2 ) z } E ( z , t ) ,
β ( ω ) = ω c n + α g i [ 1 1 + i ( ω ω 0 ) T 2 ] i α l ,
k 0 = ω 0 c n ,
k 1 = ω ( n ω c ) ω 0 + α g T 2 ,
k 2 = 1 2 2 ω 2 ( n ω c ) ω 0 i α g T 2 2 ,
( z + k 1 t ) E ( z , t ) = α g T 2 2 2 E ( z , t ) t 2 i α m [ 1 cos ( ω m t Δ β z ) ] E ( z , t ) + ( α g α l ) E ( z , t ) ,
1 cos ( ω m t Δ β z ) ½ [ ω m ( t Δ β ω m z ) ] 2 .
E ( z , t ) = E ( t z υ ) = E ( η ) .
( 1 υ + k 1 ) E = α g T 2 2 E + [ i α m 2 ( η ω m ) 2 + ( α g α l ) ] E ,
E ( η ) = exp ( ½ ω p 2 η 2 ) exp [ ½ ( 1 υ k 1 ) 1 α g T 2 2 η ] ,
ω p = ( i α m 2 α g ) 1 / 4 ( ω m T 2 ) 1 / 2
1 α l α g 1 4 ( α g T 2 ) 2 ( k 1 1 υ ) 2 = ( ω p T 2 ) 2 .
1 υ = Re ( k 1 ) = n c + Re ( α g T 2 ) = 1 υ g ,
E ( z , t ) = n = E ( η n 2 l υ ) ,
6 × ½ ω 0 c n χ ( 3 ) E m 2 = α m ,
E m 2 = n α m λ π χ ( 3 ) = 1.3 × 10 13 ( V m ) 2 .
ω 0 2 c 2 1 2 k 0 P NL ( z , t ) E 0 = α m [ 1 cos ( ω m t ) cos ( Δ β z ) ] E ( z , t ) .

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