In recent years several ways to radiometrically calibrate optical fiber-coupled detectors have been developed. However, fiber-coupled calibration methods for single photon detectors have not been compared by national metrology institutes in order to validate their equivalence or traceability to the international systems of units yet.. Here, we present the comparison of radiometric calibration methods traceable to a NIST cryogenic radiometer at the ‘few-photon’ level. The calibration methods are based on metrology grade optical power meters. The expanded (k = 2) relative standard uncertainties of the calibration methods for the detection efficiency are of the order of 0.5%. However, the results changed relatively by 10% with a different set of optical fibers and mating connectors. These results stress the importance of fiber-core dimensions and fiber-connector repeatability.
© 2017 Optical Society of America
The measurements described here are the foundation of the first bilateral comparison of the radiometric scales of National Institute of Standards and Technology (NIST, Boulder, USA) and Physikalisch-Technische Bundesanstalt (PTB, Berlin, Germany) at pW radiant power. The evaluation of the calibration methods as they will be used for customer calibrations in terms of repeatability, consistency and accuracy are crucial for the development of ’customer-available’ quantum radiometry. Thus, the main goal of this work was to show which uncertainties can be achieved under the typical conditions of a customer calibration service.
Methods to calibrate single photon detectors traceable to the International System of Units have been described before [1–8]. In recent years the accuracy for the determination of the detection efficiency of single photon detectors has increased and, hence, the achievable relative standard uncertainties were improved. For free-space detectors uncertainties as low as 0.16 % have been reported [5, 8]. Recent publications dealt with the influence of the photon statistics on the calibration result [5, 9] and introduced new methods based on fundamental quantum mechanical laws and issues that arise from the traceability of optical fiber-coupled detectors to national standards that are not fiber-coupled have been discussed [6, 10]. Here, in addition to these issues, the influence of the employed fibers on the calibration result is discussed. During the calibrations described here a strong influence of the applied fiber on the calibration was observed. During the measurements a fiber cable that connected the SNSPD to the calibration setup got damaged and was replaced yielding different measured detection efficiencies. Therefore, the influence of the fiber, i.e. a possible change of connector losses, on the measured detection efficiency will be briefly described. In classical radiometry, optical fiber-based calibrations usually take into account the influence of the optical fiber . However, publications related to radiometric calibrations in ‘few-photon’ and quantum radiometry don’t address optical fibers and mating connectors as sources of uncertainty.
Traceability of the detection efficiency of optical fiber-coupled single photon detectors is a prerequisite for applications such as remote sensing and quantum communications. However, achieving this aim is difficult due to the very different optical powers suitable for classical radiation detectors on one hand and single photon detectors on the other hand. In order to further improve the traceability, an experimental validation of the existing calibration methods is mandatory. Especially the emerging field of the so-called “quantum radiometry” , providing alternative metrological techniques to increase the accuracy of the detection of electromagnetic radiation, gains impact beyond fundamental research work if the traceability to the conventional radiometry, i.e. the cryogenic radiometer, is validated.
The experimental validation of the calibration methods traceable to cryogenic radiometers is based on a two-step approach. In the first step, which is described here, two calibration methods used at NIST are validated using a high-speed superconducting nano-wire single photon detector (SNSPD) operated by PTB. In the second step, the NIST results will be compared with calibrations obtained at the Metrology Light Source, the dedicated electron storage ring of PTB , providing an alternative calibration chain. In both steps, the radiant power that is coming out of the fiber rather than the radiant power inside the fiber is used for the radiometric calibration of the SNSPD to facilitate the traceability to the SI.
Two NIST calibration methods for optical fiber-coupled single photon detectors at telecom wavelengths are based on calibrated ‘metrology-grade’ optical power meters. One method uses a set of calibrated attenuators to set the appropriate photon flux to measure the detection efficiency of the device under test (DUT) . The other method, often referred to as direct-substitution method, is based on a power meter that has been well characterized in terms of its linearity [11, 13] and allows measuring the reference detector and the DUT at identical radiant powers, which are, however, limited to the range above 0.5 pW. Thus, a high-speed single photon detector is necessary to compare the results of both methods in the power range at or above 0.5 pW in order to avoid saturating the DUT. The direct substitution method cannot be used to calibrate the high efficiency SNSPDs developed at NIST because the count rate of these SNSPDs would be in the saturation range because of the high photon flux and the long recovery times.
