## Absolute calibration of fiber-coupled single-photon detector |

Optics Express, Vol. 22, Issue 15, pp. 18078-18092 (2014)

http://dx.doi.org/10.1364/OE.22.018078

Acrobat PDF (1174 KB)

### Abstract

We show a setup for characterising the efficiency of a single-photon-detector absolutely and with a precision better than 1%. Since the setup does not rely on calibrated devices and can be implemented with standard-optic components, it can be realised in any laboratory. Our approach is based on an Erbium-Doped-Fiber-Amplifier (EDFA) radiometer as a primary measurement standard for optical power, and on an ultra-stable source of spontaneous emission. As a proof of principle, we characterise the efficiency of an InGaAs/InP single-photon detector. We verified the correctness of the characterisation with independent measurements. In particular, the measurement of the optical power made with the EDFA radiometer has been compared to that of the Federal Institute of Metrology using a transfer power meter. Our approach is suitable for frequent characterisations of high-efficient single-photon detectors.

© 2014 Optical Society of America

## 1. Introduction

1. A. Restelli, J. C. Bienfang, and A. L. Migdall, “Single-photon detection efficiency up to 50% at 1310nm with an InGaAs/InP avalanche diode gated at 1.25 GHz,” Appl. Phys. Lett. **102**(14), 141104 (2013). [CrossRef]

2. F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. P. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics **7**(3), 210–214 (2013). [CrossRef]

3. S. Miki, T. Yamashita, H. Terai, and Z. Wang, “High performance fiber-coupled NbTiN superconducting nanowire single photon detectors with Gifford-McMahon cryocooler,” Opt. Express **21**(8), 10208 (2013). [CrossRef] [PubMed]

4. N. Gisin, S. Pironio, and N. Sangouard, “Proposal for implementing device-independent quantum key distribution based on a heralded qubit amplifier,” Phys. Rev. Lett. **105**(7), 070501 (2010). [CrossRef] [PubMed]

5. P. M. Pearle and M. Philip, “Hidden-variable example based upon data rejection,” Phys. Rev. D **2**(8), 1418–1425 (1970). [CrossRef]

6. B. G. Christensen, K. T. McCusker, J. B. Altepeter, B. Calkins, T. Gerrits, A. E. Lita, A. Miller, L. K. Shalm, Y. Zhang, Y. S. W. Nam, N. Brunner, C. C. W. Lim, N. Gisin, and P. G. Kwiat, “Detection-loophole-free test of quantum nonlocality, and applications,” Phys. Rev. Lett. **111**(13), 130406 (2013). [CrossRef] [PubMed]

7. J. Y. Cheung, C. J. Chunnilall, G. Porrovecchio, M. Smid, and E. Theocharous, “Low optical power reference detector implemented in the validation of two independent techniques for calibrating photon-counting detectors,” Opt. Express **19**(21), 20347 (2011). [CrossRef] [PubMed]

8. A. C. Parr, “The candela and photometric and radiometric measurements,” J. Res. NIST **106**(1), 151–186 (2000). [CrossRef]

*et al.*[12

12. B. Sanguinetti, T. Guerreiro, F. Monteiro, N. Gisin, and H. Zbinden, “Measuring absolute spectral radiance using an Erbium-Doped Fiber Amplifier,” Phys. Rev. A **86**(6), 062110 (2012). [CrossRef]

12. B. Sanguinetti, T. Guerreiro, F. Monteiro, N. Gisin, and H. Zbinden, “Measuring absolute spectral radiance using an Erbium-Doped Fiber Amplifier,” Phys. Rev. A **86**(6), 062110 (2012). [CrossRef]

12. B. Sanguinetti, T. Guerreiro, F. Monteiro, N. Gisin, and H. Zbinden, “Measuring absolute spectral radiance using an Erbium-Doped Fiber Amplifier,” Phys. Rev. A **86**(6), 062110 (2012). [CrossRef]

14. F. Monteiro, T. Guerreiro, B. Sanguinetti, and H. Zbinden, “Intrinsically stable light source at telecom wavelengths,” Appl. Phys. Lett. **103**(5), 051109 (2013). [CrossRef]

## 2. Experimental setup

### 2.1. Overview

_{ref}) or to the DUT. The power in the beam is attenuated in two stages,

*A*

_{0}and

*Att*, before impinging on the DUT. During the measurement PM

_{ref}monitors periodically the beam power. When calibrating PM

_{ref}, the light is also sent to the EDFA radiometer.

