Document [original]

Research Article Vol. 29, No. 15 / 19 July 2021 / Optics Express 23500

Absolute calibration of a single-photon

avalanche detector using a bright triggered

single-photon source based on an InGaAs

quantum dot

HRISTINA GEORGIEVA,1,* MARCO LÓPEZ,1HELMUTH HOFER,1

NIKLAS KANOLD,2ARSENTY KAGANSKIY,2SVEN RODT,2

STEPHAN REITZENSTEIN,2AND STEFAN KÜCK1,3

1Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany

Institut für Festkörperphysik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany

3Laboratory for Emerging Nanometrology, Langer Kamp 6, 38106 Braunschweig, Germany

*hristina.georgiev[email protected]

Abstract:

We apply an InGaAs quantum dot based single-photon source for the absolute

detection efficiency calibration of a silicon single-photon avalanche diode operating in Geiger

mode. The single-photon source delivers up to (2.55

0.02)

photons per second inside a

multimode fiber at the wavelength of 929.8 nm for above-band pulsed excitation with a repetition

rate of 80 MHz. The purity of the single-photon emission, expressed by the value of the 2

order correlation function g

(2)

(

τ=

0), is between 0.14 and 0.24 depending on the excitation power

applied to the quantum dot. The single-photon flux is sufficient to be measured with an analog

low-noise reference detector, which is traceable to the national standard for optical radiant flux.

The measured detection efficiency using the single-photon source remains constant within the

measurement uncertainty for different photon fluxes. The corresponding weighted mean thus

amounts to 0.3263 with a standard uncertainty of 0.0022.

1. Introduction

Single-photon sources (SPS) have the potential to become a new type of standard source for

optical radiation [1], as there are so far - in the classical regime - the blackbody radiator and the

synchrotron radiation source. The output power Pof an ideal SPS, emitting exactly one photon

per excitation pulse, is in fact simply given by the formula P

fhc/

, where fis the repetition rate

of the excitation laser, his the Planck constant, cis the speed of light, and

is the wavelength of

the emitted radiation. Although it is still difficult to realize an SPS with ideal photon-extraction

and collection efficiency, the advantage of high single-photon purity can be directly exploited for

the calibration of single-photon avalanche detectors (SPAD), whose detection efficiency (DE) is

strongly influenced by the photon statistics. In this way, the otherwise necessary correction of DE

when using laser light would be eliminated, which can lead to a reduced calibration uncertainty

and a simplified model of the detector response.

A narrow spectral emission bandwidth is an essential prerequisite for the successful calibration

of optical radiation detectors, whose DE depends on the wavelength. One possible approach is to

implement an SPS with broad spectral emission and then select a specific wavelength through

spectral filters. For example, a nitrogen-vacancy center in diamond was fully characterized in

a metrological sense [2]. Its emission covers the visible spectral range roughly from 650 nm

to 750 nm (half maximum values taken) with a maximum photon flux of 2.6

×105

photons/s

and a single-photon emission purity between 0.1 and 0.23. A relative SPAD calibration through

filtering of the emission of a nitrogen-vacancy center with a 19 nm wide bandpass filter has been

#430680 https://doi.org/10.1364/OE.430680

Research Article Vol. 29, No. 15 / 19 July 2021 / Optics Express 23501

demonstrated in Ref. [3]. Another approach consists in using an SPS with a narrow linewidth

emission, where different types of emitters cover different emission wavelengths. A promising

candidate for this purpose is a dibenzoterrylene molecule in an anthracene nanocrystal (DBT:Ac),

which emits narrowband photons with strong anti-bunching in the photon statistics, when cooled

to cryogenic temperatures [4–7]. A molecule based SPS has been recently applied in quantum

radiometry [4]. This SPS delivered up to 1.4

photons/s at the fiber-coupled detector, while

maintaining high purity of the single-photon emission (g

(2)

(0)

0.08

0.01) at maximum photon

flux. However, due to the continuous wave operation of the source, saturation effects caused by

the SPAD dead time were observed, resulting in a count rate dependent DE.

