1. Introduction

Quantum key distribution (QKD) is an encryption key growing protocol which provides information-theoretic security guarantees reliant only on the laws of physics [1–3]. The theoretical principles behind QKD were established by the first protocols by Bennet and Brassard [4,5] and Ekert [6]. The range of QKD systems (as well as other quantum communications protocols [7]) is limited by channel loss and background noise [8]. Without trusted nodes, fiber-based QKD is limited to 100s of km for practical key rates [9,10] and terrestrial free-space QKD is limited to 10s of km [11].

Satellite QKD overcomes these range limitations by placing a node in orbit around the planet, providing a QKD link, which has loss independent of the displacement between ground stations [12]. There have been several demonstrations of technology approaching satellite QKD [13–17]. The Micius mission has also demonstrated QKD under many different scenarios [18–20] using a dedicated satellite, while demonstrations have also been performed from the Tiangong-2 space lab [21,22]. Several missions are also proposed for near future launch [23–26]. Many of the challenges of satellite QKD are common to conventional satellite optical communications. Specifically, the issues of atmospheric turbulence [27], cloud cover [28] and point-ahead angle [29–31] are present in satellite laser communications research, while also being important to QKD performance [28,32,33]. However, in this work we will study the issue of acquisition, pointing and tracking (APT) [20,33–35].

APT is a collective term for the processes by which a satellite is located and targeted by a ground station and, similarly, a ground station is located and targeted by a satellite. APT is particularly important for Satellite QKD because of its high sensitivity to loss, short pass durations and low tolerance to background noise (which yields a small receiver field-of-view (FOV)). The use of small satellite platforms such as CubeSats [36,37] for QKD necessitates small optical systems which cause high link loss [23,25,38,39], putting significant strain on link budgets. Optical beacons are used by both transmitter and receiver nodes for APT [34], enabling both nodes to point at one another. While new single-photon detector array technologies can enable high sensitivity for the QKD channel [40], optical beacon powers of the order Watts are still used for APT with LEO satellites [33]. Optical beacon lasers can propagate through the main receiving telescope [18,20], though this can cause an increase in background noise due to imperfect spectral filtering [23] and back-reflection. While using one or more external telescopes can reduce the impact of optical fading [41], it adds cost, complexity and boresight error to the APT system. Additionally, smaller, externally mounted telescopes will cause a more divergent beacon beam. This causes more channel loss and higher requirements on the satellite APT system (which is size, weight and power (SWaP) constrained). These aspects are particularly detrimental to QKD due to its single-photon nature, which makes the channel particularly sensitive to noise [42].

In this work, we propose a method of optical beaconing through the main receiver telescope, which uses a multicore fiber to spatially separate the uplink beacon channel from the downlink QKD channel (although an identical construction could also be used for a conventional optical communications channel). This allows the benefits of using the main telescope (low divergence and complexity) while mitigating back-reflection into the QKD receiver module. As an additional benefit, such a system could be driven by separate, incoherent sources to derive a reduction in scintillation (due to atmospheric turbulence) which scales with the number of separate beams used [41], improving the reliability of the beacon. We simulate and demonstrate a reduction in back-reflected power, which is a function of the geometry of the multicore fiber, QKD receiving fiber and manipulating lenses used. In the case of our commercial-off-the-shelf, 4-core 2-by-2 fiber we show a 50 dB reduction in back-reflected power compared to the sole use of spectral filtering when using a receiving fiber with a diameter of $25\mu m$ or less. This optical beaconing system could provide lower optical noise to future free-space QKD and optical communications receivers, particularly in the satellite implementation, while maintaining low complexity and cost. This will be important as more investment is made into satellite QKD and optical communication missions and service demonstrators.

The remainder of this paper is structured as follows. Section 2 outlines the necessary components and construction of such a system, as well as the demonstrator used. Section 3 describes how we simulate the anticipated behaviour of this demonstrator, and by extension a full-scale system. Section 4 discusses measured results and how they compare to simulation. Finally, we conclude in Section 5.

2. System design

Shown in Fig. 1 is a system diagram for the back-end optics of a QKD receiver. It uses a dichroic mirror to separate outgoing uplink beacon light from incoming quantum signal light at two distinct wavelengths. However, later optics/optical surfaces in the telescope and imperfection in the dichroic beamsplitter (also directionally dependent) mean that a small proportion $\rho$ of the optical beacon is back-reflected, resulting in coupling into the QKD receiver. This causes erroneous counts in the detector system in use (for instance, a single photon avalanche diode (SPAD) [43] or superconducting nanowire single photon detector (SNSPD) [44]) when it is sensitive to the optical beacon wavelength. This increases the quantum bit error rate (QBER) of the channel. Additional noise rejection could be achieved using band-pass filtering, which will introduce extra loss to the QKD channel. This demonstration focuses on increasing SNR while maintaining a high throughput in the QKD channel. Due to the high power of the uplink optical beacon and the single-photon sensitivity of QKD detectors, even small proportions of back-reflection and effective spectral filtering can result in a significant increase in optical noise if the single-photon detector is sensitive to the beacon wavelength.

