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Abstract
High-performance single-photon detectors (SPDs) at 1550-nm band are critical for fiber-based quantum communications. Among many types of SPDs, the up-conversion SPDs based on periodically poled lithium niobate waveguides are of great interest. Combined with a strong pump laser, the telecom single-photons are converted into short wavelength ones and detected by silicon-based SPDs. However, due to the difficulty of precise controlling waveguide profile, the direct coupling between a single-mode fiber and the waveguide is not efficient. Here by utilizing fiber taper with proper diameter, optimal mode-matching is achieved and coupling efficiency up to 93% is measured. With an optimized design, a system detection efficiency of 36% and noise counting rate of 90 cps are realized. The maximum detection efficiency is characterized as 40% with a noise counting rate of 200 cps. Numerical simulation results indicate that our device can significantly improve the performance of QKD and extend the communication distance longer than 200 km.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The detection of single photons at the infrared wavelengths is essential to a wide spread of applications ranging from biomedical imaging [1] to astronomy [2] and laser ranging [3] applications. It is of particular relevance to quantum communications [4]. Practical long distance quantum key distribution (QKD) [5–10] over fiber-optic network that works at 1550-nm telecom band is of great interest [11,12], while the communication distance and key rate are limited by the detection efficiency (DE) and noise count rate (NCR) of single-photon detectors (SPDs) [13]. Of various single-photon detecting approaches, superconducting SPDs based on transition-edge sensors [14,15] or superconducting nanowire detectors [11,16–18] have impressive overall performance. However, these detectors work at cryogenic temperature, making them less appealing due to the bulky cooling system especially for field applications. Thermoelectrically cooled InGaAs/InP single-photon avalanche photodiodes (SPADs) [19–21] are the mostly used commercial detectors in the telecom band range, yet suffer from relative low DE (typical ∼20%) and high NCR even in gated mode [22–25].
On the other hand, the frequency up-conversion SPDs inherit the excellent performance of the well-developed silicon SPAD while extending its detection range to the near-infrared [26–35]. In a typical configuration, 1550-nm single-photons together with a strong continuous-wave (CW) pump laser beam are coupled into a z-cut periodically poled lithium niobate (PPLN) waveguide, in which the 1550-nm photons are up-converted to short wavelength ones via sum frequency generation and then detected by a Si SPAD. Such approach possesses several advantages. During the nonlinear conversion, the quantum characteristics of the photons are preserved when unity conversion and no loss are assumed [26]. The Si SPADs typically have higher DE and lower NCR comparing to infrared SPADs, while the infrared photons can be converted with near unity efficiency when the nonlinear waveguide is optimized. The temporal resolution of an up-conversion SPD is entirely limited by the jitter of the Si SPAD when a CW pump is used, however, it is possible to reach a time resolution smaller than 150 fs by applying a pulsed pump due to the time-domain sampling [36]. Despite of the promising future, several challenges remain such as reducing optical losses in the system and suppressing background photons originated from Raman scattering [31].
In this article we present a general analysis of frequency up-conversion SPDs. We strategically design and construct a frequency up-conversion SPD, and single-photon detection efficiency of 36% with NCR of 90 cps and 40% with NCR of 200 cps are measured. We further show that our newly designed up-conversion detector can significantly improve the performance of QKD, to be specific, it will improve the distance from 150 km to more than 200 km under the same experimental condition [37].
