Abstract

We present a two-dimensional (2D) spatial lock-in amplifier that provides a contrast ratio of more than 10,000:1 for transmitted and blocked intensity patterns using a conventional liquid-crystal spatial light modulator. The device is based on spatial-domain modulation–demodulation of intensity patterns under coherent imaging conditions. The operation of the 2D lock-in amplifier is illustrated by implementing Young’s double-slit arrangement for measurements of the mutual coherence between individual emitters of a 2D phase-coupled array of vertical cavity surface emitting lasers.

© 2006 Optical Society of America

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2005 (1)

2004 (4)

2003 (1)

2002 (1)

2000 (1)

1999 (2)

1997 (1)

Z. He, N. Mukohzaka, and K. Hotate, IEEE Photon. Technol. Lett. 9, 514 (1997).
[CrossRef]

1992 (2)

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

M. Killinger, J. L. de Bougrenet de la Tocnaye, P. Cambon, R. C. Chittick, and W. A. Crossland, Appl. Opt. 31, 3930 (1992).
[CrossRef] [PubMed]

1987 (2)

G. C. Dente, K. A. Wilson, T. C. Salvi, and D. Depatie, Appl. Phys. Lett. 51, 9 (1987).
[CrossRef]

N. W. Carlson, V. J. Masin, M. Lurie, B. Goldstein, and G. A. Evans, Appl. Phys. Lett. 51, 643 (1987).
[CrossRef]

Bagnoud, V.

Bitou, Y.

Cambon, P.

Campos, J.

Cao, Z.

Carlson, N. W.

N. W. Carlson, V. J. Masin, M. Lurie, B. Goldstein, and G. A. Evans, Appl. Phys. Lett. 51, 643 (1987).
[CrossRef]

Chittick, R. C.

Cohn, R.

Cottrell, D. M.

Crossland, W. A.

Daria, V. R.

V. R. Daria, P. J. Rodrigo, and J. Glückstad, Opt. Commun. 232, 229 (2004).
[CrossRef]

R. L. Eriksen, V. R. Daria, and J. Glückstad, Opt. Express 10, 597 (2002).
[PubMed]

Davis, J. A.

de Bougrenet de la Tocnaye, J. L.

Dente, G. C.

G. C. Dente, K. A. Wilson, T. C. Salvi, and D. Depatie, Appl. Phys. Lett. 51, 9 (1987).
[CrossRef]

Depatie, D.

G. C. Dente, K. A. Wilson, T. C. Salvi, and D. Depatie, Appl. Phys. Lett. 51, 9 (1987).
[CrossRef]

Eriksen, R. L.

Evans, G. A.

N. W. Carlson, V. J. Masin, M. Lurie, B. Goldstein, and G. A. Evans, Appl. Phys. Lett. 51, 643 (1987).
[CrossRef]

Florez, L. T.

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

Glückstad, J.

V. R. Daria, P. J. Rodrigo, and J. Glückstad, Opt. Commun. 232, 229 (2004).
[CrossRef]

R. L. Eriksen, V. R. Daria, and J. Glückstad, Opt. Express 10, 597 (2002).
[PubMed]

Goldstein, B.

N. W. Carlson, V. J. Masin, M. Lurie, B. Goldstein, and G. A. Evans, Appl. Phys. Lett. 51, 643 (1987).
[CrossRef]

Hällstig, E.

Harbison, J. P.

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

He, Z.

Z. He, N. Mukohzaka, and K. Hotate, IEEE Photon. Technol. Lett. 9, 514 (1997).
[CrossRef]

Hotate, K.

Z. He, N. Mukohzaka, and K. Hotate, IEEE Photon. Technol. Lett. 9, 514 (1997).
[CrossRef]

Hu, L.

Kapon, E.

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

Killinger, M.

Landau, L. D.

L. D. Landau and E. M. Lifshits, Electrodynamics of Continuous Media (Nauka, 1992), §94.

Li, D.

Lifshits, E. M.

L. D. Landau and E. M. Lifshits, Electrodynamics of Continuous Media (Nauka, 1992), §94.

Lindgren, M.