To resolve this, manipulation of the beam profile of the uplink beacon is proposed. By using a profile which carries very little power on the optical axis, a reduction in the amount of back-reflected power coupled into the QKD receiving fiber can be achieved. Ideally, any back-reflected power is imaged to around the QKD receiving fiber, rather than being coupled into it, though this depends on the diameter of the QKD receiving fiber and the spatial separation of the initial optical beacon. In our system design, this is achieved by using a multicore fiber to carry the optical beacon to the free-space optics; a short focal length collimating lens is used to maintain the separation of the beams. While a single collimating lens can be used for the spatial array, optimal collimation is challenging due to the short focal length required to maintain separate beams. A custom-made micro-lens collimator would allow individual beam collimation and could reduce the divergence between beams. The path difference between the beacon and QKD channels are small and fixed, so will not affect timing synchronisation.

The experimental setup described in Fig. 2 was used to demonstrate such a system. A Fibercore SM4C1500 4-core fiber was used as a beacon source, which had four $8\mu m$ mode field diameter cores separated by $50\mu m$. These cores were fed from a 1-to-4 fiber splitter from a single, laser source. The four cores were fed relative powers of $[0.9037, 1.2560, 1.0178, 0.8224]$, indicating unequal power splitting and propagation through the fibers. Section 4 demonstrates that, despite these variations in feed power, performance was not significantly altered from that anticipated from simulations (Section 3.) using equal power splitting. Existing systems include propagating an uplink beacon through the main receiving telescope in a single, gaussian, beam. To simulate this we used a Thorlabs P1-780A-FC2 single mode fiber, with a $5\mu m$ mode field diameter core. Both the single core and the multicore system were collimated using a $1.45mm$ focal length lens (Thorlabs C140TMD-B). The simulated beam profile of both of these beacon options after focussing onto the QKD receiver fiber is shown in Fig. 3.

 

Fig. 1. System diagram of quantum key distribution (QKD) back-end optics with integrated beacon laser source using a multicore fiber. The QKD downlink signal is separated from the uplink beacon by the dichroic beamsplitter, as it uses a different wavelength. However, imperfect dichroic beamsplitting and reflection from telescope optics mean that some beacon light will be back-reflected into the QKD receiver fiber.

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Fig. 2. The experimental setup used to demonstrate a reduction in back-reflection. An important difference to the system concept in Fig. 1 is that the dichroic beamsplitter reflects the uplink beacon deliberately towards the receiving fiber.

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The laser used to emulate the uplink beacon was a single continuous-wave source at 852nm (Photodigm PH852DBR). This would be compatible with a QKD signal sufficiently spectrally separated from $852nm$ (for example, $780nm$ or $910nm$). A Thorlabs AC254-030-B $30mm$ focal length lens is used as the receiving lens. To quantify the spread of beacon power, we measure the proportion of beacon power coupled into a QKD receiving fiber as a function of fiber diameter. The QKD receiving fibers used are $5\mu m$ (single mode) and $10\mu m, 25\mu m, 50\mu m, 105\mu m, 200\mu m, 300\mu m \ and \ 400\mu m$ (multimode) in diameter. These fiber diameters are shown relative to the beacon beam profile at the QKD receiver fiber in Fig. 3. Figure 3(a) shows the single core beacon fiber beacon intensity profile, while Fig. 3(b) shows the equivalent for the multicore fiber beacon. The simulations performed to produce these profiles are detailed in Section 3.

 

Fig. 3. Beam profiles at the receiving fiber resulting from a single core and multicore beacon fiber. The diameters of the receiving fibers used in this experiment are also included. These were 5, 10, 25, 50, 105, 200, 300, $400\mu m$ and are indicated by the white rings within both diagrams; $5\,\mu m$ is the most inner ring. The multicore beacon fiber generates less noise and causes fewer errors because it propagates less power down the optical axis (which is central to both diagrams) and so less power is coupled into the receiving fibers.

