1. Introduction

Single-photon detectors (SPDs) are photodetectors with quantum-limit sensitivity that play major roles in quantum information processing [1–3], space communication [4], light detection and ranging (LiDAR) [5–7], biological/medical applications [8,9], and several other spheres [10,11]. At present, more applications are being proposed that require broadband SPDs, including spectrometry for environmental science [12] and multispectral LiDAR [13]. For these applications, SPDs must have high system efficiencies at their target wavelengths, so a specific detector with efficiency over a broadband range would be preferable.

Current mainstream semiconductor SPDs such as single-photon avalanche diode (SPAD) and photomultiplier (PMT) usually show only moderate efficiency. In addition, no existing semiconducting SPDs can cover the entire wavelength range from visible to the near-infrared [14]. Because of its low superconducting gap energy (meV), the superconducting nanowire single-photon detector (SNSPD) has an intrinsically high broadband efficiency, potentially enabling broadband detectors from the near-ultraviolet (UV) to mid-infrared wavelengths [15,16]. However, to enhance the optical absorption of SNSPDs, various optical cavity structures have been adopted, that have improved the system detection efficiency (SDE) to be over 90% at various target wavelengths [17,18]. As a result, the broadband feature was sacrificed due to the resonant effect of the optical cavity structures optimized for specific target wavelengths.

Recently, a novel microfiber-coupled SNSPD was proposed by placing a microfiber (MF) atop superconducting niobium nitride (NbN) nanowires [19]. The adiabatically tapered fiber and the evanescent photon absorption constitute a nearly lossless optical structure [20], indicating the potential in high SDE characteristics for the MF-coupled SNSPD. Previous work on MF-coupled SNSPDs showed a maximum SDE of 50% at 1064 nm, however decreased to 20% at 1550 nm [21]. Such devices are unable to reach the full potential of MFs [22] and superconducting nanowires, both of which show the characteristic of broadband response.

In this paper, we first demonstrate that the absorption for MF-coupled SNSPDs can be more than 90% over a wavelength range from 350 nm to 2150 nm by numerical simulation. Then, based on the simulation, we tune the various parameters that may influence the absorption experimentally, including the diameter of the MF, the geometric parameters of the NbN nanowires and the refractive index (RI) of the low-RI adhesive (LRIA) used in the detector. We successfully produced an ultra-broadband MF-coupled SNSPD with the SDE of more than 50% from 630 nm to 1500 nm, using a 1.3-μm-diameter MF, 11 nanowires (100 μm long each) and the LRIA (with RI of 1.38 at 2 K).

2. Numerical simulations

The SDE of an SNSPD is expressed as the product of three factors: the coupling efficiency (${\eta }_{coupling}$), the absorption efficiency (${\eta }_{absorption}$) and the internal efficiency (${\eta }_{internal}$) [23]. We analyze ${\eta }_{absorption}$ for the MF-coupled SNSPD using simulation in this section, with the aim of determining the optimal design for the broadband SNSPD. The optimization of ${\eta }_{coupling}$ will be discussed in the next section. ${\eta }_{internal}$ will not be analyzed here because it has been proved to be close to unity for NbN SNSPD at 1550nm and shorter wavelengths [16,17]. The numerical simulation of ${\eta }_{absorption}$ is performed based on two-dimensional finite element method, electromagnetic waves, frequency domain (COMSOL Multiphysics). The effects of the device parameters (including the fiber diameter, and the nanowire thickness etc.) on ${\eta }_{absorption}$ were studied previously at the wavelength of 1550 nm [19]. Here, we focus on the broadband properties of the device. The RI data for the MgF₂ (001) single crystal substrate and the MF (which is mainly composed of SiO₂) as a function of wavelength were taken from an established database [24]. To guarantee a high ${\eta }_{internal}$ for wavelengths longer than 1550 nm, the nanowire parameters were set empirically as follows: Thickness T = 6.5 nm, Space S = 80 nm, Width W = 80 nm, Nanowire number N = 11, Diameter of MF D = 1.3 μm. It is noted that we were able to reduce the diameter of MF from 2.0 μm in previous work to 1.3 μm in this manuscript, since a smaller D will give a higher MF–nanowire absorptance [21]. The complex RI of the 6.5 nm-thick NbN layer that was deposited on the MgF₂ was measured using ellipsometers (M-2000DI/ IR-VASE Mark II, J.A. Woollam). We assume that the LRIA that is used to cover the whole MF and the nanowires has the same RI as the MgF₂ substrate to obtain an ideal refractive index symmetry environment around the MF.

