Abstract

Arrays consisting of coupled vertical-cavity surface-emitting lasers represent a model system for photonic lattices. Fluctuations among array elements, caused by wafer nonuniformities or processing defects, can lead to photon-mode localization, thus deteriorating the spatial coherence of such devices. The influence of cavity nonuniformities on the near-field and far-field patterns in arrays of different dimensionalities is analyzed in the framework of coupled-mode theory. It is shown that, for the same degree of disorder, photon localization is drastically reduced as the array dimensionality increases.

© 1997 Optical Society of America

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]

1996 (1)

A. Hardy and E. Kapon, IEEE J. Quantum Electron. 32, 966 (1996).
[Crossref]

1993 (1)

1992 (2)

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, J. P. Harbinson, L. T. Florez, and N. G. Stoffel, Appl. Phys. Lett. 60, 1535 (1992).
[Crossref]

1991 (1)

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

1990 (2)

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

H.-J. Yoo, A. Scherer, J. P. Harbison, L. T. Florez, E. G. Paek, B. P. van der Gaag, J. R. Hayes, A. von Lehmen, E. Kapon, and Y.-S. Kwon, Appl. Phys. Lett. 56, 1198 (1990).
[Crossref]

1986 (1)

1985 (1)

P. A. Lee and T. V. Ramakrishnan, Rev. Mod. Phys. 57, 287 (1985).
[Crossref]

1984 (2)

J. K. Butler, D. E. Ackley, and D. Botez, Appl. Phys. Lett. 44, 293 (1984).
[Crossref]

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

Ackley, D. E.

J. K. Butler, D. E. Ackley, and D. Botez, Appl. Phys. Lett. 44, 293 (1984).
[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]

Botez, D.

J. K. Butler, D. E. Ackley, and D. Botez, Appl. Phys. Lett. 44, 293 (1984).
[Crossref]

Butler, J. K.

J. K. Butler, D. E. Ackley, and D. Botez, Appl. Phys. Lett. 44, 293 (1984).
[Crossref]

Florez, L. T.

M. Orenstein, E. Kapon, J. P. Harbinson, L. T. Florez, 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]

H.-J. Yoo, A. Scherer, J. P. Harbison, L. T. Florez, E. G. Paek, B. P. van der Gaag, J. R. Hayes, A. von Lehmen, E. Kapon, and Y.-S. Kwon, Appl. Phys. Lett. 56, 1198 (1990).
[Crossref]

M. Orenstein, E. Kapon, L. T. Florez, J. P. Harbinson, and N. G. Stoffel, Integrated Photonics Research, Vol. 8 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 50.

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]

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]

Harbinson, J. P.

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

M. Orenstein, E. Kapon, L. T. Florez, J. P. Harbinson, and N. G. Stoffel, Integrated Photonics Research, Vol. 8 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 50.

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]

H.-J. Yoo, A. Scherer, J. P. Harbison, L. T. Florez, E. G. Paek, B. P. van der Gaag, J. R. Hayes, A. von Lehmen, E. Kapon, and Y.-S. Kwon, Appl. Phys. Lett. 56, 1198 (1990).
[Crossref]

Hardy, A.

Hayes, J. R.

H.-J. Yoo, A. Scherer, J. P. Harbison, L. T. Florez, E. G. Paek, B. P. van der Gaag, J. R. Hayes, A. von Lehmen, E. Kapon, and Y.-S. Kwon, Appl. Phys. Lett. 56, 1198 (1990).
[Crossref]

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

Kapon, E.

A. Hardy and E. Kapon, IEEE J. Quantum Electron. 32, 966 (1996).
[Crossref]

M. Orenstein, E. Kapon, J. P. Harbinson, L. T. Florez, 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]

H.-J. Yoo, A. Scherer, J. P. Harbison, L. T. Florez, E. G. Paek, B. P. van der Gaag, J. R. Hayes, A. von Lehmen, E. Kapon, and Y.-S. Kwon, Appl. Phys. Lett. 56, 1198 (1990).
[Crossref]

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

M. Orenstein, E. Kapon, L. T. Florez, J. P. Harbinson, and N. G. Stoffel, Integrated Photonics Research, Vol. 8 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 50.

Katz, J.

Kojima, K.

R. A. Morgan and K. Kojima, Opt. Lett. 18, 352 (1993).
[Crossref] [PubMed]

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]

Kwon, Y.-S.

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

H.-J. Yoo, A. Scherer, J. P. Harbison, L. T. Florez, E. G. Paek, B. P. van der Gaag, J. R. Hayes, A. von Lehmen, E. Kapon, and Y.-S. Kwon, Appl. Phys. Lett. 56, 1198 (1990).
[Crossref]

Lee, P. A.

P. A. Lee and T. V. Ramakrishnan, Rev. Mod. Phys. 57, 287 (1985).
[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 and K. Kojima, Opt. Lett. 18, 352 (1993).
[Crossref] [PubMed]

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.