Semiconductor materials are very well suited for the realization of a standard photon source

featuring triggered operation, robustness, durability and photostability. Moreover, the emission

wavelength of mature InGaAs quantum dots (QDs) in the near infrared enables the calibration of

both Si- and InGaAs/InP-SPADs. Highly sophisticated fabrication processes allow the design

of structures surrounding the emitting QD, so that high extraction efficiencies and thus high

photon fluxes can be obtained [8,9]. In [10], an SPS based on an InGaAs QD has been used

for the relative calibration of two Si-SPAD detectors. The source provided photon fluxes up to

3.7

photons/s at the position of the SPAD under pulsed excitation with a repetition rate of

80 MHz. In this work, we have significantly improved the efficiency of our setup and demonstrate

an absolute calibration of a Si-SPAD with an InGaAs QD as a light source. This calibration is

a proof of principle for the use of pulsed single-photon emission for a direct comparison of a

SPAD with a commercially available low-noise analog detector, which is traceable to the primary

standard for optical power, the cryogenic radiometer. With this, we have closed the traceability

gap between classical and quantum radiometry.

2. Single-photon source

The setup for the generation of single-photon emission is similar to the one used in [10]. It

consists of a home-made confocal microscope with implemented spectral filtering (see Fig. 1).

For non-resonant excitation of the QD, a diode laser (PicoQuant, LDH-D-C-850) is used, which

is operated in pulsed mode with a repetition rate of 80 MHz and a pulse width of 0.5 ns (full

width). Its relatively broadband emission is spectrally filtered with a bandpass filter at 850 nm

with a 10 nm wide transmission window. The laser beam is reflected from a dichroic beam

splitter (Semrock, 875 nm edge Bright-line) and focused on the sample, which is placed in a

cryostat keeping a constant temperature of about 10 K. The QD fluorescence is collected using

a high transmission objective (Olympus, LCPLN50XIR, NA

0.65), which has an aberration

correction for the 0.2 mm thick cryostat window. The fluorescence light passes through two

longpass and two bandpass filters and is then coupled by a high transmission objective (Olympus,

LMPLN10XIR) into a multimode optical fiber (62.5

m core diameter) that serves as a pinhole

for confocal imaging. The fiber can be connected to either a spectrometer, a SPAD detector or a

fiber based Hanbury Brown and Twiss (HBT) interferometer to analyze spectral properties, to

measure photon flux, and to determine the single-photon purity, respectively. Compared to the

setup described in [10], we have doubled the overall setup transmission (approx. 49%) by the

use of high transmission objectives. The applied aberration correction and improved vibration

damping further enhance the overall setup efficiency.

The sample structure, shown in Fig. 2(a), is grown by metal-organic chemical vapor deposition.

First, 300 nm GaAs are deposited on a (001) GaAs substrate. Next, 23 pairs of AlGaAs and

GaAs layers, with thicknesses of 78 nm and 67 nm, respectively, are forming a distributed

Bragg reflector, which reflects the light emitted into the lower hemisphere. A 67 nm thick

spacer is grown on top, followed by a thin layer of self-assembled InGaAs QDs and a capping

layer with a thickness of 420 nm. Suitable QDs at cryogenic temperatures are selected by

cathodoluminescence spectroscopy, whereas electron-beam lithography (EBL) is used to form

Research Article Vol. 29, No. 15 / 19 July 2021 / Optics Express 23502

Fig. 1.

Self-made confocal setup for the optical characterization of an InGaAs QD emitting

at around 930 nm. The sample is in a cryostat. We perform an above-band optical excitation

at 850 nm. The excitation power is adjusted with a variable neutral density filter (NDF),

whereas the bandwidth of the excitation spectrum is determined by a laser line filter (LLF).

The fluorescent emission from the QD is collected by objective 3. It is then spectrally filtered

with the help of two bandpass filters (BPF). The laser beam is blocked by two longpass

filters (LPF) with a cut-off wavelength of 900 nm. An optical fiber, which serves as a

pinhole, can be connected to different devices to measure the spectrum, the photon flux or

the single-photon purity.

micromesas at the pre-selected positions. These mesas have a cylindrical shape with a radius

between 600 nm and 640 nm and a height of 800 nm. For further information on the used in-situ

EBL nanotechnology process we refer to Ref. [11].

Fig. 2.

(a) Schematic of the sample structure. (b) Micro-photoluminescence scan of the

sample emission for emission wavelengths above 900 nm. The

PL intensity is significantly

higher for QDs integrated into micromesas by in-situ EBL, which nicely illustrates the

enhancement of photon extraction by these nanophotonic structures.

A micro-photoluminescence (

PL) scan of the sample with a color-coded emission intensity

is shown in Fig. 2(b). Only emission above 900 nm is detected due to the longpass filtering

of the fluorescent light that reaches the SPAD detector (Perkin Elmer, SPCM-AQRH-13-FC).

The QD layer has been etched away in the rectangular areas, leaving only single QDs inside the

micromesas. One of them (indicated in Fig. 2(b)) was selected for further measurements, because

it fulfills simultaneously the criteria of having high brightness and good single-photon purity.

