Efficient distributed architecture and optimized subarray control strategy to facilitate large-scale coherent beam combination.

<sec>Ultrafast fiber laser sources with mJ-level pulse energy and kilo-watt average power are of particular importance for various science fields such as attosecond lasers. Currently, several large-scale facilities for attosecond lasers, including ELI-ALPS in Europe, SECUF in China, NeXUS in America and ALFA in Japan are under construction. High-performance femtosecond driven lasers are crucial for attosecond lasers and various ultrafast laser facilities. Fiber lasers have a large surface-to-volume ratio, which enables efficient cooling and is suitable for high average power amplification. However, due to small mode area of optical fibers, detrimental nonlinear optical effects such as self-phase modulation, four-wave mixing, and stimulated Raman scattering limit the peak power of pulse to hundreds of MW, corresponding to pulse energy of hundreds of μJ for femtosecond pulses in large mode area rod-type fibers. In addition, the average power of fiber lasers is limited by transverse mode instability, which reduces the stability and quality of beams above a certain threshold. In rod-type fibers, the threshold is about 250 W. Neither average power nor pulse energy emitted by single fiber meets the requirement for attosecond laser generation.</sec><sec>The average power and pulse energy can be further scaled by coherent beam combination, which involves splitting pulses caused by an frontend laser and recombining them after amplification. It is essential for coherent beam combination to maintain the coherence of pulse replicas, which usually involves high speed photodiode detectors, piezo-driven mirrors, and other electronics forming a feedback system to actively control the phase of all replicas. We present a high-energy high-power ultrafast fiber laser system by using filled-aperture coherent combination of four ytterbium-doped rod-type fiber amplifiers. The phase control is achieved by using stochastic parallel gradient descent method. The frontend includes a passively mode-locked Yb-fiber oscillator, a stretcher, a pulse picker, and three fiber pre-amplifiers, which delivers 1 MHz stretched pulses centered at 1032 nm with 700 ps duration and 20 W average power. The pulse is split into four replicas by polarization beam-splitter and half-wave plate pairs, and the replicas pass through delay lines formed by piezo-driven mirrors before amplification. The pulse replicas are equally split and amplified to ensure the same accumulated nonlinear phase, and are combined by thin film polarizer and half-wave plate pairs. A small portion of the combined pulse is split and collected by a photodiode detector after being filtered spectrally and spatially, serving as a signal for controlling phase. The combined pulse is compressed by a compressor using a double-pass diffraction grating pair consisting of two 1739 l/mm gratings.</sec><sec>At a repetition rate of 1 MHz, our four-channel Yb-fiber coherent beam combination system generates a combined average power value of 753 W and a combination efficiency of 87%. By utilizing an adjustable pulse stretcher and compressor, a 0.67 mJ, 242 fs near transform-limited pulse can be generated with a compressing efficiency of 89%. The compressed pulse is centered at 1032 nm, and the spectrum width is 8.8-nm. In the 30 min measurement, the root-mean-square of average power is less than 1% , while the residual phase error is less than <i>λ</i>/23, indicating excellent stability on different time scales. The beam quality factor of the 0.67 mJ compressed pulses is 1.17×1.11. At 500 kHz, we obtain pulses of 1.07 mJ and 247 fs with average power of 534 W, exhibiting similar efficiency, long-term stability, and beam quality. The residual phase error decreases below <i>λ</i>/29, indicating better short-term stability. Further scaling power and energy can be achieved by increasing the number of channels. By adding the delay stabilization system and pointing stabilization system, which are currently under development, an eight-channel CBC system can be used to generate 1 kW, 2 mJ pulses.</sec><sec>In this work, we implement a four-channel coherent beam combining system based on the SPGD method, and obtain compressed pulses of 673 W, 673 µJ, and 242 fs at 1 MHz and 534 W, 1.07 mJ, and 247 fs at 500 kHz. Both power and energy can be further improved by increasing the channel number, and adding the delay stabilization system and pointing stabilization system which are under construction. By adding coherent pulse stacking amplification technology, the coherent beam combining system ought to generate pulse energy as high as 100 mJ, which constitutes the energy source for applications such as laser wake-field acceleration.</sec>

