Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, 77. Table of Contents 1

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1 Efficient single photon detection from 500 nm to 5 μm wavelength: Supporting Information F. Marsili 1, F. Bellei 1, F. Najafi 1, A. E. Dane 1, E. A. Dauler 2, R. J. Molnar 2, K. K. Berggren 1* 1 Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA 2 Lincoln Laboratory, Massachusetts Institute of Technology, 244 Wood St., Lexington, Massachusetts 02420, USA * corresponding author: berggren@mit.edu Table of Contents Table of Contents 1 Complete list of characterized devices 2 Experimental set up 3 Estimation of the device detection efficiency 4 Wavelength dependence of the numerical aperture of the optical fibers 5 Estimation of the uncertainty on the value of the detection efficiency 9 Polarization of the light 12 Photon spectra measured with 30-nm-wide SNSPDs and SNAPs 13 Detection efficiency of a 20-nm-wide 2-SNAP 14 Dark count rate measurements 15 References 16 1

2 Complete list of characterized devices Table 1 reports the details of the devices that were characterized in the wavelength range λ = µm with the dip-probe system (see section: Experimental set up). Table 1 reports, from left to right: fabrication run; type of device architecture (N-SNAP or SNSPD); nanowire width (w) and pitch (p); active area (A d ); number of devices of the same type from the same fabrication run screened with the cryogenic probe station 1 ; number of devices of the same type from the same fabrication run characterized in the dip-probe system; and average (I SW ) and standard deviation (σ ISW ) of the switching current of the devices of the same type from the same fabrication measured in the dip-probe system. Table 1. Details of the devices characterized in the wavelength range λ = µm Fabrication run Device type w - p A d Probe Dip-probe I SW σ ISW (nm) (μm μm) station (μa) (μa) 1 SNSPD SNSPD SNSPD SNAP SNSPD SNSPD SNAP SNAP SNSPD SNAP SNSPD SNAP

3 Experimental set up The detectors were tested in a dip-probe system mounted in a reservoir cryostat. The chamber where the detectors were mounted was filled with liquid 4 He. The 4 He reservoir was pumped on to reach a temperature of ~ 1.5 K, at which it became superfluid. The devices were mounted on a printed circuit board (PCB) and wire-bonded to launchers connected by ultra-miniature connectors (UMC) to low-heat-conductance coaxial cables (-3 db electrical bandwidth of 3 GHz). The devices were current-biased with a low-noise voltage source in series with a 100-kΩ resistor through the dc port of a room-temperature bias-tee (100 khz 4 GHz bandwidth on the RF port). The signals from the SNSPDs were read-out with a chain of three low-noise, room-temperature amplifiers (20 MHz 3 GHz bandwidth; 20 db gain; 2.5 db noise figure) connected to the RF port of the bias-tee. The amplified SNSPD pulses were counted with a 225-MHz-bandwidth counter. We measured the detection efficiency of SNSPDs by illuminating the detectors with two different broadband incoherent light sources (depending on the wavelength range) coupled to a 150-mm-focal-length monochromator. The light was delivered from the monochromator to the detectors by a high-numerical-aperture (NA) multimode optical fiber mounted inside the dip-probe system. The light was coupled into the fiber using uncoated, broadband CaF 2 bi-convex lenses (transmission > 90% in the range λ = µm). The devices were illuminated from the top, as the fiber connector was mounted above the detector chip. We set the distance (D) between the fiber and the device chip to ensure uniform illumination of the whole chip (see section: Wavelength-dependence of the numerical aperture of the optical fibers). The optical power coupled into the fiber was measured by a thermal powermeter (spectral range λ = µm) with a noise level of 0.5 µw peak to peak. The spatial profile of the optical beam propagating from the fiber was measured with two different rotating-slit beam profilers (depending on the wavelength range). In the range λ = µm we used a profiler based on a Si detector. In the range λ = µm we used a profiler based on an extended InGaAs detector. 3

