1. Introduction

In recent years, superconducting nanowire single-photon detectors (SNSPDs or SSPDs [1]) have emerged as promising single-photon detectors for applications in various fields such as quantum information, free space optical communication, laser detection and ranging [2–4]. Their applicability to a wide range of fields can be attributed to their high system detection efficiency (SDE), low dark count rate (DCR), high counting rate, and short timing jitter. So far, significant efforts have been made to improve the system performance of SSPDs, which are optically coupled with single-mode (SM) optical fibers at telecommunication wavelength region [5–8]. The SM fiber-coupled NbTiN-SSPDs installed in the Gifford–McMahon (GM) cryocooler achieved a high SDE of 74%, a DCR of 100 c/s and a timing jitter of 68 ps at the wavelength of 1550 nm [5]. They are already in use for specific applications, such as the ones described above, and their superiority among detectors has been demonstrated [9, 10].

Meanwhile, SSPDs for visible wavelengths have not been thoroughly developed owing to the existence of powerful competitors such as photomultiplier tubes (PMTs) and avalanche photodiodes (APDs) [11]. In spite of the wide usage of PMTs and Si APDs for commercial purposes, there still exist strong demands for better performance in many applications, including fluorescence microscopes and satellite laser ranging among others [12, 13]. If we can achieve SDE levels exceeding those of PMTs and APDs, SSPDs can be widely used as high-end detectors even at visible wavelength. Such high SDE SSPDs combined with their excellent performance as aspects of high counting rate and low DCR will give a wide dynamic range that will not be achievable in other detectors. The high counting rate and afterpulse-free nature of SSPDs are also attractive, specifically for time-correlated measurements, such as fluorescence correlation spectroscopy (FCS) in the field of cell biology [14]. Therefore, the development of SSPDs for visible wavelength will open the door to the further commercial use of SSPDs in a wide variety of fields.

Recent improvement in the SDE of SSPDs at 1550 nm encouraged us to develop the SSPD for visible wavelength, but new design and fabrication techniques of the optical cavity structure are necessary to be adapted. The optical cavity structure for back-side illumination from the Si substrate has been employed in the NbN or NbTiN SSPD for 1550 nm [15], but this cavity structure can no longer be applicable for wavelengths below 1 µm due to the photon reflection and absorption of the Si substrate. The optical cavity structure for front-side illumination will allow a flexible cavity design for various target wavelengths that are independent of the substrate material [7, 16].

Achieving efficient coupling with a multimode (MM) optical fiber is another technical requirement to use the SSPD in certain applications that need to receive photons from free space. These applications require a large detection area of the SSPD in order to achieve an efficient optical coupling with the MM optical fiber, which has a larger core diameter than that of the SM optical fiber. However, the increase of the active area of the SSPD will lead to a large kinetic inductance (L_k), resulting in a low response speed.

In this paper, we report on the development of the MM fiber-coupled SSPD at a wavelength of ~600 nm for the application in FCS. To achieve high optical absorptance for front-side photon illumination, we introduced a multi-layered dielectric mirror on a Si substrate. A circular active area with an optimized nanowire structure for visible wavelength was also employed to keep the L_k as small as possible. We evaluated the DCR, the counting rate, and the timing jitter as well as the SDE.

2. Experimental setup

Figure 1(a) shows the schematic cross-sectional view of the SSPD presented in this paper. The structure of the SSPD consists of Si substrate, dielectric mirror, SiO₂ cavity and NbN nanowire from bottom to top (illumination side). The dielectric mirror was first deposited on the Si substrate to enhance the absorptance of the nanowire for visible wavelengths. The configurations of the dielectric mirror were designed so that the reflectance for the wavelength region from 400 nm to 1000 nm becomes higher than 99%. Then a SiO₂ layer was deposited onto the dielectric mirror by RF sputtering, and the thickness was chosen to be 120 nm which corresponds to λ_eff/4 of ~600 nm (λ_eff = λ/n, n is the refractive index of SiO₂ layer) in order to confine the incident photons around the nanowire. The NbN film was deposited by DC reactive sputtering at an ambient substrate temperature, and the thickness of the film was controlled by the deposition rate and time. The nanowires were patterned by electron beam lithography and reactive ion etching. To reduce the current crowding effect, rounded boundaries were designed at the inner corner of the nanowires [17].

 

Fig. 1 (a) Schematic of stack structure of the SSPD (not to scale). (b) Scanning electron micrograph of a circular active area of SSPD with a diameter of 35 µm. The line-width of the nanowires and the space between them are 150 nm and 100 nm, respectively.