2. Optical measurement setup
The basic principle of up-conversion SPD is that by mixing a strong pump laser, the infrared single photons are efficiently converted to short wavelength ones in a nonlinear crystal via sum-frequency generation so that they can be detected by a Si SPAD. A schematic diagram of the optical measurement setup is shown in Fig. 1(a). The 1550-nm single-photon source, which is one million photons per second at the input port of a wavelength division multiplexer (WDM) with a power of −98.92 dBm, is provided by a single-frequency CW laser (Santec, TSL-710) together with two variable optical attenuators (VOAs) and a 1/99 beam splitter (BS). The 1/99 BS and a calibrated power meter are employed to monitor the input signal power. A CW seed laser at 1950nm is amplified by a thulium-doped fiber amplifier (TDFA) as pump source. The long-wavelength pumping scheme can efficiently suppress the noise originated from spontaneous Raman scattering [30,31,38]. Another WDM is used to remove unwanted photons at 1550-nm and 863-nm band. Both the pump and signal light are adjusted as transverse magnetic (TM) polarization by polarization controllers (PCs) and coupled into a reverse-proton-exchanged (RPE) PPLN waveguide. The soft-anneal depth of the waveguide is 1.84 µm. The anneal time and temperature are 23 hours and 300 °C, respectively. The RPE time and temperature are 24 hours and 300 °C, respectively. The waveguide is designed with a poling period of 20 µm, a width of 8 µm and a thickness of 6 µm. And the single-photon sum-frequency conversion efficiency (from 1550 nm to 863.6 nm) is close to 100% [39] over a length of 48 mm when the pump laser at 1950nm is 93 mW at the end of the waveguide. Here, the poling period of 20 µm is determined by quasi-phase-matching equation $\frac{{2\pi }}{\Lambda }\textrm{ = }{\textrm{k}_{pump}} + {k_{signal}} - {k_{sum}}$, where ${\textrm{k}_{pump}}$, ${k_{signal}}$, ${k_{sum}}$ are the wavenumbers of the pump, signal and sum-frequency photons in the waveguide, respectively, and $\Lambda $ is the poling period of the waveguide. The up-converted single-photons are collected by a 10x objective lens (Newport, 5720B) and a dichroic mirror is used to separate the pump laser from the up-conversion signal. In addition, a 945-nm short-pass filter, a 785-nm long-pass filter, a 857-nm band-pass filter with bandwidth of 30 nm, and two etalons with full width at half maximum (FWHM) of 0.1 nm and free spectral range of 0.5 nm are applied to block the noise photons generated during the nonlinear processes. Finally, a collimator and a multimode fiber are employed to collect the up-converted photons and a silicon SPAD (Excelitas, SPCM-850-24-FC) is used for detection.
Fig. 1. (a) Optical measurement setup for the up-conversion SPD. VOA, variable optical attenuator; WDM, wavelength division multiplexer; BS, beam splitter; DM, dichroic mirror; LP, long-pass; SP, short-pass; BP, band-pass; M1, reflective mirror. (b) Schematic diagram of the coupling structure from single-mode fiber to PPLN waveguide. MCT, microcapillary tube.
As a key component of the up-conversion SPD, the PPLN waveguide has been developed for decades with optimal conversion efficiency and minimal propagation loss. However, its performance is limited by the big optical insertion loss due to the mode mismatch between the waveguide and fiber. Spatial-mode filter at the input port of the PPLN waveguide has been introduced to minimize such mismatch. However, the coupling efficiency in general may only reach 83% by direct single-mode fiber pigtail coupling [31], because of the highly unsymmetrical waveguide mode pattern when the diameter of the waveguide mode approaches to that of the single-mode fiber. Reducing the waveguide width with linear taper can improve the mode symmetry, however, the discrepancy between the mode diameters of the waveguide and single-mode fiber can not be solved essentially. Due to the complexity and difficulty of waveguide mode profile control, here we use a more flexible coupling scheme. By tapering a single-mode fiber, the diameter of guided fundamental mode can be adjusted continuously from several tens of microns to sub-wavelength range [40], yet with nearly unity transmittance when the profile of the taper follows adiabatic shape [41–43]. Thus by applying a fiber taper with a suitable diameter, the coupling efficiency can be largely improved. As a freestanding fiber taper is not stable in the air, the fiber taper is coated with low refractive index adhesive (LRIA, n = 1.38) and supported by a microcapillary tube (MCT) for steady coupling and easy handling, as shown in Fig. 1(b). Comparing to free space coupling via fiber lens or objectives, our realization has the advantages of robustness and compactness.
