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Abstract
We report superconducting nanostrip single-photon detectors (SNSPDs) with dielectric multilayer cavities (DMCs) for a 2-µm wavelength. We designed a DMC composed of periodic SiO2/Si bilayers. Simulation results of finite element analysis showed that the optical absorptance of the NbTiN nanostrips on the DMC exceeded 95% at 2 µm. We fabricated SNSPDs with an active area of 30 µm × 30 µm, which was sufficiently large to couple with a single-mode fiber of 2 µm. The fabricated SNSPDs were evaluated using a sorption-based cryocooler at a controlled temperature. We carefully verified the sensitivity of the power meter and calibrated the optical attenuators to accurately measure the system detection efficiency (SDE) at 2 µm. When the SNSPD was connected to an optical system via a spliced optical fiber, a high SDE of 84.1% was observed at 0.76 K. We also estimated the measurement uncertainty of the SDE as ±5.08% by considering all possible uncertainties in the SDE measurements.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Single-photon detection technology at the wavelength of around 2 µm has recently attracted attention for various applications. For example, owing to the low solar irradiance around these wavelengths, it is advantageous to distinguish optical signals, even in daylight, in the application of LIDAR and free-space optical communications [1–6]. In quantum-photonic circuits based on silicon waveguides, two-photon absorption caused by nonlinear effects is a serious problem when the photons have a wavelength of 1.55 µm. However, this two-photon absorption can be avoided by using photons with a wavelength that is twice longer than those at which optical loss occurs in silicon, corresponding to λ ∼2.3 µm [7,8]. In the diagnostics of semiconductor large-scale integration chips by detecting the photons emitted from the integrated circuit, the voltage applied to the circuit decreases as the integrated circuits become highly integrated [9–12]. This causes the wavelengths of the emitted photons to shift to longer wavelengths, reaching around 2 µm. In spite that there would be various demands for the photon detectors at around 2 µm as described above, there are no single-photon avalanche diodes (SPADs) or photomultiplier tubes with a photon-counting resolution for wavelengths longer than 1.8 µm. In contrast, superconducting nanostrip single-photon detectors (SNSPDs) can have high sensitivity, even in such long wavelength regions, owing to their photon detection mechanism. In this mechanism, the superconductivity of the nanostrips is locally broken by the absorption of photons by the nanostrips because of the much smaller superconducting energy gap compared to the photon energy [13–17]. There have been several recent reports on SNSPDs designed for 2 µm [18,19], and a system detection efficiency (SDE) of 70% has been achieved [19]. In this paper, we report the highly efficient NbTiN SNSPDs by carefully tailoring the photon absorption efficiency, optical coupling efficiency, and internal detection efficiency (IDE). We designed dielectric multilayer cavities (DMCs) [20,21] placed underneath the nanowire to maximize the photon absorption efficiency at 2 µm and fabricated NbTiN nanowires on the DMC covering an area of 30 µm × 30 µm to efficiently couple with a single-mode fiber (SMF) for the 2 µm wavelength band. Since the IDE of nanostrips depends on the nanostrip parameters and the operating temperature [22], we fabricated two types of SNSPDs with different nanostrip line widths and evaluated the temperature dependences of SDE using a sorption-based cryocooling system with operation temperatures of 2.2 K–0.76 K. To perform accurate SDE measurement, we carefully established the SDE measurement setup for 2 µm with variable optical attenuators and neutral-density (ND) filters, each of which is well under the calibration level. Additionally, we estimated the measurement uncertainty of the whole system by verifying the measurement uncertainty of each component.
2. Design and fabrication
Figure 1(a) shows the device structure of a NbTiN SNSPD with a DMC for a 2-µm wavelength comprised of 11 periodic SiO2/Si bilayers on a Si wafer. Each dielectric layer is one quarter of the optical thickness at 2 µm, and the actual thicknesses of the SiO2 and Si layers are 359 and 153 nm, respectively. Figure 1(b) shows the calculated optical absorptance in the NbTiN nanostrips for transverse electric (TE)-polarized light, for which the electrical field is parallel to the nanostrips, by finite element analysis using COMSOL5.5 [20,23]. The dashed curves in Fig. 1(b) show the optical absorptance of the two designed nanostrips (Design I and Design II), whose line widths and pitches are 60 nm and 140 nm, 80 nm and 160 nm, respectively. We confirmed that the optical absorptances of Designs I and II at 2 µm were 95.6% and 98.1%, respectively. Based on the SNSPD design, the DMC was fabricated on bare silicon wafers using ion-beam sputtering deposition. Subsequently, we fabricated two types of SNSPDs (SNSPD I and SNSPD II) on the DMC. The fabrication process of SNSPDs on the DMC is like [20]: first, the surface SiO2 layer of the DMCs was cleaned by an argon ion beam. Then, the NbTiN thin film was deposited by DC reactive sputtering on the DMC. Next, nanostrip structures were fabricated using electron-beam (EB) lithography and reactive-ion etching. We estimated the NbTiN thickness of the fabricated SNSPDs to be 7 nm from the NbTiN deposition rate and the offset time due to the shutter opening/closing operation during the NbTiN deposition, which were identified by the deposition of NbTiN films with different thicknesses in advance. The fabricated SNSPD for Design II (SNSPD II) is shown in Fig. 2. The SNSPDs consist of two nanostrip avalanche photon-detector structures that improve the signal-to-noise ratio [24,25]. The mode-field diameter of the SMF for the 2-µm wavelength band (SM2000) is 13 µm, which is significantly larger than the typical beam waist (7 µm) for SNSPDs using a SMF for 1.55-µm wavelengths [26]. Therefore, we fabricated SNSPDs with an active area of 30 µm × 30 µm to maximize the coupling efficiency with SM2000. As results of analysis from the observed scanning electron microscope (SEM) image, the line widths of SNSPD I and SNSPD II (86 nm and 116 nm, respectively) became wider than expected. This is because we proceeded with EB lithography under the assumption that the proximity effect [27,28] during EB writing is similar to that for a Si substrate with a thermally oxidized layer. However, this effect on DMC was smaller than expected; hence, the nanostrip width increased. Accordingly, the optical absorptance at the actual nanostrip width should be clarified, as indicated by the solid curve in Fig. 1(b). The optical absorptance increased to over 99% for both SNSPDs at a wavelength of 2 µm because of higher fill factors than expected.
