1. Introduction

Quantum information science is one of the most significant scientific revolutions of the 20^th century [1]. The rapid development of photonic quantum technology has promoted the development of quantum communication [2–4] and quantum computation [5–7]. Over the last few decades, quantum experiments and applications have advanced from proof-of-principle demonstrations to robust implementations [8–10], bringing with them large-scale processing of many quantum information carriers and complex systems, which require the use of integrated photonic devices [11–14]. Quantum photonic circuits or chips have emerged to meet these demands due to their many advantages, which include scalability, stability, and feasibility [13]. The development of integrated quantum circuits enabled the use of highly complex apparatuses in quantum photonic state manipulation platforms and generated requirements for a large number of single-photon detectors [5].In conventional schemes, the components for manipulating and detecting quantum photon states are usually separated, and therefore the coupling losses resulting from the transmission of photons between them have scope for improvement [15,16], which leads to a demand of on-chip integration. In addition, the on-chip single-photon detectors integrated with photonic circuits may offer a solution to system miniaturization [17].

A variety of integrated photonic technologies have been proposed, such as CMOS, UV writing and femtosecond laser direct writing (FLDW) [13]. Benefiting from the precise control of material modifications, FLDW enables the use of arbitrary three-dimensional structures with complex geometries [18,19], laying a strong foundation for implementing experiments that require higher dimensional manipulation [20]. For instance, two-dimensional quantum walks are demonstrated in photonic waveguide arrays, which are fabricated using FLDW techniques [7,21], which are intractable in other integrated platforms. Besides, FLDW has the advantages of fast prototyping [22], high integration [23], and low transmission losses [24]. In addition, an FLDW waveguide is usually fabricated in a silicate substrate, which is a widely adopted material that has the benefit of high coupling efficiency with fibers. Previous research showed that the coupling efficiency between FLDW waveguides and standard single-mode fibers can be enhanced to 77% [25].

Another bottleneck that limits quantum information processors is single-photon detectors. With promising performance characteristics, such as high system detection efficiency (SDE), low time jitter, and low dark count rate (DCR) [26–29], superconducting nanowire single-photon detectors (SNSPDs) have been widely used in quantum photonic experiments and have achieved remarkable results [2–6,13,30]. Meanwhile, SNSPDs are usually made of electrically and optically accessible structures consisting of narrow (∼100 nm) and ultrathin (4–7 nm) wire strips, which are easier to integrate when compared with semiconductor detectors [17]. Many works have already been conducted to integrate SNSPDs into photonic circuits [31–40]. On this basis, here a new structure was proposed to integrate SNSPDs with waveguides fabricated by FLDW in a borosilicate wafer. SNSPDs have been proven to exhibit good performance with regard to such silicate substrates [41,42], making it possible to integrate conventional SNSPDs with an FLDW silicate waveguide.

In this work, we proposed and realized a new type of FLDW waveguide-coupled single-photon detector that combines the FLDW waveguide technology and conventional superconducting nanowires together. Light travels through a waveguide array, which is directly written inside the substrate and then absorbed by NbN nanowires engraved at the end face of the waveguides, thereby realizing array single-photon detection. We successfully demonstrated the feasibility of the proposed design, and the experimental results showed that at a wavelength of 780 nm, the device can reach a saturated SDE of 1.7% at 10 Hz DCR, which provides a new possibility for on-chip quantum optics.