4 In the visible and near-infrared wavelength range (λ = µm) the light source was a tungsten-halogen lamp (250 W) emitting in the range λ = µm. In the range λ = µm the light was diffracted by a ruled grating with a groove density of 300 grooves per millimeter (G / mm) and 0.5 µm blaze wavelength. In the range λ = µm we used a ruled grating with 600 G / mm groove density and 1.6 µm blaze wavelength. The light from the monochromator was coupled to a step-index multimode silica fiber with 600 µm core. In the near- and mid-infrared wavelength range (λ = µm) the light source was a glowbar heated at 1100 K and emitting in the range λ = 1-8 µm. The light was diffracted by a ruled grating with 150 G / mm groove density and 3 µm blaze wavelength in the range λ = µm and by a ruled grating with 150 G / mm groove density and 6 µm blaze wavelength in the range λ = µm. The light at the output of the monochromator was coupled to a step-index multimode chalcogenide fiber with an 860 µm core 2. We measured the numerical aperture of both the silica and chalcogenide fibers as a function of wavelength (see section: Wavelength-dependence of the numerical aperture of the optical fibers). The input and output slits of the monochromator were 3 mm wide. Based on the focal length of the monochromator and the groove density of the different diffraction gratings, we calculated the following spectral widths of the light collected at the output slit (using the software supplied by the manufacturer 3 ): 57 nm in the range λ = µm; 27 nm in the range λ = µm; and 118 nm in the range λ = µm. Estimation of the device detection efficiency We calculated the detection efficiency of our detectors at each wavelength (λ) as follows: η(λ) = H (CR - DCR) / N ph, where: CR is the count rate measured when the SNSPD was illuminated at wavelength λ; DCR is the count rate measured when the SNSPD was not illuminated (with the output slit of the monochromator covered by a shutter, see section: Dark count rate measurements); H is a normalization factor 1 ; and N ph is the number of photons per second at wavelength λ incident on the device active area (see Ref. 1 for a rigorous definition of the active area). 4

5 The value of N ph at each wavelength was calculated by using the detector active area, the value of D, the optical power coupled into the optical fiber measured at 300 K, and the spatial profile of the optical beam propagating from the fiber measured at 300 K or extrapolated from measurements at different wavelengths (see section: Wavelength-dependence of the numerical aperture of the optical fibers). Wavelength dependence of the numerical aperture of the optical fibers To estimate the photon flux incident on the device active area at a certain wavelength we characterized the spatial profile of the optical beam propagating from the optical fibers (silica or chalcogenide fibers) mounted on the dip-probe system as a function of wavelength. We used two different rotating-slit beam profilers (depending on the wavelength range) to measure the intensity of the beam along two orthogonal axis (which we called x and y). We used a profiler based on a Si sensor for λ = μm and a profiler based on an extended InGaAs sensor for λ = μm. Figure SI 1 shows the normalized intensity profiles along the x (Figure SI 1a) and y (Figure SI 1b) axis of the beam propagating from the silica fiber at λ = 1.3 μm. The x and y profiles were similar in shape, which indicates that the beam had radial symmetry. Although the fibers were multi-mode, we could fit the intensity profiles with Gaussian functions: I(r) = I 0 + I 1 exp[-(r r 0 ) 2 / (2σ 2 )]. We used I 0, r 0, and σ as fitting parameters. The fitted profiles are shown in Figure SI 1 (red curves). 5

6 Figure SI 1. a Normalized optical beam intensity (black squares) with Gaussian fit (red line) as a function of position on the x-axis. b Normalized optical beam intensity (black squares) with Gaussian fit (red line) as a function of position on the y-axis. The distance between the optical fiber and the beam profiler sensor was R = 4 mm. Each intensity curve was normalized by its maximum. For each wavelength, we measured the beam profile at several relative distances between the optical fiber and the beam profiler sensor (R). Figure SI 2a shows beam profiles from the silica fiber at λ = 1.3 μm on the x axis (and the relative fitting curves) for R ranging from 0 (corresponding to the minimum achievable distance between the fiber and the rotating slit) to 4 mm. Figure SI 2b shows the width of the fitting Gaussian curves (σ x ) shown in Figure SI 2a (red curves) as a function of R and the linear fit of the data. We defined the numerical aperture (NA) of a fiber at a certain wavelength as the average value of the slopes of the σ x vs R and σ y vs R fitting curves. 6

