Abstract

We derive an analytical expression for the count probability of a single photon detector for a wide range of input optical power that includes afterpulsing effects. We confirm the validity of the expression by fitting it to the data obtained from a saturated commercial Single Photon Detector by illuminating it with a cw laser. Detector efficiency and afterpulsing probability extracted from the fits agree with the manufacture specs for low repetition frequencies.

© 2010 OSA

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References

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  1. B. F. Levine, D. G. Bethea, and J. C. Campbell, “Near room temperature 1.3 um single photon counting with a InGaAs avalanche photodiode,” Electron. Lett. 20(14), 596–598 (1984).
    [CrossRef]
  2. D. Stucki, G. Ribordy, A. Stefanov, H. Zbinden, J. G. Rarity, and T. Wall, “Photon counting for quantum key distribution with Peltier cooled InGaAs/InP APD’s,” J. Mod. Opt. 48(13), 1967–1981 (2001).
    [CrossRef]
  3. M. Wegmuller, F. Scholder, and N. Gisin, “Photon counting OTDR for Local Birefringence and Fault Analysis in the Metro Environment,” J. Lightwave Technol. 22(2), 390–400 (2004).
    [CrossRef]
  4. D. S. Bethune, W. P. Risk, and G. W. Pabst, “A high performance integrated single photon detector for telecom wavelengths,” J. Mod. Opt. 51, 1359–1368 (2004).
  5. A. Yoshizawa, R. Kaji, and H. Tsuchida, “Quantum efficiency evaluation method for gated-mode single photon detector,” Electron. Lett. 38(23), 1468–1469 (2002).
    [CrossRef]
  6. PGA-600, www.princetonlightwave.com .
  7. M. A. Itzler, R. Ben-Michael, C. F. Hsu, K. Slomkowski, A. Tosi, S. Cova, F. Zappa, and R. Ispasoiu, “Single photon avalanche diodes (SPADs) for 1.5 um photon counting applications,” J. Mod. Opt. 54(2), 283–304 (2007).
    [CrossRef]
  8. X. Jiang, M. A. Itzler, R. Ben-Michael, and K. Slomkowski, “InGaAsP-InP avalanche photodiodes for single photon detection,” IEEE J. Sel. Top. Quantum Electron. 13(4), 895–905 (2007).
    [CrossRef]
  9. Y. Kang, H. X. Lu, Y.-H. Lo, D. S. Bethune, and W. P. Risk, “Dark count probability and quantum efficiency of avalanche photodiodes for single-photon detection,” Appl. Phys. Lett. 83(14), 2955 (2003).
    [CrossRef]
  10. J. Zhang, R. Thew, J. D. Gautier, N. Gisin, and H. Zbinden, “Comprehensive characterization of InGaAs/InP avalanche photodiodes at 1550 nm with an active quenching ASIC,” IEEE J. Quantum Electron. 45(7), 792–799 (2009).
    [CrossRef]
  11. S. V. Polyakov and A. L. Migdall, “High accuracy verification of a correlated-photon- based method for determining photoncounting detection efficiency,” Opt. Express 15(4), 1390–1407 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-4-1390 .
    [CrossRef] [PubMed]

2009 (1)

J. Zhang, R. Thew, J. D. Gautier, N. Gisin, and H. Zbinden, “Comprehensive characterization of InGaAs/InP avalanche photodiodes at 1550 nm with an active quenching ASIC,” IEEE J. Quantum Electron. 45(7), 792–799 (2009).
[CrossRef]

2007 (3)

M. A. Itzler, R. Ben-Michael, C. F. Hsu, K. Slomkowski, A. Tosi, S. Cova, F. Zappa, and R. Ispasoiu, “Single photon avalanche diodes (SPADs) for 1.5 um photon counting applications,” J. Mod. Opt. 54(2), 283–304 (2007).
[CrossRef]

X. Jiang, M. A. Itzler, R. Ben-Michael, and K. Slomkowski, “InGaAsP-InP avalanche photodiodes for single photon detection,” IEEE J. Sel. Top. Quantum Electron. 13(4), 895–905 (2007).
[CrossRef]

S. V. Polyakov and A. L. Migdall, “High accuracy verification of a correlated-photon- based method for determining photoncounting detection efficiency,” Opt. Express 15(4), 1390–1407 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-4-1390 .
[CrossRef] [PubMed]

2004 (2)

D. S. Bethune, W. P. Risk, and G. W. Pabst, “A high performance integrated single photon detector for telecom wavelengths,” J. Mod. Opt. 51, 1359–1368 (2004).