### 2.2. Incoherent stable source of spontaneous emission

15. J. Envall, P. Krh, and E. Ikonen, “Measurements of fibre optic power using photodiodes with and without an integrating sphere,” Metrologia **41**(4), 353 (2004). [CrossRef]

14. F. Monteiro, T. Guerreiro, B. Sanguinetti, and H. Zbinden, “Intrinsically stable light source at telecom wavelengths,” Appl. Phys. Lett. **103**(5), 051109 (2013). [CrossRef]

*et al.*[14

14. F. Monteiro, T. Guerreiro, B. Sanguinetti, and H. Zbinden, “Intrinsically stable light source at telecom wavelengths,” Appl. Phys. Lett. **103**(5), 051109 (2013). [CrossRef]

*μ*W). The relative Allan deviation of the output power shows ≤20 ppm of deviation after one day of measurement.

### 2.3. EDFA radiometer: operating principle

*k*compared to the real value. Absolute optical power measurements can be obtained with the EDFA radiometer.

*μ*exiting from an EDF depends on stimulated and spontaneous emission and is described by [12

_{out}**86**(6), 062110 (2012). [CrossRef]

*μ*is the number of input photons per mode, and

_{in}*G*is the gain of the medium. The term

*Gμ*represents the emission stimulated by the input light while the term

_{in}*G*− 1 represents the spontaneous emission. Using the formalism of Eq. (1), the measured optical powers exiting the fibre when we inject (

*ν*is the photon energy and 2/

*τ*is the number of modes per second (1/

_{c}*τ*is the number of temporal modes and the factor 2 corresponds to the number of polarisation modes).

_{c}*μ*can be derived from Eq. (2,3) [18

_{in}18. B. Sanguinetti, E. Pomarico, P. Sekatski, H. Zbinden, and N. Gisin, “Quantum cloning for absolute radiometry,” Phys. Rev. Lett. **105**, 080503 (2010). [CrossRef] [PubMed]

*μ*is an absolute measurement since

_{in}*k*. The gain

*G*(

*λ*) can always be deduced independently of

*k*using: where

*λ*dependencies introduced in Eq. (4, 5) are meant to emphasise that

*μ*is obtained for each temporal/spectral mode.

_{in}**86**(6), 062110 (2012). [CrossRef]

## 3. Absolute calibration of the reference power meter

### 3.1. EDFA radiometer characterisation

*T*

_{1},

*T*

_{2}is the transmission up to the EDF, and

*T*

_{3}is the output transmission (see Fig. 3). The pump laser is off. When connecting an optical fibre to the power meter, the reading can be affected by a systematic calibration error that can be as high as 10% [15

15. J. Envall, P. Krh, and E. Ikonen, “Measurements of fibre optic power using photodiodes with and without an integrating sphere,” Metrologia **41**(4), 353 (2004). [CrossRef]

*μ*W) therefore we perform this measurement using a commercial amplified spontaneous emission source (Trillium Photonics) as the input source. The statistical errors are reduced by repeating several times the power measurements. To correctly calibrate

*T*

_{1}we connect and disconnect repeatedly the input fibre into the input connector maximising the transmission each time in order to improve the repeatability [12

**86**(6), 062110 (2012). [CrossRef]

*T*

_{1}can be estimated from the statistics of the measured transmission factors.