7 Figure SI 2. a. Normalized intensity profiles on the x axis of the beam propagating from the silica fiber at λ = 1.3 μm at different R: R = 0 mm (blue curve); 1 mm (cyan curve); 2 mm (green curve); 3 mm (orange curve); 4 mm (gray curve). Each intensity profile was normalized by its maximum. The red solid curves are the fitting of the experimental data. b. Width of the fitting Gaussian curves (σ x ) vs R. The data (black squares) were interpolated with a linear function (red solid line). We calculated the NA of the silica and chalcogenide fibers as a function of wavelength. Figure SI 3 shows the average and standard deviation of the NA of the two fibers as a function of wavelength. The standard deviation on the values of NA was calculated by propagating the error of the Gaussian and linear fits. The NA of the two fibers was measured in different wavelength ranges because of the different transmission spectra of the fibers. We could not measure the NA of the chalcogenide fiber for λ = μm because of the limited spectral bandwidth of the extended InGaAs fiber profiler. Therefore we assumed NA = 110 μm / mm in the range λ = μm, which we calculated averaging values of the NA in the range λ = 1.6 µm µm. 7

8 Figure SI 3. NA vs λ for the silica fiber (black curve, λ = 1 µm µm) and for the chalcogenide fiber (red curve, λ = 1.6 µm µm). Figure SI 4 shows the η vs I B curves measured on the same 50-nm-wide SNSPD with the silica fiber (Figure SI 4a) and with the chalcogenide fiber (Figure SI 4b) in the range λ = μm. The values of η measured with the two fibers were in good agreement (within 10%) only for λ = 1.6 μm. For λ 1.7 μm the values of η measured with the silica fiber were up to a factor of ~ 1.4 higher than the values of η measured with the chalcogenide fiber. We attribute this discrepancy to the possibility that in the wavelength range λ = μm, the absorption loss of the silica fiber decreased when the fiber was cooled from T = 300 K (at which temperature we measured the transmission) to T = 1.5 K, which was not the case for the chalcogenide fiber, in agreement with what was reported in Ref. 4. 8

9 Figure SI 4. η vs I B / I SW curves of a 50-nm-wide SNSPD for λ = µm measured (a) with the silica and (b) with the chalcogenide fiber. The black arrow indicates the direction of increasing λ (in 100-nm steps). The colored arrows indicate the η vs I B / I SW curves at λ = 1.6 µm (violet); 2.1 µm (brown). Assuming that the NA of our fibers did not change with temperature, we expect that the shape of the optical beams measured at 300 K would not significantly differ from the shape of the beams in the superfluid He bath, because the refractive index of superfluid He is and because superfluid He does not boil. Estimation of the uncertainty on the value of the detection efficiency The uncertainty on the value of η at a certain wavelength was due to the uncertainty on the value of the photoresponse count rate (PCR = CR - DCR) and of the photon flux incident on the device active area at that wavelength (N ph ). The uncertainty on the value of the PCR was statistical (shot-noise limited), and was below 1% of the PCR value. The most significant source of uncertainty on the value of η was the uncertainty on N ph. In this section we present our estimation of the uncertainty on the value of η due to the limited accuracy and precision of our method to measure N ph. Assuming that the transmission of our silica and chalcogenide fibers did not change with temperature 4 from T = 300 K to T = 1.5 K in the wavelength range of interest (λ = μm for the silica fiber and λ = μm for the chalcogenide fiber), the systematic error on N ph depends on the systematic error on our 9

10 measurement of the NA of the fibers; of the relative distance between fiber tip and the SNSPD chip (D); and of the distance (ρ) between the device and the optical axis of the optical coupling system (i.e. the center of the core of the fiber). To experimentally estimate the systematic error on η, we measured the η vs λ curves (λ = μm) at different fiber-to-chip distances (D = 24, 30, 40 mm) of five detectors fabricated on the same chip which had different distances from the optical axis. The devices were illuminated with the silica fiber by using light from the halogen lamp. We characterized three 30-nm-wide SNSPDs (SNSPD 1.2,3 ) and two 30-nm-wide 2-SNAPs (2-SNAP 1,2 ). The devices had the same nominal nanowire width (30 nm) and fill factor (30%) and the η vs I B curves showed saturation in the wavelength range λ = μm. Therefore, the detectors were expected to have the same detection efficiency for I B > I co and I AV (the avalanche current of the 2-SNAPs 1,6 ). We estimated the systematic error in η from the discrepancy between the values of η measured at the same D for different devices (and then different ρ) and measured at different D for the same device. Figure SI 5a shows the mean and standard deviation of the η vs λ curves of each of the five devices measured at different D. Figure SI 5b shows the mean and standard deviation of all of the η vs λ curves shown in Figure SI 5a. Figure SI 5c shows the relative systematic error (ε A ) on the value of η at each wavelength, which we calculated as the ratio between the standard deviation and the mean of η shown in Figure SI 5b. 10