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Figure 1(b) shows a scanning electron micrograph of the active area with a diameter of 35 µm, which was designed to be large enough to couple efficiently with the incident light from an MM fiber as described later. The large active area leads to an increase in L_k, resulting in a lower counting rate. To reduce L_k as much as possible, we adopted a circular active area [18] instead of a square one and designed a 10.5-nm-thick and 150-nm-wide nanowire, which is thicker and wider than a typical SSPD for the telecommunication wavelength [5]. Because the energy of the single photons at visible wavelengths is higher than that for telecommunication wavelength, it is expected that the device exhibits high single photon sensitivity for visible wavelengths even when the cross section of the nanowire is larger. Furthermore, a larger switching current (I_sw) of the SSPD can be achieved, leading to a better signal-to-noise ratio of the output signal as well as a smaller timing jitter [19]. The fabricated SSPD showed a superconducting transition temperature of 7.8 K and an I_sw of 30.3 µA.

The device was mounted in a fiber-coupled package optimized for front-side illumination with an MM fiber. The graded index (GRIN) lenses were spliced to the tip of the MM fiber with a 50-µm-diameter core, and the diameter of an incident light spot was focused to ~28 µm at the active area, which has a diameter of 35 µm, enabling a good optical coupling. Because the reflectance of the dielectric mirror was designed to be less than 30% at a 1550 nm wavelength, we could perform the optical alignment precisely by monitoring an illuminated 1550-nm-wavelength light spot from the substrate side of the chip [20]. The packaged SSPD was then installed in the GM cryocooler system with the operation temperature of 2.21 K and a thermal fluctuation of 10 mK. The bias circuit used in the experiment was similar to that described in Ref [21].

While measuring the SDE, a continuous laser source with several different wavelengths was used as the photon source. A 4-channel attenuator for MM fibers was used to adjust the photon power to be P₁ and then add a calibrated attenuation of P₂ to the incident light, so that P₁ – P₂ equaled to the power of a flux of 10⁶ photons/s at a specific wavelength. The MM fibers were also used from the laser source to the input port of cryocooler system to propagate MM light and irradiate the active area of the device. Although the optical losses of the optical fibers installed in the cryocooler system were measured to be 0.1–0.3 dB, they were not included in the calibration of the input photon flux. The DCR was measured by turning off both the laser source and the attenuator. The SDE was obtained by subtracting the DCR from the output pulse rate and dividing this value by the number of the input photons.

3. Results and discussion

Figure 2 indicates the normalized bias current dependences of the SDE for the incident photons at the wavelength of 635 nm, system DCR (SDCR), and device DCR (DDCR). SDCR is the DCR when the MM fiber is connected to the detector and the input fiber to the system is blocked by a shutter, while DDCR is the DCR when the fiber is disconnected from the device inside the cryocooler. As shown in Fig. 2, the SDE curve shows saturation trend when the bias current approaches the I_sw; the SDE reaches its highest value at 73%. In practical use, the bias point for the highest SDE may not be feasible because of the high SDCR, reaching over several 10³ c/s, but even at a lower bias current of 25 µA (0.82I_sw), a high SDE value of 70% was achieved with a significantly lower SDCR of 100 c/s.

 

Fig. 2 System detection efficiency (SDE), system dark count rate (SDCR), and device dark count rate (DDCR) as a function of the normalized bias current. The SDE was measured at a wavelength of 635 nm. The triangle and pentacle indicate the SDCR and DDCR with the DCR of the SSPD measured by mounting the device in the package with and without a MM optical fiber connected, respectively.

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The SDCR at the bias region lower than 0.95I_sw increases gradually with the increase in bias current, which is not seen in the DDCR curve. Clearly, the SDCR in this bias region mainly comes from extrinsic causes such as blackbody radiation induced from the MM fiber at finite temperature [22]; filtering the radiation by either inserting a cold optical filter [23] or employing the band pass substrate [24] would be effective means to reduce this extrinsic DCR.