*T*

_{2}, instead, is calibrated by injecting the light backwards into the radiometer and measuring the light firstly in B, then in A. All the connectors belonging to

*T*

_{2}are adjusted to maximise the transmission. In this way, T

_{2}is affected only by statistical errors which scale with the square root of the number of acquisitions. Finally, we calibrate

*T*

_{3}by injecting light from the input port and measuring the light in C and then at the output. Again, all the connectors belonging to

*T*

_{3}are adjusted in order to maximise the transmission. Also in this case the uncertainty scales with the square root of the number of acquisitions. The results are tabulated in Table 1:

### 3.2. EDFA radiometer: gain measurement

_{0}(EXFO, FVA-3150 equipped with an optical shutter). After having measured the light at the input of the radiometer always with the reference power meter (

*G*using and obtaining

*Ḡ*= 6.67(2). Note, in Eq. (6), all powers must be read using the same

*k*, so we take care to use the same power-measurement-range setting during the three measurements. For simplicity, we introduce

*Ḡ*corresponding to the average gain over the spectrum of the input light. In the actual measurement we calculate the gain for each wavelength as described in [12

**86**(6), 062110 (2012). [CrossRef]

### 3.3. Absolute measurement of the input power

*λ*. With Eq. (4) we obtain

*μ*(

_{in}*λ*) and then we convert these numbers into optical power (

_{i}*P*

_{radio}) using [12

**86**(6), 062110 (2012). [CrossRef]

*λ*is the central wavelength of each measurement point and Δ

_{i}*λ*=

*λ*

_{i+1}−

*λ*the spacing. Then we just need to sum over a wavelength range which is broader than the width of the input source. By this measurement we can calibrate PM

_{i}_{ref}. We define

*k*

_{PM}as the ratio between the power measured with the radiometer and the reading of the reference power meter, i.e.

*k*

_{PM}for a single-shot measurement. We detail the analysis in the Appendix A obtaining 0.6% of relative standard error. To test the repeatability of the measurement, we repeat the entire characterisation described in Sec.3 three times. The average between the obtained

*k*

_{PM}s yields 95.2% with a standard deviation of 0.4%. This is consistent with the uncertainty of the single-shot measurement. As a confirmation, the calibration factor of PM

_{ref}has been measured at the Federal Institute of Metrology (METAS) at 1550 nm against a transfer power meter traceable to the cryogenic radiometer. In this case, the absolute-calibration factor is measured at 100

*μ*W yielding k

*=95.3±0.7%. Considering the non-linearity coefficient between 100*

_{ABS,Metas}*μ*W and 10 nW (measured at 1541 nm with a calibrated photodiode, k

_{NL,Metas,10nW}=99.754±0.001%), k

*=95.1±0.7%. We stress that the measurement with the radiometer was a*

_{METAS}*blind*test since METAS characterised the reference power meter only after we have measured

*k*

_{PM}. The two values agree within less than one standard deviation, confirming the potential of the radiometer as a measurement device for the primary standard.

## 4. Characterisation of the measurement setup

### 4.1. Testbench: actual implementation

*λ*= 1552 with 1.67 nm of FWHM (DiCon, TF500). The beam passes through A

_{t}_{0}(EXFO, FVA-3150) and goes towards the optical switch (Lightech, LT-210) that diverts the light either to PM

_{ref}(Thorlabs, S154C) or to the DUT.

*Att*consists of two variable attenuators, A

_{1},A

_{2}(EXFO, FVA-60b). All the APC connectors have been polished with the same equipment to guarantee the same angle. The number of incoming photons per second on the detector,

*N*, is derived from the measurement of the light power made with PM

_{ref}using where

*P*

_{PM}is the power measured by PM

_{ref},

*hc/λ*= 1.28 · 10

_{t}^{−19}J is the photon energy,

*Att*=

*A*

_{1}·

*A*

_{2}and

*R*is the splitting ratio.