3. Numerical simulations
To optimize the coupling efficiency, a buried waveguide with a mode filter width of 5 µm is used in our experiments, as shown in Fig. 1(b). The refractive index spatial distribution of the waveguide at the input port is calculated based on the theory of impurity diffusion [44] and plotted in Fig. 2(a). It shows a refractive index of 2.155 at the center of the waveguide, in contrast to 2.138 for extraordinary ray at 1550 nm in congruent LN crystal. The relatively higher refractive index results in a nearly symmetric confined field distribution with a diameter of 5.4 µm, as shown in Fig. 2(b).
Fig. 2. (a) Optical Numerical simulation results. (a) The refractive index distribution of the PPLN waveguide at the entrance port. (b) Normalized field distribution of guided light at 1550 nm in the waveguide. (c) Cross section of computational domain along the axis of fiber taper. The color bars indicate the refractive index. (d) The maximum coupling efficiency between the fiber taper and PPLN waveguide as a function of taper diameter. (e) The coupling efficiency as functions of misalignment for a fiber taper with a diameter of 5.8 µm. The black squares and red dots represent the misalignment along x-axis and y-axis, respectively.
The coupling efficiency between the waveguide and fiber tapers of different diameters is estimated by three-dimensional finite-difference time-domain (3D FDTD) numerical simulations. The computational domain is set as 20 µm x 11.04 µm x 35 µm which is terminated by a perfectively matched layer to avoid light reflection. As shown in Fig. 2(c), a 10-µm-long fiber taper with uniform diameter directly contacts the waveguide as butt-coupling. To mimic the experimental conditions, anti-reflection coating is applied on the input face of PPLN waveguide, and the cladding of the fiber taper has a refractive index of 1.38. The anti-reflection coating has refractive index as ${n_{film}} = \sqrt {{n_{taper}}{n_{waveguide}}}$ and thickness of ${\lambda / {4{n_{film}}}}$, where $\lambda$=1550 nm, ${n_{taper}}$ and ${n_{waveguide}}$ are the effective indices of the LRIA coated fiber taper and the PPLN waveguide (TM mode), respectively. A 1550-nm laser with fundamental taper mode profile is launched into the fiber taper from the bottom end. On the top end of the PPLN waveguide, the field distribution is collected and the fundamental waveguide mode component is calculated. By comparing the energy that is coupled to the fundamental waveguide mode to the input laser power, the coupling efficiency between fiber taper and waveguide is calculated.
To figure out the optimal fiber taper parameter, the coupling efficiency as a function of taper diameter is calculated and plotted in Fig. 2(d). For each data point shown there, the position of fiber taper is carefully adjusted to reach the optimal position before the coupling efficiency is recorded. As one can see, the coupling efficiency is > 96% for fiber tapers with diameters ranging from 5 µm to 7 µm, while the highest coupling efficiency is ∼98% when the fiber taper diameter is about 5.8 µm. This set a loose criterion for fiber taper fabrication, as the coupling efficiency is not very sensitive to the taper diameter.
On the other hand, the relative position of the fiber taper with reference to that of the waveguide is critical for coupling efficiency. Figure 2(e) shows the coupling efficiency as functions of misalignment for a fiber taper with a diameter of 5.8 µm. The coupling efficiency drops from 98% to 85% when the misalignment is 1 µm. Fortunately, a translation stage with high-resolution manual actuators (Suruga Seiki, E2200B) is still feasible.
4. Fiber taper fabrication and packing
The insertion loss introduced by fiber taper and MCT packing should be minimized to guarantee high efficiency. In our experiment, the high-quality fiber tapers are fabricated by a home-built fiber-puller system consists of a hydrogen flame torch, two motorized translation stages, optical measurement components and a computer [45]. Standard single-mode optical fiber (Corning SMF-28e) is used for tapering. During the pulling process, a CW light source at 1550 nm is coupled to the fiber and the transmittance is measured by a photodetector. When the waist diameter of the taper reaches about 5.8 µm, the translation stages stop while the transmittance for this bi-conical taper maintains 98%, as shown in Fig. 3(a). Though the one-side-taper loss of 1% indicates the satisfaction of criterion of adiabatic taper in air, the LRIA coating may possibly introduce additional radiative loss due to the increase of ambient refractive index. We measure the shape of the fabricated fiber taper by using a scanning electron microscope and plot the delineation angle as a function of fiber diameter in Fig. 3(b). The critical angle for an LRIA-cladded adiabatic taper as a function of the local taper diameter plotted in the same figure indicates that our taper is still in the adiabatic region [46] after the LRIA coating.