11 Figure SI 5. a. Mean and standard deviation of the η vs λ curves at I B = 0.9 I SW and different D of SNSPD 1 (ρ = 2.56 mm, orange) at D = 40 and 30 mm; of SNSPD 2 (ρ = 2.33 mm, black curve) at D = 40 and 24 mm; and of SNSPD 3 (ρ = 2.04 mm, blue curve) at D = 30 and 24 mm. η vs λ curves at I B = 0.9 I SW of SNAP 1 (ρ = 1.6 mm, green curve)at D = 30 mm and of SNAP 2 (ρ = 1.65 mm, red curve) at D = 40 mm. b. Mean and standard deviation of all of the η vs λ curves shown in Figure SI 5a. c. Wavelength dependence of the relative systematic error (ε A ) on the value of η. The statistical error on the value of N ph was limited by the precision of the measurement of the optical power in the fibers, which we quantified by measuring the standard deviation of 0.2 µw on the reading of the thermal power meter within a time window of 1 minute (which was the time within which the thermal drift of the power meter was lower than 0.2 μw). Figure SI 6a shows the normalized photon spectra (N ph vs λ curves) of the tungsten-halogen lamp coupled to the silica fiber (red curve) and of the glowbar coupled to the chalcogenide fiber (black curve). The error bars represent the statistical error on the value of N ph due to the precision of the power meter. Figure SI 6b shows the relative statistical error (ε P ) on the value of η at each wavelength, which we calculated propagating the statistical error on N ph. 11

12 Figure SI 6. a. Normalized photon flux vs λ of the tungsten-halogen lamp coupled to the silica fiber (red curve) and of the glowbar coupled to the chalcogenide fiber (black curve). The N ph vs λ curves were normalized by their maximum values. b. Wavelength dependence of the relative statistical error (ε P ) on the value of η. Polarization of the light We employed incoherent light sources (the halogen lamp and the glowbar), which emitted randomly polarized light. The light at the output of the monochromator was partially polarized because the gratings had different diffraction efficiencies for different polarizations of the incident light. However, the silica and chalcogenide multimode fibers used to illuminate our detectors were expected to randomize the polarization of the light due to mode mixing 7. We characterized the polarization state of the light at the output of the monochromator and the effect of mode mixing on the polarization of the light guided by silica and chalcogenide multimode fibers of different lengths. We analyzed the polarization of the light at the output of the monochromator (before coupling to the multimode fibers) at λ = 1.55 μm by using a polarizer mounted on a rotating stage. We measured the optical power out of the polarizer for different angular positions of the polarizer. We found the ellipticity of the light (E), which we defined as the ratio between the maximum and minimum power measured by rotating the polarizer, to be E =

13 We could not measure the effect of mode mixing in the multi-mode fibers used in our experiment directly on the light at the output of the monochromator because of the low coupled optical power. Therefore, we coupled a μm-wavelength continuous wave (CW) laser to a fiber-coupled polarization controller and set the polarization of the light to an arbitrary value. We then measured the ellipticity of the light at the output of the polarization controller and compared it to the ellipticity at the output of silica multi-mode fibers of different lengths connected to the polarization controller. Figure SI 7 shows the E at the output of the silica multimode fiber as a function of the fiber length (l). The value of E at l = 0 m was measured at the output of the polarization controller without multi-mode fibers connected. E decreased from 351 at l = 0 m to 5 with a 4-m-long silica fiber. As we used 3.5 m long fibers to couple the light from the monochromator to the SNSPDs, we can reasonably expect that the light impinging on the chip was randomly polarized. Figure SI 7. Ellipticity (E) of the light at the output of the silica multi-mode optical fiber as a function of fiber length (l). Photon spectra measured with 30-nm-wide SNSPDs and SNAPs We measured the wavelength dependence of the photon flux from the glowbar coupled to the chalcogenide fiber using five different detectors based on 30-nm-wide nanowires: four 30-nm-wide SNSPD (A d = 1.47 μm 0.23 μm) biased at I B = 6.5 μa, and one 30-nm-wide 2-SNAP (A d = 1.47 μm 0.53 μm) biased 13