The spectrum of the selected QD can be seen in Fig. 3(a). We use the same principle for

filtering out one single emission line as in [10], i.e. implementing two identical narrow bandpass

filters (Alluxa, 935.0–0.45 OD5), based on thin film interference, with a 0.5 nm wide transmission

Research Article Vol. 29, No. 15 / 19 July 2021 / Optics Express 23503

window and a transmission of about 90% each. The resulting filtered spectrum of the SPS is

presented in Fig. 3(b), showing one single line at λ=(929.8 ±0.1) nm with a small shoulder on

the long wavelength side, which may be attributed to a second excitonic component of the QD’s

emission due to a fine-structure splitting of about 70 pm. The spectral linewidth of the photon

emission, defined as the full width at half maximum, was determined to 31.4 pm. This value is

limited by the resolution of our spectrophotometer (approximately 36 pm for the full width at

half maximum). Noteworthy, an emission linewidth below 0.1 nm already enables very accurate

radiant flux measurements at a well-defined wavelength.

Fig. 3.

(a)

PL spectrum of the selected QD. (b) Spectrally filtered QD

PL emission with

a wavelength of λ=(929.8 ±0.1) nm.

Figure 4(a) shows the photon flux at the position of the detector and the single-photon purity

in dependence of the applied excitation power. The linear dependence at low excitation implies

that the corresponding spectral line belongs to the recombination of an exciton. Here, the photon

flux was calculated by dividing the count rate, corrected for dark counts and afterpulsing, by

the DE, calibrated in section 3. Due to the improvements in the setup transmission mentioned

earlier, we were able to achieve a photon flux of up to (2.55

0.02)

photons per second at

an excitation power of 3.5

W. This photon flux corresponds to a radiant flux of (545

4) fW,

which is high enough to be measured with a low-noise analog reference detector, thus allowing

an absolute calibration of a SPAD detector by a direct comparison with an analog detector. The

overall efficiency

ηtotal

of our source, including the optical setup for spectral and spatial filtering,

can be easily calculated by dividing the photon flux by the repetition rate, thus

ηtotal =

0.0319. An

exemplary measurement of the second-order correlation function g

(2)

is presented in Fig. 4(b).

The obtained g(2)(τ=0) value is 0.14 for low excitation powers and reaches 0.24 at saturation.

Fig. 4.

(a) Photon flux (black circles) and single-photon purity (blue squares) of the

InGaAs QD based single-photon source at the position of the SPAD detector. (b) Exemplary

second-order correlation measurement for an excitation power of 0.5

W, which yields

g(2)(0)=0.15.

Research Article Vol. 29, No. 15 / 19 July 2021 / Optics Express 23504

3. Absolute calibration of Si-SPAD

The calibration of the DE of the SPAD detector was carried out as follows. The output radiant

flux Pof the SPS was determined with a low-noise fiber-coupled reference detector (Femto,

FWPR-20-S) according to: P

s, where sis the spectral responsivity in volt per watt and U

is the voltage. Traceability to the primary standard for optical power, the cryogenic radiometer, is

achieved by a calibration of the spectral responsivity. This calibration was conducted according

to the double attenuator technique, presented in detail in Ref. [12]. For this purpose, the

optical power from a laser (PicoQuant, LDH-D-C-930) at zero attenuation was measured with

a calibrated optical power meter (HP, 81530A). Two calibrated variable attenuators were used

to vary the optical power in the range between 57 fW and 12.3 pW, and the corresponding

voltage was read out from the low-noise analog detector. We did not observe any nonlinearity of

the spectral responsivity within the measurement uncertainty in the optical power range stated

above. Therefore, the final value for the responsivity s

=(0.5886 ±0.0031) · 1012 VW−1

was

calculated by taking the weighted mean. The uncertainty of the spectral responsivity considers

both the standard deviation of the weighted mean and the repeatability of the calibration results.

The SPAD calibration is performed according to the substitution method. First, the x,yand z

coordinates of the selected QD are confirmed with a

PL scan (objective realignment is performed

if necessary). The multimode fiber with the spatially and spectrally filtered single-photon emission

is connected to the Si-SPAD (Perkin Elmer, SPCM-AQRH-13-FC) to measure the count rate

Ntotal

, then it is connected to the already calibrated low-noise detector to determine the absolute

radiant flux. Since the dark current of the low-noise detector is sensitive to changes in the ambient

conditions and may vary over time, its value was measured immediately after the previous step.