Fig. 3. (a) Fiber taper characterization. (a) The normalized transmission curve of 1550-nm laser as a function of time during the tapering process. (b) The declination angle of the adiabaticity criteria taper and fabricated fiber taper with LRIA are plotted by black blocks and red dots, respectively.
After the fiber taper reaches its desired diameter and the hydrogen flame stops heating, the fiber is stretched a little (0.2 mm) to make it tight. With the assistance of an optical microscope, the taper is cut by a diamond blade perpendicularly and breaks into halves in the middle. Figure 4(a) shows a typical optical microscope image of the taper after cutting. Then the taper is removed from the fiber-pulling system and carefully slides into an MCT with an inner diameter of 130 µm. After the tip of the taper reaches the end of the MCT, a drop of LRIA is applied on it and gradually fills the entire gap due to capillary action, as shown in Figs. 4(b) and 4(c). After verifying that the fiber taper is free from sticking to the MCT inner wall, the LRIA is cured by UV light. Finally, the end-face of the MCT is polished by a zirconia plate until the exposed taper diameter reaches desired diameter. The LRIA cladding and the MCT jacket can protect the fiber taper from contamination and greatly improve the stability and handling for butt-coupling.
Fig. 4. (a) Fiber taper packing and coupling with PPLN waveguide. (a) Optical microscope image of a free-standing fiber taper. Scale bar: 0.2 mm. (b) Image of the fiber taper slid into an MCT with an inner diameter of 130 µm. Scale bar: 2 mm. (c) Image of MCT filled with LRIA. Note that the length of taper region is about 9 mm. Scale bar: 2 mm. (d) Schematic diagram of optical setup for measuring coupling efficiency between the fiber and the PPLN waveguide. (e) The calibrated coupling efficiency for fiber tapers with various diameters.
To achieve optimal coupling between the fiber taper and the PPLN waveguide, the MCT is mounted on a 6-axis stage with differential actuators for fine adjustment. Figure 4(d) shows that a narrow-bandwidth CW tunable /diode laser (Santec, TSL-710) at 1550 nm is launched into the fiber, and the input power is monitored by a power meter after a 50/50 fiber optic splitter. The laser coupled to the waveguide is adjusted as TM polarization by an online fiber polarization controller. The laser coupled out of the waveguide is collected by a 10x objective lens (NA = 0.15) and is measured by another power meter. The MCT is firstly aligned with waveguide coarsely, and a drop of LRIA is applied on the contacting region. The position and angles of the MCT are carefully adjusted until the output power from the waveguide reached a maximum. Then the LRIA is cured by UV light to fix the relative position between the MCT and waveguide. Figure 4(e) plots the measured maximum coupling efficiency from a series of samples as a function of taper diameter when the fiber taper transmittance is taking into account. Here optical loss from objective lens and mirror is excluded, as well as the propagation loss of the waveguide. The trend agrees well with the numerical calculation result shown in Fig. 2(d), with a maximum coupling efficiency of 93% for a taper of 5.8 µm in diameter.
5. Detector performance
The overall optical properties of the up-conversion SPD following the setup shown in Fig. 1(a) are characterized. Firstly, the system optical loss is estimated. The WDM2 introduces an insertion loss of 0.22 dB. The single-mode fiber to PPLN waveguide coupling efficiency is measured as 93%, including the taper transmittance. While the propagation loss of the PPLN waveguide is ∼0.1 dB/cm estimated by the Fabry-Perot fringe-contrast method [47]. The two etalons introduce a loss of 0.27 dB. And the overall transmittance from the waveguide to the silicon SPAD is measured as 92%, taking the objective lens, filters, collimator and multimode fiber into account.
