Coherent beam combination of a hexagonal distributed high power fiber amplifier array

Traditional coherent beam combination (CBC) system architecture has revealed inadequacies in meeting the concurrent demands of large-scale deployment and high-bandwidth requirements. Addressing this challenge, we propose a distributed CBC system architecture based on the optimized stochastic parallel gradient descent (SPGD) algorithm. Our strategy segments the large-scale laser array into multiple independent smaller-scale subarrays, ensuring their efficient phase convergence through the introduction of corresponding reference lasers while avoiding interference when integrating different subarrays. Moreover, the piecewise SPGD algorithm is proposed and the intensity of the reference laser is modulated to further improve the convergence speed and accuracy within subarrays, enhancing the algorithm's compatibility across laser arrays of varying scales. We have validated the feasibility of the distributed CBC architecture through numerical analysis and assessed the strategy's performance in both static and dynamic environments using simulation software. The simulation findings indicate that, compared to traditional CBC systems, distributed architecture with 3, 7, and 19 subarrays and utilizing the piecewise SPGD algorithm, has experienced phase control bandwidth enhancements by factors of approximately 3.6, 10.4, and 32.5 respectively, maintaining superior average power output in dynamic noise environments. The proposed architecture and strategy also accommodate subarrays of variable scales and obviates the necessity for large-aperture optical components on the emitted plane, demonstrating exceptional scalability and adaptability.

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.

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.

We report on active coherent beam combining of two single-frequency nanosecond fiber amplifiers by using stochastic parallel gradient descent algorithm. Each fiber amplifier produces an average power of more than 100 W by using three-stage cascaded amplification. The two laser beams are actively phase-locked with a total average power of 215.8 W, producing ~8 ns pulses at 10 MHz repetition rate. The contrast of the far-field intensity pattern of the coherently combined beam is more than 83%.

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.

In this chapter, several beam combining architectures suitable for DE applications have been reported, and are divided into two distinct categories: incoherent beam combination (IBC) and coherent beam combination (CBC). The purpose of each method is to increase the far field intensity when brightness and power of a single fiber amplifier is limited. In IBC, an array of fiber lasers is superimposed in the far field without control of the relative spectra or phases of the different fibers. No brightness enhancement is obtained from this method, limiting the maximum intensity in the far field. Although such beam combining has been successfully demonstrated by the Navy [5], this approach is limited to propagation ranges on the order of a few kilometers. In spectral beam combining (SBC), a separate class of IBC, incoherent beams of different wavelengths are spatially overlapped to create a single output beam of multiple colors. The brightness of the propagating beam can be increased at the cost of increased spectral bandwidth. Similarly, SBC has the advantage of not requiring active phase control or mutual temporal coherence of the individual beams. Alternatively, coherent beam combining (CBC) schemes require proper phase, frequency, and polarization relationships for efficient beam combination. Overall, due to their brightness enhancements, for longer range and higher power/ intensity DE applications, SBC and CBC are potentially more appealing.

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.

Coherent beam combination laser system using SBS-PCM for high repetition rate solid-state lasers

The development of high-power fiber lasers is of great interest due to the advantages they offer relative to other laser technologies. Currently, the maximum power from a reportedly single-mode fiber amplifier stands at 10 kW. Though impressive, this power level was achieved at the cost of a large spectral linewidth, making the laser unsuitable for coherent or spectral beam combination techniques required to reach power levels necessary for airborne tactical applications. An effective approach in limiting the SBS effect is to insert an electro-optic phase modulator at the low-power end of a master oscillator power amplifier (MOPA) system. As a result, the optical power is spread among spectral sidebands; thus raising the overall SBS threshold of the amplifier. It is the purpose of this work to present a comprehensive numerical scheme that is based on the extended nonlinear Schrodinger equations that allows for accurate analysis of phase modulated fiber amplifier systems in relation to the group velocity dispersion and Kerr nonlinearities and their effect on the coherent beam combining efficiency. As such, we have simulated a high-power MOPA system modulated via filtered pseudo-random bit sequence format for different clock rates and power levels. We show that at clock rates of ≥30 GHz, the combination of GVD and self-phase modulation may lead to a drastic drop in beam combining efficiency at the multi-kW level. Furthermore, we extend our work to study the effect of cross-phase modulation where an amplifier is seeded with two laser sources.

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.

The XCAN project, which is a three years project and began in 2015, carried out by Thales and the Ecole Polytechnique aims at developing a laser system based on the coherent combination of laser beams produced through a network of amplifying optical fibers. This technique provides an attractive mean of reaching simultaneously the high peak and high average powers required for various industrial, scientific and defense applications. The architecture has to be compatible with very large number of fibers (1000-10000). The goal of XCAN is to overcome all the key scientific and technological barriers to the design and development of an experimental laser demonstrator. The coherent addition of multiple individual phased beams is aimed to provide tens of Gigawatt peak power at 50 kHz repetition rate. Coherent beam combining (CBC) of fiber amplifiers involves a master oscillator which is split into N fiber channels and then amplified through series of polarization maintaining fiber pre-amplifiers and amplifiers. In the so-called tiled aperture configuration, the N fibers are arranged in an array and collimated in the near field of the laser output. The N beamlets then interfere constructively in the far field, and give a bright central lobe. CBC techniques with active phase locking involve phase mismatch detection, calculation of the correction and phase compensation of each amplifier by means of phase modulators. Interferometric phase measurement has proven to be particularly well suited to phase-lock a very large number of fibers in continuous regime. A small fraction of the N beamlets is imaged onto a camera. The beamlets interfere separately with a reference beam. The phase mismatch of each beam is then calculated from the interferences' position. In this presentation, we demonstrate the phase locking of 19 fibers in femtosecond pulse regime with this technique. In our first experiment, a master oscillator generates pulses of 300 fs (chirped at 200 ps). The beam is split into 19 passive channels. Prior to phase locking, the optical path differences are adjusted down to 10 μm with optical delay lines. Interferograms of the 19 fibers are recorded at 1 kHz with a camera. A dedicated algorithm is developed to measure both the phase and the delay between the fibers on a measurement path. The delay and phase shift are thus calculated collectively from a single image and piezo-electric fiber stretchers are controlled in order to ensure compensation of time-varying phase and delay variations. The residual phase shift error is below λ/60 rms. The coherent beam combining is obtained after propagation and compression. The combined pulse width is measured at 315fs. A second experiment was done to coherently combine two amplified channels of the XCAN demonstrator. A residual phase shift error of λ/30 rms was measured in this case.

The single frequency dithering technique for coherent beam combination with one single modulation frequency and without a reference beam is presented for the first time to our knowledge. Coherent beam combination of four fiber amplifiers is successfully demonstrated by using the single-dithering technique. When the phase control system is in the closed loop, the fringe contrast of far-field intensity pattern is improved by more than 85% from 8% in open loop, and the residual phase error is less than lambda/20. Experimental results reveal that the single-dithering technique has great potential in scaling to a large number of beamlets with a simple phase control system and low cost.

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.

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.