Free-space optical (FSO) communications give out higher data rates, larger unlicensed bandwidth, better security, and lower power consumption when compared with radio frequency links [1]. FSO with data rates up to 100 Gbps for the downlinks from the low Earth orbit satellites to ground is on the time schedule of NASA [2]. Mitigation of aberrations distributed in the whole optical path from a local transceiver to the target point is critical and difficult for FSO, especially for coherent FSO [3–5]. The internal phase distortions are caused by the aberrated optical mirrors and lenses. The external distortions are represented by the turbulence-induced dynamic aberrations and lead to extreme undulating of the received beam intensity and serious signal-to-noise ratio degradation. Adaptive optics (AO) techniques are commonly adopted in the large monolithic-aperture telescopes to alleviate the effect of aberrations [6]. However, such AO systems are bulk, complex, and expensive.

The optical transmission system of the distributed fiber laser array has been proven to be a promising approach to entitle the system with smaller size and lower weight. With advantages of easy heat management, extendable structure, and keeping high beam quality while promoting the output power, the array systems composed of compactly packed small size subapertures might replace common large monolithic transceivers. Several coherent beam combining (CBC) experiments indoors [7–9] have demonstrated these functions. Excellent AO correction capacity of such tiled fiber laser arrays [10,11] could be obtained through manipulating the subaperture phase, like pistons and tip/tilts [12–14]. Eliminating the turbulence-induced aberrations to get efficient CBC at the target over 7 km with 21-element adaptive fiber-optics collimators (AFOCs) has been demonstrated by Weyrauch et al. [15]. They adopt the target-in-the-loop (TIL) method to obtain the power-in-the-bucket (PIB) metric, which is defined as the power located in a circular region on the target. Stochastic parallel gradient descent (SPGD) [16] optimization algorithm is used to iteratively calculate the turbulence-induced and subaperture averaged pistons and tip/tilts to maximize the PIB metric. TIL could work with noncooperative targets in distance of dozens of kilometers (not far-field) where the laser array works under a conformal way, while TIL suffers from disadvantages of inherent optical transmission delay especially for future long-distance FSO communications, where the delay in the control loop would disable the convergence of the optimization control algorithms. Meanwhile, the multiple control variables increase sharply as the array scale increases to hundreds and would decrease the effective control bandwidth. All these factors would give challenges to the applications of this adaptive distributed aperture array in FSO communications.

In fact, the distributed fiber laser array presents its advantages not only for laser beam emission, but also could act as an efficient aperture receiver [17,18]. A laser beam reflected by or originating from the target reaches the array aperture and is divided by the subapertures. The coupling efficiency from space to the single-mode fiber in each subaperture could reach 0.81 for a plane wave input laser beam [19]. When facing turbulence, the coupling efficiency could be highly improved by eliminating the subaperture tip/tilts, because tip/tilts take most part of the turbulence-induced aberrations. The coupled laser beams could be merged together with fiber power combiners. But, the combined beams are basically with multiple modes and degraded beam quality, which is not suitable for coherent FSO communications. As an alternative, through polarization-maintaining fiber (PMF) couplers with multiple-level and active phase control, all the coupled laser beams could be coherently combined into a single PMF and maintain good beam quality [3].

 

Fig. 1. Experimental scheme of the adaptive optics correction of distributed 19-element fiber laser array. HVA, high voltage amplifier.

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Fig. 2. Scheme of the cophasing module.

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Current researches are mainly focused on the CBC function of the distributed fiber laser array for laser emission, and minor attention has been spent on the laser beam receiving, while basically no researches report the bidirectional transceiving of the distributed aperture array with full capability of eliminating the subapertures’ pistons and tip/tilts phase distortions. In this Letter, we demonstrate the AO correction for both the CBC of the outgoing laser beams and the cophasing control of the coupled laser beams from space with a 19-element AFOCs array for the first time, to our best knowledge.