The mode field distribution of light at different wavelengths propagating within the 1.3-μm-diameter MF without any NbN nanowire was simulated to ensure light can be confined within the MF before it contacts the NbN nanowires. In this simulation, the fundamental TE mode (where the electric field is parallel to the surface of the substrate, X direction shown in the insert of Fig. 1(b)) and TM mode (where the electric field is perpendicular to the surface of the substrate, Y direction shown in the insert of Fig. 1(b)) were only considered. The TE mode corresponds to light with polarization that is perpendicular to the optical axis of the MgF₂ (001) single crystal substrate, with an RI of n(o), while the TM mode is in the direction of the optical axis, with an RI of n(e). As shown in Fig. 1(a), the calculated effective indices of both the TE and TM modes are higher than their corresponding RIs of the surrounding materials for each wavelength over the wavelength range drawn in the graph (250–2300 nm), indicating that there is no cutoff for the fundamental modes in such a symmetrical structure [19]. As the wavelength increases, the curves move closer to the curves of the ambient RI, as a result of increasing evanescent fields (see the inset of Fig. 1(a) for 250 and 2300 nm).

 

Fig. 1 (a) Blue solid square dots and hollow dots represent the calculated effective mode indices of the TE and TM modes in the symmetrical structure respectively, when the diameter of the MF is 1.3 μm. The solid red line and dotted line represent the RIs of MgF₂ (o) and MgF₂ (e) respectively. Inset: profiles of the TE and TM modes at the wavelengths of 250 nm and 2300 nm. The two figures on the left and the two on the right have different length scales in order to make the images of the mode field clear. (b) TE modal absorption versus wavelength for various L values of the nanowire array (indicated using different colors). Inset: 2D schematic of the structure. The number of nanowires is N and the length of a single nanowire in the array is L; the total length of the nanowire is thus N × L. D represents the diameter of the MF, and T, W, and S are the thickness, width, and space of the NbN nanowires.

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Next, an array of 11 NbN nanowires with the parameters listed above is added to the simulation model. The 2D cross section of the structure is illustrated in the inset of Fig. 1(b). The superconducting nanowire has a meander structure and each parallel segment has a length of L [21]. When the length L of the nanowire is increased, the absorption also increases. Figure 1(b) shows the relationship between the TE modal absorption and the wavelength for different lengths L of the nanowire only. The fundamental mode propagating in the MF is considered in this case, and the higher-order modes that are supported in the MF for shorter waves are neglected. In addition, because the TM mode absorption is much lower than that of the TE mode [19], the TE mode only is considered here. The square dots in Fig. 1(b) indicate that, in a 50-μm-long nanowires array, the TE absorption rate initially increases and then decreases with increasing wavelength, as a result of when the distribution of the evanescent field confined within the MF varies with the optical wavelength, the absorption of the MF-coupled nanowire also changes with the wavelength. There is a plateau in the absorption in the middle-range wavelengths that will increase with increasing L. When L is 300 μm, the entire curve represented by the golden triangles becomes very flat, indicating near-100% absorption from 400 nm to 1900 nm. The absorption is more than 90% from 350 nm to 2150 nm. It should be noted here that the curves in Fig. 1(b) do not exhibit any of absorption dips that usually appear in fiber-coupled SNSPDs, which are caused by optical cavity resonances [25–27]. As a result, the MF-coupled SNSPD can achieve both broadband operation and high absorption, which indicates that the MF-coupled SNSPD is likely to have a high and ultra-broadband SDE.

The above analysis describes the ideal situation where the LRIA has the same RI with the substrate. In practice, the difference between RIs of the LRIA and the substrate will cause the light to leak toward the larger RI side from the MF, particularly at longer wavelengths [28]. The analysis will be discussed along with the experimental results in the next section. However, many adhesives with RIs close to that of MgF₂ are ultraviolet-light-curable and the absorption of these adhesives is high for wavelengths below 400 nm, the transmittance even reaches zero at 370 nm [29]. The lower wavelength limit for practical devices is thus usually around 400 nm.