M. Wegmuller, F. Scholder, and N. Gisin, “Photon counting OTDR for Local Birefringence and Fault Analysis in the Metro Environment,” J. Lightwave Technol. 22(2), 390–400 (2004).
[CrossRef]

2003 (1)

Y. Kang, H. X. Lu, Y.-H. Lo, D. S. Bethune, and W. P. Risk, “Dark count probability and quantum efficiency of avalanche photodiodes for single-photon detection,” Appl. Phys. Lett. 83(14), 2955 (2003).
[CrossRef]

2002 (1)

A. Yoshizawa, R. Kaji, and H. Tsuchida, “Quantum efficiency evaluation method for gated-mode single photon detector,” Electron. Lett. 38(23), 1468–1469 (2002).
[CrossRef]

2001 (1)

D. Stucki, G. Ribordy, A. Stefanov, H. Zbinden, J. G. Rarity, and T. Wall, “Photon counting for quantum key distribution with Peltier cooled InGaAs/InP APD’s,” J. Mod. Opt. 48(13), 1967–1981 (2001).
[CrossRef]

1984 (1)

B. F. Levine, D. G. Bethea, and J. C. Campbell, “Near room temperature 1.3 um single photon counting with a InGaAs avalanche photodiode,” Electron. Lett. 20(14), 596–598 (1984).
[CrossRef]

Ben-Michael, R.

X. Jiang, M. A. Itzler, R. Ben-Michael, and K. Slomkowski, “InGaAsP-InP avalanche photodiodes for single photon detection,” IEEE J. Sel. Top. Quantum Electron. 13(4), 895–905 (2007).
[CrossRef]

M. A. Itzler, R. Ben-Michael, C. F. Hsu, K. Slomkowski, A. Tosi, S. Cova, F. Zappa, and R. Ispasoiu, “Single photon avalanche diodes (SPADs) for 1.5 um photon counting applications,” J. Mod. Opt. 54(2), 283–304 (2007).
[CrossRef]

Bethea, D. G.

B. F. Levine, D. G. Bethea, and J. C. Campbell, “Near room temperature 1.3 um single photon counting with a InGaAs avalanche photodiode,” Electron. Lett. 20(14), 596–598 (1984).
[CrossRef]

Bethune, D. S.

D. S. Bethune, W. P. Risk, and G. W. Pabst, “A high performance integrated single photon detector for telecom wavelengths,” J. Mod. Opt. 51, 1359–1368 (2004).

Y. Kang, H. X. Lu, Y.-H. Lo, D. S. Bethune, and W. P. Risk, “Dark count probability and quantum efficiency of avalanche photodiodes for single-photon detection,” Appl. Phys. Lett. 83(14), 2955 (2003).
[CrossRef]

Campbell, J. C.

B. F. Levine, D. G. Bethea, and J. C. Campbell, “Near room temperature 1.3 um single photon counting with a InGaAs avalanche photodiode,” Electron. Lett. 20(14), 596–598 (1984).
[CrossRef]

Cova, S.

M. A. Itzler, R. Ben-Michael, C. F. Hsu, K. Slomkowski, A. Tosi, S. Cova, F. Zappa, and R. Ispasoiu, “Single photon avalanche diodes (SPADs) for 1.5 um photon counting applications,” J. Mod. Opt. 54(2), 283–304 (2007).
[CrossRef]

Gautier, J. D.

J. Zhang, R. Thew, J. D. Gautier, N. Gisin, and H. Zbinden, “Comprehensive characterization of InGaAs/InP avalanche photodiodes at 1550 nm with an active quenching ASIC,” IEEE J. Quantum Electron. 45(7), 792–799 (2009).
[CrossRef]

Gisin, N.

J. Zhang, R. Thew, J. D. Gautier, N. Gisin, and H. Zbinden, “Comprehensive characterization of InGaAs/InP avalanche photodiodes at 1550 nm with an active quenching ASIC,” IEEE J. Quantum Electron. 45(7), 792–799 (2009).
[CrossRef]

M. Wegmuller, F. Scholder, and N. Gisin, “Photon counting OTDR for Local Birefringence and Fault Analysis in the Metro Environment,” J. Lightwave Technol. 22(2), 390–400 (2004).
[CrossRef]

Hsu, C. F.