Fig. 1. (a) Device structure of SNSPDs with a DMC for 2-µm wavelength and (b) calculated optical absorptance of TE-polarized light for designed and fabricated nanostrips. The thickness of NbTiN nanostrips is assumed to be 7 nm. The parenthetical values in the legend of (b) denote (line width, pitch).
Fig. 2. Microphotographs of the fabricated design II. The active area is 30 µm × 30 µm, and the measured line width and pitch are 116 nm and 160 nm, respectively. The inset shows a SEM image.
3. Measurements and results
3.1 Measurement setup and SDE measurements
Figure 3 shows the measurement setup used to evaluate the SDE. The fabricated SNSPDs were mounted on a fiber-coupled package [29] and placed in a sorption-based cryocooler with operation temperatures of 2.2 K–0.76 K. The output signals of the SNSPD under testing were amplified using a low-noise amplifier (RF Bay, LNA-545) outside the cryocooler, and the output count rate was observed using a pulse counter (Stanford Research Systems, SR400). The optical systems for measuring the SDE were composed of a thulium-doped laser source (Thorlabs, LFL2000), a fiber-coupled beam splitter, three variable optical attenuators (VOAs; Thorlabs, V2000F), a free-space fiber-to-fiber coupler module including ND filters and a polarization controller, and optical power meters (PM1 and PM2; Thorlabs, S148C).
Fig. 3. Measurement system to evaluate SDE of SNSPDs. All optical components are connected via optical fibers for 2 µm, SM2000. The current biasing to SNSPDs and extracting their output signals are via coaxial cables.
To adjust the input photon flux at the single-photon level, we calibrated all optical attenuators using a power meter and estimated the actual sensitivity of the power meter to guarantee the accuracy of the attenuators (details are provided in Supplement 1). The initial input power emerging from the fiber-to-fiber coupler was measured by PM2, with all VOAs set to 0 dB and the ND filters removed. Subsequently, the optical input power was attenuated to approximately −110 dBm using the VOAs and ND filters. To address the laser power fluctuations, PM1 monitored the laser power, and the input photon flux was calculated in real time during the SDE measurements.
To evaluate the SDE, the optical fiber from the fiber-to-fiber coupler was connected to the SNSPD under testing (SNSPD I and SNSPD II) via the FC/PC connectors (Fig. 3(a)). Here, the SDE was evaluated as (CR–DCR)/PN, where CR is the count rate of the output signals from the SNSPD when the photon flux is the input, DCR (dark count rate) is the count rate from the SNSPD when the photon flux is blanked off at the fiber-to-fiber coupler module, and PN is the input photon number per second. The polarization of the input photon flux was adjusted to maximize the CR using a polarization controller. The measured bias current dependences of the SDE and DCR are shown in Fig. 4. During the SDE measurements, the laser power was observed by PM1 each time and reflected in the PN identification, which varied from 97.646 × 103 to 98.453 × 103 photons per second. The measured DCRs were three orders of magnitude higher than those of typical SNSPDs at a wavelength of 1.55 µm [25]. This was due to the drastic increase of blackbody radiation entering the SNSPDs because the cutoff wavelength of SM2000 (∼ 2.3 µm) was longer than that of SMF28e fiber (∼1.63 µm), which was consistent with a previous study [18,19]. At an operating temperature of 2.2 K, which was similar to the temperature of typical Gifford–McMahon cryocoolers [25], the SDE of SNSPD I was saturated and reached 74.2%. Meanwhile, the SDE of SNSPD II was 68.7%, which was lower than that of SNSPD I because of the insufficient IDE caused by the wide nanostrip width. In addition, the wide nanostrip of SNSPD II may have induced a current crowding effect at the bend edge of the nanostrip, which reduced the critical current of the nanostrip, resulting in a reduction in IDE [30,31]. On the other hand, at an operating temperature of 0.77 K, the SDEs of SNSPD I and SNSPD II reached 74.6% and 78.5%, respectively, owing to the improvement in the IDE. Note that SNSPD II had a higher SDE, despite SNSPD I having a higher IDE, and the simulated optical absorptances were not significantly different between the two devices. This discrepancy can be attributed to the controllability of the incident photon polarization state and the optical properties of the SNSPDs. As mentioned above, the incident photons were polarized to achieve the maximum count rate of the SNSPDs, which corresponded to tuning the incident photons to TE-polarized light. However, because of the slight movement or vibration of the SMF after passing through the polarizer, the incident photon may have fluctuated from the TE-polarized light or shifted slightly from linear polarization to elliptical polarization, resulting in a decrease in SDEs. Although both SNSPDs had polarization sensitivity (details of the optical properties of SNSPD I and SNSPD II are provided in Supplement 1), the optical absorption of the TM-polarized light of SNSPD II was higher than that of SNSPD I, which may have caused a larger decrease in the SDE of SNSPD I. Therefore, we believe that the SDE can be further improved by optimizing the thickness of each layer in the DMC to suppress the polarization sensitivity [20].