The last step consists in measuring the count rate a second time with the SPAD for an uncertainty

estimation of the temporal stability

ftemp

of our SPS. These steps are repeated for each data point

in Fig. 5(a) at different laser excitation powers. The apparent DE ηSPAD is determined by:

ηSPAD =hc

U(Ntotal −Ndark)(1−pa)ftemp fconn. (1)

Fig. 5.

Si-SPAD detector calibration. (a) Calibration using the spectrally filtered QD

emission [for

PL spectrum, see Fig. 3(b)] for a direct comparison with an analog reference

detector. The pink area represents the expanded uncertainty (k

2) of the weighted mean.

(b) Calibration using a strongly attenuated laser source, where the incoming photon flux

has been indirectly determined from a calibration of two variable attenuators. The error

bars in (a) and (b) indicate the standard measurement uncertainty. Inset: comparison of the

weighted mean of the DE from (a) with the DE from (b) for the lowest measured photon flux,

where the error bars show the corresponding expanded uncertainties (k=2).

Research Article Vol. 29, No. 15 / 19 July 2021 / Optics Express 23505

Here, his the Planck constant, and cis the speed of light, both having no uncertainty with

the current definition of the SI units. The wavelength of the emitted radiation is denoted by

, whereas

Ndark

is the dark count rate of the SPAD, and

is the afterpulsing probability. It

was obtained from additional correlation measurements. The value for

did not change with

the photon flux within the measurement uncertainty, which justifies the absence of higher order

terms in

in Eq. (1). Finally, the term

fconn

takes into account the change of the coupling losses

of the FC/PC connector, estimated to 0.5%. This is an empirical value confirmed by connecting

and disconnecting the fiber patch cord several times and looking at the relative change of the

count rate from a SPAD with a stable laser as a light source.

It is important to note that we are using the conventional definition of the apparent DE, given

by the measured count rate, corrected for dark counts and afterpulsing, divided by the incident

photon flux. This value depends on the properties of the light source and of the SPAD detector

and is in general count rate dependent.

An exemplary measurement uncertainty budget of the third data point in Fig. 5(a) is shown in

Table 1. The largest contribution stems from the temporal stability of the QD emission. The

traceable calibration of the spectral responsivity of the low-noise analog detector as well as

the change of the coupling loss of the FC/PC connector are two further significant sources of

uncertainty. The smallest uncertainty contribution arises from the dark count rate, since the high

count rate leads to an excellent signal-to-noise ratio. The uncertainty in the wavelength has also

a small contribution to the overall uncertainty of the DE because of the very narrow linewidth of

the QD emission.

Table 1. Measurement Uncertainty Budget for the Calibration of a Si-SPAD Detector Against a

Low-Noise Analog Reference Detector for the Third Data Point in Fig. 5(a)

Relative Standard

Source of Uncertainty Value Uncertainty (%) Distribution Contribution (%)

Planck constant h6.62607015 ×10−34 J s 0 - 0

Speed of light c299792458 m s−10 - 0

Wavelength λ929.8 nm 0.01 Rectangular 0.01

Spectral responsivity s0.5886×1012 V W−10.53 Standard 17.97

Voltage U0.3082 V 0.13 Standard 1.03

Count rate Ntotal 825500 s−10.08 Standard 0.39

Dark count rate Ndark 231 s−11.02 Standard 0.002

Afterpulsing probability pa0.0208 4.81 Standard 0.68

Temporal stability ftemp 1 0.99 Rectangular 63.73

Connect/disconnect fiber factor fconn 1 0.50 Rectangular 16.19

Combined uncertainty uc1.24 Standard 100

The results of the DE calibration are shown in Fig. 5(a), where the DE is plotted against the

photon flux impinging on the detection area for the calibration using the QD based SPS. The

different size of the error bars is mainly due to variations of the uncertainty of the temporal

stability

ftemp

, which was estimated independently for each data point. Note that the calibration

was performed on a different day than the recording of the saturation curve, which explains

the nonidentical maximum photon flux. As can be seen, the measured DE is independent of

the incoming photon flux within the stated uncertainties. We determined a weighted mean of

0.3263

0.0022 for the apparent DE. One would expect a small decrease with increasing photon

flux because of the dead time of the SPAD detector. In order to quantify this contribution, we

derived an equation (based on the model in Ref. [13]) describing the dead time effect for an ideal

Research Article Vol. 29, No. 15 / 19 July 2021 / Optics Express 23506

SPS with an efficiency of φ/f:

ηSPAD =η0

1+Int(fD)ϕ

fη0

, (2)

where

η0

is the intrinsic detection efficiency,

is the photon flux, and Int is the integer part of the

product of source frequency fand SPAD dead time D

=(29.2 ±0.2)ns

. Therefore, we expect

an absolute change of the apparent DE by 0.005 between the first and last data point in Fig. 5(a).