2. Design and simulation

A three-dimensional diagram of the FLDW waveguide-coupled SNSPD is illustrated in Fig. 1. An array of waveguides was fabricated by FLDW in a 20 mm × 20 mm borosilicate glass substrate with the thickness of 1 mm (EAGLE XG Slim Glass, Corning). There are two types of waveguides: detector waveguides, which are bent upward to the surface, and auxiliary waveguides, which horizontally extend through the entire chip. All the detector waveguides were parallel to each other and located at the same depth within the chip. Each detector waveguide in the array was composed of three sections: a horizontal section, an inclined section, and a curved section connecting these two sections. The horizontal section is parallel to the substrate surface and extends from the sidewall of the substrate to within. A part of the horizontal section can be replaced with more complicated structures, which can be used for quantum photonic experiments in the future. The inclined section is connected to the horizontal section by a short curved waveguide, at an inclination angle β to the upper surface of the substrate. The inclined section ends at the top surface of the substrate, leaving an oval cross-section. This section is used to guide light to the substrate surface, and therefore, NbN nanowires can be prepared on the chip surface using mature fabrication technologies. The refractive index (RI) of the waveguides was higher than that of a surrounding substrate, allowing light to be confined therein. In our work, the RI of the substrate and waveguide were around 1.50475 and 1.50625 at a target of 780-nm wavelength, respectively. With proper fabrication parameters, such as the pulse energy, we successfully prepared single-mode waveguides at 780-nm wavelength. In addition, several auxiliary straight waveguides were prepared for calibration. These auxiliary waveguides penetrated the entire chip and were parallel to the bottom surface of the chip. The NbN nanowire array was arranged in a meandering line shape, as shown in Fig. 1, where the active area covered directly above the waveguide cross-section on the surface. An incident light was coupled to the waveguides embedded into the chip through a V-groove, and the light traveled along the waveguides until it was absorbed by the nanowires deposited on the upper surface of the chip. An optical adhesive (OA) was used to cover the top of the nanowires and played a role in adjusting the environmental RI and protecting the nanowires. The whole device was placed at a cryogenic temperature (∼2 K) to achieve a superconducting state in the NbN nanowires. Once a single photon was absorbed, the superconducting state was destroyed, resulting in a measurable output voltage signal to detect the event. Each waveguide and the nanowires on its top formed a detector, and worked independently.

 

Fig. 1. Schematic of the FLDW waveguide-coupled SNSPD. The gray square block represents the chip, and the blue square block represents the V-groove. The dark gray cylinder represents the waveguides, and the three colors of green, yellow, and purple indicate the horizontal, curving, and inclined sections of the waveguide. The red area represents NbN. Only the approximate nanowire structure on one of the detector waveguides is shown, and it is present on each detector waveguide. Moreover, cladding was used to cover the nanowire area, but it was not shown in the figure for clarity purpose.

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The optical absorption property of the detector was numerically analyzed using the three-dimensional (3D) finite element method (FEM) (COMSOL Multiphysics). Because the entire area of the NbN nanowire array in our device was much larger than the size of a single nanowire, we could choose a small region of a single line in the nanowire array as a simulation unit, as shown in Fig. 1. A schematic 3D diagram of the simulation unit model is illustrated in Fig. 2(a). The simulation model was periodically repeated along the x-axis at a pitch of 200 nm, extending infinitely along the y-axis. The computational domain was set to 200 × 200 × 3000 nm³, where the NbN nanowire (red area in Fig. 2(a)) on the x-y plane had a width w = 100 nm, a length d = 200 nm, and a thickness t = 6.5 nm. Figure 2(b) shows a schematic of the light propagation direction in the waveguide. For clarity, the figure only shows the x-y plane in which the nanowire (red area) is located and the y-z plane (gray area) in which the light propagates. As seen in Fig. 1, the long side of the nanowire is in the same direction of the waveguide extension, so light propagates in the y-z plane in Fig. 2(b). Since the waveguide obliquely extends to the upper surface of the substrate, the light is incident on the nanowire at an angle α, which is the complementary angle of β. For the cladding covering the nanowire, we analyzed two cases, which were composed of air or OA. Considering that the device operates at cryogenic temperatures, the RI data of the used materials in the device needed to be modified. The waveguide was mainly composed of borosilicate glass, which has low temperature dependence. However, using the cryogenic RI measurement method, the RI of the OA cladding at cryogenic temperature was estimated to be 1.3841 at a wavelength of 780 nm [43]. It is obvious that the incident angle α greatly affected the distribution of the evanescent field near the nanowire, leading to differing coupling efficiency. Thus, we analyzed the relationship between the nanowire absorption and α.