Fig. 4. Bias current dependences of SDE and DCR of fabricated SNSPDs with operational temperatures of 2.2 K and 0.77 K.
To avoid deterioration of the SDE due to the optical loss of the FC/PC connectors, we connected the optical system to SNSPD II via a spliced optical fiber (Fig. 3(b)). The fiber end of the SNSPD II package was cut and fusion-spliced with an optical fiber without cable jackets in the cryocooler. After re-cooling to the cryogenic temperature, the initial power of the optical system was measured using PM2, and the optical input power was adjusted to −110 dBm, as previously stated. Subsequently, the fiber end from the fiber-to-fiber coupler was cut and fusion-spliced to the other end of the optical fiber without cable jackets. Figure 5 shows the measurement results of the fiber-spliced SNSPD II. We measured the CR and DCR five times at each bias current to estimate the measurement uncertainty of the SDE [32,33] (discussed later), and the mean values of the SDE and DCR are shown in Fig. 5(a). The measurement results of the SNSPDs by connection type are summarized in Table 1. Note that the DCR of the fiber-spliced SNSPD II increased owing to blackbody radiation and stray light entering from the room-temperature environment through the spliced fiber without cable jackets. By changing the connection between the optical system and SNSPD II from FC/PC connectors to fusion splicing, the SDE improved to 84.1%, which is the highest among the SNSPDs for the 2 µm wavelength reported thus far.
Fig. 5. Measurement results of SNSPD II connected via spliced optical fiber. (a) Bias current dependences of SDE and DCR using the mean value of five measurements, (b) estimated relative uncertainties of CR and DCR, and (c) PN and its relative uncertainty during SDE measurements.
Table 1. Summary of measurement results of SNSPD I and SNSPD II
3.2 Estimation of SDE uncertainty
To verify the accuracy of the measurements, we estimated the SDE uncertainty. In the SDE measurement, the relative uncertainty of the SDE (σSDE) was determined by all possible uncertainties in the measurements as follows:
Table 2. Possible uncertainties in SDE measurements
4. Conclusion
In summary, we presented NbTiN SNSPDs with a dielectric multilayer cavity (DMC) for a 2-µm wavelength. By fabricating nanostrips on DMCs with an active area sufficiently larger than the mode field diameter of the optical fiber coupled to SNSPDs, the optical absorptance and coupling efficiency of the nanostrips were maximized. We fabricated two types of SNSPDs with different nanostrip line widths of 86 and 116 nm. These were shifted toward higher fill factors than expected by the proximity effect of EB lithography on the DMCs. The fabricated SNSPDs were evaluated using a sorption-based cryocooler at a controlled temperature. For accurate SDE measurements at 2 µm, we experimentally evaluated the actual sensitivity of the power meter and carefully calibrated all the optical attenuators. In measurements at 2.2 K, we obtained a saturated SDE of 74.2% for the SNSPD with an 86-nm line width. On the other hand, in the measurements of the SNSPD with a line width of 116 nm, the SDE was not saturated and was 68.7%. The SDE reached 78.5% at 0.77 K by improving the IDE. In addition, we connected the SNSPD with a line width of 116 nm to the optical system via a spliced optical fiber instead of FC/PC connectors. Consequently, we successfully demonstrated the high SDE of 84.1% at 2 µm and estimated the measurement uncertainty of the SDE as ±5.08%. The results presented in this paper indicate that the SNSPD with DMCs is an effective approach for obtaining a high SDE, even in the mid-infrared wavelength region, and the design flexibility of DMCs enables the development of various applications for the 2-µm wavelength band.
Funding
MEXT Quantum Leap Flagship Program (MEXT Q-LEAP) (JPMXS0118067634); Japan Society for the Promotion of Science (21K20438).
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.
Supplemental document
See Supplement 1 for supporting content.
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