Abstract

It is not widely appreciated that many subtleties are involved in the accurate measurement of intensity-correlated photons; even for the original experiments of Hanbury Brown and Twiss (HBT). Using a monolithic 4×4 array of single-photon avalanche diodes (SPADs), together with an off-chip algorithm for processing streaming data, we investigate the difficulties of measuring second-order photon correlations g (2)(x′, t′,x, t) in a wide variety of light fields that exhibit dramatically different correlation statistics: a multimode He-Ne laser, an incoherent intensity-modulated lamp-light source and a thermal light source. Our off-chip algorithm treats multiple photon-arrivals at pixel-array pairs, in any observation interval, with photon fluxes limited by detector saturation, in such a way that a correctly normalized g (2) function is guaranteed. The impact of detector background correlations between SPAD pixels and afterpulsing effects on second-order coherence measurements is discussed. These results demonstrate that our monolithic SPAD array enables access to effects that are otherwise impossible to measure with stand-alone detectors.

© 2009 Optical Society of America

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    [CrossRef] [PubMed]
  4. H. Deng, D. Press, S. G¨otzinger, G. S. Solomon, R. Hey, K. H. Ploog, and Y. Yamamoto, "Quantum Degenerate Exciton-Polaritons in Thermal Equilibrium," Phys. Rev. Lett. 97, 146402-4 (2006).
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    [CrossRef]
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2009 (1)

D. L. Boiko, N. J. Gunther, N. Brauer, M. Sergio, C. Niclass, G. B. Beretta, and E. Charbon, "A quantum imager for intensity correlated photons," New J. Phys. 11, 013001-7 (2009).
[CrossRef]

2007 (5)

L. D. A. Lundeberg, G. P. Lousberg, D. L. Boiko, and E. Kapon, "Spatial coherence measurements in arrays of coupled vertical cavity surface emitting lasers," Appl. Phys. Lett. 90, 021103-3 (2007).
[CrossRef]

S. Christopoulos, G. Baldassarri Hoger von Hogersthal, A. J. D. Grundy, P. G. Lagoudakis, A.V. Kavokin, J. J. Baumberg, G. Christmann, R. Butt’e, E. Feltin, J.-F. Carlin, and N. Grandjean, "Room-Temperature Polariton Lasing in Semiconductor Microcavities," Phys. Rev. Lett. 98, 126405-4 (2007).
[CrossRef]

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, "Bose-Einstein Condensation of Microcavity Polaritons in a Trap," Science 316, 1007-1010 (2007).
[CrossRef] [PubMed]

C. W. Oh, S. Moon, SuhasP. Veetil, and D. Y. Kim, "An angular offset launching technique for bandwidth enhancement in multimode fiber links," Micro. Opt. Technol. Lett. 50, 165-168 (2007).
[CrossRef]

R. J. Glauber, "Nobel Lecture: One hundred years of light quanta," Ann. Phys. (Leipzig) 16, 6-24 (2007).
[CrossRef]

2006 (2)

H. Deng, D. Press, S. G¨otzinger, G. S. Solomon, R. Hey, K. H. Ploog, and Y. Yamamoto, "Quantum Degenerate Exciton-Polaritons in Thermal Equilibrium," Phys. Rev. Lett. 97, 146402-4 (2006).
[CrossRef] [PubMed]

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szyma’nska, R. Andr’e, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and Le Si Dang, "Bose-Einstein condensation of exciton polaritons," Nature 443, 409-414 (2006).
[CrossRef] [PubMed]

2005 (3)

J. Enderlein, and I. Gregor, "Using fluorescence lifetime for discriminating detector afterpulsing in fluorescencecorrelation spectroscopy," Rev. Sci. Instrum. 76, 033102-5 (2005).
[CrossRef]

C. Niclass, A. Rochas, P. A. Besse, and E. Charbon, "Design and Characterization of a CMOS 3-D Image Sensor Based on Single Photon Avalanche Diodes," IEEE J. Solid-State Circuits 40, 1847-1854 (2005).
[CrossRef]

E. I. Chaikina, S. Stepanov, A. G. Navarrete, E. R. M’endez, and T. A. Leskova, "Formation of angular power profile via ballistic light transport in multimode optical fibers with corrugated surfaces," Phys. Rev. B 71, 085419-9 (2005).
[CrossRef]

2004 (1)

G. Scarcelli, A. Valencia, and Y. Shih, "Two-photon interference with thermal light," Europhys. Lett.,  68, 618-624 (2004).
[CrossRef]

2003 (1)

D. W. Snoke, "When should we say we have observed Bose condensation of excitons?" Phys. Stat. Sol.(b) 238, 389-396 (2003).
[CrossRef]

2002 (1)

H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, "Condensation of Semiconductor Microcavity Exciton Polaritons," Science 298, 199-202 (2002).
[CrossRef] [PubMed]

2001 (1)

J. Zhang, Q. Li, W. Pan, and Y. Chen, "Ring-Shaped Field Pattern: The Fundamental Mode of a Multimode Optical Fiber," Fiber Integ. Opt. 20, 403-410 (2001).
[CrossRef]

1998 (1)

