Abstract

The selection of a transverse traveling wave by an inhomogeneous pump profile has been experimentally observed in a class B laser structure. The laser structure consisted of a wide-aperture edge-emitting laser diode operating in pulsed mode to avoid thermal guiding effects. The injection current’s profile was modified from the usual top-hat configuration to a Lorentzian-like profile by the inclusion of a 10μm p-type expitaxial spreading layer. Spatial dependance of the far field on the near field was observed. The same behavior is also demonstrated numerically by use of Maxwell–Bloch equations for semiconductor lasers.

© 2001 Optical Society of America

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References

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  1. L. A. Lugiato, M. Brambilla, and A. Gatti, in Advances in Atomic, Molecular and Optical Physics, B. Bedersen and H. Walther, eds., (Academic, San Diego, Calif., 1998), pp. 277–282.
  2. T. Ackemann, Yu. A. Logvin, A. Heuer, and W. Lange, Phys. Rev. Lett. 75, 3450 (1995).
    [CrossRef] [PubMed]
  3. E. Pampaloni, P. L. Ramazza, S. Residori, and F. T. Arecchi, Phys. Rev. Lett. 74, 258 (1995).
    [CrossRef] [PubMed]
  4. F. T. Arecchi, G. Giacomelli, P. L. Ramazza, and S. Residori, Phys. Rev. Lett. 67, 3749 (1991).
    [CrossRef] [PubMed]
  5. K. Staliunas, G. Slekys, and C. O. Weiss, Phys. Rev. Lett. 79, 2658 (1997).
    [CrossRef]
  6. P. Lodahl, M. Bache, and M. Saffman, Phys. Rev. Lett. 85, 4506 (2000).
    [CrossRef] [PubMed]
  7. D. Dangoisse, D. Hennequin, C. Lepers, E. Louvergnaux, and P. Glorieux, Phys. Rev. A 46, 5955 (1992).
    [CrossRef] [PubMed]
  8. G. Huyet, C. Martinoni, J. R. Tredicce, and S. Rica, Phys. Rev. Lett. 75, 4027 (1995).
    [CrossRef] [PubMed]
  9. F. Encinas-Sanz, I. Leyva, and J. M. Guerra, Phys. Rev. Lett. 84, 883 (2000).
    [CrossRef] [PubMed]
  10. R. Lang, A. Larsson, and J. Cody, IEEE J. Quantum Electron. 27, 312 (1991).
    [CrossRef]
  11. S. P. Hegarty, G. Huyet, J. G. McInerney, and K. D. Choquette, Phys. Rev. Lett. 82, 1434 (1999).
    [CrossRef]
  12. See R. Diehl, ed. High-Power Diode Laser, Fundamentals, Technology, Applications, Vol. 78 of Topics in Applied Physics (Springer-Verlag, Berlin, 2000)
  13. P. Kirkby, A. Goodwin, G. Thompson, and P. Selway, IEEE J. Quantum Electron. 13, 705 (1977).
    [CrossRef]
  14. A. Mosser, E. Latta, and D. Webb, Appl. Phys. Lett. 55, 1152 (1989).
    [CrossRef]
  15. C. Lindsey, P. Derry, and A. Yariv, Electron. Lett. 21, 671 (1985).
    [CrossRef]
  16. P. O’Brien, P. M. W. Skovgaard, J. G. McInerney, and J. S. Roberts, Electron. Lett. 34, 20 1943 (1998).
  17. J. Martin-Regalado, S. Balle, and N. B. Abraham, IEE Proc. Optoelectron. 143, 17 (1996).
    [CrossRef]
  18. C. Ning, R. Indik, and J. Moloney, IEEE J. Quantum Electron. 33, 1543 (1997).
    [CrossRef]
  19. J. Moloney, R. Indik, J. Hader, and S. Koch, J. Opt. Soc. Am. B 16, 2023 (1999).
    [CrossRef]
  20. J. Marciante and G. Agrawal, IEEE J. Quantum Electron. 33, 1174 (1997).
    [CrossRef]
  21. K. Petermann, Opt. Quantum Electron. 13, 323 (1981).
    [CrossRef]
  22. C. Chang-Hasnain, E. Kapon, and R. Bhat, Appl. Phys. Lett. 54, 205 (1989).
    [CrossRef]

