Abstract

Large two-dimensional arrays of vertical cavity semiconductor lasers, unlike similar one-dimensional arrays, exhibit a single lasing mode because of their immunity to defects and inhomogeneities. Both experiments and theoretical study of the coherence of the arrays verified this improved performance and attributed it to possible bypass routes for the propagation of phase information in the two-dimensional structure, which ensured the locking of remote array elements even in the presence of defects.

© 1997 Optical Society of America

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References

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  1. M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florez, and J. Wullert, Appl. Phys. Lett. 58, 804 (1991).
    [CrossRef]
  2. J. P. van der Ziel, D. G. Deppe, N. Chand, G. J. Zydzik, and S. N. G. Chu, IEEE J. Quantum Electron. 26, 1873 (1990).
    [CrossRef]
  3. P. L. Gourley, M. E. Warren, G. R. Hadley, G. A. Vawter, T. M. Brennan, and B. E. Hammons, Appl. Phys. Lett. 58, 890 (1991).
    [CrossRef]
  4. M. Orenstein, E. Kapon, L. T. Florez, J. P. Harbison, and N. G. Stoffel, Appl. Phys. Lett. 60, 1535 (1992).
    [CrossRef]
  5. R. A. Morgan, K. Kojima, T. Mullally, G. D. Guth, M. W. Focht, R. E. Leibenguth, and M. Asom, Appl. Phys. Lett. 61, 1160 (1992).
    [CrossRef]
  6. M. Orenstein, E. Kapon, N. G. Stoffel, L. T. Florez, and J. P. Harbison, presented at the 1990 LEOS Annual Meeting, Boston, Mass.
  7. H. G. Winful, Phys. Rev. A 46, 6093 (1992).
    [CrossRef] [PubMed]
  8. T. Fishman and M. Orenstein, Opt. Lett. 21, 600 (1996).
    [CrossRef] [PubMed]
  9. A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1988), pp. 606–611.
  10. M. Orenstein and T. Fishman, presented at the 13th International Semiconductor Laser Conference, Takamatsu, Japan, 1992.

1996 (1)

1992 (3)

M. Orenstein, E. Kapon, L. T. Florez, J. P. Harbison, and N. G. Stoffel, Appl. Phys. Lett. 60, 1535 (1992).
[CrossRef]

R. A. Morgan, K. Kojima, T. Mullally, G. D. Guth, M. W. Focht, R. E. Leibenguth, and M. Asom, Appl. Phys. Lett. 61, 1160 (1992).
[CrossRef]

H. G. Winful, Phys. Rev. A 46, 6093 (1992).
[CrossRef] [PubMed]

1991 (2)

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

P. L. Gourley, M. E. Warren, G. R. Hadley, G. A. Vawter, T. M. Brennan, and B. E. Hammons, Appl. Phys. Lett. 58, 890 (1991).
[CrossRef]

1990 (1)

J. P. van der Ziel, D. G. Deppe, N. Chand, G. J. Zydzik, and S. N. G. Chu, IEEE J. Quantum Electron. 26, 1873 (1990).
[CrossRef]

Asom, M.

R. A. Morgan, K. Kojima, T. Mullally, G. D. Guth, M. W. Focht, R. E. Leibenguth, and M. Asom, Appl. Phys. Lett. 61, 1160 (1992).
[CrossRef]

Brennan, T. M.

P. L. Gourley, M. E. Warren, G. R. Hadley, G. A. Vawter, T. M. Brennan, and B. E. Hammons, Appl. Phys. Lett. 58, 890 (1991).
[CrossRef]

Chand, N.

J. P. van der Ziel, D. G. Deppe, N. Chand, G. J. Zydzik, and S. N. G. Chu, IEEE J. Quantum Electron. 26, 1873 (1990).
[CrossRef]

Chu, S. N. G.

J. P. van der Ziel, D. G. Deppe, N. Chand, G. J. Zydzik, and S. N. G. Chu, IEEE J. Quantum Electron. 26, 1873 (1990).
[CrossRef]

Deppe, D. G.