E. Overbeck, and C. Sinn, "Silicon avalanche photodiodes as detectors for photon correlation experiments," Rev. Sci. Instrum. 69, 3515-3523 (1998).
[CrossRef]

1969 (1)

A. A. Grutter, H. P. Weber, and R. Dandliker, "Imperfectly Mode-Locked Laser Emission and Its Effects on Nonlinear Optics," Phys. Rev. 185, 629-643 (1969).
[CrossRef]

1966 (1)

D. B. Scarl, "Measurement Of Photon Time-Of-Arrival Distribution In Partially Coherent Light," Phys. Rev. Lett. 17, 663-666 (1966).
[CrossRef]

1964 (1)

P. L. Kelley, and W. H. Kleiner, "Theory of Electromagnetic Field Measurement and Photoelectron Counting," Phys. Rev. 136, A316-A334 (1964).
[CrossRef]

1963 (2)

R. J. Glauber, "The Quantum Theory of Optical Coherence," Phys. Rev. 130, 2529-2539 (1963).
[CrossRef]

R. J. Glauber, "Coherent and incoherent states of the radiation field," Phys. Rev. 131, 2766-2788 (1963).
[CrossRef]

1956 (5)

R. Hanbury Brown, and R. Q. Twiss, "Correlation between photons in two coherent beams of light," Nature 177, 27-29 (1956).
[CrossRef]

R. Hanbury Brown, and R. Q. Twiss, "A test of a new type of stellar interferometer on Sirius," Nature 178, 1046-1048 (1956).
[CrossRef]

E. Brannen, and H. I. S. Ferguson, "The question of correlation between photons in coherent light beams," Nature 178, 481-482 (1956).
[CrossRef]

R. H. Brown, and R. Q. Twiss, "The question of corelation between photons in coherent light rays," Nature 178, 1447-1448 (1956).
[CrossRef]

E. M. Purcell, "The question of corelation between photons in coherent light rays," Nature 178, 1449-1450 (1956).
[CrossRef]

1955 (1)

A. Adam, L. Janossy, and R. Varga, "Coincidences between photons contained in coherent light rays," Acta Physica Hungarica 4, 301-315 (1955).

Ad’am, A.

A. Adam, L. Janossy, and R. Varga, "Coincidences between photons contained in coherent light rays," Acta Physica Hungarica 4, 301-315 (1955).

Baas, A.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szyma’nska, R. Andr’e, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and Le Si Dang, "Bose-Einstein condensation of exciton polaritons," Nature 443, 409-414 (2006).
[CrossRef] [PubMed]

Baldassarri H¨oger von H¨ogersthal, G.

S. Christopoulos, G. Baldassarri Hoger von Hogersthal, A. J. D. Grundy, P. G. Lagoudakis, A.V. Kavokin, J. J. Baumberg, G. Christmann, R. Butt’e, E. Feltin, J.-F. Carlin, and N. Grandjean, "Room-Temperature Polariton Lasing in Semiconductor Microcavities," Phys. Rev. Lett. 98, 126405-4 (2007).
[CrossRef]

Balili, R.

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, "Bose-Einstein Condensation of Microcavity Polaritons in a Trap," Science 316, 1007-1010 (2007).
[CrossRef] [PubMed]

Baumberg, J. J.

S. Christopoulos, G. Baldassarri Hoger von Hogersthal, A. J. D. Grundy, P. G. Lagoudakis, A.V. Kavokin, J. J. Baumberg, G. Christmann, R. Butt’e, E. Feltin, J.-F. Carlin, and N. Grandjean, "Room-Temperature Polariton Lasing in Semiconductor Microcavities," Phys. Rev. Lett. 98, 126405-4 (2007).
[CrossRef]

Beretta, G. B.

D. L. Boiko, N. J. Gunther, N. Brauer, M. Sergio, C. Niclass, G. B. Beretta, and E. Charbon, "A quantum imager for intensity correlated photons," New J. Phys. 11, 013001-7 (2009).
[CrossRef]

Besse, P. A.

C. Niclass, A. Rochas, P. A. Besse, and E. Charbon, "Design and Characterization of a CMOS 3-D Image Sensor Based on Single Photon Avalanche Diodes," IEEE J. Solid-State Circuits 40, 1847-1854 (2005).
[CrossRef]

Bloch, J.

H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, "Condensation of Semiconductor Microcavity Exciton Polaritons," Science 298, 199-202 (2002).
[CrossRef] [PubMed]

Boiko, D. L.

D. L. Boiko, N. J. Gunther, N. Brauer, M. Sergio, C. Niclass, G. B. Beretta, and E. Charbon, "A quantum imager for intensity correlated photons," New J. Phys. 11, 013001-7 (2009).
[CrossRef]

L. D. A. Lundeberg, G. P. Lousberg, D. L. Boiko, and E. Kapon, "Spatial coherence measurements in arrays of coupled vertical cavity surface emitting lasers," Appl. Phys. Lett. 90, 021103-3 (2007).
[CrossRef]

Brannen, E.

E. Brannen, and H. I. S. Ferguson, "The question of correlation between photons in coherent light beams," Nature 178, 481-482 (1956).
[CrossRef]

Brauer, N.

