Abstract

We investigate the spatial structure of broad-area vertical-cavity regenerative amplifiers injected with a homogeneous beam. The emerging patterns have a predominantly sixfold rotational symmetry, verifying the recent prediction of formation of hexagons. The length scale is controllable by means of detuning and follows the prediction for tilted waves.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. J. Lang, D. Mehuys, A. Hardy, K. M. Dzurko, and D. F. Welch, Appl. Phys. Lett. 62, 1209 (1993).
    [CrossRef]
  2. I. Fischer, O. Hess, W. Elsässer, and E. Göbel, Europhys. Lett. 35, 579 (1997).
    [CrossRef]
  3. S. Hegarty, G. Huyet, J. G. McInerney, and K. D. Choquette, Phys. Rev. Lett. 82, 1434 (1999).
    [CrossRef]
  4. R. Michalzik, M. Grabherr, and K. J. Ebeling, Proc. SPIE 3286, 206 (1998).
    [CrossRef]
  5. G. S. McDonald and W. J. Firth, J. Opt. Soc. Am. B 7, 1328 (1990).
    [CrossRef]
  6. N. N. Rozanov, Proc. SPIE 1840, 130 (1991).
    [CrossRef]
  7. M. A. Vorontsov and W. B. Miller, eds., Self-Organization in Optical Systems and Application in Information Technology, Vol. 66 of Springer Series in Synergetics (Springer-Verlag, Berlin, 1995).
    [CrossRef]
  8. M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, and W. J. Firth, Phys. Rev. Lett. 79, 2042 (1997).
    [CrossRef]
  9. L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, Phys. Rev. A 58, 2542 (1998).
    [CrossRef]
  10. M. Grabherr, R. Jäger, M. Miller, C. Thalmaier, J. Herlein, and K. J. Ebeling, IEEE Photon. Technol. Lett. 10, 1061 (1998).
    [CrossRef]
  11. P. Jakobsen, J. Moloney, A. Newell, and R. Indik, Phys. Rev. A 45, 8129 (1992).
    [CrossRef] [PubMed]
  12. K. Staliunas, Phys. Rev. A 48, 1573 (1993).
    [CrossRef] [PubMed]
  13. W. J. Firth and A. J. Scroggie, Europhys. Lett. 26, 521 (1994).
    [CrossRef]
  14. S. Coen, M. Tlidi, P. Emplit, and M. Haelterman, Phys. Rev. Lett. 83, 2328 (1999).
    [CrossRef]

1999 (2)

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

S. Coen, M. Tlidi, P. Emplit, and M. Haelterman, Phys. Rev. Lett. 83, 2328 (1999).
[CrossRef]

1998 (3)

R. Michalzik, M. Grabherr, and K. J. Ebeling, Proc. SPIE 3286, 206 (1998).
[CrossRef]

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, Phys. Rev. A 58, 2542 (1998).
[CrossRef]

M. Grabherr, R. Jäger, M. Miller, C. Thalmaier, J. Herlein, and K. J. Ebeling, IEEE Photon. Technol. Lett. 10, 1061 (1998).
[CrossRef]

1997 (2)

M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, and W. J. Firth, Phys. Rev. Lett. 79, 2042 (1997).
[CrossRef]

I. Fischer, O. Hess, W. Elsässer, and E. Göbel, Europhys. Lett. 35, 579 (1997).
[CrossRef]

1994 (1)

W. J. Firth and A. J. Scroggie, Europhys. Lett. 26, 521 (1994).
[CrossRef]

1993 (2)

K. Staliunas, Phys. Rev. A 48, 1573 (1993).
[CrossRef] [PubMed]

R. J. Lang, D. Mehuys, A. Hardy, K. M. Dzurko, and D. F. Welch, Appl. Phys. Lett. 62, 1209 (1993).
[CrossRef]

1992 (1)

P. Jakobsen, J. Moloney, A. Newell, and R. Indik, Phys. Rev. A 45, 8129 (1992).
[CrossRef] [PubMed]

1991 (1)

N. N. Rozanov, Proc. SPIE 1840, 130 (1991).
[CrossRef]

1990 (1)

Brambilla, M.

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, Phys. Rev. A 58, 2542 (1998).
[CrossRef]

M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, and W. J. Firth, Phys. Rev. Lett. 79, 2042 (1997).
[CrossRef]

Choquette, K. D.

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

Coen, S.

S. Coen, M. Tlidi, P. Emplit, and M. Haelterman, Phys. Rev. Lett. 83, 2328 (1999).
[CrossRef]

Dzurko, K. M.

R. J. Lang, D. Mehuys, A. Hardy, K. M. Dzurko, and D. F. Welch, Appl. Phys. Lett. 62, 1209 (1993).
[CrossRef]

Ebeling, K. J.

