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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  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]
  2. D. W. Snoke, “When should we say we have observed Bose condensation of excitons?” Phys. Stat. Sol. (b) 238, 389–396 (2003).
    [CrossRef]
  3. H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, “Condensation of Semiconductor Microcavity Exciton Polaritons,” Science 298, 199–202 (2002).
    [CrossRef] [PubMed]
  4. H. Deng, D. Press, S. Götzinger, 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]
  5. J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, 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]
  6. S. Christopoulos, G. Baldassarri Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A.V. Kavokin, J. J. Baumberg, G. Christmann, R. Butté, E. Feltin, J.-F. Carlin, and N. Grandjean, “Room-Temperature Polariton Lasing in Semiconductor Microcavities,” Phys. Rev. Lett. 98, 126405-4 (2007).
    [CrossRef]
  7. D. Bajoni, P. Senellart, A. Lemaître, and J. Bloch, “Photon lasing in GaAs microcavity: Similarities with a polariton condensate,” Phys. Rev. B 76, 201305(R)-4 (2007).
    [CrossRef]
  8. J. Bloch, D. Bajoni, P. Senellart, E. Wertz, I. Sagnes, A. Miard, and A. Lemaître, “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.
  9. 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]
  10. 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).
  11. R. J. Glauber, “Coherent and incoherent states of the radiation field,” Phys. Rev. 131, 2766–2788 (1963).
    [CrossRef]
  12. G. Scarcelli, A. Valencia, and Y. Shih, “Two-photon interference with thermal light,” Europhys. Lett.,  68, 618–624 (2004).
    [CrossRef]
  13. R. Hanbury Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature 177, 27–29 (1956).
    [CrossRef]
  14. A. Adám, L. Jánossy, and R. Varga, “Coincidences between photons contained in coherent light rays,” Acta Physica Hungarica 4, 301–315 (1955).
  15. E. Brannen and H. I. S. Ferguson, “The question of correlation between photons in coherent light beams,” Nature 178, 481–482 (1956).
    [CrossRef]
  16. R. Hanbury Brown and R. Q. Twiss, “The question of corelation between photons in coherent light rays,” Nature 178, 1447–1448 (1956).
    [CrossRef]
  17. E. M. Purcell, “The question of corelation between photons in coherent light rays,” Nature 178, 1449–1450 (1956).
    [CrossRef]
  18. 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]
  19. R. Hanbury Brown and R. Q. Twiss, “A test of a new type of stellar interferometer on Sirius,” Nature 178, 1046–1048 (1956).
    [CrossRef]
  20. C. Niclass, M. Sergio, and E. Charbon, “A Single Photon Avalanche Diode Array Fabricated in 0.35 µm 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.
  21. R. J. Glauber, “The Quantum Theory of Optical Coherence,” Phys. Rev. 130, 2529–2539 (1963).
    [CrossRef]
  22. P. L. Kelley and W. H. Kleiner, “Theory of Electromagnetic Field Measurement and Photoelectron Counting,” Phys. Rev. 136, A316–A334 (1964).
    [CrossRef]
  23. J. Enderlein and I. Gregor, “Using fluorescence lifetime for discriminating detector afterpulsing in fluorescence-correlation spectroscopy,” Rev. Sci. Instrum. 76, 033102–5 (2005).
    [CrossRef]
  24. E. Overbeck and C. Sinn, “Silicon avalanche photodiodes as detectors for photon correlation experiments,” Rev. Sci. Instrum. 69, 3515–3523 (1998).
    [CrossRef]
  25. 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]
  26. R. J. Glauber, “Nobel Lecture: One hundred years of light quanta,” Ann. Phys. (Leipzig) 16, 6–24 (2007).
    [CrossRef]
  27. 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]
  28. C. W. Oh, S. Moon, Suhas P. 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]
  29. E. I. Chaikina, S. Stepanov, A. G. Navarrete, E. R. Méndez, 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]
  30. A. A. Grütter, H. P. Weber, and R. Dändliker, “Imperfectly Mode-Locked Laser Emission and Its Effects on Nonlinear Optics,” Phys. Rev. 185, 629–643 (1969).
    [CrossRef]
  31. D. B. Scarl, “Measurement Of Photon Time-Of-Arrival Distribution In Partially Coherent Light,” Phys. Rev. Lett. 17, 663–666 (1966).
    [CrossRef]