D. L. Boiko, N. J. Gunther, N. Brauer, M. Sergio, C. Niclass, G. B. Beretta, and E. Charbon, "A quantum imager for intensity correlated photons," New J. Phys. 11, 013001-7 (2009).
[CrossRef]

Brown, R. H.

R. H. Brown, and R. Q. Twiss, "The question of corelation between photons in coherent light rays," Nature 178, 1447-1448 (1956).
[CrossRef]

Chaikina, E. I.

E. I. Chaikina, S. Stepanov, A. G. Navarrete, E. R. M’endez, and T. A. Leskova, "Formation of angular power profile via ballistic light transport in multimode optical fibers with corrugated surfaces," Phys. Rev. B 71, 085419-9 (2005).
[CrossRef]

Charbon, E.

D. L. Boiko, N. J. Gunther, N. Brauer, M. Sergio, C. Niclass, G. B. Beretta, and E. Charbon, "A quantum imager for intensity correlated photons," New J. Phys. 11, 013001-7 (2009).
[CrossRef]

C. Niclass, A. Rochas, P. A. Besse, and E. Charbon, "Design and Characterization of a CMOS 3-D Image Sensor Based on Single Photon Avalanche Diodes," IEEE J. Solid-State Circuits 40, 1847-1854 (2005).
[CrossRef]

Chen, Y.

J. Zhang, Q. Li, W. Pan, and Y. Chen, "Ring-Shaped Field Pattern: The Fundamental Mode of a Multimode Optical Fiber," Fiber Integ. Opt. 20, 403-410 (2001).
[CrossRef]

Christmann, G.

S. Christopoulos, G. Baldassarri Hoger von Hogersthal, A. J. D. Grundy, P. G. Lagoudakis, A.V. Kavokin, J. J. Baumberg, G. Christmann, R. Butt’e, E. Feltin, J.-F. Carlin, and N. Grandjean, "Room-Temperature Polariton Lasing in Semiconductor Microcavities," Phys. Rev. Lett. 98, 126405-4 (2007).
[CrossRef]

Christopoulos, S.

S. Christopoulos, G. Baldassarri Hoger von Hogersthal, A. J. D. Grundy, P. G. Lagoudakis, A.V. Kavokin, J. J. Baumberg, G. Christmann, R. Butt’e, E. Feltin, J.-F. Carlin, and N. Grandjean, "Room-Temperature Polariton Lasing in Semiconductor Microcavities," Phys. Rev. Lett. 98, 126405-4 (2007).
[CrossRef]

D¨andliker, R.

A. A. Grutter, H. P. Weber, and R. Dandliker, "Imperfectly Mode-Locked Laser Emission and Its Effects on Nonlinear Optics," Phys. Rev. 185, 629-643 (1969).
[CrossRef]

Deng, H.

H. Deng, D. Press, S. G¨otzinger, G. S. Solomon, R. Hey, K. H. Ploog, and Y. Yamamoto, "Quantum Degenerate Exciton-Polaritons in Thermal Equilibrium," Phys. Rev. Lett. 97, 146402-4 (2006).
[CrossRef] [PubMed]

H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, "Condensation of Semiconductor Microcavity Exciton Polaritons," Science 298, 199-202 (2002).
[CrossRef] [PubMed]

Enderlein, J.

J. Enderlein, and I. Gregor, "Using fluorescence lifetime for discriminating detector afterpulsing in fluorescencecorrelation spectroscopy," Rev. Sci. Instrum. 76, 033102-5 (2005).
[CrossRef]

Ferguson, H. I. S.

E. Brannen, and H. I. S. Ferguson, "The question of correlation between photons in coherent light beams," Nature 178, 481-482 (1956).
[CrossRef]

G¨otzinger, S.

H. Deng, D. Press, S. G¨otzinger, G. S. Solomon, R. Hey, K. H. Ploog, and Y. Yamamoto, "Quantum Degenerate Exciton-Polaritons in Thermal Equilibrium," Phys. Rev. Lett. 97, 146402-4 (2006).
[CrossRef] [PubMed]

Glauber, R. J.

R. J. Glauber, "Nobel Lecture: One hundred years of light quanta," Ann. Phys. (Leipzig) 16, 6-24 (2007).
[CrossRef]

R. J. Glauber, "Coherent and incoherent states of the radiation field," Phys. Rev. 131, 2766-2788 (1963).
[CrossRef]

R. J. Glauber, "The Quantum Theory of Optical Coherence," Phys. Rev. 130, 2529-2539 (1963).
[CrossRef]

Gr¨utter, A. A.

A. A. Grutter, H. P. Weber, and R. Dandliker, "Imperfectly Mode-Locked Laser Emission and Its Effects on Nonlinear Optics," Phys. Rev. 185, 629-643 (1969).
[CrossRef]

Gregor, I.

J. Enderlein, and I. Gregor, "Using fluorescence lifetime for discriminating detector afterpulsing in fluorescencecorrelation spectroscopy," Rev. Sci. Instrum. 76, 033102-5 (2005).
[CrossRef]

Grundy, A. J. D.