Secondary, the phase-matching of the up-conversion waveguide is characterized by fixing the pumping laser at 1950nm while sweeping the signal wavelength around 1550 nm. When the PPLN waveguide is kept at 33.4 °C with a PID temperature controller, the phase-matching wavelength is 1550 nm with a FWHM of 0.64 nm, as shown in Fig. 5(a). The asymmetry of the tuning curve of the phase-matching is mainly induced by the nonuniformities in waveguide width and poling quality. The width matches well with the theoretical value of 0.63 nm calculated by its dispersion relation and grating length. Such linewidth indicates the bandwidth of the up-conversion SPD which is much narrower comparing to that of InGaAs/InP detectors. However, it is sufficient for QKD applications.
Fig. 5. (a) The phase matching tuning curve. The red dots represent the experimental results. (b) Detection efficiency (black squires) and NCR (red triangles) as a function of pump power.
Finally, the system photon DE is measured under optimal phase-matching condition. Figure 5(b) shows overall system DE and NCR as functions of pump power. DE of 36% is measured with NCR of merely 90 cps when the pump power is set as 58 mW. As the pump power increases to 93 mW, DE reaches a maximum value of 40% while the NCR is 200 cps. Other than spontaneous Raman scattering, nonlinear processes such as second harmonic generation, third harmonic generation, spontaneous parametric downconversion and their combinations may also contribute to the background noise which causes the nonlinearly increasing of NCR with the pump power. Such performance is remarkable, considering the silicon SPAD used in our experiments has a DE of 55% at 863 nm and an intrinsic NCR of 40 cps. Further increasing of the pump power results in slightly decreasing of DE.
6. Discussion
Though the up-conversion SPD demonstrated in this work can not directly compete with superconducting SPDs that need bulky cryogenic systems, it outperforms the rest SPDs in terms of DE and NCR. Table 1 shows the comparison of our fiber taper coupling method to free-space coupling and single mode fiber coupling methods. The free-space coupling method gives a relatively high coupling efficiency, however bulky optical system is needed. Table 2 shows the comparison of our device to the best up-conversion one that have been reported [31] and one of the best performance InGaAs/InP SPAD [37]. For the two fiber coupled up-conversion SPDs, the great enhancement of overall optical system efficiency from 63.7% to 73.2% is mainly due to increasing of fiber to waveguide coupling efficiency by adapting new coupling scheme. Meanwhile the reduction of NCR by more than one order of magnitude (from 7000 cps to 200 cps at maximum detection efficiency, as shown in Table 2) contributes to the using of longer pump wavelength. Besides, our new coupling scheme also reduces the requirement for complex waveguide profile control. Nevertheless, our detector shows much better performance comparing to the InGaAs/InP detectors [37] unless bandwidth is concerned.
Table 1. Efficiency comparison between up-conversion SPDs.
Table 2. Performance comparison between SPDs.