M. A. Itzler, R. Ben-Michael, C. F. Hsu, K. Slomkowski, A. Tosi, S. Cova, F. Zappa, and R. Ispasoiu, “Single photon avalanche diodes (SPADs) for 1.5 um photon counting applications,” J. Mod. Opt. 54(2), 283–304 (2007).
[CrossRef]

Ispasoiu, R.

M. A. Itzler, R. Ben-Michael, C. F. Hsu, K. Slomkowski, A. Tosi, S. Cova, F. Zappa, and R. Ispasoiu, “Single photon avalanche diodes (SPADs) for 1.5 um photon counting applications,” J. Mod. Opt. 54(2), 283–304 (2007).
[CrossRef]

Itzler, M. A.

M. A. Itzler, R. Ben-Michael, C. F. Hsu, K. Slomkowski, A. Tosi, S. Cova, F. Zappa, and R. Ispasoiu, “Single photon avalanche diodes (SPADs) for 1.5 um photon counting applications,” J. Mod. Opt. 54(2), 283–304 (2007).
[CrossRef]

X. Jiang, M. A. Itzler, R. Ben-Michael, and K. Slomkowski, “InGaAsP-InP avalanche photodiodes for single photon detection,” IEEE J. Sel. Top. Quantum Electron. 13(4), 895–905 (2007).
[CrossRef]

Jiang, X.

X. Jiang, M. A. Itzler, R. Ben-Michael, and K. Slomkowski, “InGaAsP-InP avalanche photodiodes for single photon detection,” IEEE J. Sel. Top. Quantum Electron. 13(4), 895–905 (2007).
[CrossRef]

Kaji, R.

A. Yoshizawa, R. Kaji, and H. Tsuchida, “Quantum efficiency evaluation method for gated-mode single photon detector,” Electron. Lett. 38(23), 1468–1469 (2002).
[CrossRef]

Kang, Y.

Y. Kang, H. X. Lu, Y.-H. Lo, D. S. Bethune, and W. P. Risk, “Dark count probability and quantum efficiency of avalanche photodiodes for single-photon detection,” Appl. Phys. Lett. 83(14), 2955 (2003).
[CrossRef]

Levine, B. F.

B. F. Levine, D. G. Bethea, and J. C. Campbell, “Near room temperature 1.3 um single photon counting with a InGaAs avalanche photodiode,” Electron. Lett. 20(14), 596–598 (1984).
[CrossRef]

Lo, Y.-H.

Y. Kang, H. X. Lu, Y.-H. Lo, D. S. Bethune, and W. P. Risk, “Dark count probability and quantum efficiency of avalanche photodiodes for single-photon detection,” Appl. Phys. Lett. 83(14), 2955 (2003).
[CrossRef]

Lu, H. X.

Y. Kang, H. X. Lu, Y.-H. Lo, D. S. Bethune, and W. P. Risk, “Dark count probability and quantum efficiency of avalanche photodiodes for single-photon detection,” Appl. Phys. Lett. 83(14), 2955 (2003).
[CrossRef]

Migdall, A. L.

Pabst, G. W.

D. S. Bethune, W. P. Risk, and G. W. Pabst, “A high performance integrated single photon detector for telecom wavelengths,” J. Mod. Opt. 51, 1359–1368 (2004).

Polyakov, S. V.

Rarity, J. G.

D. Stucki, G. Ribordy, A. Stefanov, H. Zbinden, J. G. Rarity, and T. Wall, “Photon counting for quantum key distribution with Peltier cooled InGaAs/InP APD’s,” J. Mod. Opt. 48(13), 1967–1981 (2001).
[CrossRef]

Ribordy, G.

D. Stucki, G. Ribordy, A. Stefanov, H. Zbinden, J. G. Rarity, and T. Wall, “Photon counting for quantum key distribution with Peltier cooled InGaAs/InP APD’s,” J. Mod. Opt. 48(13), 1967–1981 (2001).
[CrossRef]

Risk, W. P.

D. S. Bethune, W. P. Risk, and G. W. Pabst, “A high performance integrated single photon detector for telecom wavelengths,” J. Mod. Opt. 51, 1359–1368 (2004).