S. Christopoulos, G. Baldassarri Hoger von Hogersthal, A. J. D. Grundy, P. G. Lagoudakis, A.V. Kavokin, J. J. Baumberg, G. Christmann, R. Butt’e, E. Feltin, J.-F. Carlin, and N. Grandjean, "Room-Temperature Polariton Lasing in Semiconductor Microcavities," Phys. Rev. Lett. 98, 126405-4 (2007).
[CrossRef]

Gunther, N. J.

D. L. Boiko, N. J. Gunther, N. Brauer, M. Sergio, C. Niclass, G. B. Beretta, and E. Charbon, "A quantum imager for intensity correlated photons," New J. Phys. 11, 013001-7 (2009).
[CrossRef]

Hanbury Brown, R.

R. Hanbury Brown, and R. Q. Twiss, "A test of a new type of stellar interferometer on Sirius," Nature 178, 1046-1048 (1956).
[CrossRef]

R. Hanbury Brown, and R. Q. Twiss, "Correlation between photons in two coherent beams of light," Nature 177, 27-29 (1956).
[CrossRef]

Hartwell, V.

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, "Bose-Einstein Condensation of Microcavity Polaritons in a Trap," Science 316, 1007-1010 (2007).
[CrossRef] [PubMed]

Hey, R.

H. Deng, D. Press, S. G¨otzinger, G. S. Solomon, R. Hey, K. H. Ploog, and Y. Yamamoto, "Quantum Degenerate Exciton-Polaritons in Thermal Equilibrium," Phys. Rev. Lett. 97, 146402-4 (2006).
[CrossRef] [PubMed]

Jeambrun, P.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szyma’nska, R. Andr’e, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and Le Si Dang, "Bose-Einstein condensation of exciton polaritons," Nature 443, 409-414 (2006).
[CrossRef] [PubMed]

Kapon, E.

L. D. A. Lundeberg, G. P. Lousberg, D. L. Boiko, and E. Kapon, "Spatial coherence measurements in arrays of coupled vertical cavity surface emitting lasers," Appl. Phys. Lett. 90, 021103-3 (2007).
[CrossRef]

Kasprzak, J.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szyma’nska, R. Andr’e, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and Le Si Dang, "Bose-Einstein condensation of exciton polaritons," Nature 443, 409-414 (2006).
[CrossRef] [PubMed]

Kavokin, A.V.

S. Christopoulos, G. Baldassarri Hoger von Hogersthal, A. J. D. Grundy, P. G. Lagoudakis, A.V. Kavokin, J. J. Baumberg, G. Christmann, R. Butt’e, E. Feltin, J.-F. Carlin, and N. Grandjean, "Room-Temperature Polariton Lasing in Semiconductor Microcavities," Phys. Rev. Lett. 98, 126405-4 (2007).
[CrossRef]

Keeling, J. M. J.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szyma’nska, R. Andr’e, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and Le Si Dang, "Bose-Einstein condensation of exciton polaritons," Nature 443, 409-414 (2006).
[CrossRef] [PubMed]

Kelley, P. L.

P. L. Kelley, and W. H. Kleiner, "Theory of Electromagnetic Field Measurement and Photoelectron Counting," Phys. Rev. 136, A316-A334 (1964).
[CrossRef]

Kleiner, W. H.

P. L. Kelley, and W. H. Kleiner, "Theory of Electromagnetic Field Measurement and Photoelectron Counting," Phys. Rev. 136, A316-A334 (1964).
[CrossRef]

Kundermann, S.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szyma’nska, R. Andr’e, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and Le Si Dang, "Bose-Einstein condensation of exciton polaritons," Nature 443, 409-414 (2006).
[CrossRef] [PubMed]

Lagoudakis, P. G.

S. Christopoulos, G. Baldassarri Hoger von Hogersthal, A. J. D. Grundy, P. G. Lagoudakis, A.V. Kavokin, J. J. Baumberg, G. Christmann, R. Butt’e, E. Feltin, J.-F. Carlin, and N. Grandjean, "Room-Temperature Polariton Lasing in Semiconductor Microcavities," Phys. Rev. Lett. 98, 126405-4 (2007).
[CrossRef]

Li, Q.

J. Zhang, Q. Li, W. Pan, and Y. Chen, "Ring-Shaped Field Pattern: The Fundamental Mode of a Multimode Optical Fiber," Fiber Integ. Opt. 20, 403-410 (2001).
[CrossRef]

Lousberg, G. P.

L. D. A. Lundeberg, G. P. Lousberg, D. L. Boiko, and E. Kapon, "Spatial coherence measurements in arrays of coupled vertical cavity surface emitting lasers," Appl. Phys. Lett. 90, 021103-3 (2007).
[CrossRef]

Lundeberg, L. D. A.

L. D. A. Lundeberg, G. P. Lousberg, D. L. Boiko, and E. Kapon, "Spatial coherence measurements in arrays of coupled vertical cavity surface emitting lasers," Appl. Phys. Lett. 90, 021103-3 (2007).
[CrossRef]

Marchetti, F. M.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szyma’nska, R. Andr’e, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and Le Si Dang, "Bose-Einstein condensation of exciton polaritons," Nature 443, 409-414 (2006).
[CrossRef] [PubMed]

Moon, S.