Coherent beam combining (CBC) of fiber laser array is a promising way to achieve high output power. Phase control is one key point to implement CBC. Appropriate feedback structures should be established to achieve phase control. Most feedback structures of CBC are established after the lasers emit to free space and consist of a set of lenses or mirrors. Those optical elements in free space may hinder array size and integration. In this paper, we demonstrated an all-fiber structured CBC method with distributed phase-locking. By adding an all-fiber measurement loop beside the main laser chain, the phase of main laser chain is appended to the measuring loop. Phases of each main laser chain are locked indirectly though the measurement loops by using stochastic parallel gradient descent (SPGD) algorithm. The principle of distributed phase-locking is also illustrated. Corresponding simulations are carried out and two-channel fiber lasers are coherently combined by this method. The experimental results show that the structure can achieve phase-locking effectively. Stable and distinct interference fringe is observed. Additionally, the structure proposed in this paper is straightforwardly building and expanding.

Supercontinuum laser, as a new type of laser source, compared with monochromatic or quasi-monochromatic light, has incandescent wide spectra and the brightness of the laser. However,the beam quality in high power is usually bad and greatly affected by atmospheric turbulence in the transmission process. Therefore, how to improve the beam quality to ensure the energy transmission and image quality has become a popular topic. According to the measurement results of the near field wavefront characteristics of the supercontinuum laser in different wavelength, we know that the wavefront phase of the light source is relatively stable and change slowly over time. The types of wavefront distortion at each wavelength are basically the same, mainly made up of defocus and astigmatism. In order to conform to the wavefront characteristics of supercontinuum laser, the input of simulation is low-order static distortion wavefront generated by using Zernike polynomia with defocus and astigmatism. Stochastic Parallel Gradient Descent (SPGD) algorithm with the thorlabs DMP40 deformable mirror and CCD camera as the imaging sensor, is used to construct a simulation model for wavefront correction of low-order static distortion aberrations. Since B-SPGD algorithm is superior to U-SPGD in terms of convergence speed and correction effect, as well as adaptability to the near field wavefront distortion [1], we use B-SPGD algorithm to construct the simulation program for wavefront correction simulation research. The ability and convergence of SPGD algorithm to correct wavefront distortion are studied, mainly about the random disturbance amplitude and influence coefficient of the core parameters. In order to get close to the evaluation standard of laser in practical application, Strehl Ratio(SR) is selected as the performance evaluation function. According to the effective diameter of deformable mirror and the distance between electrodes, the influence function of deformable mirror is normalized to the unit circle to meet the requirements of simulation calculation. In order to improve the stability of SPGD algorithm and reduce the possibility of SPGD algorithm falling into local extreme values, we use Hessian matrix to optimize SPGD algorithm. After simulation and analysis of distortion correction of Supercontinuum laser wavefront, deformable mirror controlled by SPGD algorithm has good correction capability for low-order static aberration.

Owing to the unique features in intensity and phase structures, optical vortex lattices (OVLs) have attracted intensive attention and promoted various applications. However, the power scaling of OVLs always presents a critical challenge. Here we take advantage of the brightness enhancement of coherent beam combining (CBC) technology and propose an architecture for creating OVLs based on the CBC system. In the experiment, by utilizing the stochastic parallel gradient descent algorithm, the dynamic phase noises were compensated. The desired piston phase shifting of each element for tailoring the structured wavefront was implemented by the liquid crystal. When the system in a closed loop, hexagonal close-packed OVL consists of spatially distributed orbital angular momentum, beams can be generated in the far-field. This work is an important step toward future implementation of high-power structured light beams.

Beam combination of fiber laser array is an effective technique contributed to improve the brightness of fiber lasers. In order to realize high-efficiency CBC, challenges like phase distortion (mainly including piston and tilt phase aberrations) should be taken into consideration. Resent years, tilt phase aberrations control has been come true by adaptive fiber optics collimator using the stochastic parallel gradient descent (SPGD) algorithm. However, the convergence rate of tilt control system still cannot satisfy the needs of practical application. In order to increase the tilt control bandwidth, a new idea is put forward that applying the orthogonal single frequency dithering (OSFD) technique into tilt control, and numerical simulation has been completed. A hexagonal laser array with 7 elements has been simulated, and each element has a pair of initial tilt angles in horizontal and vertical direction. The initial tilt angles comply with normal distribution. In the same condition, tilt phase control has been realized through SPGD and OSFD individually, and the convergence steps (defined as the iteration steps that improve the normalized PIB above 0.9) with appropriate parameters are respectively about 20 (SPGD) and 7 (OSFD). Furthermore, tilt phase control of large number hexagonal array is simulated, and the results are as follows: for 19/37 elements, the least convergence steps are about 80/160(SPGD) and 19/55(OSFD). Comparing with SPGD algorithm, it is obvious that the OSFD has higher convergence rate and greater potential for tilt control application in large number coherent fiber laser array.