One of the main aims of this work was to define a procedure to deal with the uncertainties that occur during the calibration. One way is to compile an uncertainty budget and to estimate the type A and B uncertainties that come from, e.g., the polarization controller, the fiber connections and so on. Here, the uncertainty budget of the direct-substitution method has been obtained by treating the setup as a “black box”. This system is described with the known systematic type B uncertainties of the power meter and, additionally, a set of random effects that affect the calibration result .
1.1. Description of the artefact
In this work, commercially available niobium nitride (NbN)-SNSPDs  have been used in order to mimic customer calibration conditions. The detector system has not been spliced to the calibration setup to estimate the influence of the repeatability of the fiber connections. SNSPDs can achieve high quantum efficiency, and very low dark-count rates. Furthermore, photon-number-resolving capabilities can be achieved by using interleaved or multiple meanders. These specifications are a prerequisite to enable a number of applications in the field of quantum information, photon source and detector calibration as well to test the hypothesis that nature is governed by local realism [16, 17]. The most important feature of the NbN-SNSPDs used in these experiments is the maximum count-rate that can reach values above 100 Mcounts/s before saturating the detector, i.e. these detectors can be exposed to radiant powers well above 10 pW making them suitable artefacts for the comparison of the different calibration techniques. The SNSPD is installed in a cryo-insert that is placed in a liquid helium storage unit. The cryo-insert is capable of cooling the SNSPD to 1.70(5) K by pumping on the liquid helium in the storage Dewar. The detector was biased with DC current through a bias-T (or bias-tee) at room temperature. The pulses from the SNSPD were amplified after the bias-T using 2 amplifiers with a nominal gain of 28 dB and a 2 GHz bandwidth. The performance of the detector is evaluated at a bias current of 19.445(5) µA which is 90 % of the SNSPD switching current, where it switches to the normal state. The switching current has been determined in the absence of optical radiation. The detector is equipped with an FC/PC optical fiber connector and uses a standard telecom single-mode fiber to couple the radiation onto the SNSPD. The detection efficiency of the NbN-SNSPD shows a strong polarization dependence and can change by more than 50 % for radiation incident parallel or perpendicular to the meander wires [18, 19]. Thus, the state of polarization was adjusted in order to achieve the maximum count rate.
The measurements with the calibrated attenuator method and the direct substitution method were performed using a fiber-pigtailed laser diode source (without coherence control) at a wavelength of 1547 nm. Additional measurements employing a cw-laser at 1302 nm were performed using the direct substitution method only. The power meters were calibrated against the NIST cryogenic radiometer and the linearity was measured down to the pW radiant power range . Standard telecom optical single-mode fibers were used in the measurements. Within approximately 3 months we performed several hundred measurements using both methods. We found that the detection efficiency of the SNSPD, that was used during the calibration campaign, was stable and showed no signs of thermal instability, that would affect the detection efficiency, or other degradations.
2.1. Calibrated attenuators method
This method (see Fig. 1) uses a calibrated optical power meter to determine the attenuation factors of a set of attenuators. Here, the calibrated optical power meter is used to absolutely measure the radiant power coming from the polarizer and is then used relatively to determine the attenuation of each of the attenuators in turn. The laser is connected to a polarization controller. The polarization controller uses the feedback from the SNSPD to be calibrated to set the ideal polarization in order to get the maximum detection efficiency of the SNSPD. To achieve this the polarization controller scans all possible polarization states to determine the elliptical state that maximizes the SNSPD response. The polarizer is connected to a set of 3 variable attenuators that are used to set the appropriate photon flux that can be varied over up to nine orders of magnitude. The range of each attenuator is 30 dB. An optical switch is used to guide the photon flux either to the calibrated power meter or the SNSPD to be calibrated. The setup is all fiber and employs a 1 mW laser as the radiation source. The calibration routine was:
- First step: The polarization state is optimized using an automated algorithm in order to maximize the SNSPD count rate. After the measurements were finished we remeasured the ideal polarization state. If there was a noticeable change this measurement was repeated.