C. W. Oh, S. Moon, SuhasP. Veetil, and D. Y. Kim, "An angular offset launching technique for bandwidth enhancement in multimode fiber links," Micro. Opt. Technol. Lett. 50, 165-168 (2007).
[CrossRef]

Navarrete, A. G.

E. I. Chaikina, S. Stepanov, A. G. Navarrete, E. R. M’endez, and T. A. Leskova, "Formation of angular power profile via ballistic light transport in multimode optical fibers with corrugated surfaces," Phys. Rev. B 71, 085419-9 (2005).
[CrossRef]

Niclass, C.

D. L. Boiko, N. J. Gunther, N. Brauer, M. Sergio, C. Niclass, G. B. Beretta, and E. Charbon, "A quantum imager for intensity correlated photons," New J. Phys. 11, 013001-7 (2009).
[CrossRef]

C. Niclass, A. Rochas, P. A. Besse, and E. Charbon, "Design and Characterization of a CMOS 3-D Image Sensor Based on Single Photon Avalanche Diodes," IEEE J. Solid-State Circuits 40, 1847-1854 (2005).
[CrossRef]

Oh, C. W.

C. W. Oh, S. Moon, SuhasP. Veetil, and D. Y. Kim, "An angular offset launching technique for bandwidth enhancement in multimode fiber links," Micro. Opt. Technol. Lett. 50, 165-168 (2007).
[CrossRef]

Overbeck, E.

E. Overbeck, and C. Sinn, "Silicon avalanche photodiodes as detectors for photon correlation experiments," Rev. Sci. Instrum. 69, 3515-3523 (1998).
[CrossRef]

Pan, W.

J. Zhang, Q. Li, W. Pan, and Y. Chen, "Ring-Shaped Field Pattern: The Fundamental Mode of a Multimode Optical Fiber," Fiber Integ. Opt. 20, 403-410 (2001).
[CrossRef]

Pfeiffer, L.

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, "Bose-Einstein Condensation of Microcavity Polaritons in a Trap," Science 316, 1007-1010 (2007).
[CrossRef] [PubMed]

Ploog, K. H.

H. Deng, D. Press, S. G¨otzinger, G. S. Solomon, R. Hey, K. H. Ploog, and Y. Yamamoto, "Quantum Degenerate Exciton-Polaritons in Thermal Equilibrium," Phys. Rev. Lett. 97, 146402-4 (2006).
[CrossRef] [PubMed]

Press, D.

H. Deng, D. Press, S. G¨otzinger, G. S. Solomon, R. Hey, K. H. Ploog, and Y. Yamamoto, "Quantum Degenerate Exciton-Polaritons in Thermal Equilibrium," Phys. Rev. Lett. 97, 146402-4 (2006).
[CrossRef] [PubMed]

Purcell, E. M.

E. M. Purcell, "The question of corelation between photons in coherent light rays," Nature 178, 1449-1450 (1956).
[CrossRef]

Richard, M.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szyma’nska, R. Andr’e, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and Le Si Dang, "Bose-Einstein condensation of exciton polaritons," Nature 443, 409-414 (2006).
[CrossRef] [PubMed]

Rochas, A.

C. Niclass, A. Rochas, P. A. Besse, and E. Charbon, "Design and Characterization of a CMOS 3-D Image Sensor Based on Single Photon Avalanche Diodes," IEEE J. Solid-State Circuits 40, 1847-1854 (2005).
[CrossRef]

Santori, C.

H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, "Condensation of Semiconductor Microcavity Exciton Polaritons," Science 298, 199-202 (2002).
[CrossRef] [PubMed]

Scarcelli, G.

G. Scarcelli, A. Valencia, and Y. Shih, "Two-photon interference with thermal light," Europhys. Lett.,  68, 618-624 (2004).
[CrossRef]

Scarl, D. B.

D. B. Scarl, "Measurement Of Photon Time-Of-Arrival Distribution In Partially Coherent Light," Phys. Rev. Lett. 17, 663-666 (1966).
[CrossRef]

Sergio, M.

D. L. Boiko, N. J. Gunther, N. Brauer, M. Sergio, C. Niclass, G. B. Beretta, and E. Charbon, "A quantum imager for intensity correlated photons," New J. Phys. 11, 013001-7 (2009).
[CrossRef]

Shih, Y.

G. Scarcelli, A. Valencia, and Y. Shih, "Two-photon interference with thermal light," Europhys. Lett.,  68, 618-624 (2004).
[CrossRef]

Sinn, C.

E. Overbeck, and C. Sinn, "Silicon avalanche photodiodes as detectors for photon correlation experiments," Rev. Sci. Instrum. 69, 3515-3523 (1998).
[CrossRef]

Snoke, D.

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, "Bose-Einstein Condensation of Microcavity Polaritons in a Trap," Science 316, 1007-1010 (2007).
[CrossRef] [PubMed]

Snoke, D. W.

D. W. Snoke, "When should we say we have observed Bose condensation of excitons?" Phys. Stat. Sol.(b) 238, 389-396 (2003).
[CrossRef]

Solomon, G. S.

H. Deng, D. Press, S. G¨otzinger, G. S. Solomon, R. Hey, K. H. Ploog, and Y. Yamamoto, "Quantum Degenerate Exciton-Polaritons in Thermal Equilibrium," Phys. Rev. Lett. 97, 146402-4 (2006).
[CrossRef] [PubMed]

Stepanov, S.