3. Fabrication and experimental setup

Figure 2(a) shows a photograph of the chip-mounting block used for the MF-coupled SNSPD. The SNSPD chip with dimensions of 10 × 10 × 0.4 mm³ is located inside the red dotted frame. The NbN thin film was magnetron-sputtering deposited onto an MgF₂ (001) substrate with thickness of 6.5 nm. The film was then patterned into a meandered nanowire with a line width and pitch of 80 nm and 160 nm, respectively, using electron beam lithography (EBL) and reactive ion etching (RIE). The final active area of the nanowires was designed as an array of 11 parallel nanowires, where each nanowire has length L = 100 μm (a scanning electron microscope (SEM) image of the nanowires is shown in the inset of Fig. 2(b)). We selected L = 100 μm rather than 300 μm to avoid a high dynamic inductance, and it is twice the L of the device in our previous work to assure the broadband absorption [21]. Indeed, the writing field of the EBL equipment is 62.5 × 62.5 μm², and each nanowire was stitched once to reach the length of 100 μm with no visible misalignment, as was depicted in the inset of the Fig. 2(b).

 

Fig. 2 (a) Photograph of chip-mounting block with the MF-coupled SNSPD. The SNSPD chip is located within the red dotted frame. The MF was bent into a U-shape and then placed on the chip, its location is highlighted using a yellow dotted line because the MF is too thin to be seen in the photograph. (b) Optical image of the MF-coupled SNSPD. The inset (c) shows the SEM image of the nanowires without the MF on top (with red pseudo-coloring), and insert (d) shows a partial enlargement of the nanowires.

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As shown in Fig. 2(b), the 1.3-μm-diameter, tapered from standard SMF-28e fiber, was precisely aligned to the nanowires using a microscope [21]. Several improvements had also been made to enhance the ${\eta }_{coupling}$. The first was to perform the coupling process at a dust-free workbench to protect the MF from dust contamination, which could degrade the MF and reduce its transmittance [30]. Another improvement was to select an LRIA with an appropriate RI at low temperatures. The new LRIA used for our MF-coupled SNSPD was a UV-cured adhesive (MY-133-EA, MY Polymers LTD). The RI of the LRIA at the wavelength of 1550 nm changes from 1.33 at 300 K to approximately 1.38 at 2 K, while the changes of the other materials including MgF₂ and SiO₂ were negligible [31,32]. The RI of the new LRIA at 2 K is lower than the RI of LRIA (1.41 at 2 K) used in our previous work [21]. The value is close to the n(e) of MgF₂, which enables us to use 1.3 μm-MF without a light leakage. Assuming that the temperature dependence of the RI is the same for different wavelengths, we calculated the other RIs for the different wavelengths at various temperatures. With this LRIA, the simulations indicated that the TE modal absorption is more than 90% over the wavelength range from 300 nm to 1950 nm when L = 300 μm, and when L = 100 μm, the wavelength range is from 500 nm to 1700 nm, while the other parameters are consistent with the case we studied in simulation part above. In addition, the MF and nanowires were firmly bonded together via the LRIA after curing.

Figure 3 shows a schematic of the measurement system. A supercontinuum laser (EXB-3, NKT) was used together with an acousto-optic tunable filter (SuperK SELECT, NKT) to provide incident photons at different wavelengths. Two attenuators were used to obtain the single-photon-level pulse, and the input photon rate was set to at 10⁶ photon/s. All fibers used in the optical system were standard SMF-28e fibers, except for those used in the polarization controller and the filter, to minimize the optical link losses. Single-mode fibers using for different wavelengths were wrapped within the paddle of the polarization controller (FPC560, Thorlabs) to combine the polarization controller with the filter. Since the polarization of the transmitted photons of different wavelengths cannot be predicted, this configuration gives us the freedom to alter the polarization of the transmitted photons to be the TE mode, i.e. the maximum absorptance to the nanowire. However, we have to tune the polarization for each wavelength. In addition, it also filters out the higher-order modes of shorter waves that may possibly be generated in the SMF-28e fiber before they enter the polarization controller. The MF-coupled SNSPD was packaged in a copper block and then mounted on the cold head of a two-stage Gifford-McMahon (G-M) refrigerator operating at 2.1 K. A bias tee and a room-temperature 50 dB low-noise amplifier (LNA-650, RF Bay Inc.) were used to read out and amplify the voltage pulses generated by the SNSPD. The amplified signal was then fed into an oscilloscope or a photon counter to characterize the device performance.