 

Fig. 2. (a) 3D schematic of the simulation unit. The simulation model was set to periodically repeat along the x-axis at a pitch of 200 nm and to extend infinitely along the y-axis. The NbN nanowire (red area) is on the x-y plane and extends infinitely in the y-direction. (b) A schematic of the light field propagation in the waveguide with the orange arrow representing the direction of the light field propagation in the y-z plane and the blue arrow representing the electric field direction. (c) The TE and TM mode absorption of the NbN nanowire as a function of the waveguide inclination angle α. The red and blue dotted lines represent the nanowire covered using an optical adhesive (OA) and air, respectively. The TE mode is defined as the incident light of the electric field in the y-z plane, and the TM mode is in the x-y plane.

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Figure 2(c) shows the nanowire absorption dependence of the incident angle α. Here, the TE mode is defined as the incident light of the electric field in the y-z plane, and the TM mode is that in the x-y plane. As seen in the figure, different claddings and fundamental optical modes have different maximum absorption values. A local minimum absorption close to zero can also be observed on the TE absorptance curve at the angle (41.60° for air and α = 66.76° for OA) corresponding to the total internal reflection at the waveguide-cladding interface, which is in accordance with the simulation results presented in previous literature [44,45]. For the air cladding, the maximum absorption occurred at α = 55° for TE and at 50° for TM. For the OA cladding, the maximum absorption occurred at α = 75° for TE and nearly reached unity for TM when α was 70°. However, for the FLDW waveguide fabrication, the achievable α was subject to the limitations of the manufacturing process, such as, the inclination angle β. When the bending radius of the curved waveguide was fixed, β increased, and the curving arc became longer. Since the transmission loss of the curved waveguide was much larger compared with the straight one [24], β was maintained below 10° to allow a shorter curved waveguide and fewer losses. As shown in Fig. 2(b), for β ≤ 10° (α ≥ 80°), the greater the angle, the higher the absorption. The simulation results showed that in the case of OA cladding, for α = 80°, the highest absorption of 87% can be reached for the TM mode.

3. Device fabrication

The device fabrication included four steps: waveguide preparation, nanowire engraving, fiber coupling, and chip packaging. First, we fabricated the waveguides in a borosilicate substrate. Both the detector and auxiliary waveguides were written using a femtosecond laser that has a repetition rate of 1 MHz, a pulse duration of 290 fs, a central wavelength of 513 nm, and a pulse energy of 270 nJ. Beam shaping was achieved with a cylindrical lens. The laser beam was focused by a 50× objective with a numerical aperture of 0.55 in the borosilicate substrate at a depth of 500 µm. Besides, the translational stage moved at a constant speed of 15 mm/s. 12 detector waveguides and 12 auxiliary waveguides were made and arranged in parallel, which were 127 µm apart. The length of the horizontal section was approximately 5–6 mm, and the curved section had a bending radius of 30 mm. Considering the bending loss, the angle β of the inclined section was set to 7°. In this case, an array of elliptical waveguide cross-sections with a long axis of ∼49 µm and a short axis of ∼6 µm was formed on the chip surface (see Fig. 1). Careful characterization of waveguide qualities that are dependent on fabrication parameters was performed.

After the waveguide preparation completed, the surface of the chip was polished to a flatness of a magnitude 10⁻¹⁰ m to meet the necessary requirements for the NbN film preparation. The next procedure was nanowire engraving. A 6.5 nm thick NbN film was deposited using magnetron sputtering and then patterned using a PMMA resist layer and electron-beam lithography (EBL) tool. Then the electron-beam resist pattern was transferred onto the NbN layer using a CF₄ reactive-ion etch (RIE) recipe. The position of the polished waveguide cross-sections was calibrated through a series of mark arrays (small black crosses in Fig. 3(b)) using an optical microscope to accurately engrave the nanowire array onto the waveguide cross-sections. As shown in Fig. 3(b) and Fig. 3(c), the waveguides and nanowires were marked in pseudo-colored yellow and red, respectively. These two optical images were obtained using a transmission microscope, so the waveguides inside the chip could be seen directly below the NbN electrode but not actually in contact with it. The right ends of the waveguides were considered as the locations of the cross-sections, and no visible misalignment was observed. The width and pitch of the nanowires were 100 and 200 nm, respectively, and the nanowire area was set to be a square whose details can be seen in the inset of Fig. 3(c), where it had a length of 60 µm and a width of 10 µm. After the electrodes made from NbN were formed, the FLDW waveguide-coupled SNSPD chip was complete.