2000 (2)

P. Lodahl, M. Bache, and M. Saffman, Phys. Rev. Lett. 85, 4506 (2000).
[CrossRef] [PubMed]

F. Encinas-Sanz, I. Leyva, and J. M. Guerra, Phys. Rev. Lett. 84, 883 (2000).
[CrossRef] [PubMed]

1999 (2)

S. P. Hegarty, G. Huyet, J. G. McInerney, and K. D. Choquette, Phys. Rev. Lett. 82, 1434 (1999).
[CrossRef]

J. Moloney, R. Indik, J. Hader, and S. Koch, J. Opt. Soc. Am. B 16, 2023 (1999).
[CrossRef]

1998 (1)

P. O’Brien, P. M. W. Skovgaard, J. G. McInerney, and J. S. Roberts, Electron. Lett. 34, 20 1943 (1998).

1997 (3)

C. Ning, R. Indik, and J. Moloney, IEEE J. Quantum Electron. 33, 1543 (1997).
[CrossRef]

J. Marciante and G. Agrawal, IEEE J. Quantum Electron. 33, 1174 (1997).
[CrossRef]

K. Staliunas, G. Slekys, and C. O. Weiss, Phys. Rev. Lett. 79, 2658 (1997).
[CrossRef]

1996 (1)

J. Martin-Regalado, S. Balle, and N. B. Abraham, IEE Proc. Optoelectron. 143, 17 (1996).
[CrossRef]

1995 (3)

G. Huyet, C. Martinoni, J. R. Tredicce, and S. Rica, Phys. Rev. Lett. 75, 4027 (1995).
[CrossRef] [PubMed]

T. Ackemann, Yu. A. Logvin, A. Heuer, and W. Lange, Phys. Rev. Lett. 75, 3450 (1995).
[CrossRef] [PubMed]

E. Pampaloni, P. L. Ramazza, S. Residori, and F. T. Arecchi, Phys. Rev. Lett. 74, 258 (1995).
[CrossRef] [PubMed]

1992 (1)

D. Dangoisse, D. Hennequin, C. Lepers, E. Louvergnaux, and P. Glorieux, Phys. Rev. A 46, 5955 (1992).
[CrossRef] [PubMed]

1991 (2)

F. T. Arecchi, G. Giacomelli, P. L. Ramazza, and S. Residori, Phys. Rev. Lett. 67, 3749 (1991).
[CrossRef] [PubMed]

R. Lang, A. Larsson, and J. Cody, IEEE J. Quantum Electron. 27, 312 (1991).
[CrossRef]

1989 (2)

A. Mosser, E. Latta, and D. Webb, Appl. Phys. Lett. 55, 1152 (1989).
[CrossRef]

C. Chang-Hasnain, E. Kapon, and R. Bhat, Appl. Phys. Lett. 54, 205 (1989).
[CrossRef]

1985 (1)

C. Lindsey, P. Derry, and A. Yariv, Electron. Lett. 21, 671 (1985).
[CrossRef]

1981 (1)

K. Petermann, Opt. Quantum Electron. 13, 323 (1981).
[CrossRef]

1977 (1)

P. Kirkby, A. Goodwin, G. Thompson, and P. Selway, IEEE J. Quantum Electron. 13, 705 (1977).
[CrossRef]

Abraham, N. B.

J. Martin-Regalado, S. Balle, and N. B. Abraham, IEE Proc. Optoelectron. 143, 17 (1996).
[CrossRef]

Ackemann, T.

T. Ackemann, Yu. A. Logvin, A. Heuer, and W. Lange, Phys. Rev. Lett. 75, 3450 (1995).
[CrossRef] [PubMed]

Agrawal, G.

J. Marciante and G. Agrawal, IEEE J. Quantum Electron. 33, 1174 (1997).
[CrossRef]

Arecchi, F. T.

E. Pampaloni, P. L. Ramazza, S. Residori, and F. T. Arecchi, Phys. Rev. Lett. 74, 258 (1995).
[CrossRef] [PubMed]

F. T. Arecchi, G. Giacomelli, P. L. Ramazza, and S. Residori, Phys. Rev. Lett. 67, 3749 (1991).
[CrossRef] [PubMed]

Bache, M.