- Second step: Measurement of the switching ratio of the optical switch using a second InGaAs power meter and the reference InGaAs power meter.
- Third step: The reference optical power meter is used to calibrate the attenuation ratios of the variable attenuators and to thereby absolutely determine the power coming out of the polarization controller and the attenuators.
- Fourth step: The SNSPD is irradiated with the set and stabilized photon flux and the count rate is measured.
- Fifth step: From the known photon flux and the measured count rate of the SNSPD the system detection efficiency is calculated.
The uncertainties associated with the reference detector are stated in Table 1. The combined relative standard uncertainty of the detection efficiency was modeled assuming a gaussion distribution of the measured detection efficiencies. A detailed description of the calibration method using spliced fibers can be found in . The calibration routine used here does not account for the optical fiber connection to the device under test. Hence, the efficiency of the fiber connection has to be taken into account separately. Here, this has been done by taking several measurement runs that include a reconnection of the optical fibers.
2.2. Direct substitution method
This method exploits the large dynamic range of the optical power meter that is used in the measurements and that has been calibrated traceable to a cryogenic radiometer at NIST. Here, the SNSPD and the calibrated power meter are irradiated with the identical spectral radiant power (see Fig. 3), i.e. the count rate of the SNSPD and the radiant power measured with the reference are directly compared. The uncertainties associated with the reference detector used for the direct substitution measurements are stated in Table 2. The signal to noise ratio of the power meter increases with decreasing radiant power and the lower limit of the detectable radiant power is 0.5 pW, which is approximately 4 · 106 photons per second at 1547 nm. A set of monitor detectors at different powers is used to correct for any changes of the radiant power during the measurements. The calibration routine was:
- First step: The radiant power was set to a level compatible with the reference power meter and the SNSPD. During the measurements the radiant power was sequentially reduced by 3 dB by means of the variable attenuator starting at approximately 12 pW down to approximately 0.5 pW. For each radiant power the calibration sequence was restarted beginning at step 2.
- Second step: The optical fiber cable was connected to the SNSPD. Then the polarizer was used to determine the proper polarization state in order to achieve the maximum count rate of the SNSPD. At 1547 nm an automated algorithm was used to determine the ideal state of polarization. After the measurements were finished we remeasured the ideal polarization state. If there was a noticeable change this measurement was repeated. At 1302 nm the polarization was adjusted by manual control of the polarization using iterative steps in order to obtain the maximum count rate.
- Third step: The fiber connector was cleaned and connected to the reference power meter and the average radiant power over a period of 30 seconds was recorded.
- Fourth step: The fiber connector was cleaned again and connected to the SNSPD. Then the average count rate of the SNSPD within 30 seconds is measured. The steps 3 to 4 are repeated at least six times at each radiant power.
- Fifth step: After the set of measurements has been recorded the polarization state ideal for the SNSPD was measured again to see if a possibly occurring drift of the measured detection efficiency could be explained by a change of the polarization state.
3. Results and discussion
3.1. Calibrated attenuator method
The averaged results of measurement runs on 3 subsequent days are shown in Fig. 4. The runs were performed at different photon fluxes ranging from approximately 6 105 photons per second up to about 7.4 · 107 photons per second. There was no systematic dependence of the detection efficiency on the photon flux (see Fig. 5) observed. However, the blocking loss for the NbN-SNSPD has to be taken into account for count rates above 1 Mcounts/s (see Fig. 2). Additionally, possible double triggering of a single SNSPD pulse was investigated by changing the threshold voltage of the photon counter. No double triggering was observed (data not shown). The bias current was swept from 10 µA up to the switching current of the SNSPD. The results plotted in Fig. 4 show an agreement of the results of the first two days (darker green and green markers) within 1 %. The measured detection efficiency obtained on the third day (red markers) is 2 % higher than the values of the first two days. This can be easily explained by a reconnection of the optical fiber cable yielding a different coupling efficiency of the SNSPD to the calibration setup. The fiber was disconnected to measure the switching ratio of the optical switch used in this setup. However, this coincides with an increased detection efficiency of the SNSPD that was noticed during the measurements with the direct substitution method (see below). The overall detection efficiency taking into account the results obtained during the three calibration days is ηca = 13.50(±0.07) % (k = 2) at a bias current of 19.445(5) µA.