 

Fig. 3. (a) Photograph of the chip-mounting block with the FLDW waveguide-coupled SNSPD. (b) Optical image of the FLDW waveguide-coupled SNSPD without OA cover. For clarity, both the waveguide (yellow) and NbN (red) were pseudo colored. (c) Partial enlargement of the waveguide and NbN nanowires. Inset: SEM image of a single nanowire in the meandering structure.

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An 8-channel V-groove was used to couple light into the detector chip. The V-groove and the chip were placed on 6D precise adjustment frames, and an alignment operation was performed with the help of the auxiliary waveguides. Half of the channels were used to couple with the detector waveguides, and the left channels were coupled with the auxiliary waveguides to calibrate the relative position between the V-groove and the chip. Calibration light was injected into one end of the auxiliary waveguide through the V-groove. The best coupling between the V-groove and the chip was considered to be obtained when the strongest output light is detected at the other end of all the auxiliary waveguides. After this, they were fixed together with optical glue (Norland Optical Adhesive 61, Norland Products). The chip was packaged in a copper block with 16 SMP connectors, as shown in Fig. 3(a), and then a chip-mounting block was mounted on the cold head of a two-stage Gifford (G-M) refrigerator operating at 2.1 K. The positive electrode of each detector was connected to an SMP, and because four waveguides were selected to access the optical channel on this chip, only four electric channels worked effectively. A supercontinuum laser source (EXB-3, NKT) and an attenuator (LTK-1-1, EXFO) were used to provide incident single-photon-level photons at 780-nm wavelength, and the input photon rate was set at 10⁶ photon/s. All the used fibers in the optical system, including those wrapped within the paddle of the polarization controller (FPC560, Thorlabs), were single-mode fibers for the 780-nm wavelength. The polarization of the transmitted photons was altered for polarization-optimized SDE. For the electric circuit, 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 signals were then fed into an oscilloscope to characterize the device performance.

4. Device characteristics and discussion

We characterized the performance of the detector system by measuring the SDE and DCR as functions of the bias current. The SDE was defined as the output pulse rate subtracted from the DCR and then divided by the number of incident photons. We were able to obtain saturated SDEs for three out of four detectors of our device due to imperfect processing. Each detector was labeled after its corresponding waveguide number. At 10 Hz DCR, the SDEs of the FLDW waveguide-coupled SNSPD for the waveguide numbers 10#, 11#, and 12# were 1.2%, 1.7%, and 0.6%, respectively. The SDE performance of 11# is displayed in Fig. 4(a). The saturated plateau indicates that the intrinsic detection efficiency (IDE) of the device reached near unity, [26,28]. The result shown in Fig. 4(a) indicates that our FLDW waveguide-coupled SNSPD successfully obtained an optical response. The SDEs of the detectors based on multiple waveguides on the same chip have demonstrated the potential of implementing large-scale on-chip integrated detectors. We also examined the influence of the scattered photons from the neighboring fibers, which may cause SDE to be overestimated. During the measurement of one detector, we checked counts on the neighboring detectors which were negligible small.

 

Fig. 4. (a) SDE and DCR versus bias current for waveguide-11#. (b) Oscilloscope persistence map of the response at a bias current of 17 µA. (c) Histograms of the time-correlated photon counts measured at 780 nm.

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The SDE is the product of the photon loss (PL) and on-chip detection efficiency (OCDE). The photon loss is the loss during the transmission from the input fiber to the chip. The main source of PL comes from the V-groove, such as the mismatch between the V-groove fiber and waveguide mode fields, poor alignment, and the offset due to thermal expansion at low temperatures. With the help of the auxiliary waveguides, we were able to measure the PL of our device at room temperature, which was 3.2 dB, and thus the OCDE could be calculated to be 3.5%. The OCDE was relatively low compared with the reported performance [46].