E. I. Chaikina, S. Stepanov, A. G. Navarrete, E. R. M’endez, and T. A. Leskova, "Formation of angular power profile via ballistic light transport in multimode optical fibers with corrugated surfaces," Phys. Rev. B 71, 085419-9 (2005).
[CrossRef]

Suhas, S.

C. W. Oh, S. Moon, SuhasP. Veetil, and D. Y. Kim, "An angular offset launching technique for bandwidth enhancement in multimode fiber links," Micro. Opt. Technol. Lett. 50, 165-168 (2007).
[CrossRef]

Szyma’nska, M. H.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szyma’nska, R. Andr’e, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and Le Si Dang, "Bose-Einstein condensation of exciton polaritons," Nature 443, 409-414 (2006).
[CrossRef] [PubMed]

Twiss, R. Q.

R. Hanbury Brown, and R. Q. Twiss, "Correlation between photons in two coherent beams of light," Nature 177, 27-29 (1956).
[CrossRef]

R. H. Brown, and R. Q. Twiss, "The question of corelation between photons in coherent light rays," Nature 178, 1447-1448 (1956).
[CrossRef]

R. Hanbury Brown, and R. Q. Twiss, "A test of a new type of stellar interferometer on Sirius," Nature 178, 1046-1048 (1956).
[CrossRef]

Valencia, A.

G. Scarcelli, A. Valencia, and Y. Shih, "Two-photon interference with thermal light," Europhys. Lett.,  68, 618-624 (2004).
[CrossRef]

Weber, H. P.

A. A. Grutter, H. P. Weber, and R. Dandliker, "Imperfectly Mode-Locked Laser Emission and Its Effects on Nonlinear Optics," Phys. Rev. 185, 629-643 (1969).
[CrossRef]

Weihs, G.

H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, "Condensation of Semiconductor Microcavity Exciton Polaritons," Science 298, 199-202 (2002).
[CrossRef] [PubMed]

West, K.

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, "Bose-Einstein Condensation of Microcavity Polaritons in a Trap," Science 316, 1007-1010 (2007).
[CrossRef] [PubMed]

Yamamoto, Y.

H. Deng, D. Press, S. G¨otzinger, G. S. Solomon, R. Hey, K. H. Ploog, and Y. Yamamoto, "Quantum Degenerate Exciton-Polaritons in Thermal Equilibrium," Phys. Rev. Lett. 97, 146402-4 (2006).
[CrossRef] [PubMed]

H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, "Condensation of Semiconductor Microcavity Exciton Polaritons," Science 298, 199-202 (2002).
[CrossRef] [PubMed]

Zhang, J.

J. Zhang, Q. Li, W. Pan, and Y. Chen, "Ring-Shaped Field Pattern: The Fundamental Mode of a Multimode Optical Fiber," Fiber Integ. Opt. 20, 403-410 (2001).
[CrossRef]

Acta Physica Hungarica (1)

A. Adam, L. Janossy, and R. Varga, "Coincidences between photons contained in coherent light rays," Acta Physica Hungarica 4, 301-315 (1955).

Ann. Phys. (Leipzig) (1)

R. J. Glauber, "Nobel Lecture: One hundred years of light quanta," Ann. Phys. (Leipzig) 16, 6-24 (2007).
[CrossRef]

Appl. Phys. Lett. (1)

L. D. A. Lundeberg, G. P. Lousberg, D. L. Boiko, and E. Kapon, "Spatial coherence measurements in arrays of coupled vertical cavity surface emitting lasers," Appl. Phys. Lett. 90, 021103-3 (2007).
[CrossRef]

Europhys. Lett. (1)

G. Scarcelli, A. Valencia, and Y. Shih, "Two-photon interference with thermal light," Europhys. Lett.,  68, 618-624 (2004).
[CrossRef]

Fiber Integ. Opt. (1)

J. Zhang, Q. Li, W. Pan, and Y. Chen, "Ring-Shaped Field Pattern: The Fundamental Mode of a Multimode Optical Fiber," Fiber Integ. Opt. 20, 403-410 (2001).
[CrossRef]

IEEE J. Solid-State Circuits (1)

C. Niclass, A. Rochas, P. A. Besse, and E. Charbon, "Design and Characterization of a CMOS 3-D Image Sensor Based on Single Photon Avalanche Diodes," IEEE J. Solid-State Circuits 40, 1847-1854 (2005).
[CrossRef]

Micro. Opt. Technol. Lett. (1)

C. W. Oh, S. Moon, SuhasP. Veetil, and D. Y. Kim, "An angular offset launching technique for bandwidth enhancement in multimode fiber links," Micro. Opt. Technol. Lett. 50, 165-168 (2007).
[CrossRef]

Nature (6)

R. Hanbury Brown, and R. Q. Twiss, "A test of a new type of stellar interferometer on Sirius," Nature 178, 1046-1048 (1956).
[CrossRef]

R. Hanbury Brown, and R. Q. Twiss, "Correlation between photons in two coherent beams of light," Nature 177, 27-29 (1956).
[CrossRef]