3.2. Direct substitution method
The results obtained with this method can be separated into two groups depending on the fiber and mating connector used during the calibration. The detection efficiency of the SNSPD changed during the measurements after the optical fiber cable and the mating connector that were used to connect the SNSPD to the laser source had to be replaced. We replaced the optical fiber with one of the same type, SMF-28e, and used an identical but different mating connector. The SNSPD detection efficiency at 1302 nm plotted over the photon flux range is shown in Fig. 6. Figure 7 shows the measured detection efficiency at 1547 nm at a bias current of 19.445 µA plotted over the photon flux. The measurements that were finished before the fiber and mating connector were changed are plotted using red (circular-shaped) markers. The measurements performed after the change are plotted using green (square-shaped) markers. At both wavelengths, the measured detection efficiency changed by approximately 10 % after the conversion. Before the conversion the measured detection efficiency was at 1302 nm and at 1547 nm. After the conversion the measured detection efficiency of the SNSPD increased and reached values of at 1302 nm and at 1547 nm. This behavior ± can be explained by a change of the fiber connector losses. The combined relative standard type B uncertainty of the reference power meter including linearity and power calibration was 0.18 % at 1302 nm and 0.19 % at 1547 nm (see Table 2).
The direct substitution detection efficiency measurements qi were modeled by a random effects modelFig. 8 reveals an additional heterogeneity which is not explained by the uncertainties indicated by the error bars. The term λi in Eq. (3) models these additional fluctuations due to switching of the fiber connections and the λi are assumed to be Gaussian distributed as with unknown variance . Each of the two data sets of the direct substitution measurements recorded at 1547 nm (see Fig. 7) before and after changing the fiber and the mate connector were analyzed separately in terms of the statistical model [Eq. (3)] by applying a Bayesian inference approach . In the analysis, the parameters q and are treated as unknowns and the inference aims at determining their posterior distribution given the detection efficiency measurements qi and the associated uncertainties . As described in , when employing a non-informative reference prior the posterior distribution can be calculated by a numerical integration. Figure 8 shows the resulting posterior distributions obtained for the detection efficiency for the two groups (red and green curves). In addition, a Gaussian distribution representing the mean of the calibrated attenuator measurements (ca) is plotted in Fig. 8 (black curve).
The results obtained during these measurements demonstrate that the expanded relative calibration uncertainty of the detection efficiency of single photon detectors, is very good at 0.5 % (see Table 3). However, the absolute calibration is strongly influenced by fiber coupling issues, which introduce an additional systematic uncertainty of approximately 10 % in agreement with the specification of the coupling losses of FC-fiber connections of 0.5 dB. This can be explained by a change of the coupling efficiency between the last fiber of the calibration setup to the DUT fiber caused by 2.5 µm displacement of the fiber cores. The impact of different fiber core diameters and fiber core displacements is shown in Figs. 9 and 10. For spliced setups this source of uncertainty does not occur and, hence, the relative combined standard uncertainties of the two calibration methods are stated without this source of uncertainty (Uex) for better comparison with spliced calibrations.
In conclusion, we are forced to question how fiber-coupled single photon detectors can be calibrated as a customer service with high accuracy, using standard fibers and mating fiber connectors. The current optical FC-connectors specify insertion losses of approximately 0.5 dB. To our experience there are high quality connectors but no metrology grade fiber connectors available. A possible way to reduce the fiber displacement would be to use a fiber launch system with auto-alignment functionality. In this way good repeatability of the fiber connection could be achieved by minimizing the fiber core displacement. A second way could be to introduce a set of standardized, well characterized, low tolerance optical fibers and connectors.
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