Abstract

Emission of symmetric flower-shaped light patterns from coherently locked hexagonal vertical-cavity semiconductor laser arrays is reported. The flower patterns preserve their shape while propagating in free space. The emission of these unique light distributions is explained as being due to the combined effects of thermal lensing and the loss patterns employed for array definition. A theoretical model for strongly coupled arrays matches the results.

© 2002 Optical Society of America

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References

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  1. C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. Von Lehman, L. T. Florez, and N. G. Stoffel, IEEE J. Quantum Electron. 27, 1402 (1991).
    [CrossRef]
  2. J. Scheuer and M. Orenstein, Science 285, 230 (1999).
    [CrossRef] [PubMed]
  3. S. P. Hegarty, G. Huyet, J. G. McInerney, and K. D. Choquette, Phys. Rev. Lett. 82, 1434 (1999).
    [CrossRef]
  4. J. Martin-Regalado, S. Balle, M. San Miguel, A. Valle, and L. Pesquera, Quantum Semiclass. Opt. 9, 713 (1997).
    [CrossRef]
  5. M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florez, and J. Wullert, Appl. Phys. Lett. 58, 804 (1991).
    [CrossRef]
  6. H.-J. Yoo, J. R. Hayes, E. G. Paek, A. Scherer, and S.-K. Young, IEEE J. Quantum Electron. 26, 1039 (1990).
    [CrossRef]
  7. T. Fishman and M. Orenstein, Opt. Lett. 21, 600 (1996).
    [CrossRef] [PubMed]
  8. E. Kapon, J. Katz, and A. Yariv, Opt. Lett. 9, 125 (1984).
    [CrossRef] [PubMed]
  9. H. A. Haus, W. P. Huang, S. Kawakami, and N. A. Whitaker, J. Lightwave Technol. 5, 16 (1987).
    [CrossRef]
  10. G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. W. Corzine, IEEE J. Quantum Electron. 32, 607 (1996).
    [CrossRef]
  11. J. Scheuer, “Multiple elements optical patterns in nonlinear complex media,” Ph.D. dissertation (Technion, Haifa, Israel, 2001), Chap. 4.1.

1999 (2)

J. Scheuer and M. Orenstein, Science 285, 230 (1999).
[CrossRef] [PubMed]

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

1997 (1)

J. Martin-Regalado, S. Balle, M. San Miguel, A. Valle, and L. Pesquera, Quantum Semiclass. Opt. 9, 713 (1997).
[CrossRef]

1996 (2)

T. Fishman and M. Orenstein, Opt. Lett. 21, 600 (1996).
[CrossRef] [PubMed]

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. W. Corzine, IEEE J. Quantum Electron. 32, 607 (1996).
[CrossRef]

1991 (2)

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. Von Lehman, L. T. Florez, and N. G. Stoffel, IEEE J. Quantum Electron. 27, 1402 (1991).
[CrossRef]

M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florez, and J. Wullert, Appl. Phys. Lett. 58, 804 (1991).
[CrossRef]

1990 (1)

H.-J. Yoo, J. R. Hayes, E. G. Paek, A. Scherer, and S.-K. Young, IEEE J. Quantum Electron. 26, 1039 (1990).
[CrossRef]

1987 (1)

H. A. Haus, W. P. Huang, S. Kawakami, and N. A. Whitaker, J. Lightwave Technol. 5, 16 (1987).
[CrossRef]

1984 (1)

Balle, S.

J. Martin-Regalado, S. Balle, M. San Miguel, A. Valle, and L. Pesquera, Quantum Semiclass. Opt. 9, 713 (1997).
[CrossRef]

Chang-Hasnain, C. J.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. Von Lehman, L. T. Florez, and N. G. Stoffel, IEEE J. Quantum Electron. 27, 1402 (1991).
[CrossRef]

Choquette, K. D.

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

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. W. Corzine, IEEE J. Quantum Electron. 32, 607 (1996).
[CrossRef]

Corzine, S. W.

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. W. Corzine, IEEE J. Quantum Electron. 32, 607 (1996).
[CrossRef]

Fishman, T.

Florez, L. T.