Y. Kang, H. X. Lu, Y.-H. Lo, D. S. Bethune, and W. P. Risk, “Dark count probability and quantum efficiency of avalanche photodiodes for single-photon detection,” Appl. Phys. Lett. 83(14), 2955 (2003).
[CrossRef]

Scholder, F.

Slomkowski, K.

X. Jiang, M. A. Itzler, R. Ben-Michael, and K. Slomkowski, “InGaAsP-InP avalanche photodiodes for single photon detection,” IEEE J. Sel. Top. Quantum Electron. 13(4), 895–905 (2007).
[CrossRef]

M. A. Itzler, R. Ben-Michael, C. F. Hsu, K. Slomkowski, A. Tosi, S. Cova, F. Zappa, and R. Ispasoiu, “Single photon avalanche diodes (SPADs) for 1.5 um photon counting applications,” J. Mod. Opt. 54(2), 283–304 (2007).
[CrossRef]

Stefanov, A.

D. Stucki, G. Ribordy, A. Stefanov, H. Zbinden, J. G. Rarity, and T. Wall, “Photon counting for quantum key distribution with Peltier cooled InGaAs/InP APD’s,” J. Mod. Opt. 48(13), 1967–1981 (2001).
[CrossRef]

Stucki, D.

D. Stucki, G. Ribordy, A. Stefanov, H. Zbinden, J. G. Rarity, and T. Wall, “Photon counting for quantum key distribution with Peltier cooled InGaAs/InP APD’s,” J. Mod. Opt. 48(13), 1967–1981 (2001).
[CrossRef]

Thew, R.

J. Zhang, R. Thew, J. D. Gautier, N. Gisin, and H. Zbinden, “Comprehensive characterization of InGaAs/InP avalanche photodiodes at 1550 nm with an active quenching ASIC,” IEEE J. Quantum Electron. 45(7), 792–799 (2009).
[CrossRef]

Tosi, A.

M. A. Itzler, R. Ben-Michael, C. F. Hsu, K. Slomkowski, A. Tosi, S. Cova, F. Zappa, and R. Ispasoiu, “Single photon avalanche diodes (SPADs) for 1.5 um photon counting applications,” J. Mod. Opt. 54(2), 283–304 (2007).
[CrossRef]

Tsuchida, H.

A. Yoshizawa, R. Kaji, and H. Tsuchida, “Quantum efficiency evaluation method for gated-mode single photon detector,” Electron. Lett. 38(23), 1468–1469 (2002).
[CrossRef]

Wall, T.

D. Stucki, G. Ribordy, A. Stefanov, H. Zbinden, J. G. Rarity, and T. Wall, “Photon counting for quantum key distribution with Peltier cooled InGaAs/InP APD’s,” J. Mod. Opt. 48(13), 1967–1981 (2001).
[CrossRef]

Wegmuller, M.

Yoshizawa, A.

A. Yoshizawa, R. Kaji, and H. Tsuchida, “Quantum efficiency evaluation method for gated-mode single photon detector,” Electron. Lett. 38(23), 1468–1469 (2002).
[CrossRef]

Zappa, F.

M. A. Itzler, R. Ben-Michael, C. F. Hsu, K. Slomkowski, A. Tosi, S. Cova, F. Zappa, and R. Ispasoiu, “Single photon avalanche diodes (SPADs) for 1.5 um photon counting applications,” J. Mod. Opt. 54(2), 283–304 (2007).
[CrossRef]

Zbinden, H.

J. Zhang, R. Thew, J. D. Gautier, N. Gisin, and H. Zbinden, “Comprehensive characterization of InGaAs/InP avalanche photodiodes at 1550 nm with an active quenching ASIC,” IEEE J. Quantum Electron. 45(7), 792–799 (2009).
[CrossRef]

D. Stucki, G. Ribordy, A. Stefanov, H. Zbinden, J. G. Rarity, and T. Wall, “Photon counting for quantum key distribution with Peltier cooled InGaAs/InP APD’s,” J. Mod. Opt. 48(13), 1967–1981 (2001).
[CrossRef]

Zhang, J.