R. Michalzik, M. Grabherr, and K. J. Ebeling, Proc. SPIE 3286, 206 (1998).
[CrossRef]

M. Grabherr, R. Jäger, M. Miller, C. Thalmaier, J. Herlein, and K. J. Ebeling, IEEE Photon. Technol. Lett. 10, 1061 (1998).
[CrossRef]

Elsässer, W.

I. Fischer, O. Hess, W. Elsässer, and E. Göbel, Europhys. Lett. 35, 579 (1997).
[CrossRef]

Emplit, P.

S. Coen, M. Tlidi, P. Emplit, and M. Haelterman, Phys. Rev. Lett. 83, 2328 (1999).
[CrossRef]

Firth, W. J.

M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, and W. J. Firth, Phys. Rev. Lett. 79, 2042 (1997).
[CrossRef]

W. J. Firth and A. J. Scroggie, Europhys. Lett. 26, 521 (1994).
[CrossRef]

G. S. McDonald and W. J. Firth, J. Opt. Soc. Am. B 7, 1328 (1990).
[CrossRef]

Fischer, I.

I. Fischer, O. Hess, W. Elsässer, and E. Göbel, Europhys. Lett. 35, 579 (1997).
[CrossRef]

Göbel, E.

I. Fischer, O. Hess, W. Elsässer, and E. Göbel, Europhys. Lett. 35, 579 (1997).
[CrossRef]

Grabherr, M.

R. Michalzik, M. Grabherr, and K. J. Ebeling, Proc. SPIE 3286, 206 (1998).
[CrossRef]

M. Grabherr, R. Jäger, M. Miller, C. Thalmaier, J. Herlein, and K. J. Ebeling, IEEE Photon. Technol. Lett. 10, 1061 (1998).
[CrossRef]

Haelterman, M.

S. Coen, M. Tlidi, P. Emplit, and M. Haelterman, Phys. Rev. Lett. 83, 2328 (1999).
[CrossRef]

Hardy, A.

R. J. Lang, D. Mehuys, A. Hardy, K. M. Dzurko, and D. F. Welch, Appl. Phys. Lett. 62, 1209 (1993).
[CrossRef]

Hegarty, S.

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

Herlein, J.

M. Grabherr, R. Jäger, M. Miller, C. Thalmaier, J. Herlein, and K. J. Ebeling, IEEE Photon. Technol. Lett. 10, 1061 (1998).
[CrossRef]

Hess, O.

I. Fischer, O. Hess, W. Elsässer, and E. Göbel, Europhys. Lett. 35, 579 (1997).
[CrossRef]

Huyet, G.

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

Indik, R.

P. Jakobsen, J. Moloney, A. Newell, and R. Indik, Phys. Rev. A 45, 8129 (1992).
[CrossRef] [PubMed]

Jäger, R.

M. Grabherr, R. Jäger, M. Miller, C. Thalmaier, J. Herlein, and K. J. Ebeling, IEEE Photon. Technol. Lett. 10, 1061 (1998).
[CrossRef]

Jakobsen, P.

P. Jakobsen, J. Moloney, A. Newell, and R. Indik, Phys. Rev. A 45, 8129 (1992).
[CrossRef] [PubMed]

Lang, R. J.

R. J. Lang, D. Mehuys, A. Hardy, K. M. Dzurko, and D. F. Welch, Appl. Phys. Lett. 62, 1209 (1993).
[CrossRef]

Lugiato, L. A.

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, Phys. Rev. A 58, 2542 (1998).
[CrossRef]

M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, and W. J. Firth, Phys. Rev. Lett. 79, 2042 (1997).
[CrossRef]

McDonald, G. S.

McInerney, J. G.

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

Mehuys, D.

R. J. Lang, D. Mehuys, A. Hardy, K. M. Dzurko, and D. F. Welch, Appl. Phys. Lett. 62, 1209 (1993).
[CrossRef]

Michalzik, R.

R. Michalzik, M. Grabherr, and K. J. Ebeling, Proc. SPIE 3286, 206 (1998).
[CrossRef]

Miller, M.

M. Grabherr, R. Jäger, M. Miller, C. Thalmaier, J. Herlein, and K. J. Ebeling, IEEE Photon. Technol. Lett. 10, 1061 (1998).
[CrossRef]

Moloney, J.

P. Jakobsen, J. Moloney, A. Newell, and R. Indik, Phys. Rev. A 45, 8129 (1992).
[CrossRef] [PubMed]

Newell, A.

P. Jakobsen, J. Moloney, A. Newell, and R. Indik, Phys. Rev. A 45, 8129 (1992).
[CrossRef] [PubMed]

Prati, F.