P. Lodahl, M. Bache, and M. Saffman, Phys. Rev. Lett. 85, 4506 (2000).
[CrossRef] [PubMed]

Balle, S.

J. Martin-Regalado, S. Balle, and N. B. Abraham, IEE Proc. Optoelectron. 143, 17 (1996).
[CrossRef]

Bhat, R.

C. Chang-Hasnain, E. Kapon, and R. Bhat, Appl. Phys. Lett. 54, 205 (1989).
[CrossRef]

Brambilla, M.

L. A. Lugiato, M. Brambilla, and A. Gatti, in Advances in Atomic, Molecular and Optical Physics, B. Bedersen and H. Walther, eds., (Academic, San Diego, Calif., 1998), pp. 277–282.

Chang-Hasnain, C.

C. Chang-Hasnain, E. Kapon, and R. Bhat, Appl. Phys. Lett. 54, 205 (1989).
[CrossRef]

Choquette, K. D.

S. P. Hegarty, G. Huyet, J. G. McInerney, and K. D. Choquette, Phys. Rev. Lett. 82, 1434 (1999).
[CrossRef]

Cody, J.

R. Lang, A. Larsson, and J. Cody, IEEE J. Quantum Electron. 27, 312 (1991).
[CrossRef]

Dangoisse, D.

D. Dangoisse, D. Hennequin, C. Lepers, E. Louvergnaux, and P. Glorieux, Phys. Rev. A 46, 5955 (1992).
[CrossRef] [PubMed]

Derry, P.

C. Lindsey, P. Derry, and A. Yariv, Electron. Lett. 21, 671 (1985).
[CrossRef]

Encinas-Sanz, F.

F. Encinas-Sanz, I. Leyva, and J. M. Guerra, Phys. Rev. Lett. 84, 883 (2000).
[CrossRef] [PubMed]

Gatti, A.

L. A. Lugiato, M. Brambilla, and A. Gatti, in Advances in Atomic, Molecular and Optical Physics, B. Bedersen and H. Walther, eds., (Academic, San Diego, Calif., 1998), pp. 277–282.

Giacomelli, G.

F. T. Arecchi, G. Giacomelli, P. L. Ramazza, and S. Residori, Phys. Rev. Lett. 67, 3749 (1991).
[CrossRef] [PubMed]

Glorieux, P.

D. Dangoisse, D. Hennequin, C. Lepers, E. Louvergnaux, and P. Glorieux, Phys. Rev. A 46, 5955 (1992).
[CrossRef] [PubMed]

Goodwin, A.

P. Kirkby, A. Goodwin, G. Thompson, and P. Selway, IEEE J. Quantum Electron. 13, 705 (1977).
[CrossRef]

Guerra, J. M.

F. Encinas-Sanz, I. Leyva, and J. M. Guerra, Phys. Rev. Lett. 84, 883 (2000).
[CrossRef] [PubMed]

Hader, J.

Hegarty, S. P.

S. P. Hegarty, G. Huyet, J. G. McInerney, and K. D. Choquette, Phys. Rev. Lett. 82, 1434 (1999).
[CrossRef]

Hennequin, D.

D. Dangoisse, D. Hennequin, C. Lepers, E. Louvergnaux, and P. Glorieux, Phys. Rev. A 46, 5955 (1992).
[CrossRef] [PubMed]

Heuer, A.

T. Ackemann, Yu. A. Logvin, A. Heuer, and W. Lange, Phys. Rev. Lett. 75, 3450 (1995).
[CrossRef] [PubMed]

Huyet, G.

S. P. Hegarty, G. Huyet, J. G. McInerney, and K. D. Choquette, Phys. Rev. Lett. 82, 1434 (1999).
[CrossRef]

G. Huyet, C. Martinoni, J. R. Tredicce, and S. Rica, Phys. Rev. Lett. 75, 4027 (1995).
[CrossRef] [PubMed]

Indik, R.