E. Brannen, and H. I. S. Ferguson, "The question of correlation between photons in coherent light beams," Nature 178, 481-482 (1956).
[CrossRef]

R. H. Brown, and R. Q. Twiss, "The question of corelation between photons in coherent light rays," Nature 178, 1447-1448 (1956).
[CrossRef]

E. M. Purcell, "The question of corelation between photons in coherent light rays," Nature 178, 1449-1450 (1956).
[CrossRef]

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szyma’nska, R. Andr’e, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and Le Si Dang, "Bose-Einstein condensation of exciton polaritons," Nature 443, 409-414 (2006).
[CrossRef] [PubMed]

New J. Phys. (1)

D. L. Boiko, N. J. Gunther, N. Brauer, M. Sergio, C. Niclass, G. B. Beretta, and E. Charbon, "A quantum imager for intensity correlated photons," New J. Phys. 11, 013001-7 (2009).
[CrossRef]

Phys. Rev. (4)

R. J. Glauber, "Coherent and incoherent states of the radiation field," Phys. Rev. 131, 2766-2788 (1963).
[CrossRef]

A. A. Grutter, H. P. Weber, and R. Dandliker, "Imperfectly Mode-Locked Laser Emission and Its Effects on Nonlinear Optics," Phys. Rev. 185, 629-643 (1969).
[CrossRef]

R. J. Glauber, "The Quantum Theory of Optical Coherence," Phys. Rev. 130, 2529-2539 (1963).
[CrossRef]

P. L. Kelley, and W. H. Kleiner, "Theory of Electromagnetic Field Measurement and Photoelectron Counting," Phys. Rev. 136, A316-A334 (1964).
[CrossRef]

Phys. Rev. B (1)

E. I. Chaikina, S. Stepanov, A. G. Navarrete, E. R. M’endez, and T. A. Leskova, "Formation of angular power profile via ballistic light transport in multimode optical fibers with corrugated surfaces," Phys. Rev. B 71, 085419-9 (2005).
[CrossRef]

Phys. Rev. Lett. (3)

D. B. Scarl, "Measurement Of Photon Time-Of-Arrival Distribution In Partially Coherent Light," Phys. Rev. Lett. 17, 663-666 (1966).
[CrossRef]

H. Deng, D. Press, S. G¨otzinger, G. S. Solomon, R. Hey, K. H. Ploog, and Y. Yamamoto, "Quantum Degenerate Exciton-Polaritons in Thermal Equilibrium," Phys. Rev. Lett. 97, 146402-4 (2006).
[CrossRef] [PubMed]

S. Christopoulos, G. Baldassarri Hoger von Hogersthal, A. J. D. Grundy, P. G. Lagoudakis, A.V. Kavokin, J. J. Baumberg, G. Christmann, R. Butt’e, E. Feltin, J.-F. Carlin, and N. Grandjean, "Room-Temperature Polariton Lasing in Semiconductor Microcavities," Phys. Rev. Lett. 98, 126405-4 (2007).
[CrossRef]

Phys. Stat. Sol. (1)

D. W. Snoke, "When should we say we have observed Bose condensation of excitons?" Phys. Stat. Sol.(b) 238, 389-396 (2003).
[CrossRef]

Rev. Sci. Instrum. (2)

J. Enderlein, and I. Gregor, "Using fluorescence lifetime for discriminating detector afterpulsing in fluorescencecorrelation spectroscopy," Rev. Sci. Instrum. 76, 033102-5 (2005).
[CrossRef]

E. Overbeck, and C. Sinn, "Silicon avalanche photodiodes as detectors for photon correlation experiments," Rev. Sci. Instrum. 69, 3515-3523 (1998).
[CrossRef]

Science (2)

H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, "Condensation of Semiconductor Microcavity Exciton Polaritons," Science 298, 199-202 (2002).
[CrossRef] [PubMed]

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, "Bose-Einstein Condensation of Microcavity Polaritons in a Trap," Science 316, 1007-1010 (2007).
[CrossRef] [PubMed]

Other (4)

D. L. Boiko, "Towards r-space Bose-Einstein condensation of photonic crystal exciton polaritons," in Proceedings of the Progress in Electromagnetics Research Symposium PIERS 2008, (Cambridge MA, USA, July 2-6, 2008), pp 659-665 (2008); idem, PIERS Online 4, 831-837 (2008).

D. Bajoni, P. Senellart, A. Lema?tre, and J. Bloch, "Photon lasing in GaAs microcavity: Similarities with a polariton condensate," Phys. Rev. B 76, 201305(R)-4 (2007).
[CrossRef]

J. Bloch, D. Bajoni, P. Senellart, E. Wertz, I. Sagnes, A. Miard, and A. Lema?tre,"Polariton quantum degeneracy in GaAs microcavities," presented at the 2008 Latsis Symposium at EPFL on Bose Einstein Condensation in dilute atomic gases and in condensed matter, Lausanne, Switzerland, 28-30 Januarry 2008.

C. Niclass, M. Sergio, and E. Charbon, "A Single Photon Avalanche Diode Array Fabricated in 0.35 um CMOS and based on an Event-Driven Readout for TCSPC Experiments" in Proc. SPIE Opt. East (Boston) vol 6372 (Bellingham, WA, SPIE Optical Engineering Press, 2006) p 63720S-12.