J. P. van der Ziel, D. G. Deppe, N. Chand, G. J. Zydzik, and S. N. G. Chu, IEEE J. Quantum Electron. 26, 1873 (1990).
[CrossRef]

Fishman, T.

Florez, L. T.

M. Orenstein, E. Kapon, L. T. Florez, J. P. Harbison, and N. G. Stoffel, Appl. Phys. Lett. 60, 1535 (1992).
[CrossRef]

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

Focht, M. W.

R. A. Morgan, K. Kojima, T. Mullally, G. D. Guth, M. W. Focht, R. E. Leibenguth, and M. Asom, Appl. Phys. Lett. 61, 1160 (1992).
[CrossRef]

Gourley, P. L.

P. L. Gourley, M. E. Warren, G. R. Hadley, G. A. Vawter, T. M. Brennan, and B. E. Hammons, Appl. Phys. Lett. 58, 890 (1991).
[CrossRef]

Guth, G. D.

R. A. Morgan, K. Kojima, T. Mullally, G. D. Guth, M. W. Focht, R. E. Leibenguth, and M. Asom, Appl. Phys. Lett. 61, 1160 (1992).
[CrossRef]

Hadley, G. R.

P. L. Gourley, M. E. Warren, G. R. Hadley, G. A. Vawter, T. M. Brennan, and B. E. Hammons, Appl. Phys. Lett. 58, 890 (1991).
[CrossRef]

Hammons, B. E.

P. L. Gourley, M. E. Warren, G. R. Hadley, G. A. Vawter, T. M. Brennan, and B. E. Hammons, Appl. Phys. Lett. 58, 890 (1991).
[CrossRef]

Harbison, J. P.

M. Orenstein, E. Kapon, L. T. Florez, J. P. Harbison, and N. G. Stoffel, Appl. Phys. Lett. 60, 1535 (1992).
[CrossRef]

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

Kapon, E.

M. Orenstein, E. Kapon, L. T. Florez, J. P. Harbison, and N. G. Stoffel, Appl. Phys. Lett. 60, 1535 (1992).
[CrossRef]

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

Kojima, K.

R. A. Morgan, K. Kojima, T. Mullally, G. D. Guth, M. W. Focht, R. E. Leibenguth, and M. Asom, Appl. Phys. Lett. 61, 1160 (1992).
[CrossRef]

Leibenguth, R. E.

R. A. Morgan, K. Kojima, T. Mullally, G. D. Guth, M. W. Focht, R. E. Leibenguth, and M. Asom, Appl. Phys. Lett. 61, 1160 (1992).
[CrossRef]

Morgan, R. A.

R. A. Morgan, K. Kojima, T. Mullally, G. D. Guth, M. W. Focht, R. E. Leibenguth, and M. Asom, Appl. Phys. Lett. 61, 1160 (1992).
[CrossRef]

Mullally, T.

R. A. Morgan, K. Kojima, T. Mullally, G. D. Guth, M. W. Focht, R. E. Leibenguth, and M. Asom, Appl. Phys. Lett. 61, 1160 (1992).
[CrossRef]

Orenstein, M.

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

M. Orenstein, E. Kapon, L. T. Florez, J. P. Harbison, and N. G. Stoffel, Appl. Phys. Lett. 60, 1535 (1992).
[CrossRef]

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

Stoffel, N. G.

M. Orenstein, E. Kapon, L. T. Florez, J. P. Harbison, and N. G. Stoffel, Appl. Phys. Lett. 60, 1535 (1992).
[CrossRef]

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

van der Ziel, J. P.

J. P. van der Ziel, D. G. Deppe, N. Chand, G. J. Zydzik, and S. N. G. Chu, IEEE J. Quantum Electron. 26, 1873 (1990).
[CrossRef]

Vawter, G. A.