J. Moloney, R. Indik, J. Hader, and S. Koch, J. Opt. Soc. Am. B 16, 2023 (1999).
[CrossRef]

C. Ning, R. Indik, and J. Moloney, IEEE J. Quantum Electron. 33, 1543 (1997).
[CrossRef]

Kapon, E.

C. Chang-Hasnain, E. Kapon, and R. Bhat, Appl. Phys. Lett. 54, 205 (1989).
[CrossRef]

Kirkby, P.

P. Kirkby, A. Goodwin, G. Thompson, and P. Selway, IEEE J. Quantum Electron. 13, 705 (1977).
[CrossRef]

Koch, S.

Lang, R.

R. Lang, A. Larsson, and J. Cody, IEEE J. Quantum Electron. 27, 312 (1991).
[CrossRef]

Lange, W.

T. Ackemann, Yu. A. Logvin, A. Heuer, and W. Lange, Phys. Rev. Lett. 75, 3450 (1995).
[CrossRef] [PubMed]

Larsson, A.

R. Lang, A. Larsson, and J. Cody, IEEE J. Quantum Electron. 27, 312 (1991).
[CrossRef]

Latta, E.

A. Mosser, E. Latta, and D. Webb, Appl. Phys. Lett. 55, 1152 (1989).
[CrossRef]

Lepers, C.

D. Dangoisse, D. Hennequin, C. Lepers, E. Louvergnaux, and P. Glorieux, Phys. Rev. A 46, 5955 (1992).
[CrossRef] [PubMed]

Leyva, I.

F. Encinas-Sanz, I. Leyva, and J. M. Guerra, Phys. Rev. Lett. 84, 883 (2000).
[CrossRef] [PubMed]

Lindsey, C.

C. Lindsey, P. Derry, and A. Yariv, Electron. Lett. 21, 671 (1985).
[CrossRef]

Lodahl, P.

P. Lodahl, M. Bache, and M. Saffman, Phys. Rev. Lett. 85, 4506 (2000).
[CrossRef] [PubMed]

Logvin, Yu. A.

T. Ackemann, Yu. A. Logvin, A. Heuer, and W. Lange, Phys. Rev. Lett. 75, 3450 (1995).
[CrossRef] [PubMed]

Louvergnaux, E.

D. Dangoisse, D. Hennequin, C. Lepers, E. Louvergnaux, and P. Glorieux, Phys. Rev. A 46, 5955 (1992).
[CrossRef] [PubMed]

Lugiato, L. A.

L. A. Lugiato, M. Brambilla, and A. Gatti, in Advances in Atomic, Molecular and Optical Physics, B. Bedersen and H. Walther, eds., (Academic, San Diego, Calif., 1998), pp. 277–282.

Marciante, J.

J. Marciante and G. Agrawal, IEEE J. Quantum Electron. 33, 1174 (1997).
[CrossRef]

Martinoni, C.

G. Huyet, C. Martinoni, J. R. Tredicce, and S. Rica, Phys. Rev. Lett. 75, 4027 (1995).
[CrossRef] [PubMed]

Martin-Regalado, J.

J. Martin-Regalado, S. Balle, and N. B. Abraham, IEE Proc. Optoelectron. 143, 17 (1996).
[CrossRef]

McInerney, J. G.

S. P. Hegarty, G. Huyet, J. G. McInerney, and K. D. Choquette, Phys. Rev. Lett. 82, 1434 (1999).
[CrossRef]

P. O’Brien, P. M. W. Skovgaard, J. G. McInerney, and J. S. Roberts, Electron. Lett. 34, 20 1943 (1998).

Moloney, J.

J. Moloney, R. Indik, J. Hader, and S. Koch, J. Opt. Soc. Am. B 16, 2023 (1999).
[CrossRef]

C. Ning, R. Indik, and J. Moloney, IEEE J. Quantum Electron. 33, 1543 (1997).
[CrossRef]

Mosser, A.

A. Mosser, E. Latta, and D. Webb, Appl. Phys. Lett. 55, 1152 (1989).
[CrossRef]

Ning, C.

C. Ning, R. Indik, and J. Moloney, IEEE J. Quantum Electron. 33, 1543 (1997).
[CrossRef]

O’Brien, P.