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Figures (6)

Fig. 1.
Fig. 1.

Micrograph of the 4×4 SPAD array (a), schematics of the SPAD pixel structure (b) and electronic readout circuit (c). For a typical operation conditions V OP=-21V, which by 4 V exceeds the breakdown voltage, V DD=3.3V and VBIAS=0V.

Fig. 2.
Fig. 2.

Second-order correlation functions g (2)(x ij ,τ) of SPAD array pixels (a) and the maps of correlation maxima g (2)(x ij ,0) [(b) and (c)] measured for incoherent light using detector D8 [(a) and (b)] or D9 (c) as a reference. The time resolution is 1 ns. The panels corresponding to individual SPAD pixels are arranged in the same order in which they appear in the imager pattern and corresponds to SPAD pixel position in Fig. 1. Green scale curves in (a) show autocorrelation curves g (2)(0,τ) in linear (olive curve, left axis) and logarithmic (green curve, right axis) scales

Fig. 3.
Fig. 3.

a) shows the correlation function g̃(2) 5,9(τ) [Eq. (2)] measured by two detectors in the middle of array (detectors D5 and D9) at 30 µm baseline. The background component due to a spurious crosstalk at the same detector pair g̃(2), bg 5,9 (τ), which was measured with an incoherent broadband light source, is shown in (b). The corresponding correlation function of the multimode laser beam g(2)(x5,9,τ) calculated from Eq. (4) after corrections for background correlations and afterpulsing effects in the detectors is plotted in (c). It can be seen that this procedure is an efficient tool for removing spurious (anti-) correlations seen as a dip in both the measured correlations g̃(2) ij (τ) and reference background g̃(2), bg ij (τ).

Fig. 4.
Fig. 4.

Multimode coherent state emitted by a He-Ne laser at 632.8 nm wavelength. (a): Acquired second order coherence function g̃(2) 5,9(τ) [Eq. (2)]. (b): Spurious correlations background g (2), bg 5,9 (τ) measured with the help of an incandescent light bulb. (c): Second order correlation function of the field g (2)(x5,9,τ) corrected for spurious correlations.

Fig. 5.
Fig. 5.

Extended quasi-monochromatic thermal light source (546nm line of mercury). (a): Young’s interference fringes indicate phase correlation |g (1)|>0. (b) and (c): Measured second order correlation function g (2) 5,9 in the near field of the source obtained after corrections (4) at temporal resolution 100ps (b) and 100ns (c). The oscillations are due to the AC power supply of the Hg-Ar discharge lamp.

Fig. 6.
Fig. 6.

(a) Experimental setup of the table-top stellar HBT interferometer. (b) Correlations measured at various detector separation xi j and distance L to the fiber end. The Fresnel parameter F N =wxijλL is indicated in the panels. (c) Measured (points) and modeled (curves) second-order correlations in function of detector separation for the model Eq. (6) (dashed blue curve) and Eq. (8) (solid red curve). The inset shows the corresponding near field distributions at the fiber end (indicated with same type). (d) shows the corresponding modelled g(2)max (r) patterns (top line of panels) and far field patterns (bottom line of panels). (e) Imaged second-order correlation maxima along the row of the array. Its position in the g (2) plane is indicated in (d) with green solid lines. It is assumed that g (2)=2 along the diagonal. The green line of Hg (546nm) is used. Temporal resolution.

Tables (1)

Tables Icon

Table 1. Values of first and second order correlation functions for incoherent, coherent and thermal light states as well as entangled two-photon state produced as a result of spontaneous parametric down conversion [12]. Single-mode states are considered, θ is the angular width of the source, λ is the wavelength, τ c is the coherence length. Integration effects due to limited detector response times and resolution of coincidence counter are not indicated.

Equations (9)

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

g(2) (xij,τ)=Tr(ρ̂âi+âj+âjâi)Tr(ρâi+âi)Tr(ρâj+âj)
g˜ij(2) (τ)=g˜(2)(Xij,τ) =NMΣm=0MΣn=N2N2Xi(m)(n)ΛXj(m)(n+1)Σm=0MΣn=N2N2Xi(m)(n)Σm=0MΣn=N2N2Xj(m)(n+l)
g˜ii(2) (τ) = 1+PA(τ)(1+ε)2μ , τ >τD,
g˜ij(2) (τ) = 1+ gij(2)(τ)1(1+ε)2 +(g˜ij(2),bg(τ)1) , ij
gij(2) (τ) =1+α (gij(2),α(τ)1) Ii(α)Ij(α)IiIj
g(2) ( xij , τ ) =1+12 g(1)xijτ2 =1+12sinc2 (πwλLxij) exp (πτ2τc2) ,
g(2) xijτ =1+12 I0xyexp(i2πxλLxij)dxdyI0xydxdy2 exp (πτ2τc2) ,
g(2) xijτ = 1+ 12 sinc(πFN)+γ2sinc(πFN+12Ωw)+γ2sinc(πFN12Ωw)1+γsinc(12Ωw)2
×exp (πτ2τc2)

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