14 at I B = 13 μa. Figure SI 8 shows the average and standard deviation of the normalized photon flux vs λ curves measured with the different detectors. Figure SI 8. Average and standard deviation of the normalized photon flux vs λ curves from the glowbar coupled to the chalcogenide fiber. The photon flux was measured with five different 30-nm-nanowire-width detectors. The curves were normalized by their value at λ = 2400 nm. Detection efficiency of a 20-nm-wide 2-SNAP Figure SI 9 shows the bias and wavelength dependence of the detection efficiency of a 2-SNAP based on 20-nm-wide nanowires. For short wavelengths, λ < 2.5 μm, the I co of the 2-SNAP does not show wavelength dependence because the I co is limited by the avalanche current of the device: I AV ~ 0.67I 1 SW (see dashed line in Figure SI 9). 14

15 Figure SI 9. Detection efficiency (η, in color scale) vs λ and normalized bias current (I B / I SW ) for a 2-SNAP based on 20-nm-wide nanowires. Each pixel of the color map corresponds to an experimental data point. The switching current and the active area (A d ) of the device were: I SW = 8 µa and A d = 1.22 μm 0.52 µm. The dashed line corresponds to the avalanche current (I AV ) of the detector. Dark count rate measurements We measured the DCR that we used to calculate the PCR by covering the output slit of the monochromator with a metal shutter. The DCR measured in this condition was due to the intrinsic DCR of the detector and to stray photons from the background illumination of the room and from 300 K blackbody radiation. We measured the intrinsic DCR of the detectors by mounting a metal screen between the fiber and the detectors inside the dip-probe system. Figure SI 10 shows the DCR vs I B curves of (a) a 30-nm-wide SNSPD and (b) an 85-nm-wide SNSPD measured with the chalcogenide fiber (blue curves) the silica fiber (green curves) or the shield (red curves) mounted on the dip probe. We attributed the fact that the DCR measured with the chalcogenide fiber mounted on the dip probe was higher than the DCR measured with the silica fiber to the fact that the transmission bandwidth and the core of the chalcogenide fiber were larger than the silica fiber, so the chalcogenide fiber coupled more stray photons to the detectors. 15

16 Figure SI 10. DCR vs bias current of (a) a 30-nm-wide SNSPD and (b) an 85-nm-wide SNSPD measured with the chalcogenide fiber (blue curves), the silica fiber (green curves) or the shield (red curves) mounted on the dip probe. We used the same discriminator trigger level of -100 mv in all cases. The acquisition times of the count rates were 10 s (for Figure a and for the red curve in Figure b) or 0.5 s (for the blue and green curves in Figure b). References 1 Marsili, F. et al. Single-photon detectors based on ultra-narrow superconducting nanowires. Nano Lett. 11, (2011) Nguyen, V. Q., Sanghera, J. S., Kung, F. H., Aggarwal, I. D. & Lloyd, I. K. Effect of Temperature on the Absorption Loss of Chalcogenide Glass Fibers. Appl. Opt. 38, (1999). 5 Edwards, M. H. Refractive Index of He 4 : Liquid. Can. J. Phys. 36, (1958). 6 Marsili, F., Najafi, F., Herder, C. & Berggren, K. K. Electrothermal simulation of superconducting nanowire avalanche photodetectors. Appl. Phys. Lett. 98, (2011). 7 McMichael, I., Yeh, P. & Beckwith, P. Correction of polarization and modal scrambling in multimode fibers by phase conjugation. Opt. Lett. 12, (1987). 16