The schematic of the experimental setup is depicted in Fig. 1. The optical transceiver is composed of a hexagonally distributed array of 19 AFOCs with the whole equivalent aperture $D = {152}\;{\rm mm}$ (subaperture size $d = {28}\;{\rm mm}$). The array’s fill factor is 0.903, larger than others reported [15,20]. The 19 sub-beams received by the transceiver are then coherently combined into one PMF (RX port) by the cophasing (CP) module shown in Fig. 2. Two control loops named as fiber coupling (FC) and CP are built to correct the aberrations of tip/tilts and pistons in subapertures and maximize the receiving light intensity. For each AFOC, 5% of the coupled power (separated by the fiber splitter) is detected by a photo-detector and used as the SPGD metric for FC control. The fiber-tip’s position at the AFOC’s focal plane varies with the driving voltages, so the coupling efficiency or the deflection angle of the outgoing beamlet is changed correspondingly. SPGD algorithm iteratively calculates the driving voltages applied on the AFOC to optimize the coupled power [11], and then the subaperture’s tip/tilts carried by the incident beam are corrected. The deflection angle of the AFOCs is bigger than $ \pm {200}\;\unicode{x00B5} {\rm rad}$, and the 3 dB bandwidth is about 1.3 kHz. The FC control works in parallel for each AFOC. The proportion of the received power used for FC could be compressed down to small enough with the help of more sensitive detectors in practical engineering applications. The CP course controls the phase of the 19 coupled laser beams (rest 95%) for merging into one PMF using a special all-fiber CBC structure, with the help of the homemade phase-compensators (PCs) shown in Fig. 2. The intensity of coupled and combined beams is detected and used as the SPGD metric of the CP control to calculate the PCs’ driving voltages and finally maximize the receiving light intensity [3]. Pistons deriving from the incident wavefront aberrations and fiber path’s random phase are then eliminated. In fact, this metric voltage could also be utilized as the signal in FSO communications. The incident laser beam above is generated from the fiber tip located at the focal point of the transforming lens with a focal length of 2.5 m. This simulated far-field laser beam (50 mW) comes from the laser source with wavelength $\lambda $ of 1.064 µm and linewidth of 3 kHz. The transmitting laser beam (TX port) of the fiber array transceiver is separated from the same laser source and with power of 135 µW. With the help of a fiber circulator, this beam shares the same optical path as the array’s incident laser beam. According to the reversibility of the optical path, wavefront aberrations of the 19 outgoing beamlets are precompensated, and an ideal CBC pattern would be obtained at the far-field port.

 

Fig. 3. Curves of normalized light intensity coupled by the AFOC array.

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The SPGD iteration rate of the FC control is 0.93 kHz with a computer-based controller (Intel core i7-4790, NI 6723 and NI 6254). The 19 curves of the normalized light intensity coupled by the AFOCs are illustrated in Fig. 3. The durations of the open and closed loops are 10 s and 20 s correspondingly. Most metrics converge to their maximal values within 50 ms. The averaged metric is 0.975 in the closed loop, 2.48 times of that value equal to 0.393 in open loop. The metrics’ RMS decreases from 0.0108 in open loop to 0.0071 in closed loop. Low coupling efficiency in the open loop is mainly caused by the optical alignment errors and environmental weak vibration. The results show that the coupling efficiency could be improved and more stable under the FC control. Such control is parallel for each of the AFOCs, so the effective control bandwidth would not decrease as the array scale enlarges.

The CP module shown in Fig. 2 is composed of 19 piezoelectric-based PCs and a combiner of fiber couplers with five levels. The PCs are with half-wave voltage of about 1.3 V and first-order resonance frequency of about 32 kHz. Sixteen fiber couplers (black) are with coupling ratio of 50:50. The remaining two couplers are with special coupling ratio. The electric field ${E_o}$ of the output laser beam is function of the coupled laser beams’ power ${I_n}$ ($n = {1}$ to 19), phase ${\varphi _n}$, and PCs’ phase ${\psi _n}$ as

Normalized light intensity curves of the coupled and combined laser beams at the laser receiving port are shown in Fig. 4. Each of the three stages lasts 10 s. The two curves are different in stage II where CP control (red) or FC control (blue) operates alone. The iteration rate of the CP SPGD control is 9.56 kHz. The CP control takes about 150 ms to promote the metric to its maximum. The control speed could be optimized by using improved phase-locking methods [21,22] and a hardware-based controller. The averaged values of the metrics in stage I are different between the two curves, due to the random phase distribution in the open loop. The metric increases to 0.36 under CP control, 25.7 times of that in open loop. FC control just improves the metric from 0.028 to 0.099. So, the influence of the subapertures’ pistons is larger than tip/tilts for receiving in a distributed fiber laser array. The metric is maximized rapidly when both the FC and CP control are carried out. The averaged metric then is raised to 0.968 and 0.972 for the two curves, equaling about 69 and 35 times as against the open loop. For objectivity, the two multiples’ mean of 52 is adopted. So, the aberrations located in the path from the simulated far-field point to the receiving port of the distributed fiber laser array are eliminated through the parallel FC and CP control.

 

Fig. 4. Normalized light intensity curves of the coupled and combined laser beams at the laser receiving port.

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The outgoing laser beams of the 19 AFOCs generating from the same local source share the uniform optical path as the receiving beam. According to the principle of optical reciprocity, the aberrations in the transmission path should be precompensated for the outgoing laser beams of the AFOC array.

The far-field long exposure patterns (frame averaged) during the experiment are shown in Fig. 5. The four subplots Figs. 4(a)–4(d) correspond to the stage I, stage II-FC, stage II-CP, and stage III, respectively. The pixel values are all normalized and divided by the maximum in Fig. 5(d). In Fig. 5(a), the far-field pattern is flat, and the coherent stripes are barely visible, due to the alignment-induced beam direction deviation between the AFOCs and the optical-path-difference-induced random pistons. The peak intensity is improved slightly, and the energy concentration is obviously promoted when adaptive fiber coupling is carried out in Fig. 5(b). Single CP generates obvious fringe visibility, while the energy distribution tilts to the left bottom corner as shown in Fig. 5(c). Both the peak intensity and fringe visibility are maximized under both adaptive FC and CP control, as shown in Fig. 5(d).