 

Fig. 3 Schematics of the measurement system which contains the optical system, the cryocooler and the circuit system. The optical system is composed by a supercontinuum laser, an acousto-optic tunable filter (AOTF), two attenuators, a polarization controller, power meters for the detector port and monitor port, and SMF-28e fibers to connect all of them together; the cryocooler is prepared to provide a 2.1 K environment for the MF-coupled SNSPD; the circuit system consists of a bias tee, a 100 KΩ resistor, a DC voltage and a room-temperature 50 dB low-noise amplifier (AMP) to amplify the voltage pulses generated by the SNSPD, and an oscilloscope or a photon counter to monitor and count the amplified signals.

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4. Results and discussion

We characterized the performance of the detector system by measuring the SDE and the dark count rate (DCR) as a function of the bias current over the wavelength range from 500 nm to 1700 nm. The SDE is defined as the number of detected counts subtracting the number of dark counts divided by the number of incident photons from the detector port marked in Fig. 3. The polarization of the input photons was adjusted to obtain the maximum photon count (in the TE mode) using a polarization controller. Figure 4(a) shows broadband SDE and DCR response to wavelength from 530 to 1550 nm. The saturated plateau can be found at wavelengths shorter than 850 nm and the SDE reached 66% at a wavelength of 785 nm. The SDE at 1550 nm was 45% at a DCR of 50 Hz. The unsaturated SDE for the longer wavelengths offers an opportunity for improving the internal efficiency of the SNSPD.

 

Fig. 4 (a) SDE versus bias current at various wavelengths (indicated using different colors). The hollow dotted line represents the dark count rate as a function of bias current. (b) SDE versus wavelength over the range from 500 to 1700 nm. The red dashed line represents the simulated TE modal absorption, while the measured SDE is the black dotted line, the yellow diamond and blue dotted lines represent calculated SDEs with and without saturation correction, respectively, and the purple dotted line is the measured initial optical loss of the MF.

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Figure 4(b) shows the wavelength dependence of the measured SDE, the simulated optical absorption, the calculated SDE, and the initial optical loss of the MF. The measured SDE is represented by the maximum value measured in experiments for each wavelength. Figure 4(a) shows that the MF-coupled device exhibits a remarkably broadband SDE, with the criterion of an SDE of more than 50%, the bandwidth is 630–1500 nm. When the criterion of SDE is more than 30%, the bandwidth is 530–1650 nm. To the best of our knowledge, this is the best bandwidth reported for broadband SPDs that can operate at both the visible and near-infrared wavelengths. The simulated TE modal absorption ${\eta }_{absorption}$, which is represented by the red dashed line, was obtained using the simulation that was introduced in the previous section, with the 1.38-RI-LRIA. When compared with the simulated ${\eta }_{absorption}$, there are losses that may be contributed by ${\eta }_{coupling}$ and ${\eta }_{internal}$.

Because the connection loss between the MF fiber and the standard SMF-28e fiber can be neglected, ${\eta }_{coupling}$ is mainly determined by the initial optical loss of the MF. The initial optical loss was measured and is plotted in Fig. 4(b) using triangles. We coupled the 1.3-μm-diameter MF to the bare MgF₂ substrate using the LRIA and evaluated the loss of the structure at 2.1 K. The optical system of the measurements is the same as that shown in Fig. 3. We measured the power at the input of the detector port and at the monitor port in Fig. 3. The difference between these powers is the initial optical loss of the MF. The loss is less than 1 dB over a wide wavelength range from 750 nm to 1600 nm. However, the loss increases rapidly when the wavelength is lower than 750 nm or higher than 1600 nm.