P. O’Brien, P. M. W. Skovgaard, J. G. McInerney, and J. S. Roberts, Electron. Lett. 34, 20 1943 (1998).

Pampaloni, E.

E. Pampaloni, P. L. Ramazza, S. Residori, and F. T. Arecchi, Phys. Rev. Lett. 74, 258 (1995).
[CrossRef] [PubMed]

Petermann, K.

K. Petermann, Opt. Quantum Electron. 13, 323 (1981).
[CrossRef]

Ramazza, P. L.

E. Pampaloni, P. L. Ramazza, S. Residori, and F. T. Arecchi, Phys. Rev. Lett. 74, 258 (1995).
[CrossRef] [PubMed]

F. T. Arecchi, G. Giacomelli, P. L. Ramazza, and S. Residori, Phys. Rev. Lett. 67, 3749 (1991).
[CrossRef] [PubMed]

Residori, S.

E. Pampaloni, P. L. Ramazza, S. Residori, and F. T. Arecchi, Phys. Rev. Lett. 74, 258 (1995).
[CrossRef] [PubMed]

F. T. Arecchi, G. Giacomelli, P. L. Ramazza, and S. Residori, Phys. Rev. Lett. 67, 3749 (1991).
[CrossRef] [PubMed]

Rica, S.

G. Huyet, C. Martinoni, J. R. Tredicce, and S. Rica, Phys. Rev. Lett. 75, 4027 (1995).
[CrossRef] [PubMed]

Roberts, J. S.

P. O’Brien, P. M. W. Skovgaard, J. G. McInerney, and J. S. Roberts, Electron. Lett. 34, 20 1943 (1998).

Saffman, M.

P. Lodahl, M. Bache, and M. Saffman, Phys. Rev. Lett. 85, 4506 (2000).
[CrossRef] [PubMed]

Selway, P.

P. Kirkby, A. Goodwin, G. Thompson, and P. Selway, IEEE J. Quantum Electron. 13, 705 (1977).
[CrossRef]

Skovgaard, P. M. W.

P. O’Brien, P. M. W. Skovgaard, J. G. McInerney, and J. S. Roberts, Electron. Lett. 34, 20 1943 (1998).

Slekys, G.

K. Staliunas, G. Slekys, and C. O. Weiss, Phys. Rev. Lett. 79, 2658 (1997).
[CrossRef]

Staliunas, K.

K. Staliunas, G. Slekys, and C. O. Weiss, Phys. Rev. Lett. 79, 2658 (1997).
[CrossRef]

Thompson, G.

P. Kirkby, A. Goodwin, G. Thompson, and P. Selway, IEEE J. Quantum Electron. 13, 705 (1977).
[CrossRef]

Tredicce, J. R.

G. Huyet, C. Martinoni, J. R. Tredicce, and S. Rica, Phys. Rev. Lett. 75, 4027 (1995).
[CrossRef] [PubMed]

Webb, D.

A. Mosser, E. Latta, and D. Webb, Appl. Phys. Lett. 55, 1152 (1989).
[CrossRef]

Weiss, C. O.

K. Staliunas, G. Slekys, and C. O. Weiss, Phys. Rev. Lett. 79, 2658 (1997).
[CrossRef]

Yariv, A.

C. Lindsey, P. Derry, and A. Yariv, Electron. Lett. 21, 671 (1985).
[CrossRef]

Appl. Phys. Lett. (2)

A. Mosser, E. Latta, and D. Webb, Appl. Phys. Lett. 55, 1152 (1989).
[CrossRef]

C. Chang-Hasnain, E. Kapon, and R. Bhat, Appl. Phys. Lett. 54, 205 (1989).
[CrossRef]

Electron. Lett. (2)

C. Lindsey, P. Derry, and A. Yariv, Electron. Lett. 21, 671 (1985).
[CrossRef]

P. O’Brien, P. M. W. Skovgaard, J. G. McInerney, and J. S. Roberts, Electron. Lett. 34, 20 1943 (1998).

IEE Proc. Optoelectron. (1)

J. Martin-Regalado, S. Balle, and N. B. Abraham, IEE Proc. Optoelectron. 143, 17 (1996).
[CrossRef]

IEEE J. Quantum Electron. (4)