M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florez, and J. Wullert, Appl. Phys. Lett. 58, 804 (1991).
[CrossRef]

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. Von Lehman, L. T. Florez, and N. G. Stoffel, IEEE J. Quantum Electron. 27, 1402 (1991).
[CrossRef]

Hadley, G. R.

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. W. Corzine, IEEE J. Quantum Electron. 32, 607 (1996).
[CrossRef]

Harbison, J. P.

M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florez, and J. Wullert, Appl. Phys. Lett. 58, 804 (1991).
[CrossRef]

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. Von Lehman, L. T. Florez, and N. G. Stoffel, IEEE J. Quantum Electron. 27, 1402 (1991).
[CrossRef]

Hasnain, G.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. Von Lehman, L. T. Florez, and N. G. Stoffel, IEEE J. Quantum Electron. 27, 1402 (1991).
[CrossRef]

Haus, H. A.

H. A. Haus, W. P. Huang, S. Kawakami, and N. A. Whitaker, J. Lightwave Technol. 5, 16 (1987).
[CrossRef]

Hayes, J. R.

H.-J. Yoo, J. R. Hayes, E. G. Paek, A. Scherer, and S.-K. Young, IEEE J. Quantum Electron. 26, 1039 (1990).
[CrossRef]

Hegarty, S. P.

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

Huang, W. P.

H. A. Haus, W. P. Huang, S. Kawakami, and N. A. Whitaker, J. Lightwave Technol. 5, 16 (1987).
[CrossRef]

Huyet, G.

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

Kapon, E.

M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florez, and J. Wullert, Appl. Phys. Lett. 58, 804 (1991).
[CrossRef]

E. Kapon, J. Katz, and A. Yariv, Opt. Lett. 9, 125 (1984).
[CrossRef] [PubMed]

Katz, J.

Kawakami, S.

H. A. Haus, W. P. Huang, S. Kawakami, and N. A. Whitaker, J. Lightwave Technol. 5, 16 (1987).
[CrossRef]

Lear, K. L.

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. W. Corzine, IEEE J. Quantum Electron. 32, 607 (1996).
[CrossRef]

Martin-Regalado, J.

J. Martin-Regalado, S. Balle, M. San Miguel, A. Valle, and L. Pesquera, Quantum Semiclass. Opt. 9, 713 (1997).
[CrossRef]

McInerney, J. G.

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

Orenstein, M.

J. Scheuer and M. Orenstein, Science 285, 230 (1999).
[CrossRef] [PubMed]

T. Fishman and M. Orenstein, Opt. Lett. 21, 600 (1996).
[CrossRef] [PubMed]

M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florez, and J. Wullert, Appl. Phys. Lett. 58, 804 (1991).
[CrossRef]

Paek, E. G.

H.-J. Yoo, J. R. Hayes, E. G. Paek, A. Scherer, and S.-K. Young, IEEE J. Quantum Electron. 26, 1039 (1990).
[CrossRef]

Pesquera, L.

J. Martin-Regalado, S. Balle, M. San Miguel, A. Valle, and L. Pesquera, Quantum Semiclass. Opt. 9, 713 (1997).
[CrossRef]

San Miguel, M.

J. Martin-Regalado, S. Balle, M. San Miguel, A. Valle, and L. Pesquera, Quantum Semiclass. Opt. 9, 713 (1997).
[CrossRef]

Scherer, A.

H.-J. Yoo, J. R. Hayes, E. G. Paek, A. Scherer, and S.-K. Young, IEEE J. Quantum Electron. 26, 1039 (1990).
[CrossRef]

Scheuer, J.

J. Scheuer and M. Orenstein, Science 285, 230 (1999).
[CrossRef] [PubMed]

J. Scheuer, “Multiple elements optical patterns in nonlinear complex media,” Ph.D. dissertation (Technion, Haifa, Israel, 2001), Chap. 4.1.

Scott, J. W.

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. W. Corzine, IEEE J. Quantum Electron. 32, 607 (1996).
[CrossRef]

Stoffel, N. G.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. Von Lehman, L. T. Florez, and N. G. Stoffel, IEEE J. Quantum Electron. 27, 1402 (1991).
[CrossRef]

M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florez, and J. Wullert, Appl. Phys. Lett. 58, 804 (1991).
[CrossRef]

Valle, A.