However, such a small change lies within the expanded measurement uncertainty of each of the

four DE values. The imperfection of our SPS, namely the nonzero second-order correlation at

zero delay, could also influence the apparent DE. The magnitude of this change depends on the

product

φ·g(2)(

)

. With the use of the equation from Ref. [10] and with the data from Fig. 4(a)

we estimate a maximum decrease of the apparent DE with the photon flux by about 0.4%, which

is clearly below the relative standard uncertainties (between 0.91% and 3.18%) in Fig. 5(a).

In Fig. 5(b), the measured DE is shown for a calibration using attenuated laser pulses (PicoQuant,

LDH-D-C-930) with the same repetition rate of 80 MHz. A decrease of the measured DE with

increasing photon flux can be observed, as expected from the photon statistics of the laser light in

combination with the dead time of the Si-SPAD detector. The saturation of the count rate at high

optical powers is enhanced by the presence of multiphoton events due to the Poisson nature of

the laser emission.

Both calibration methods in Fig. 5yield consistent results at low photon fluxes, where dead

time and photon statistics have a negligible effect. In the inset in Fig. 5(b), the weighted mean

from the calibration with the SPS is compared with the DE at the lowest photon flux measured

with an attenuated laser. The values agree within their expanded uncertainties (k

2). Both QD

and laser have about the same emission wavelength: 929.8 nm and 930 nm, respectively. The QD

possesses a smaller spectral linewidth; its pulse width in the time domain is determined by the

decay time of the excited state (1.7 ns), which could be improved by exploiting the Purcell effect

in a cavity-enhanced SPS [8,14,15]. Just by improving the temporal stability of the QD emission

it would be possible to reduce the overall measurement uncertainty by a factor of two, so that it

becomes comparable or even lower than the uncertainty of the calibration with attenuated laser

light.

The presented calibration method has several advantages over the classical method with

attenuated laser light. The QD emission falls directly in the desired photon flux range, whereas

laser light has to be attenuated by about ten orders of magnitude for traditional calibration

methods [12,16], which implies an additional calibration of the attenuators contributing to the

measurement uncertainty. Moreover, pulsed QD operation with a repetition period below the

dead time of the SPAD detector would completely remove any saturation effects caused by

its dead time. Therefore, this calibration method has the potential of reaching a simple linear

dependence between incoming photon flux and measured count rate which would further reduce

the measurement uncertainty. In contrast, even for fD

1, the Poisson statistics of laser light lead

to a strong saturation of the count rate at high photon fluxes because of the large mean photon

number. This saturation effect is hard to be precisely modelled and limits the usable detection

range.

4. Summary

We have developed a pulsed InGaAs QD based single-photon source applied for the direct

calibration of a single-photon avalanche detector against a classical analog reference detector.

The single-photon source was metrologically characterized with respect to its total radiant flux,

which was up to (2.55

0.02)

photons/s, corresponding to (545

4) fW at an emission

wavelength of

λ=

929.8 nm, and with a single-photon purity of g

(2)

(0)

0.25. This development

can be considered as a significant improvement in the field of quantum radiometry, since, due

Research Article Vol. 29, No. 15 / 19 July 2021 / Optics Express 23507

to the pulsed operation and sub-Poisson statistics of the light source, any count rate saturation

effects of the single-photon detector are diminished.

Funding.

Deutsche Forschungsgemeinschaft (390837967, Re2974/23-1, RTG 1952); European Metrology Programme

for Innovation and Research (17FUN06 SIQUST).

Acknowledgments.

This work was funded by the project EMPIR-17FUN06 SIQUST. This project received funding

from the EMPIR program co-financed by the Participating States and from the European Union Horizon 2020 research

and innovation program. We gratefully acknowledge the support of the Braunschweig International Graduate School

of Metrology B-IGSM and the DFG Research Training Group 1952 Metrology for Complex Nanosystems. This work

was also supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s

Excellence Strategy—EXC- 2123 QuantumFrontiers—390837967 and via the project Re2974/23-1.

Disclosures. The authors declare no conflicts of interest.

Data availability.

Data underlying the results presented in this paper are not publicly available at this time but may

be obtained from the authors upon reasonable request.

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