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 (6)

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 Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A.V. Kavokin, J. J. Baumberg, G. Christmann, R. Butté, E. Feltin, J.-F. Carlin, and N. Grandjean, “Room-Temperature Polariton Lasing in Semiconductor Microcavities,” Phys. Rev. Lett. 98, 126405-4 (2007).
[CrossRef]

D. Bajoni, P. Senellart, A. Lemaître, and J. Bloch, “Photon lasing in GaAs microcavity: Similarities with a polariton condensate,” Phys. Rev. B 76, 201305(R)-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, Suhas P. 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 (3)

H. Deng, D. Press, S. Götzinger, 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. Szymańska, R. André, 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]

C. Niclass, M. Sergio, and E. Charbon, “A Single Photon Avalanche Diode Array Fabricated in 0.35 µm 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.

2005 (3)

E. I. Chaikina, S. Stepanov, A. G. Navarrete, E. R. Méndez, 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]

J. Enderlein and I. Gregor, “Using fluorescence lifetime for discriminating detector afterpulsing in fluorescence-correlation 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]

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. Grütter, H. P. Weber, and R. Dändliker, “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, “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]

1956 (5)

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. Hanbury 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. Adám, L. Jánossy, and R. Varga, “Coincidences between photons contained in coherent light rays,” Acta Physica Hungarica 4, 301–315 (1955).

Adám, A.

A. Adám, L. Jánossy, and R. Varga, “Coincidences between photons contained in coherent light rays,” Acta Physica Hungarica 4, 301–315 (1955).

André, R.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, 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]

Baas, A.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, 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]

Bajoni, D.

D. Bajoni, P. Senellart, A. Lemaître, 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. Lemaître, “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.

Baldassarri Höger von Högersthal, G.

S. Christopoulos, G. Baldassarri Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A.V. Kavokin, J. J. Baumberg, G. Christmann, R. Butté, 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 Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A.V. Kavokin, J. J. Baumberg, G. Christmann, R. Butté, 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.

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

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

J. Bloch, D. Bajoni, P. Senellart, E. Wertz, I. Sagnes, A. Miard, and A. Lemaître, “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.

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]

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).

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]

Butté, R.

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

Carlin, J.-F.

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

Chaikina, E. I.

E. I. Chaikina, S. Stepanov, A. G. Navarrete, E. R. Méndez, 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, M. Sergio, and E. Charbon, “A Single Photon Avalanche Diode Array Fabricated in 0.35 µm 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.

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 Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A.V. Kavokin, J. J. Baumberg, G. Christmann, R. Butté, 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 Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A.V. Kavokin, J. J. Baumberg, G. Christmann, R. Butté, E. Feltin, J.-F. Carlin, and N. Grandjean, “Room-Temperature Polariton Lasing in Semiconductor Microcavities,” Phys. Rev. Lett. 98, 126405-4 (2007).
[CrossRef]

Dändliker, R.

A. A. Grütter, H. P. Weber, and R. Dändliker, “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. Götzinger, 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]

Deveaud, B.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, 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]

Enderlein, J.

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

Feltin, E.

S. Christopoulos, G. Baldassarri Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A.V. Kavokin, J. J. Baumberg, G. Christmann, R. Butté, E. Feltin, J.-F. Carlin, and N. Grandjean, “Room-Temperature Polariton Lasing in Semiconductor Microcavities,” Phys. Rev. Lett. 98, 126405-4 (2007).
[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]

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, “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]

Götzinger, S.

H. Deng, D. Press, S. Götzinger, 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]

Grandjean, N.

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

Gregor, I.

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

Grundy, A. J. D.

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

Grütter, A. A.

A. A. Grütter, H. P. Weber, and R. Dändliker, “Imperfectly Mode-Locked Laser Emission and Its Effects on Nonlinear Optics,” Phys. Rev. 185, 629–643 (1969).
[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, “The question of corelation between photons in coherent light rays,” Nature 178, 1447–1448 (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. Götzinger, 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]

Jánossy, L.