Utilizing our detector will significantly enhance the performance of QKD. Numerical results of QKD simulation for the InGaAs/InP and up-conversion SPDs compared in Table 2 are illustrated in Fig. 6. The system frequencies for up-conversion SPDs and InGaAs/InP SPAD are 625 MHz and 1.82 GHz respectively, which are limited by the timing resolutions of them. In our simulation, the optical loss in fiber and insertion loss of the receiver are set as 0.2 dB/km and 3 dB. The secure key rate is calculated following the standard Decoy state BB84 protocol [48,49], with the analytical estimation [50]: $R \ge q - {Q_\mu } \times f \times {H_2}({E_\mu }) + {Q_1}[1 - {H_2}({e_1})]$, where ${H_2}(x)$ is the binary entropy function: ${H_2}(x) ={-} x \times lo{g_2}(x) - (1 - x) \times lo{g_2}(1 - x)$, and q is an efficiency factor for the protocol. Here the mean photon number of signal (µ) and decoy ($v$) state are set to be 0.6 and 0.2. The time ratio of signal/decoy/vacuum are fixed to be 0.75/0.125/0.125. The error correction efficiency is select as $f = 1.2$. ${Q_\mu }$ and ${E_\mu }$ are the measured gain and the QBER for signal states. The gain and error rate of signal photon state ${Q_1}$ and ${e_1}$ are estimated with ${Q_1} \ge Q_1^L = \frac{{{\mu ^2}{e^{ - \mu }}}}{{\mu v - {v^2}}}(Q_v^L{e^v} - {Q_\mu }{e^\mu }\frac{{{v^2}}}{{{\mu ^2}}} - Y_0^U\frac{{{\mu ^2} - {v^2}}}{{{\mu ^2}}})$ and ${e_1} \le e_1^U = \frac{{{E_\mu }{Q_\mu } - {{Y_0^L{e^{ - \mu }}} / 2}}}{{Q_1^L}}$, respectively, where the lower bounds are estimated with Gaussian distribution: $Q_v^L = {Q_v}(1 - \frac{{10}}{{\sqrt {{N_v}{Q_v}} }})$, $Y_0^L = {Y_0}(1 - \frac{{10}}{{\sqrt {{N_0}{Y_0}} }})$, $Y_0^U = {Y_0}(1\textrm{ + }\frac{{10}}{{\sqrt {{N_0}{Y_0}} }})$. Here ${N_v}$ and ${N_0}$ are the pulse number of decoy and vacuum states, respectively, ${Q_v}$ is the gain of decoy state, and ${Y_0}$ is the yield of vacuum. The comparison shows that our up-conversion SPD performs excellently in short distance QKD with a high secret key rate, and can work in long distance QKD more than 200 km.
We would like to note that there still exists some room for improvement with optimized waveguide and fiber taper parameters as well as careful alignment, as the numerical simulation results predict near unity single-mode fiber to PPLN waveguide coupling efficiency. Moreover, if a Si SPAD that is optimum for detection at 863 nm is adapted, significant enhancement is possible to be achieved. As CW pump is used in the demonstration, the temporal resolution of our up-conversion SPD is restrained by the timing jitter of Si SPAD which is about 450 ps at 863 nm, and that for a high-performance InGaAs/InP is about 130 ps [51]. However the detector timing jitter down to 10 ps is possible to reach with high conversion efficiency when a ps pulsed pump is adapted [52], as the short fiber taper we introduced in the structure has similar dispersion as single-mode fiber.
7. Summary
To summarize, we have demonstrated a new coupling scheme between single-mode fiber and PPLN waveguide via fiber taper structure toward perfecting up-conversion SPDs. Though fiber-pigtailed devices have already been obtained in different scenarios [53], as fabricating a waveguide that matches well with single-mode fiber is difficult, our approach is much easier by controlling the fiber taper diameter. Coupling efficiency as high as 98% can be realized by numerical simulation, and efficiency of 93% is measured experimentally when the taper transmittance is taking into account. Other than bulky superconducting based SPDs, the up-conversion SPD with a system DE of 36% and NCR of 90 cps realized in this work outperforms all reported SPDs at 1550-nm band. Numerical simulation result indicates that utilizing of our detector can extend QKD distance longer than 200 km. Our MCT protected fiber taper structure is robust and compatible with all-fiber systems, and may be applied to other integrated photonic device applications.
Funding
National Key Research and Development Program of China (2018YFB0504300, 2018YFB2200400); National Natural Science Foundation of China (61635009); Fundamental Research Funds for the Central Universities; SAICT Experts Program; Shandong Peninsula National Innovation Park Development Project; 5150 Program for Talents Introduction; Major Scientific Research Project of Zhejiang Lab (2019MC0AD01); Taishan Scholar Project of Shandong Province.
Acknowledgments
We thank Dai-Ying Wei for the packaging of the waveguides and Yang Gao for the help in the fabrication process.
Disclosures
The authors declare no conflicts of interest.
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