C. Ning, R. Indik, and J. Moloney, IEEE J. Quantum Electron. 33, 1543 (1997).
[CrossRef]

J. Marciante and G. Agrawal, IEEE J. Quantum Electron. 33, 1174 (1997).
[CrossRef]

P. Kirkby, A. Goodwin, G. Thompson, and P. Selway, IEEE J. Quantum Electron. 13, 705 (1977).
[CrossRef]

R. Lang, A. Larsson, and J. Cody, IEEE J. Quantum Electron. 27, 312 (1991).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Quantum Electron. (1)

K. Petermann, Opt. Quantum Electron. 13, 323 (1981).
[CrossRef]

Phys. Rev. A (1)

D. Dangoisse, D. Hennequin, C. Lepers, E. Louvergnaux, and P. Glorieux, Phys. Rev. A 46, 5955 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett. (8)

G. Huyet, C. Martinoni, J. R. Tredicce, and S. Rica, Phys. Rev. Lett. 75, 4027 (1995).
[CrossRef] [PubMed]

F. Encinas-Sanz, I. Leyva, and J. M. Guerra, Phys. Rev. Lett. 84, 883 (2000).
[CrossRef] [PubMed]

S. P. Hegarty, G. Huyet, J. G. McInerney, and K. D. Choquette, Phys. Rev. Lett. 82, 1434 (1999).
[CrossRef]

T. Ackemann, Yu. A. Logvin, A. Heuer, and W. Lange, Phys. Rev. Lett. 75, 3450 (1995).
[CrossRef] [PubMed]

E. Pampaloni, P. L. Ramazza, S. Residori, and F. T. Arecchi, Phys. Rev. Lett. 74, 258 (1995).
[CrossRef] [PubMed]

F. T. Arecchi, G. Giacomelli, P. L. Ramazza, and S. Residori, Phys. Rev. Lett. 67, 3749 (1991).
[CrossRef] [PubMed]

K. Staliunas, G. Slekys, and C. O. Weiss, Phys. Rev. Lett. 79, 2658 (1997).
[CrossRef]

P. Lodahl, M. Bache, and M. Saffman, Phys. Rev. Lett. 85, 4506 (2000).
[CrossRef] [PubMed]

Other (2)

See R. Diehl, ed. High-Power Diode Laser, Fundamentals, Technology, Applications, Vol. 78 of Topics in Applied Physics (Springer-Verlag, Berlin, 2000)

L. A. Lugiato, M. Brambilla, and A. Gatti, in Advances in Atomic, Molecular and Optical Physics, B. Bedersen and H. Walther, eds., (Academic, San Diego, Calif., 1998), pp. 277–282.

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Figures (5)

Fig. 1
Fig. 1

Cross section of the p-spreading layer device. The thick p layer allows the carriers to spread, thus smoothing the injection profile in the active region.

Fig. 2
Fig. 2

Characteristic far fields (left) and near fields (right) of the laser. In the pulsed regime (solid curves) the single-lobed near field results in a double-lobed far field, whereas in the thermal regime (dashed curves) the far field is single lobed.

Fig. 3
Fig. 3

Re-imaged near fields when a spatial filter is progressively inserted into the far field from the right-hand side. Top, total near field. Middle, all the right-hand lobe is cut. Bottom, all the right-hand lobe and part of the left-hand lobe are cut. Thus spatial interdependence between the near and the far fields is demonstrated.

Fig. 4
Fig. 4

Characteristic far field (left) and near field (right) given by the simulation. The far-field intensity exhibits two lobes, as in the experiment. The near field is composed of two counterpropagating traveling waves (bottom curve, real part of electric field), whereas its intensity (top curve) follows the pump profile.

Fig. 5
Fig. 5

Re-formed near field after part of the far field of Fig.  4 has been removed (1, no filter; 2, angles >3.4° removed; 3, angles >-2.3° removed). Note the appearance of fringes, whose frequency depends on the position of the filter, as seen in the experiment (Fig.  3).

Equations (1)

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tE=-κ1-iδ-iαD-1-ia/22E-κP,tP=-γDE+1+iδP,tD=-γ-12E*P+EP*+D-jx,

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