_{DC}### 4.2. Splitting ratio

*Att*affect the uncertainty of

*N*. After setting

*Att*to the minimum value, we characterise the splitting ratio, defined as

*(P*

_{C}*) is the power measured at the point C (point D). We measure the light firstly in the upper path then in the bottom path over an extended period (∼10 hours). We use PM*

_{D}_{ref}to monitor the light at C (see Fig. 1) and an EXFO PM1100 power meter calibrated against PM

_{ref}to monitor the light at D. Each power measurement is averaged for 1 second and repeated 10 times on each path. We obtain R

*=0.3441 (3) which corresponds to a relative standard error of 0.09%.*

_{DC}### 4.3. Attenuation stage

*P*

_{PM}=9 nW we set A

_{1}=A

_{2}= 30 dB. The remaining attenuation is introduced adjusting A

_{0}(see Table 2). To characterise the variable attenuator over 30 dB of attenuation we can not use the stable source since its output power is low, so we use the commercial source of amplified spontaneous emission, filtered at

*λ*= 1552±1.67 nm again. A

_{t}*is obtained measuring the incoming light when the attenuation is set to the minimum (*

_{i}*μ*W range) and when the attenuation is increased by 30 dB. Each power measurement is averaged over 1 s and repeated 10 times. The attenuation value is where

*k*is the linearity measurement of the reference power meter performed at METAS and

_{NLrange,i}*i*= 1, 2. The standard error is From that we can deduce the standard error on

*Att*

### 4.4. Overall stability

### 4.5. Uncertainty budget

## 5. Measurement of the detection efficiency

19. B. Korzh, N. Walenta, T. Lunghi, N. Gisin, and H. Zbinden, “Free-running InGaAs single photon detector with 1 cps dark count rate at 10% efficiency,” Appl. Phys. Lett. **104**(8), 081108 (2014). [CrossRef]

21. D. W. Scott, “On optimal and data-based histograms,” Biometrika **66**(3), 605–610 (1979). [CrossRef]

_{ref}, to estimate the detection efficiency (

*η*) of an ideal single-photon detector it would be sufficient to record, with two independent measurements, the avalanche rate sending or not photons to the detector. Then

*η*is derived using: where

*r*is the avalanche rate originated by both photons and dark counts and

_{det}*r*is the avalanche rate originated only by dark counts.

_{dc}*η*is underestimated. On the other hand, the afterpulses increase the detection rate bringing an overestimation of

*η*. The impact of the hold-off times on the detection rate can be corrected introducing a duty-cycle corresponding to the time when the detector is on. To correct for the afterpulsing we consider that after any detection an afterpulse is generated with probability p

*. These corrections are introduced modifying*

_{ap}*r*and

_{det}*r*with where

_{dc}*τ*is the hold-off time and

**measured**detection rate (dark-count rate). We can now plug Eq. (14, 15) into Eq. (13) to get [13

13. T. Lunghi, C. Barreiro, O. Guinnard, R. Houlmann, X. Jiang, M. A. Itzler, and H. Zbinden, “Free-running single-photon detection based on a negative feedback InGaAs APD,” J. Mod. Opt. **59**(17), 1481–1488 (2012). [CrossRef]

*η*,

*τ*and p

*for different hold-off times. This would allow to calculate*

_{ap}*N*in any measurement conditions simply by measuring

*μ*s) and different nominal efficiencies (15% and 20%). As one may notice, it can happen that an afterpulse is originated by another afterpulse. To consider this, p

*should correspond to the total afterpulsing probability and include also higher-order afterpulses p*

_{ap}*can be measured reconstructing the temporal evolution of the avalanche rate given that an avalanche has occurred at time zero,*

_{ap}*P*(

_{c}*t*| 0). For very long delays there will be no correlation between two events and the probability that a pulse occurs will be determined only by the mean count rate,

*n*. We calculate p

*using We use two independent measurement procedures (see Appendix B):*

_{ap}- The first method, described in [22], records the time interval between successive avalanches. This is the easiest measurement procedure and requires only a Time To Digital Converter device to register the time-stamp.
- The second method, described in [13], uses a pulsed laser to trigger the first avalanche. The temporal evolution is recorded with an FPGA board which controls the setup to record data only when the detector is in a well-defined condition. This method has the advantage of precise control of the detector but it requires a dedicated setup.
13. T. Lunghi, C. Barreiro, O. Guinnard, R. Houlmann, X. Jiang, M. A. Itzler, and H. Zbinden, “Free-running single-photon detection based on a negative feedback InGaAs APD,” J. Mod. Opt.