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This is a simplification of a QKD receive in which a single silicon SPAD is used to capture the number of photons received by the optical beacon. In the most common QKD protocol, known as BB84 [4], photons are shared by polarization filtering between four detectors. Back-reflected light is therefore shared (although not necessarily equally) between these four detectors. The result, in terms of quantum bit error rate (QBER) is the same. Dichroic splitting is provided by a Thorlabs DMSP805 dichroic beamsplitter. In order to receive reflected power measurable on a Thorlabs power meter, we used this to reflect the 852nm beacon light into the QKD receiver, with reflectivity $\rho = 0.9904$. In Section 4, any QBER results are rescaled to represent the transmissivity of this beamsplitter, so that photon count rates are representative of a system using it to transmit beacon light and reflect QKD signal. In this case, beacon light can be reflected into the QKD receiver.

3. Simulation

The propagation of both types of optical beacon (sourced from single mode and multicore fibers) through the setup described in Section 2 was simulated. This was done by assuming Gaussian intensity distributions at each core, with known mode field diameter and separation, propagating each through a collimating and focussing lens, and observing the intensity distribution which is incident at the QKD receiving fiber. Tracking the separation of the four beams from the multicore fiber is challenging as it depends on non-ideal behaviour away from the centre of each lens due to aberrations. Multicore beam separation (a single variable) is fitted to experimental data. The result is intensity distributions for both beacon fibers which are incident at the QKD receiver fiber. Quantities such as coupled back-reflected power and QBER are computed using these theoretical intensity distributions, though in most cases these computations are not analytic and require numerical integration.

Details of the simulations performed (including an exemplar analytic result) are included in Supplement 1.

4. Results

4.1 Back-reflected power

Figure 4, shows the back-reflected power coupled into the receiving fiber as a function of receiving fiber diameter. This is shown for both the single-mode beacon fiber (an example of previous technology) and for the multicore beacon fiber we propose, and for both experiment and the simulation explained in Section 3. Coupled power is normalized by $P_t \rho \eta$, the total beacon power $P_t$ used, multiplied by the reflectivity of the dichroic mirror $\rho$ used at the beacon wavelength and the transmissivity of the channel from beacon to receiver fiber $\eta$ (which accounts for reflections at the faces of fibers at both ends). Two points are apparent from this figure. The first is that there is a significant reduction in coupled back-reflected power when using the multicore fiber over the single-mode beacon. This improvement is most marked when using a small QKD receiving fiber, as this gives both the highest mean intensity at the receiving fiber in the single-mode fiber beacon case, and the lowest mean intensity at the receiving fiber in the multicore fiber beacon case (see the intensity profiles predicted in Section 3, shown in Fig. 3.). The total reduction in back-reflection coupling is shown in Fig. 4. We see a maximum of 50 dB reduction in back-reflected power from the multicore fiber predicted and achieved. This value depends on some of the geometric parameters of the beacon optics. In particular:

A custom-made multicore fiber and collimator could improve significantly on the result shown here, particularly by increasing core spacing $d_{spacing}$. Intensity at the optical axis (where the receiving optical fiber is located) scales with $\exp (-(d_{spacing}/2)^2)$, which gives rapid drop-off in intensity as $d_{spacing}$ increases. Separation into four beams can also reduce the peak intensity of the beacon (see Fig. 3), which reduces requirements on optical components and coatings.

Due to both beam spreading and turbulence in the uplink channel, the beacon beams will overlap to form a single gaussian beam at long range. The distance at which this occurs depends on the telescope used. This overlapping means that the fiber geometry chosen has little effect on the beam profile at the satellite.

 

Fig. 4. back-reflected (BR) beacon power coupled into the QKD receiver fiber from a single mode and multicore beacon fiber. Improvement from the single mode to the multicore case is also shown. Greater improvement between single mode and multicore fibers could be observed if multicore fiber core spacing were improved. Data available in [45].

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The second point is that there is an agreement between experiment and theory. There is a higher proportional error in the agreement between multicore theory and experiment, which can be accounted for by a combination of three factors:

Despite these factors, experimental results agree in form with simulation. This validates the use of simulation to predict performance of different multicore fibers as beacon sources.

4.2 Quantum bit error rate (QBER)

The effect of back-reflected power on a QKD system is to erroneously trigger the single-photon detectors in use. This causes bit errors and increases the quantum bit error rate (QBER). We predict the QBER resulting from back-reflected power for each of the two optical beacons systems in this paper using the following scaling:

The results of this process are shown in Fig. 5. The relationship used to compute QBER was

While the QBER limit above which a QKD system cannot operate varies between protocols and can be much higher, the secret key rate (SKR) of a QKD system is very sensitive to QBER. With finite error correction efficiency ($f=1.2$), SKR tends to zero at around $QBER=7\%$[47]. Other parts of the QKD system (detector dark counts, light pollution coupling, source polarization error) will also contribute QBER. The total QBER should be designed to lie below the fundamental limit of the protocol (for BB84 this is $11\%$[26]). In practical systems QBER is designed to lie well below this limit in order to yield practical SKR [18,25]. Therefore we consider $QBER_{BR} < 1\%$ an objective for this single component.