OCDE can also be composed of IDE, nanowire absorption (Abs) and on-chip coupling efficiency (OCE). Here, the first factor IDE was near unity. For Abs, with the actually used 7° inclination angle in the device, the nanowire absorption was calculated to be 73%. The alignment error during the nanowire engraving may have affected the nanowire absorption. The statistically obtained alignment error in the x-direction was ∼0.5 µm, and the alignment error in the y-direction was ∼2 µm, where both of them were much smaller than the width of the nanowire area in the x-direction (10 µm) and the length in the y-direction (60 µm). As a result, the impact of the alignment error was negligible. OCE is mainly affected by the transmission losses in the FLDW waveguides, where the loss of a straight waveguide section is ∼0.2 dB/cm. For one single waveguide with an estimated propagation length of ∼7 mm, the loss is ∼0.14 dB. The curved section of the waveguide introduced a bending loss. We have deliberately written an array of waveguides in the same silica chip with the same parameters to estimate the bending loss, which is called loss waveguides. The ending segment of the loss waveguide was parallel to the top surface of the chip. By comparing a loss waveguide with a reference waveguide, the bending loss can be calculated, which is treated as an estimation of the bending loss of the detector waveguides. For an inclination angle of β = 7°, the measured bending loss was ∼0.8 dB, and the total transmission loss was ∼0.94 dB when the two were added. No polarization dependence was observed during the measurement of both transmission loss and bending loss. In summary, using this method, the calculated OCDE was 58%, which is significantly higher than 3.5%. Therefore, it is believed the actual PL value should be greater than the measured result at a room temperature of 3.2 dB.

From room temperature to low temperature, the thermal expansion and contraction caused by the temperature change will cause the alignment position of the V-groove end face and the waveguide light input end face in the chip to shift, thereby leading to an evident loss. For a simple model including a waveguide with a diameter of 6 µm, and a 780 nm single-mode fiber with a diameter of 4.6 µm, a misplacement of 3 µm will give a PL of 5 dB according to the simulation. The properties of optical glues used for bonding usually change significantly with temperature [43]. Especially, the RI change may affect the matching of the mode field between the waveguide and the optical fiber and reduce the coupling efficiency. The above two losses resulted in a difference between the PL at low temperature and room temperature, leading to an extremely inaccurate OCDE, which was calculated from the PL. Due to technical limitations, it is currently only possible to measure the PL at room temperature, while its value at low temperature is unknown and changes based on the differences between different devices. Thus, the PL needs to be separately measured for each device at low temperature. A low-temperature translation stage can be used to correct the position of the V-groove at low temperature to obtain a better coupling efficiency and a smaller PL in the future [47]. The performance of the device, such as the real-time SDE and low-temperature PL, can also be tested in real time while adjusting the position of the V-groove at low temperature to calculate the true OCDE of the device. In addition, the performance of the device can be improved by increasing β to obtain a higher nanowire absorption, together with a designed Fabry–Pérot cavity [48].

The recovery time and timing jitter of the FLDW waveguide-coupled SNSPD were also measured. Figure 4(b) shows the oscilloscope persistence map of the response of the device based on waveguide-11# at a bias current of 17 µA. The recovery time was obtained from the averaged response waveform, and it was found to be 40 ns, which corresponds to a count rate of 25 MHz. The timing jitter of the device was achieved using a time-correlated single-photon counting module [49] (Fig. 4(c)), and it was estimated to be 40 ps at a wavelength of 780 nm. Both the recovery time and timing jitter were found to be typical values when compared with the corresponding values of conventional SNSPDs.

5. Conclusions

In this work, we designed and fabricated a novel FLDW waveguide-coupled SNSPD in which three detectors in one chip achieved effective single-photon responses. A maximum SDE of 1.7% at 10 Hz DCR was achieved. The measurement results demonstrated the feasibility of integrating SNSPDs in FLDW waveguides. In the future, the horizontal section of the FLDW waveguides in our device can be replaced with a complex quantum optical logic structure, offering potential as a quantum photonic chip integrated with manipulation circuits and a large array of detectors.