**59**(17), 1481–1488 (2012). [CrossRef]

### 5.1. Results

*τ*≤ 100 ns) and we pay attention not to saturate the detector (the detector is inactive less than 10% the time). The afterpulse correction is more delicate as it is illustrated in Table 5. The table reports the efficiencies with different hold-off times before and after correcting for the afterpulsing (for p

*obtained by the 2 methods).*

_{ap}*is measured with the second method. This indicates that the values obtained with this method are more appropriate. Note that, differences above 0.23% are significant according to Table 6. However for smaller efficiencies, P*

_{ap}*obtained by the simpler first method can give still satisfactory results, in particular for longer hold-off times. We expect the values for longer hold-off times being a better estimate of the real detection efficiency. The uncertainty of the detection efficiency introduced by imperfection of the afterpulses compensation depends on the settings. For 20% efficiency and 20*

_{ap}*μ*s of hold-off time, we assume conservatively the introduced uncertainty to be smaller than 0.4%, which is the difference between the values obtained with 20

*μ*s and 10

*μ*s, respectively. Finally, we can provide the total uncertainty budget for the detection efficiency characterisation, see Table 6 for an overview.

## 6. Conclusions

## A. Uncertainty analysis of the calibration factor

*P*can be deduced from Eq. (8) using: The calibration factor is where

_{radio}_{PM}. Table 7 shows in details each contribution to the uncertainty of the calibration factor.

## B. Afterpulsing characterisation

**subsequent**avalanches [24

24. S. Cova, A. Lacaita, and G. Ripamonti, “Trapping phenomena in avalanche photodiodes on nanosecond scale,” IEEE Electron. Dev. Lett. **12**(12), 685–687 (1991). [CrossRef]

**any**pairs of avalanches with no assumption on what is happening between them. The difference between the two distributions is mainly due to higher order afterpulsing. We implemented two independent methods able to reconstruct the avalanche rate at time t conditioned on having an avalanche at time zero,

*P*(

_{c}*t*| 0).

**59**(17), 1481–1488 (2012). [CrossRef]

*μ*s. Then an FPGA triggers a laser pulse which is sent to the detector. When the pulse is detected, the FPGA records all the avalanches occurring in the next 75

*μ*s, building

*h*[

*i*Δ

*T*]. This time,

*N*corresponds to the total number of avalanches originated by the laser pulses.

_{Tot}*p*, obtained with these methods are reported in Table 8 for different settings of efficiency and hold-off times (HO). For the first method we also estimate the repeatability of the measurement doing the measurement 4 times. The two methods produce significantly different results. Since the measurement conditions can be well controlled for the second method, we believe that this method gives better results. This hypothesis is reinforced by the analysis of the results in chapter 5.1. However, more work will be necessary to understand the systematic difference between the two methods. It has to be noted that these discrepancies are small (for p

_{ap}*<<1) and, and finally not limiting the precision of the efficieny measurement.*

_{ap}## Acknowledgments

## References and links

1. | A. Restelli, J. C. Bienfang, and A. L. Migdall, “Single-photon detection efficiency up to 50% at 1310nm with an InGaAs/InP avalanche diode gated at 1.25 GHz,” Appl. Phys. Lett. |

2. | F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. P. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics |

3. | S. Miki, T. Yamashita, H. Terai, and Z. Wang, “High performance fiber-coupled NbTiN superconducting nanowire single photon detectors with Gifford-McMahon cryocooler,” Opt. Express |

4. | N. Gisin, S. Pironio, and N. Sangouard, “Proposal for implementing device-independent quantum key distribution based on a heralded qubit amplifier,” Phys. Rev. Lett. |