J. Martin-Regalado, S. Balle, M. San Miguel, A. Valle, and L. Pesquera, Quantum Semiclass. Opt. 9, 713 (1997).
[CrossRef]

Von Lehman, A.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. Von Lehman, L. T. Florez, and N. G. Stoffel, IEEE J. Quantum Electron. 27, 1402 (1991).
[CrossRef]

Warren, M. E.

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. W. Corzine, IEEE J. Quantum Electron. 32, 607 (1996).
[CrossRef]

Whitaker, N. A.

H. A. Haus, W. P. Huang, S. Kawakami, and N. A. Whitaker, J. Lightwave Technol. 5, 16 (1987).
[CrossRef]

Wullert, J.

M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florez, and J. Wullert, Appl. Phys. Lett. 58, 804 (1991).
[CrossRef]

Yariv, A.

Yoo, H.-J.

H.-J. Yoo, J. R. Hayes, E. G. Paek, A. Scherer, and S.-K. Young, IEEE J. Quantum Electron. 26, 1039 (1990).
[CrossRef]

Young, S.-K.

H.-J. Yoo, J. R. Hayes, E. G. Paek, A. Scherer, and S.-K. Young, IEEE J. Quantum Electron. 26, 1039 (1990).
[CrossRef]

Appl. Phys. Lett. (1)

M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florez, and J. Wullert, Appl. Phys. Lett. 58, 804 (1991).
[CrossRef]

IEEE J. Quantum Electron. (3)

H.-J. Yoo, J. R. Hayes, E. G. Paek, A. Scherer, and S.-K. Young, IEEE J. Quantum Electron. 26, 1039 (1990).
[CrossRef]

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. Von Lehman, L. T. Florez, and N. G. Stoffel, IEEE J. Quantum Electron. 27, 1402 (1991).
[CrossRef]

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. W. Corzine, IEEE J. Quantum Electron. 32, 607 (1996).
[CrossRef]

J. Lightwave Technol. (1)

H. A. Haus, W. P. Huang, S. Kawakami, and N. A. Whitaker, J. Lightwave Technol. 5, 16 (1987).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. Lett. (1)

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

Quantum Semiclass. Opt. (1)

J. Martin-Regalado, S. Balle, M. San Miguel, A. Valle, and L. Pesquera, Quantum Semiclass. Opt. 9, 713 (1997).
[CrossRef]

Science (1)

J. Scheuer and M. Orenstein, Science 285, 230 (1999).
[CrossRef] [PubMed]

Other (1)

J. Scheuer, “Multiple elements optical patterns in nonlinear complex media,” Ph.D. dissertation (Technion, Haifa, Israel, 2001), Chap. 4.1.

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Figures (4)

Fig. 1
Fig. 1

(a) Top view of the hexagonal laser array. (b) NF emission for low injection currents, I<30 mA; (c) the corresponding FF patterns.

Fig. 2
Fig. 2

NF emission patterns at higher injection currents [injection current (milliamperes), pulse length (microseconds)]: (a) 40, 1.5; (b) 40, 10; (c) 60, 1; (d) 70, 1.5; (e) 80, 2.5; (f) 75, 2.

Fig. 3
Fig. 3

FF compared with NF emission [injection current (milliamperes), pulse length (microseconds)]: (a) 40, 1.5; (b) 60, 1; (c) 70, 1.5; (d) 80, 2.5.

Fig. 4
Fig. 4

Comparison of experimentally observed and theoretically predicted patterns. Experimental [injection current (milliamperes), pulse length (microseconds)]: (a) 40, 10; (b) 70, 1.5; (c) 60, 1. Theoretical [injection current I mode waist (micrometers)]: (a) 2, 9; (b) 3, 9; (c) 3, 10.

Equations (2)

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ψp,l,±r,φ=2l+1/2πp!p+l!1/2×rlLpl2r2exp-r2exp±ilφ.
ddtEx,y=cμΓ1-iRgx,y-αx,yEx,y,ddtNx,y=Jx,yed-Nx,yτ-Γgx,yμ02k0Ex,y2,gx,y=aNx,y-Ntr1+Ex,y2,    =0μ22ηω.

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