A phase controller for coherent beam combining (CBC) of fibre lasers has been designed and manufactured based on a stochastic parallel gradient descent (SPGD) algorithm and a field programmable gate array (FPGA). The theoretical analysis shows that the iteration rate is higher than , and the average compensation bandwidth of CBC for 5 or 20 channels is or , respectively. The tests show that the phase controller ensures reliable phase locking of lasers: When the phases of five lasers are locked by the improved control strategy with a variable gain, the energy encircled in the target is increased by than that in the single output, the phase control accuracy is better than , and the combining efficiency is 92 %.

Coherent beam combination (CBC) of laser arrays is an efficient way to scale brightness. We demonstrate CBC of two slab laser amplifiers based on active phase locking. Instead of the complex phase detection system, intensity detection is used and the feedback control signal is calculated based on the stochastic parallel gradient descent (SPGD) algorithm. The experimental investigation on a 101.5-W CBC of two slab amplifiers shows that the entire system in a closed loop performs well for long-time observation. A combination efficiency of nearly 81% is realized. The slab amplifier laser arrays are the coherent beams efficiently combined by active phase locking based on the SPGD.

IERUS Technologies, Inc. and the University of Alabama in Huntsville have partnered to perform characterization and development of algorithms and hardware for adaptive optics. To date the algorithm work has focused on implementation of the stochastic parallel gradient descent (SPGD) algorithm. SPGD is a metric-based approach in which a scalar metric is optimized by taking random perturbative steps for many actuators simultaneously. This approach scales to systems with a large number of actuators while maintaining bandwidth, while conventional methods are negatively impacted by the very large matrix multiplications that are required. The metric approach enables the use of higher speed sensors with fewer (or even a single) sensing element(s), enabling a higher control bandwidth. Furthermore, the SPGD algorithm is model-free, and thus is not strongly impacted by the presence of nonlinearities which degrade the performance of conventional phase reconstruction methods. Finally, for high energy laser applications, SPGD can be performed using the primary laser beam without the need for an additional beacon laser. The conventional SPGD algorithm was modified to use an adaptive gain to improve convergence while maintaining low steady state error. Results from laboratory experiments using phase plates as atmosphere surrogates will be presented, demonstrating areas in which the adaptive gain yields better performance and areas which require further investigation.

The adaptive polarization conversion system which converts the non-polarization maintaining laser to polarization maintaining one based on stochastic parallel gradient descent (SPGD) algorithm is reported in this paper. Using polarization controller to control polarized component in X and Y direction directly, adopting SPGD optimization technology to optimize the output extinction ratio, it finally realizes polarization conversion of non-polarization maintaining laser to polarization maintaining one. In theory, the model of adaptive polarization conversion is built based on the principle of the controller and the SPGD algorithm. In experiment, we first realized adaptive conversion of non-polarization maintaining laser to polarization maintaining one with an extinction ratio of 14.1 dB. Then we used the system to change the polarization direction of the linearly polarized laser from any direction (0-360) to the expected direction with high extinction ratio, and the average extinction ratio is about 12 dB.

Stochastic parallel gradient descent (SPGD) algorithm is one of the most promising methods for effective coherent beam combination. However, the algorithm also has some disadvantages, such as slow convergence speed and local extremum. This paper proposes an AdaDelSPGD algorithm, which combines an AdaDelta algorithm with a SPGD algorithm, and improves the traditional AdaDelta algorithm with adaptive gain coefficient. It is worth noting that the adaptive gain coefficient can be adjusted in real time to improve the convergence rate. The effectiveness of the proposed algorithm is verified by relevant simulation experiments, and the results show that the proposed algorithm can significantly improve the convergence speed. Following the experiments with the fiber laser-phased array multiplex communication system, we can draw the conclusion that the addition of communication modulation reduces the beam quality, and the higher the modulation frequency, the worse the beam quality. However, adding the SPGD algorithm can improve the beam quality. The AdaDelSPGD algorithm proposed in this paper can further improve the beam quality, and the bit error rate of communication is also decreased after testing. This provides a foundation for further research on the fiber laser-phased array multiplex communication system.