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, Phys. Rev. A 58, 2542 (1998).
[CrossRef]

M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, and W. J. Firth, Phys. Rev. Lett. 79, 2042 (1997).
[CrossRef]

Rozanov, N. N.

N. N. Rozanov, Proc. SPIE 1840, 130 (1991).
[CrossRef]

Scroggie, A. J.

W. J. Firth and A. J. Scroggie, Europhys. Lett. 26, 521 (1994).
[CrossRef]

Spinelli, L.

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, Phys. Rev. A 58, 2542 (1998).
[CrossRef]

M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, and W. J. Firth, Phys. Rev. Lett. 79, 2042 (1997).
[CrossRef]

Staliunas, K.

K. Staliunas, Phys. Rev. A 48, 1573 (1993).
[CrossRef] [PubMed]

Thalmaier, C.

M. Grabherr, R. Jäger, M. Miller, C. Thalmaier, J. Herlein, and K. J. Ebeling, IEEE Photon. Technol. Lett. 10, 1061 (1998).
[CrossRef]

Tissoni, G.

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, Phys. Rev. A 58, 2542 (1998).
[CrossRef]

Tlidi, M.

S. Coen, M. Tlidi, P. Emplit, and M. Haelterman, Phys. Rev. Lett. 83, 2328 (1999).
[CrossRef]

Welch, D. F.

R. J. Lang, D. Mehuys, A. Hardy, K. M. Dzurko, and D. F. Welch, Appl. Phys. Lett. 62, 1209 (1993).
[CrossRef]

Appl. Phys. Lett. (1)

R. J. Lang, D. Mehuys, A. Hardy, K. M. Dzurko, and D. F. Welch, Appl. Phys. Lett. 62, 1209 (1993).
[CrossRef]

Europhys. Lett. (2)

I. Fischer, O. Hess, W. Elsässer, and E. Göbel, Europhys. Lett. 35, 579 (1997).
[CrossRef]

W. J. Firth and A. J. Scroggie, Europhys. Lett. 26, 521 (1994).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

M. Grabherr, R. Jäger, M. Miller, C. Thalmaier, J. Herlein, and K. J. Ebeling, IEEE Photon. Technol. Lett. 10, 1061 (1998).
[CrossRef]

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

Phys. Rev. A (3)

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, Phys. Rev. A 58, 2542 (1998).
[CrossRef]

P. Jakobsen, J. Moloney, A. Newell, and R. Indik, Phys. Rev. A 45, 8129 (1992).
[CrossRef] [PubMed]

K. Staliunas, Phys. Rev. A 48, 1573 (1993).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

S. Coen, M. Tlidi, P. Emplit, and M. Haelterman, Phys. Rev. Lett. 83, 2328 (1999).
[CrossRef]

M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, and W. J. Firth, Phys. Rev. Lett. 79, 2042 (1997).
[CrossRef]

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

Proc. SPIE (2)

R. Michalzik, M. Grabherr, and K. J. Ebeling, Proc. SPIE 3286, 206 (1998).
[CrossRef]

N. N. Rozanov, Proc. SPIE 1840, 130 (1991).
[CrossRef]

Other (1)

M. A. Vorontsov and W. B. Miller, eds., Self-Organization in Optical Systems and Application in Information Technology, Vol. 66 of Springer Series in Synergetics (Springer-Verlag, Berlin, 1995).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Schematic of the experimental setup: EGTL, external grating tunable laser; OD’s, optical diodes; AOM, acousto-optical modulator; ANP, anamorphic prism pair; SF, spatial filter; λ/2, half-wave plate; LP, linear polarizer; SFPI’s, scanning Fabry–Perot interferometers; MO, monochromator; D1, D2, photodetectors. The darker line denotes the beam of the master oscillator; the lighter line, the beam emitted by the VCSEL.

Fig. 2
Fig. 2

Dependence of the amplification of the total injected power on the injection wavelength for constant injected power. The wavelength of the free-running VCSEL at threshold is denoted by the solid vertical line. The distance between the points is 54 GHz and is determined by the free spectral range of the internal cavity of the master laser diode.

Fig. 3
Fig. 3

Dependence of the spatial structure on the injection wavelength. Top, the near-field images; bottom, the corresponding far-field images. The dynamic range of each of the images is optimized for maximum contrast; therefore a comparison of the absolute intensity levels in different images is not possible. The frame size of the near-field images is 40 µm×40 µm.

Fig. 4
Fig. 4

Dependence of the square of the transverse wave vector on the injection wavelength. Solid curve, the prediction from Eq. (1).

Equations (1)

Equations on this page are rendered with MathJax. Learn more.

q2=8π2n02λ0-λinj/λ03,

Metrics