Besides the wavelength of 635 nm, the SDEs of the SSPD at other visible wavelengths were measured and shown in Fig. 3. The SDE curve at the wavelength of 635 nm is also included for comparison. As shown clearly in the figure, the maximum SDE reached on a given curve was the highest for the wavelength of 635 nm (73.0%) and decreased with increased wavelength. Maximum SDEs of 60.7%, 50.9%, and 42.6% were obtained for wavelengths of 785, 904, and 980 nm, respectively. The trend of saturation appears only at 635 nm, becoming weaker and disappearing for longer wavelengths due to the reduction of the intrinsic pulse generation probability of the device for incident photons with lower energy. Thus, it was shown that the present cross-section size of the nanowire (10.5 nm thick and 150 nm wide) was adequate to achieve the high pulse generation probability for the wavelength of 635 nm. In combination with the high optical absorptance optimized for 635-nm wavelength by SiO₂ cavity, the fabricated device actually achieved the high SDE of 73% for the target wavelength of 635 nm.

 

Fig. 3 The normalized bias current dependence of the SDE for incident photons with wavelengths of 635 nm (red circle), 785 nm (green square), 904 nm (blue triangle), and 980 nm (purple quadrangle).

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Next, the counting rate of the present SSPD was investigated. The counting rate of the SSPD is limited by the large L_k of the nanowire because the time constant for the bias current flowing back to the detector after a photon detection is equal to L_k/R_L, where R_L is the impedance of load side [25]. To estimate the response speed, we measured L_k by fitting the phase of the reflection coefficient using a network analyzer [26]. As a result, we obtained an L_k of 2.46 µH, which was comparable with the value of 15 × 15 µm² active area SSPD with thinner and narrower nanowires, even though the nanowire length was quite long at ~3.9 mm [6]. Figure 4 shows the response counting rate dependence of the SDE at 0.92I_sw when the DCR is 10³ c/s. When response counting rate varies from 0.05 to 1 Mega counts per second (Mcps), the SDE remains almost constant, equaling 71.7 ± 1.4%. The minor uncertainty of the SDE is because of the calibration deviation of the ultraweak photon power. With the increase of the response counting rate, the detector could not respond to the large number of incoming photons, resulting in the decrease of the measured SDE. When the SDE shifted 3 dB from its maximum value, response counting rate was 8.5 Mcps, which is indicated as the arrow in Fig. 4. Since the readout circuit used in the measurement is conventional, the counting rate of the SSPD can be further enhanced closer to its theoretical limits by an improved capacitor-grounded readout circuit [27] or by a DC coupled cryogenic circuit [28].

 

Fig. 4 Response counting rate dependence of the SDE. The wavelength of the incident photons was 635 nm, and the detector was biased at 0.92I_sw.

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Finally, the timing jitter of the SSPD was measured using the time-correlated single-photon counting (TCSPC) module with a resolution of 813 fs (SPC-150 board card from Becker & Hickl GmbH). The instrument jitter of the SPC-150 is 6.6 ps full-width at half-maximum (FWHM), which is very small compared to the timing jitter of the device and can be neglected. As the photon source, a 1550-nm-wavelength pulsed laser with a 100 fs pulse width and 80 MHz repetition rate was used, and the incident light illuminating the detector was attenuated to a photon flux of 0.01 photons/pulse. Then the TCSPC module built up a statistical distribution of the intervals between the synchronization trigger pulse of the laser and the response pulse from the SSPD. Figure 5 shows the measured histograms of the time-correlated counts when the incident light was induced through the MM fiber and SM fiber at a bias current of 28.0 µA (0.92I_sw). The timing jitter defined by FWHM of the histogram for the MM fiber coupling was 75.7 ps, which was slightly larger than the value for the SM fiber coupling (52.2 ps) because of the modal dispersion inside the MM fiber [29]. In the actual applications where timing jitter is the key parameter, the total length of the MM fiber of the system should be as short as possible in order to reduce the modal dispersion effect. However, compared to most semiconductor single-photon detectors and transition edge sensors, the timing jitter of the SSPD coupled with MM fiber is still small [11], bringing in a precise depth resolution in the laser ranging and imaging applications.

 

Fig. 5 Histograms of the time-correlated photon counts measured at the wavelength of 1550 nm. Circles and stars indicate the histograms when the device was coupled with multi-mode (MM) fiber and single-mode (SM) fiber, respectively. The red lines are the fitted curves using the Gaussian distribution.

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4. Conclusions

In summary, we have developed and characterized the MM fiber-coupled NbN-SSPD for the visible wavelength region. The device showed a high SDE of 70% for the incident photons with 635 nm wavelength at a DCR of 100 c/s. The 3 dB roll-off response counting rate of the SSPD was 8.5 Mcps, and the timing jitter was obtained as 75.7 ps using the MM fiber coupling. The developed practical SSPD presented in this paper could open a new frontier for a wide range of applications at visible wavelength.