## Method for characterizing single photon detectors in saturation regime by cw laser

Optics Express, Vol. 18, Issue 6, pp. 5906-5911 (2010)

http://dx.doi.org/10.1364/OE.18.005906

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### 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

## 1. Introduction

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]

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]

*μ*, of 3 – 20). First, we measure probability of a count over a range of power and trigger rates for both pulsed and cw lasers. The data suggest higher afterpulsing probability at higher rates, which, unexpectedly, is accompanied by a slight decrease in detector efficiency. These tendencies are more pronounced with cw lasers than with pulsed lasers. Then, we fit the experimental results by a newly derived analytical expression using the detector efficiency and afterpulsing probability as fitting parameters. Our fits perfectly match the data within rms deviation of < 0.03%. Extracted efficiencies of 20%, and conditional afterpulsing probability in the range of 0.01 - 0.03 for 250 kHz trigger rate (device dependent) are similar to the values reported in manufacturer tests performed at the conventional low power regime of

*μ=0.1*[4]. We found that in the cw regime the afterpulsing is somewhat stronger and decays faster with the characteristic time of 2.5-3μs, which is shorter than the 4-5μs measured for pulsed laser. This observation suggests that different processes dominate in the cw and pulsed regime. But when the trigger rates are below 200 kHz the results obtained by cw and pulsed methods are nearly identical.

## 2. Experimental setup

6. PGA-600, www.princetonlightwave.com.

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]

*μ*, was adjusted down to 0.02 for both cw and pulsed sources. The detector produces an electrical NIM pulse (Nuclear Instrumentation Module Standard) for each detection event. These NIM pulses were then integrated by an electronic counter.

*η*achieved at the peak of the bias pulse is measured with a properly aligned narrow optical pulse [4] and serves as the major spec for SPDs. On the other hand, cw light experience efficiency that changes during the bias pulse in a nonlinear fashion. To simplify calculations, we model the SPD in the cw regime as operating at its maximal efficiency value

_{0}*η*for an effective gate window

_{0}*P*over a wide power range of each cw and pulsed laser. The repetition rate of the detector is

_{c}*R=*100kHz in both cases, and the pulsed laser is synchronized with the detector. Then we pick the values of the cw laser power

*P*and the average pulsed laser power

_{cw}*P*that equates the corresponding count probabilities

_{p}*P*and

_{p}*P*are in dBm. When averaged over the entire power range this procedure results in

_{cw}*h*is the Planck constant and

*ν*is optical frequency. Here the value

## 3. Derivation of the detector count probability

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]

*P*is the probability of a dark count,

_{dc}*μ*is the average number of photons per SPD gate and

*η*is the detector efficiency. However, we find that our data deviates from such dependence in two ways. First, we find that the measured probability is somewhat higher at lower

*μ*values, which suggests the presence of afterpulses [7

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]

*μ*indicating a slight decrease in efficiency. These two effects become more pronounced with higher repetition rates. To account for these deviations we modify the expression for the count probability to include the afterpulsing effect.

*t*since the successful detection event. We further assume that this conditional probability decays exponentially with a time constant

*τ*:

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]

*n*clock cycles in the detector that is gated with the trigger rate

*R*:Within this model the overall probability of a registered event

*n*denotes that the corresponding probability is evaluated at the

*n*-th time interval. Note that

## 4. Experimental results

*R*the experimental dependence of

*R*. This allows us to extract the efficiency for each trigger rate

*τ*by fitting Eq. (3) to the data.

*τ*extracted by the fits. Again we obtain for the two regimes very similar results for times longer than

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]

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]

## 5. Conclusion

## References and links

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. |

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. |

3. | M. Wegmuller, F. Scholder, and N. Gisin, “Photon counting OTDR for Local Birefringence and Fault Analysis in the Metro Environment,” J. Lightwave Technol. |

4. | D. S. Bethune, W. P. Risk, and G. W. Pabst, “A high performance integrated single photon detector for telecom wavelengths,” J. Mod. Opt. |

5. | A. Yoshizawa, R. Kaji, and H. Tsuchida, “Quantum efficiency evaluation method for gated-mode single photon detector,” Electron. Lett. |

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. |

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. |

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. |

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. |

11. | S. V. Polyakov and A. L. Migdall, “High accuracy verification of a correlated-photon- based method for determining photoncounting detection efficiency,” Opt. Express |

**OCIS Codes**

(060.2380) Fiber optics and optical communications : Fiber optics sources and detectors

(270.5290) Quantum optics : Photon statistics

(270.5570) Quantum optics : Quantum detectors

**ToC Category:**

Detectors

**History**

Original Manuscript: November 20, 2009

Revised Manuscript: January 12, 2010

Manuscript Accepted: January 25, 2010

Published: March 10, 2010

**Citation**

Jungmi Oh, Cristian Antonelli, Moshe Tur, and Misha Brodsky, "Method for characterizing single photon detectors in saturation regime by cw laser," Opt. Express **18**, 5906-5911 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-6-5906

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### References

- 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]
- 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]
- 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]
- 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).
- 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]
- PGA-600, www.princetonlightwave.com .
- 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]
- 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]
- 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]
- 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]

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