P. L. Gourley, M. E. Warren, G. R. Hadley, G. A. Vawter, T. M. Brennan, and B. E. Hammons, Appl. Phys. Lett. 58, 890 (1991).
[CrossRef]

Warren, M. E.

P. L. Gourley, M. E. Warren, G. R. Hadley, G. A. Vawter, T. M. Brennan, and B. E. Hammons, Appl. Phys. Lett. 58, 890 (1991).
[CrossRef]

Winful, H. G.

H. G. Winful, Phys. Rev. A 46, 6093 (1992).
[CrossRef] [PubMed]

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]

Zydzik, G. J.

J. P. van der Ziel, D. G. Deppe, N. Chand, G. J. Zydzik, and S. N. G. Chu, IEEE J. Quantum Electron. 26, 1873 (1990).
[CrossRef]

Appl. Phys. Lett. (4)

P. L. Gourley, M. E. Warren, G. R. Hadley, G. A. Vawter, T. M. Brennan, and B. E. Hammons, Appl. Phys. Lett. 58, 890 (1991).
[CrossRef]

M. Orenstein, E. Kapon, L. T. Florez, J. P. Harbison, and N. G. Stoffel, Appl. Phys. Lett. 60, 1535 (1992).
[CrossRef]

R. A. Morgan, K. Kojima, T. Mullally, G. D. Guth, M. W. Focht, R. E. Leibenguth, and M. Asom, Appl. Phys. Lett. 61, 1160 (1992).
[CrossRef]

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. (1)

J. P. van der Ziel, D. G. Deppe, N. Chand, G. J. Zydzik, and S. N. G. Chu, IEEE J. Quantum Electron. 26, 1873 (1990).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (1)

H. G. Winful, Phys. Rev. A 46, 6093 (1992).
[CrossRef] [PubMed]

Other (3)

A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1988), pp. 606–611.

M. Orenstein and T. Fishman, presented at the 13th International Semiconductor Laser Conference, Takamatsu, Japan, 1992.

M. Orenstein, E. Kapon, N. G. Stoffel, L. T. Florez, and J. P. Harbison, presented at the 1990 LEOS Annual Meeting, Boston, Mass.

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Figures (5)

Fig. 1
Fig. 1

Experimental results of a 1D, 16-element VCSEL array. (a) NF intensity distribution, (b) spectrally resolved near field (NFRS), (c) FF intensity distribution. The FF photo is distorted to save space: the actual height-to-width ratio of each lobe is approximately 10:1.

Fig. 2
Fig. 2

Localized modes of a 10-element 1D array with a single defect (on laser 5), calculated by the complex CMT.

Fig. 3
Fig. 3

Lasing modes of both perfect and nonhomogeneous 2D arrays calculated by the complex CMT. (a) A 2×10 array. Defects were located on lasers 1, 5 and 2, 2. (b) A 10×10 array. Defects can be seen as the darker lasers in the NF pattern.

Fig. 4
Fig. 4

Experimental results for 2D arrays. (a) Homogenous 20×20 array. (b) 3×3 and 5×5 arrays with intentional defects, produced by reducing for some lasers the deposited top mirror area by one half. Defects are located at 1, 1, 2, 1, and 3, 3 for the 3×3 and 1, 4, 2, 4, 3, 3, 4, 4, and 5, 3 for the 5×5 arrays.

Fig. 5
Fig. 5

Phase transfer functions of 2D and 1D arrays. Dashed curves, transfer function for an array with random defects. (a) 1×25 and 5×5 arrays. (b) 1×5 and 5×5 arrays. τp is the photon cavity lifetime, and ω=-js.

Equations (3)

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dEn,mdt=-jβn,mEn,m-jκcnexp(-jφ)(En+1,m+En-1,m+En,m+1+En,m-1),
dδϕn,mdt=p(a(n,m),p)δϕn,m-p a(n,m),pδϕp,
A=Ai,i=j ai,jAi,j=-ai,j.

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