 

Fig. 5. Long exposure patterns in far field (frame averaged) during the experiment: (a) open loop; (b) adaptive fiber coupling only; (c) cophasing only; (d) both cophasing and adaptive fiber coupling.

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Fig. 6. PIB metric proportion as the function of time.

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PIB metric proportion, defined as the ratio between PIB and the total transmitting power, is the key value to estimate the performance of the far-field CBC pattern. Here the angular diameter of the PIB bucket is ${2}.{44}\lambda /D$ (Airy disk diameter). The PIB metric proportion calculated from the image sequence captured by the camera is depicted in Fig. 6. The two curves correspond to the two in Fig. 4. The embedded image is the ideal CBC pattern of the 19 AFOCs array and with PIB proportion of 0.51. The far-field pattern shown in Fig. 5(d) is very close to the ideal distribution. The mean PIB proportion of the two curves in open loop is 0.06 (0.069 and 0.051, respectively) and increased to 0.194 (0.196 and 0.192 for single FC and CP control, respectively). Finally, this value reaches 0.496 (0.494 and 0.498, respectively), which is 8.27 times of the open loop value and approaches the ideal value (about 97%).

The experimental results above show the effectiveness of the AO capabilities of the distributed fiber laser array for beams’ transmitting and receiving. All-fiber active CP, together with active FC, gives out efficient and fast correction of the aberrations distributed in the transmission path from the array to the target. A laser beacon could be the cooperative targets’ lasers in FSO communications, or the light launched by the array and reflected by the in-cooperative target. Correction of quasi-static phase wavefront aberrations has been demonstrated in the experiment. Effective FC bandwidth of 400 Hz is obtained in early studies [23], and the phase-locking control’s bandwidth even could reach 500 Hz [15] for a 21-AFOC array. So, dynamic aberrations of atmospheric turbulence with typical frequency about 100 Hz could be corrected theoretically under improved controller platform and with higher bandwidth devices in the near future. It should be noticed that the transmitting and the receiving of laser beams come from the same laser source, so they keep the same aberrations when sharing the uniform optical path in fiber and space in the opposite directions. This is different from the actual FSO scenario, where the signal laser and the local laser are different. Rigid control of the length difference of the fiber path between each subaperture would reduce the influence of the optical frequency difference. Meanwhile, the optic phase-locked loop could help and should be researched.

 

Fig. 7. Fiber coupling efficiency and cophasing efficiency vary as the array element number under a certain turbulence intensity of $D/{r_0} = {10}$.

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One of the key issues for future applications of this adaptive transceiver in FSO communications is the choice of array unit number $N$ and subaperture’s size $d$, under the given whole aperture diameter $D$ varying as the transmission distance and signal rate. Optimal $N$ and $d$ generate the best reception efficiency of signal beam from the whole aperture to the single-mode-fiber under certain Kolmogorov turbulence intensity $D/{r_0}$ (${r_0}$ is the Fried parameter). Figure 7 illustrates the numerical results of the coupled and combined efficiency varying as $N$. Here the excess loss ratio for each order of fiber couplers in the CP module is set as 0.2 dB (commercial standards). $D/{r_0}$ is set as 10 for common turbulence condition. The transmission distance is set as larger than Fraunhofer distance (tens of kilometers). Obviously, the FC efficiency increases as $N$ enlarges, due to the reduction of $d/{r_0}$. The CP combining efficiency decreases for larger $N$, where the order of the CP module is higher. The optimal $N$ is about 250, and the total receiving efficiency is 0.455 (loss ratio of 3.42 dB), which is hard to achieve for the conventional AO-enhanced monolithic telescope. Based on the analysis above, when $D$ drifts from 100 mm to 1 m, the $d$ is from 5 mm to 50 mm under $N = {250}$. For $d = {28}\;{\rm mm}$ in our system, the optimal $D$ would reach about 0.5 m for the hexagonal arrangement, which is suited for FSO communications with a distance up to thousands of kilometers. Furthermore, such a system is with smaller size and lower weight.

In conclusion, we have shown an efficient adaptive optical correction of a distributed 19-element fiber laser array for both beam sending and receiving. Such a system has advantages of good scalability, compactness, lower costs, and superior reliability. Active beam coupling from space into PMFs and all-fiber active CP combining with multiple-level fiber couplers are demonstrated. Aberrations distributed in the whole fiber path from the target to the receiving port are eliminated, and nearly ideal coherent combining is achieved. Coherent reception efficiency is raised up to 52 times with the whole aperture of 152 mm and the far-field PIB metric up to 8.27 times. Adaptive correction for dynamic turbulence-induced aberrations with more AFOC elements and higher control speed with a hardware circuit should be researched experimentally in the future.