 

Fig. 5. Quantum bit error rate due to beacon back-reflection ($QBER_{BR}$) using single mode and multicore beacon fibers for a range of single-photon detector time gate widths. In practice, further spectral filtering could reduce $QBER_{BR}$. Data available in [45].

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To yield $QBER_{BR}$ in the practical range $QBER_{BR}<1\%$, the count rate $\mu$ must satisfy $\mu T<0.02$. In this range it is valid to consider the approximation in Eq. (2) which linearizes $\exp (-\mu T)$ to $1-\mu T$ and neglects higher order terms which are quadratic and above in $\mu T$. This approximation is equivalent to assuming that no more than one noise photon arrives in a single time gate $T$.

No practical $QBER_{BR}$ is achieved by the single-mode fiber beacon due to the large amount of back-reflected power which lies on the optical axis. Even with spectral filtering provided by the dichroic mirror, the power of the beacon is enough to completely overwhelm a QKD receiver using any practical receiver fiber and even short (10ps) time gating. However, the multicore fiber beacon can achieve $QBER_{BR}<1\%$ at up to $10\mu m$ of fiber diameter provided that $10ps$ time gating is available. Time gating in the $10ps$ domain is not compatible with single-photon avalanche detectors (SPADs) in the visible or near-infrared bands, but can be achieved by using superconducting nanowire single photon detectors (SNSPDs) [48,49]. These devices are costly and require cryogenic refrigeration, but would allow a low-error QKD channel with no further filtering or intervention.

While the $100ps$ and $1ns$ time gate measurements (and simulations) have $QBER>1\%$ for any reasonable fiber diameter, this can be improved by other methods of filtering. For instance, the inclusion of an additional spectral filter at the QKD receiver fiber may be expected to provide an extra $20dB$ of beacon light rejection. This would result in the $1ns$ time gated multicore fiber system having similar QBER characteristics to the $10ps$ filtering in Fig. 5. This would introduce a small increase in QKD channel loss and system complexity, but would also be effective at rejecting background light. Reducing the optical power of the beacon would also reduce $QBER_{BR}$. This is limited by systems engineering, as there is a requirement on the beacon to be detectable by the transmitter node. Finally, since $QBER_{BR}$ depends approximately linearly on back-reflected count rate and therefore power, the improvements suggested in Section 4.1 would yield reduced $QBER_{BR}$ here. In particular, increasing the spacing of the multicore fiber used would cause an exponential reduction in coupled back-reflected photons. One or more of these modifications, combined with the significant reduction in back-reflected power shown in Fig. 4 could allow optical beaconing and QKD through the same telescope without the need for time multiplexing with existing SPAD technology limited to $100ps-1ns$ time gate widths [50].

5. Conclusion

Optical beacons are an important component of optical satellite and mobile free-space communications systems, including for QKD. However, the sensitivity of QKD receivers to noise means that propagating a single beacon beam through a receiving telescope will provide prohibitive noise count rates. Using separate telescopes for beaconing increases complexity and cost and requires boresighting. In this work, the use of a multicore fiber to spatially separate beacon and signal light in a receiving telescope is proposed. This reduces the noise due to back-reflected beacon light from the receiver optics while maintaining the simplicity and pointing precision intrinsic to using the same telescope for beaconing and signal receiving.

A reduction in coupled back-reflected power from a single-mode beacon fiber to a multicore beacon fiber was demonstrated. This reduction is greater for narrower QKD receiving fibers and for greater spacing between beacon cores. For the particular 4-core multicore fiber used in this experiment, there was a $50~dB$ reduction in coupled back-reflected power for a receiving fiber diameter of $25\mu m$ or below. For a realistic set of QKD receiver and beacon parameters, this was predicted to yield $QBER$ due to back-reflection of less than 1% for fibers below $10\mu m$ diameter when $10ps$ time gating is used. Both back-reflected power and $QBER$ could be further improved by using spectral filtering, reducing beacon power or changing the beacon multicore fiber geometry.

This method of beaconing yields lower noise characteristics for both conventional and quantum optical communications, while maintaining a simple, low-cost telescope architecture which remains compatible with time-division multiplexing to further reduce noise. This could be used to improve free-space and satellite quantum communications receivers being designed and built in the near future.