5. | P. M. Pearle and M. Philip, “Hidden-variable example based upon data rejection,” Phys. Rev. D |

6. | B. G. Christensen, K. T. McCusker, J. B. Altepeter, B. Calkins, T. Gerrits, A. E. Lita, A. Miller, L. K. Shalm, Y. Zhang, Y. S. W. Nam, N. Brunner, C. C. W. Lim, N. Gisin, and P. G. Kwiat, “Detection-loophole-free test of quantum nonlocality, and applications,” Phys. Rev. Lett. |

7. | J. Y. Cheung, C. J. Chunnilall, G. Porrovecchio, M. Smid, and E. Theocharous, “Low optical power reference detector implemented in the validation of two independent techniques for calibrating photon-counting detectors,” Opt. Express |

8. | A. C. Parr, “The candela and photometric and radiometric measurements,” J. Res. NIST |

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

10. | S. V. Polyakov and A. L. Migdall, “Quantum radiometry,” J. Mod. Opt. |

11. | M. Ware and A. L. Migdall, “Single-photon detector characterization using correlated photons: The march from feasibility to metrology,” J. Mod. Opt. |

12. | B. Sanguinetti, T. Guerreiro, F. Monteiro, N. Gisin, and H. Zbinden, “Measuring absolute spectral radiance using an Erbium-Doped Fiber Amplifier,” Phys. Rev. A |

13. | T. Lunghi, C. Barreiro, O. Guinnard, R. Houlmann, X. Jiang, M. A. Itzler, and H. Zbinden, “Free-running single-photon detection based on a negative feedback InGaAs APD,” J. Mod. Opt. |

14. | F. Monteiro, T. Guerreiro, B. Sanguinetti, and H. Zbinden, “Intrinsically stable light source at telecom wavelengths,” Appl. Phys. Lett. |

15. | J. Envall, P. Krh, and E. Ikonen, “Measurements of fibre optic power using photodiodes with and without an integrating sphere,” Metrologia |

16. | |

17. | see e.g. EXFO Tunable laser source: IQS/FLS 2600. |

18. | B. Sanguinetti, E. Pomarico, P. Sekatski, H. Zbinden, and N. Gisin, “Quantum cloning for absolute radiometry,” Phys. Rev. Lett. |

19. | B. Korzh, N. Walenta, T. Lunghi, N. Gisin, and H. Zbinden, “Free-running InGaAs single photon detector with 1 cps dark count rate at 10% efficiency,” Appl. Phys. Lett. |

20. | I. Vayshenker, S. Yang, X. Li, T. R. Scott, and C. L. Cromer, “Optical fiber power meter nonlinearity calibrations at NIST,” NIST special publications250–256 (2000). |

21. | D. W. Scott, “On optimal and data-based histograms,” Biometrika |

22. | J. W. Kindt, |

23. | 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. |

24. | S. Cova, A. Lacaita, and G. Ripamonti, “Trapping phenomena in avalanche photodiodes on nanosecond scale,” IEEE Electron. Dev. Lett. |

**OCIS Codes**

(120.1880) Instrumentation, measurement, and metrology : Detection

(120.5630) Instrumentation, measurement, and metrology : Radiometry

**ToC Category:**

Detectors

**History**

Original Manuscript: April 14, 2014

Revised Manuscript: July 7, 2014

Manuscript Accepted: July 8, 2014

Published: July 18, 2014

**Citation**

Tommaso Lunghi, Boris Korzh, Bruno Sanguinetti, and Hugo Zbinden, "Absolute calibration of fiber-coupled single-photon detector," Opt. Express **22**, 18078-18092 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-15-18078