There are three factors that contribute to the MF’s initial optical loss, the mode loss, the MF fabrication loss and the bending loss. The mode loss comes from the successive disappearance of the higher-order modes when the fiber diameter decreases in the transition section of the MF [33]. Although there was a single-mode filter inserted into the optical system before the incident photons entered the detector port, there still existed a section of SMF-28e fiber which was included in the MF might cause the higher-order modes. As a result, we see in Fig. 4(b) that the MF’s initial optical loss increases rapidly as the wavelength decreases below 750 nm. We can choose single mode fiber with wider operating wavelength (e.g. HI1060-J9, Thorlabs, operating wavelength: 980–1650 nm) to fabricate the MF, and then the multi-mode loss for low wavelength will be reduced. However, the high-transmittance taper process based on a new type of fiber still requires quite a lot experimental work. While the initial MFs have very high transmittance (the typical value is more than 90%), the transmittance may decrease because of the possible contamination during the fabrication process, which is called as the MF fabrication loss of MF-coupled SNSPD. The transmission of photons with larger wavelengths is more sensitive to asymmetric mode field distribution caused by fiber bending, leading to a bending loss. The main bending loss occurs on the corners of the U-shaped MF structure, so this part of loss will disappear if we redesign the coupling module and choose the straight MF in future. In summary, the MF fabrication loss contributes to the background of the MF initial optical loss over the whole wavelength range. The mode loss causes extra losses at shorter wavelengths and the bending loss contributes to these extra losses at longer wavelengths.

By adding the measured initial loss to the measured SDE, we obtained the expected calculated SDE shown as a blue dotted line in Fig. 4(b), which was lower than the simulated absorption. As Fig. 4(a) shows, the SDE curve is unsaturated when the wavelength is longer than 1250 nm due to the worse nanowire uniformity compared with shorter nanowires, which indicates that ${\eta }_{internal}$ is less than 100% at these wavelengths. Optimized fabrication process may solve this issue. After ${\eta }_{internal}$ was taken into consideration, we corrected the unsaturated SDEs of the wavelengths above 1250 nm using a sigmoid function fitting [34] and obtained the yellow diamond dotted line shown in Fig. 4(b). The calculated saturated curve is consistent with the simulated absorption, with an offset of 1.3 ± 0.2 dB over the range from 600 nm to 1600 nm. This offset may be related to the difference in the whole fabrication losses between the MF-coupled SNSPD and the MF on the bare MgF₂ substrate. At the shorter wavelengths, the larger offset is caused by imperfect polarization control. At longer wavelengths, the offset is higher because of the scattering of impurities within the LRIA; at longer wavelengths, a larger evanescent field occurs around the MF (the evanescent field distribution is shown in Fig. 1(a)), which is more susceptible to the environmental effects.

6.5 nm is a typical film thickness for NbN SNSPDs on Si substrate with high performance (high DE, low timing jitter) [17]. The RI of 6.5 nm thick NbN thin film is well understood from the previous measurements, which is used for the simulation. On the other hand, thinner NbN nanowires fabricated on insulated MgF₂ substrate have larger resistance, which make the sample more susceptible to electrostatic burnout. As a result, we chose the thickness of 6.5 nm. However, we have to admit that more studies should be done to optimize the thickness and other parameters of the film on MgF₂ substrate to improve the performance of the MF-coupled SNSPD.

The recovery time and the timing jitter of the MF-coupled SNSPD were also measured. The recovery time was obtained from the averaged response waveform at a bias current of 18.0 μA, and had a value 19.4 ns, corresponding to a count rate of ~50 MHz. The timing jitter of the device was achieved using a time correlated single-photon counting module [35], and it was estimated to be 56.1 ps at a wavelength of 1550 nm. Both the recovery time and the timing jitter are typical values when compared with the corresponding values of conventional SNSPDs.

5. Conclusions

In this work, we first showed the MF-coupled SNSPD can achieve optical absorption of more than 90% over the 350–2150 nm wavelength range using numerical simulations. We then experimentally demonstrated an MF-coupled SNSPD with an unparalleled broadband SDE of more than 50% over the range from 630 nm to 1500 nm. The SDE was 66% at 785 nm and was 45% at 1550 nm. This ultra-broadband SPD may find interesting applications in a variety of fields, such as spectrometer. In future work, we will optimize the device to further increase both the SDE and the operating wavelength range. Reduction of the MF’s initial optical loss may increase the SDE over the whole wavelength rage, and the SDE at longer wavelengths can be improved by optimizing the superconducting nanowires.