Liu, Y.

Lurie, M.

N. W. Carlson, V. J. Masin, M. Lurie, B. Goldstein, and G. A. Evans, Appl. Phys. Lett. 51, 643 (1987).
[CrossRef]

Martin, T.

Masin, V. J.

N. W. Carlson, V. J. Masin, M. Lurie, B. Goldstein, and G. A. Evans, Appl. Phys. Lett. 51, 643 (1987).
[CrossRef]

McCabe, E. M.

Moreno, I.

Mu, Q. Q.

Mukohzaka, N.

Z. He, N. Mukohzaka, and K. Hotate, IEEE Photon. Technol. Lett. 9, 514 (1997).
[CrossRef]

Orenstein, M.

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

Rodrigo, P. J.

V. R. Daria, P. J. Rodrigo, and J. Glückstad, Opt. Commun. 232, 229 (2004).
[CrossRef]

Salvi, T. C.

G. C. Dente, K. A. Wilson, T. C. Salvi, and D. Depatie, Appl. Phys. Lett. 51, 9 (1987).
[CrossRef]

Shaw, A. J.

Shen, S.

S. Shen and A. M. Weiner, IEEE Photon. Technol. Lett. 11, 566 (1999).
[CrossRef]

Sjöqvist, L.

Smith, P. J.

Stoffel, N. G.

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

Taylor, C. M.

Weiner, A. M.

S. Shen and A. M. Weiner, IEEE Photon. Technol. Lett. 11, 566 (1999).
[CrossRef]

Wilson, K. A.

G. C. Dente, K. A. Wilson, T. C. Salvi, and D. Depatie, Appl. Phys. Lett. 51, 9 (1987).
[CrossRef]

Xuan, L.

Xun, X.

Yzuel, M. J.

Zuegel, J. D.

Appl. Opt. (4)

Appl. Phys. Lett. (3)

G. C. Dente, K. A. Wilson, T. C. Salvi, and D. Depatie, Appl. Phys. Lett. 51, 9 (1987).
[CrossRef]

N. W. Carlson, V. J. Masin, M. Lurie, B. Goldstein, and G. A. Evans, Appl. Phys. Lett. 51, 643 (1987).
[CrossRef]

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

IEEE Photon. Technol. Lett. (2)

Z. He, N. Mukohzaka, and K. Hotate, IEEE Photon. Technol. Lett. 9, 514 (1997).
[CrossRef]

S. Shen and A. M. Weiner, IEEE Photon. Technol. Lett. 11, 566 (1999).
[CrossRef]

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

Opt. Commun. (1)

V. R. Daria, P. J. Rodrigo, and J. Glückstad, Opt. Commun. 232, 229 (2004).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Other (1)

L. D. Landau and E. M. Lifshits, Electrodynamics of Continuous Media (Nauka, 1992), §94.

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Figures (3)

Fig. 1
Fig. 1

Schematic of the 2D lock-in amplifier for spatial coherence measurements in VCSEL arrays. SLM, spatial light modulator; DP, Dove prism; WP, wave plate; BS, beam splitter; P1,P2, polarizers; A, aperture; CCD, camera; IR, iris diaphragm; M, mirror; f1, microscope objective ( f 1 = 8.55 mm , NA = 0.4 ); f2–f4, lenses ( f 2 = 400 , f 3 = 300 , and f 4 = 163 mm ). Distances a and b are 215 and 600 mm , respectively.

Fig. 2
Fig. 2

Contrast ratio of the lock-in amplifier as a function of the gray level of the uniform SLM pattern.

Fig. 3
Fig. 3

(a) Near-field and (b) far-field patterns of the lasing 10 × 10 VCSEL array. (c) NF and (d) FF patterns of two selected VCSEL pixels [the arrows in (a) indicate their row and column positions]. (e) FF line scans of the solitary VCSEL pixels (dashed curves 1 and 2) and of the interference pattern of the two VCSELs (solid curve 3) along the dashed line in (d). (f) Normalized correlation function of the selected VCSEL pixels.

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