J. Zhang, R. Thew, J. D. Gautier, N. Gisin, and H. Zbinden, “Comprehensive characterization of InGaAs/InP avalanche photodiodes at 1550 nm with an active quenching ASIC,” IEEE J. Quantum Electron. 45(7), 792–799 (2009).
[CrossRef]

Appl. Phys. Lett. (1)

Y. Kang, H. X. Lu, Y.-H. Lo, D. S. Bethune, and W. P. Risk, “Dark count probability and quantum efficiency of avalanche photodiodes for single-photon detection,” Appl. Phys. Lett. 83(14), 2955 (2003).
[CrossRef]

Electron. Lett. (2)

B. F. Levine, D. G. Bethea, and J. C. Campbell, “Near room temperature 1.3 um single photon counting with a InGaAs avalanche photodiode,” Electron. Lett. 20(14), 596–598 (1984).
[CrossRef]

A. Yoshizawa, R. Kaji, and H. Tsuchida, “Quantum efficiency evaluation method for gated-mode single photon detector,” Electron. Lett. 38(23), 1468–1469 (2002).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. Zhang, R. Thew, J. D. Gautier, N. Gisin, and H. Zbinden, “Comprehensive characterization of InGaAs/InP avalanche photodiodes at 1550 nm with an active quenching ASIC,” IEEE J. Quantum Electron. 45(7), 792–799 (2009).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

X. Jiang, M. A. Itzler, R. Ben-Michael, and K. Slomkowski, “InGaAsP-InP avalanche photodiodes for single photon detection,” IEEE J. Sel. Top. Quantum Electron. 13(4), 895–905 (2007).
[CrossRef]

J. Lightwave Technol. (1)

J. Mod. Opt. (3)

D. Stucki, G. Ribordy, A. Stefanov, H. Zbinden, J. G. Rarity, and T. Wall, “Photon counting for quantum key distribution with Peltier cooled InGaAs/InP APD’s,” J. Mod. Opt. 48(13), 1967–1981 (2001).
[CrossRef]

D. S. Bethune, W. P. Risk, and G. W. Pabst, “A high performance integrated single photon detector for telecom wavelengths,” J. Mod. Opt. 51, 1359–1368 (2004).

M. A. Itzler, R. Ben-Michael, C. F. Hsu, K. Slomkowski, A. Tosi, S. Cova, F. Zappa, and R. Ispasoiu, “Single photon avalanche diodes (SPADs) for 1.5 um photon counting applications,” J. Mod. Opt. 54(2), 283–304 (2007).
[CrossRef]

Opt. Express (1)

Other (1)

PGA-600, www.princetonlightwave.com .

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Figures (4)

Fig. 1
Fig. 1

The experimental setup.

Fig. 2
Fig. 2

Measured count probability P c as a function of the average number of photons per gate μ for pulsed (●) and cw (□) laser. Here τ g = 0.49 n s .

Fig. 3
Fig. 3

Count probability P c versus average number of photons per gate μ c w = 0.1 20 for cw laser at different trigger rates of 100 kHz (□) and 1 MHz(○). Inset: a zoom in with more trigger rates. Data is shown by symbols, lines are fits.

Fig. 4
Fig. 4

Top: extracted detector efficiency η at different trigger rates R for cw (□) and pulsed (●) lasers. Bottom: conditional afterpulsing probability for cw (red thin line) and pulsed (blue thick line) measurements.

Equations (6)

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

P c = 1 ( 1 P d c ) × exp ( μ η )
Q n = Q 0 exp ( n R τ )
P c = 2 e 1 R τ ( 1 P d c ) ( 1 P p h ) ( 1 Q 0 ) 2 + 1 2 [ 2 e 1 R τ ( 1 P d c ) ( 1 P p h ) ( 1 Q 0 ) ] 2 + 4 ( e 1 R τ 1 ) [ 1 ( 1 P d c ) ( 1 P p h ) ]
P a p ( n ) = P c ( n 1 ) Q 1 + ( 1 P c ( n 1 ) ) P c ( n 2 ) Q 2 + ( 1 P c ( n 1 ) ) ( 1 P c ( n 2 ) ) P c ( n 3 ) Q 3 + ...
P a p ( n ) = P c ( n 1 ) Q 1 + P a p ( n 1 ) ( 1 P c ( n 1 ) ) Q 1 / Q 0
P a p = P c Q 1 1 ( 1 P c ) Q 1 / Q 0

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