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### References

- A. Restelli, J. C. Bienfang, and A. L. Migdall, “Single-photon detection efficiency up to 50% at 1310nm with an InGaAs/InP avalanche diode gated at 1.25 GHz,” Appl. Phys. Lett.102(14), 141104 (2013). [CrossRef]
- F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. P. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics7(3), 210–214 (2013). [CrossRef]
- S. Miki, T. Yamashita, H. Terai, and Z. Wang, “High performance fiber-coupled NbTiN superconducting nanowire single photon detectors with Gifford-McMahon cryocooler,” Opt. Express21(8), 10208 (2013). [CrossRef] [PubMed]
- N. Gisin, S. Pironio, and N. Sangouard, “Proposal for implementing device-independent quantum key distribution based on a heralded qubit amplifier,” Phys. Rev. Lett.105(7), 070501 (2010). [CrossRef] [PubMed]
- P. M. Pearle and M. Philip, “Hidden-variable example based upon data rejection,” Phys. Rev. D2(8), 1418–1425 (1970). [CrossRef]
- B. G. Christensen, K. T. McCusker, J. B. Altepeter, B. Calkins, T. Gerrits, A. E. Lita, A. Miller, L. K. Shalm, Y. Zhang, Y. S. W. Nam, N. Brunner, C. C. W. Lim, N. Gisin, and P. G. Kwiat, “Detection-loophole-free test of quantum nonlocality, and applications,” Phys. Rev. Lett.111(13), 130406 (2013). [CrossRef] [PubMed]
- J. Y. Cheung, C. J. Chunnilall, G. Porrovecchio, M. Smid, and E. Theocharous, “Low optical power reference detector implemented in the validation of two independent techniques for calibrating photon-counting detectors,” Opt. Express19(21), 20347 (2011). [CrossRef] [PubMed]
- A. C. Parr, “The candela and photometric and radiometric measurements,” J. Res. NIST106(1), 151–186 (2000). [CrossRef]
- S. V. Polyakov and A. L. Migdall, “High accuracy verification of a correlated-photon- based method for determining photoncounting detection efficiency,” Opt. Express15(4), 1390–1407 (2007). [CrossRef] [PubMed]
- S. V. Polyakov and A. L. Migdall, “Quantum radiometry,” J. Mod. Opt.569, 1045–1052 (2009). [CrossRef]
- M. Ware and A. L. Migdall, “Single-photon detector characterization using correlated photons: The march from feasibility to metrology,” J. Mod. Opt.51(9), 1549–1557 (2004). [CrossRef]
- B. Sanguinetti, T. Guerreiro, F. Monteiro, N. Gisin, and H. Zbinden, “Measuring absolute spectral radiance using an Erbium-Doped Fiber Amplifier,” Phys. Rev. A86(6), 062110 (2012). [CrossRef]
- T. Lunghi, C. Barreiro, O. Guinnard, R. Houlmann, X. Jiang, M. A. Itzler, and H. Zbinden, “Free-running single-photon detection based on a negative feedback InGaAs APD,” J. Mod. Opt.59(17), 1481–1488 (2012). [CrossRef]
- F. Monteiro, T. Guerreiro, B. Sanguinetti, and H. Zbinden, “Intrinsically stable light source at telecom wavelengths,” Appl. Phys. Lett.103(5), 051109 (2013). [CrossRef]
- J. Envall, P. Krh, and E. Ikonen, “Measurements of fibre optic power using photodiodes with and without an integrating sphere,” Metrologia41(4), 353 (2004). [CrossRef]
- http://refractiveindex.info .
- see e.g. EXFO Tunable laser source: IQS/FLS 2600.
- B. Sanguinetti, E. Pomarico, P. Sekatski, H. Zbinden, and N. Gisin, “Quantum cloning for absolute radiometry,” Phys. Rev. Lett.105, 080503 (2010). [CrossRef] [PubMed]
- B. Korzh, N. Walenta, T. Lunghi, N. Gisin, and H. Zbinden, “Free-running InGaAs single photon detector with 1 cps dark count rate at 10% efficiency,” Appl. Phys. Lett.104(8), 081108 (2014). [CrossRef]
- I. Vayshenker, S. Yang, X. Li, T. R. Scott, and C. L. Cromer, “Optical fiber power meter nonlinearity calibrations at NIST,” NIST special publications250–256 (2000).
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