Abstract

If an incident pulse is chirped, the critical parameters for self-induced transparency to occur in coherent pulse propagation can no longer be obtained from the well-known McCall-Hahn area theorem. We have been able to obtain these parameters by solving the Zakharov-Shabat eigenvalue equation for the bound-state eigenvalues. We find that critical (threshold) areas will be increased for a chirped incident pulse in almost all cases, except for a box profile or for a pulse that is approximately box-like in shape. In these latter cases, the chirped critical areas will instead decrease for the second and all higher branches. The first branch’s critical area is <i>always</i> increased due to chirping.

© 1979 Optical Society of America

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  1. S. L. McCall and E. L. Hahn, Phys. Rev. Lett. 18, 908 (1967).
  2. S. L. McCall and E. L. Hahn, Phys. Rev. 183, 457 (1967).
  3. J. C. Diels and E. L. Hahn, Phys. Rev. 8, 1084 (1973).
  4. G. L. Lamb, Phys. Rev. Lett. 31, 196 (1973).
  5. D. J. Kaup, Phys. Rev. A 16, 704 (1977).
  6. M. J. Ablowitz, D. J. Kaup, and A. C. Newell, J. of Math Phys. 1852 (1974).
  7. R. E. Slusher and H. M. Gibbs, Phys. Rev. A 5, 1634 (1972).
  8. Gardner, Green, Kruskal, and Miura, Phys. Rev. Lett. 19, 1095 (1967).
  9. G. L. Lamb, Physica 66, 298 (1973).
  10. D. W. McLaughlin and J. Corones, Phys. Rev. A 10, 2051 (1974).
  11. V. E. Zakharov and A. B. Shabat, Soc. Phys. JETP 34, 62 (1972).
  12. M. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, Stud. in App. Math. 53, 249 (1974).
  13. R. T. Deck and G. L. Lamb, Phys. Rev. A 12, 1503 (1975).
  14. D. F. Dubois, D. W. Forslund, and E. A. Williams, Phys. Rev. Lett. 33, 1013 (1974).
  15. D. D. Schnack and G. L. Lamb, Jr., in Coherence and Quantum Optics edited by L. Mandel & E. Wolf. (Plenum, New York, 1973), p. 23–33.

Ablowitz, M. J.

M. J. Ablowitz, D. J. Kaup, and A. C. Newell, J. of Math Phys. 1852 (1974).

M. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, Stud. in App. Math. 53, 249 (1974).

Corones, J.

D. W. McLaughlin and J. Corones, Phys. Rev. A 10, 2051 (1974).

Deck, R. T.

R. T. Deck and G. L. Lamb, Phys. Rev. A 12, 1503 (1975).

Diels, J. C.

J. C. Diels and E. L. Hahn, Phys. Rev. 8, 1084 (1973).

Dubois, D. F.

D. F. Dubois, D. W. Forslund, and E. A. Williams, Phys. Rev. Lett. 33, 1013 (1974).

Forslund, D. W.

D. F. Dubois, D. W. Forslund, and E. A. Williams, Phys. Rev. Lett. 33, 1013 (1974).

Gibbs, H. M.

R. E. Slusher and H. M. Gibbs, Phys. Rev. A 5, 1634 (1972).

Hahn, E. L.

J. C. Diels and E. L. Hahn, Phys. Rev. 8, 1084 (1973).

S. L. McCall and E. L. Hahn, Phys. Rev. Lett. 18, 908 (1967).

S. L. McCall and E. L. Hahn, Phys. Rev. 183, 457 (1967).

Kaup, D. J.

M. J. Ablowitz, D. J. Kaup, and A. C. Newell, J. of Math Phys. 1852 (1974).

D. J. Kaup, Phys. Rev. A 16, 704 (1977).

M. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, Stud. in App. Math. 53, 249 (1974).

Lamb, G. L.

R. T. Deck and G. L. Lamb, Phys. Rev. A 12, 1503 (1975).

G. L. Lamb, Phys. Rev. Lett. 31, 196 (1973).

G. L. Lamb, Physica 66, 298 (1973).

Lamb, Jr., G. L.

D. D. Schnack and G. L. Lamb, Jr., in Coherence and Quantum Optics edited by L. Mandel & E. Wolf. (Plenum, New York, 1973), p. 23–33.

McCall, S. L.

S. L. McCall and E. L. Hahn, Phys. Rev. Lett. 18, 908 (1967).

S. L. McCall and E. L. Hahn, Phys. Rev. 183, 457 (1967).

McLaughlin, D. W.

D. W. McLaughlin and J. Corones, Phys. Rev. A 10, 2051 (1974).

Newell, A. C.

M. J. Ablowitz, D. J. Kaup, and A. C. Newell, J. of Math Phys. 1852 (1974).

M. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, Stud. in App. Math. 53, 249 (1974).

Schnack, D. D.

D. D. Schnack and G. L. Lamb, Jr., in Coherence and Quantum Optics edited by L. Mandel & E. Wolf. (Plenum, New York, 1973), p. 23–33.

Segur, H.

M. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, Stud. in App. Math. 53, 249 (1974).

Shabat, A. B.

V. E. Zakharov and A. B. Shabat, Soc. Phys. JETP 34, 62 (1972).

Slusher, R. E.

R. E. Slusher and H. M. Gibbs, Phys. Rev. A 5, 1634 (1972).

Williams, E. A.

D. F. Dubois, D. W. Forslund, and E. A. Williams, Phys. Rev. Lett. 33, 1013 (1974).

Zakharov, V. E.

V. E. Zakharov and A. B. Shabat, Soc. Phys. JETP 34, 62 (1972).

Other (15)

S. L. McCall and E. L. Hahn, Phys. Rev. Lett. 18, 908 (1967).

S. L. McCall and E. L. Hahn, Phys. Rev. 183, 457 (1967).

J. C. Diels and E. L. Hahn, Phys. Rev. 8, 1084 (1973).

G. L. Lamb, Phys. Rev. Lett. 31, 196 (1973).

D. J. Kaup, Phys. Rev. A 16, 704 (1977).

M. J. Ablowitz, D. J. Kaup, and A. C. Newell, J. of Math Phys. 1852 (1974).

R. E. Slusher and H. M. Gibbs, Phys. Rev. A 5, 1634 (1972).

Gardner, Green, Kruskal, and Miura, Phys. Rev. Lett. 19, 1095 (1967).

G. L. Lamb, Physica 66, 298 (1973).

D. W. McLaughlin and J. Corones, Phys. Rev. A 10, 2051 (1974).

V. E. Zakharov and A. B. Shabat, Soc. Phys. JETP 34, 62 (1972).

M. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, Stud. in App. Math. 53, 249 (1974).

R. T. Deck and G. L. Lamb, Phys. Rev. A 12, 1503 (1975).

D. F. Dubois, D. W. Forslund, and E. A. Williams, Phys. Rev. Lett. 33, 1013 (1974).

D. D. Schnack and G. L. Lamb, Jr., in Coherence and Quantum Optics edited by L. Mandel & E. Wolf. (Plenum, New York, 1973), p. 23–33.

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