M. Orenstein, E. Kapon, J. P. Harbinson, L. T. Florez, 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]

M. Orenstein, E. Kapon, L. T. Florez, J. P. Harbinson, and N. G. Stoffel, Integrated Photonics Research, Vol. 8 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 50.

Osinski, M.

Paek, E. G.

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

H.-J. Yoo, A. Scherer, J. P. Harbison, L. T. Florez, E. G. Paek, B. P. van der Gaag, J. R. Hayes, A. von Lehmen, E. Kapon, and Y.-S. Kwon, Appl. Phys. Lett. 56, 1198 (1990).
[Crossref]

Ramakrishnan, T. V.

P. A. Lee and T. V. Ramakrishnan, Rev. Mod. Phys. 57, 287 (1985).
[Crossref]

Scherer, A.

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

H.-J. Yoo, A. Scherer, J. P. Harbison, L. T. Florez, E. G. Paek, B. P. van der Gaag, J. R. Hayes, A. von Lehmen, E. Kapon, and Y.-S. Kwon, Appl. Phys. Lett. 56, 1198 (1990).
[Crossref]

Stoffel, N. G.

M. Orenstein, E. Kapon, J. P. Harbinson, L. T. Florez, 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]

M. Orenstein, E. Kapon, L. T. Florez, J. P. Harbinson, and N. G. Stoffel, Integrated Photonics Research, Vol. 8 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 50.

Streifer, W.

van der Gaag, B. P.

H.-J. Yoo, A. Scherer, J. P. Harbison, L. T. Florez, E. G. Paek, B. P. van der Gaag, J. R. Hayes, A. von Lehmen, E. Kapon, and Y.-S. Kwon, Appl. Phys. Lett. 56, 1198 (1990).
[Crossref]

von Lehmen, A.

H.-J. Yoo, A. Scherer, J. P. Harbison, L. T. Florez, E. G. Paek, B. P. van der Gaag, J. R. Hayes, A. von Lehmen, E. Kapon, and Y.-S. Kwon, Appl. Phys. Lett. 56, 1198 (1990).
[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, A. Scherer, J. P. Harbison, L. T. Florez, E. G. Paek, B. P. van der Gaag, J. R. Hayes, A. von Lehmen, E. Kapon, and Y.-S. Kwon, Appl. Phys. Lett. 56, 1198 (1990).
[Crossref]

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

Appl. Phys. Lett. (5)

J. K. Butler, D. E. Ackley, and D. Botez, Appl. Phys. Lett. 44, 293 (1984).
[Crossref]

M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florez, and J. Wullert, Appl. Phys. Lett. 58, 804 (1991).
[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, J. P. Harbinson, L. T. Florez, and N. G. Stoffel, Appl. Phys. Lett. 60, 1535 (1992).
[Crossref]

H.-J. Yoo, A. Scherer, J. P. Harbison, L. T. Florez, E. G. Paek, B. P. van der Gaag, J. R. Hayes, A. von Lehmen, E. Kapon, and Y.-S. Kwon, Appl. Phys. Lett. 56, 1198 (1990).
[Crossref]

IEEE J. Quantum Electron. (2)

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

A. Hardy and E. Kapon, IEEE J. Quantum Electron. 32, 966 (1996).
[Crossref]

Opt. Lett. (3)

Rev. Mod. Phys. (1)

P. A. Lee and T. V. Ramakrishnan, Rev. Mod. Phys. 57, 287 (1985).
[Crossref]

Other (1)

M. Orenstein, E. Kapon, L. T. Florez, J. P. Harbinson, and N. G. Stoffel, Integrated Photonics Research, Vol. 8 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 50.

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Figures (5)

Fig. 1
Fig. 1

Near-field (left) and far-field (right) intensity distributions of the highest-order supermode in (a) 1×25, (b) 2×25, (c) 4×25, and (d) 8×25 arrays, each with an impurity at position (1, 7), marked by an arrow. The wavelength is 980  nm, and the array pitch is 5  µm.

Fig. 2
Fig. 2

Localization lengths of the highest-order supermode of N×25N=1, 2, 4, 8, 25 arrays (from bottom to top) with a single impurity, as shown in Fig. 1, but kept in the center of the array. The inset shows a magnified view of the region 0Δβ/κ1.

Fig. 3
Fig. 3

FWHM of the far-field lobes of the highest-order supermode in N×25 arrays versus the disorder parameter, calculated along the long dimension of the array, for 0<βmax/κ<1.

Fig. 4
Fig. 4

(a) Sierpinski-carpet array with DH=1.89. (b) Near-field intensity pattern of the fundamental supermode of the array in (a) with an impurity at position (9, 13), marked by the arrow.

Fig. 5
Fig. 5

Far-field widths of the fundamental supermode in a 1D array, Sierpinski-carpet arrays with DH=1.77, DH=1.89, and a 2D array, with a single optical impurity, versus the effective disorder parameter.

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