Sensor-less adaptive optics (AO) technology is an effective method to compensate the wave front distortion caused by atmospheric turbulence in free space optical communication (FSOC) system. In general, a lot of iterations are required to update the control voltage vector step by step for the stochastic parallel gradient descent (SPGD) algorithm which is a conventional and often considered model-free algorithm. The newly developed model-based algorithms have certain constraints and difficulties for the construction of the models. Therefore, in order to develop a rapid wave front distortion compensation algorithm with better performance, we present a hybrid method which combines a model-based algorithm presented by Martin J. Booth and SPGD algorithm to correct the low-order aberration and high-order aberration respectively. Simulations show that this hybrid method can compensate wave front aberrations with higher convergence speed than that of SPGD algorithm and finally reach higher Strehl ratio (SR) and better bit error rate (BER) with same iterations, particularly under strong turbulence. This result means that our hybrid method can improve coupling efficiency and quality of FSOC system.

In this paper, we report a coherent beam combining (CBC) system that involves two thulium-doped all-polarization maintaining (PM) fiber chirped pulse amplifiers. Through phase-locking the two channels via a fiber stretcher by using the stochastic parallel gradient descent (SPGD) algorithm, a maximum average power of 265 W is obtained, with a CBC efficiency of 81% and a residual phase error of λ/17. After de-chirping by a pair of diffraction gratings, the duration of the combined laser pulse is compressed to 690 fs. Taking into account the compression efficiency of 90% and the main peak energy proportion of 91%, the corresponding peak power is calculated to be 4 MW. The laser noise characteristics before and after CBC are examined, and the results indicate that the CBC would degrade the low frequency relative intensity noise (RIN), of which the integration is 1.74% in [100 Hz, 2 MHz] at the maximum combined output power. In addition, the effects of the nonlinear spectrum broadening during chirped pulse amplification on the CBC efficiency are also investigated, showing that a higher extent of pulse stretching is effective in alleviating the spectrum broadening and realizing a higher output power with decent combining efficiency.Graphical

Owing to the restriction of the stimulated Brillouin scattering (SBS) and other nonlinear effects, the output power of the single frequency amplifier is ar a level of about hundred watts. Multi-wavelength and non-single frequency seed laser will mitigate the SBS and improve the output power of the fiber laser amplifier. The coherent beam combining of the non-single frequency and/or multi-wavelength laser will greatly increase the total output power of the coherent beam combining as compared with the coherent beam combining of a single frequency laser. Based on the stochastic parallel gradient descent (SPGD) algorithm, coherent combining of four channel four-wavelength lasers is realized. In the close loop state, the mean power of the main-lobe is four times higher than that of the open-loop, approaching 75% of its ideal value. The coherent combining of the multi-wavelength and non-single frequency laser is demonstrated and an approach to the high power coherent beam combining is provided.

To speed up the convergence rate of Stochastic Parallel Gradient Descent(SPGD) algorithm that was used to control a deformable mirror for wavefront shaping and to enhance the capability of real-time wave-front shaping,a simulation model was established by using wave-front distortion described by 12 Zernike polynomials and a 32-unit deformable mirror.Two constant matrixes were obtained with the orthogonality of Zernike polynomials in a unit circle,which simplizes computations and speeds up the running time of the algorithm.After 660 iterations,the Strehl ratio is 0.8.Comparison results of 6 kinds of SPGD algorithms with Matlab7.8.0 show that indirect-fixed-bilateral SPGD algorithm can be used in the conditions of low Strehl ratio,and indirect-varied-bilateral SPGD algorithm can be used in the conditions of high Strehl ratio,which will speed up the convergence rate of SPGD algorithm and provide the theoretical guidance for laser shaping.

We demonstrate the coherent beam combination of a hexagonal distributed high power fiber amplifier array. Six polarization-maintained fiber amplifiers are tiled into a hexagonal array by use of a novel beam combiner. The phase control signal for fiber amplifiers is generated by running a stochastic parallel gradient descent algorithm on a digital signal processor. The coherent beam combination with a total output power of 73.5 W is demonstrated. The contrast of the coherent combined beam profile is as high as 81% when the system is closed-loop controlled.