A. Adám, L. Jánossy, and R. Varga, “Coincidences between photons contained in coherent light rays,” Acta Physica Hungarica 4, 301–315 (1955).

Jeambrun, P.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, 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. Szymańska, R. André, 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 Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A.V. Kavokin, J. J. Baumberg, G. Christmann, R. Butté, 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. Szymańska, R. André, 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]

Kim, D. Y.

C. W. Oh, S. Moon, Suhas P. 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]

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. Szymańska, R. André, 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 Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A.V. Kavokin, J. J. Baumberg, G. Christmann, R. Butté, E. Feltin, J.-F. Carlin, and N. Grandjean, “Room-Temperature Polariton Lasing in Semiconductor Microcavities,” Phys. Rev. Lett. 98, 126405-4 (2007).
[CrossRef]

Le Si Dang,

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, 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]

Lemaître, A.

D. Bajoni, P. Senellart, A. Lemaître, 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. Lemaître, “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.

Leskova, T. A.

E. I. Chaikina, S. Stepanov, A. G. Navarrete, E. R. Méndez, 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]

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]

Littlewood, P. B.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, 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]

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. Szymańska, R. André, 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]

Méndez, E. R.

E. I. Chaikina, S. Stepanov, A. G. Navarrete, E. R. Méndez, 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]

Miard, A.

J. Bloch, D. Bajoni, P. Senellart, E. Wertz, I. Sagnes, A. Miard, and A. Lemaître, “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.

Moon, S.

C. W. Oh, S. Moon, Suhas P. 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. Méndez, 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, M. Sergio, and E. Charbon, “A Single Photon Avalanche Diode Array Fabricated in 0.35 µm 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.

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, Suhas P. 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. Götzinger, 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. Götzinger, 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. Szymańska, R. André, 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]

Sagnes, I.

J. Bloch, D. Bajoni, P. Senellart, E. Wertz, I. Sagnes, A. Miard, and A. Lemaître, “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.

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]

Savona, V.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, 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]

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]

Senellart, P.

D. Bajoni, P. Senellart, A. Lemaître, 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. Lemaître, “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.

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]

C. Niclass, M. Sergio, and E. Charbon, “A Single Photon Avalanche Diode Array Fabricated in 0.35 µm 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.

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. Götzinger, 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]

Staehli, J. L.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, 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]

Stepanov, S.

E. I. Chaikina, S. Stepanov, A. G. Navarrete, E. R. Méndez, 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]

Szymanska, M. H.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, 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. Hanbury 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]

Varga, R.

A. Adám, L. Jánossy, and R. Varga, “Coincidences between photons contained in coherent light rays,” Acta Physica Hungarica 4, 301–315 (1955).

Veetil, Suhas P.

C. W. Oh, S. Moon, Suhas P. 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]

Weber, H. P.

A. A. Grütter, H. P. Weber, and R. Dändliker, “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]

Wertz, E.

J. Bloch, D. Bajoni, P. Senellart, E. Wertz, I. Sagnes, A. Miard, and A. Lemaître, “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.

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. Götzinger, 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. Adám, L. Jánossy, 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]

in Proc. SPIE Opt. East (Boston) (1)

C. Niclass, M. Sergio, and E. Charbon, “A Single Photon Avalanche Diode Array Fabricated in 0.35 µm 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.

Micro. Opt. Technol. Lett. (1)

C. W. Oh, S. Moon, Suhas P. 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. Hanbury 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. Szymańska, R. André, 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. Grütter, H. P. Weber, and R. Dändliker, “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 (2)

E. I. Chaikina, S. Stepanov, A. G. Navarrete, E. R. Méndez, 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]

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

Phys. Rev. Lett. (3)

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

H. Deng, D. Press, S. Götzinger, 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]

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

Phys. Stat. Sol. (b) (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 fluorescence-correlation 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 (2)

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).

J. Bloch, D. Bajoni, P. Senellart, E. Wertz, I. Sagnes, A. Miard, and A. Lemaître, “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.

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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)

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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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