Stochastic Parallel Gradient Descent Algorithm Research Articles

Coherent beam combining of 137 W 2 × 2 fiber amplifier array

We demonstrate coherent beam combining of two-dimensional fiber amplifier arrays with a total of 137W output power using stochastic parallel gradient descent (SPGD) algorithm. Compact all-fiber polarization-maintained single frequency fiber amplifier chains are developed and four fiber amplifiers are arranged to 2×2 laser array with a fill factor of 70% in the near-field. Active phase control is implemented by a digital signal processor (DSP) based SPGD controller. The fringe visibility of the coherent combined beam profile is as high as 81% when the system is closed-loop controlled despite perturbations of the environment.

基于并行梯度下降算法的自适应任意口径光束整形

基于并行梯度下降算法的自适应任意口径光束整形

基于并行梯度下降算法模拟高功率固体激光装置的相干合成

基于并行梯度下降算法模拟高功率固体激光装置的相干合成

Adaptive generation of a near-diffraction-limited square flattop beam with dual phase onlyliquid crystal spatial light modulators

We demonstrate the adaptive conversion of a quasi-Gaussian beam into anear-diffraction-limited square flattop beam in the near field based on the combination ofdual phase only liquid crystal spatial light modulators (LC-SLMs) and a stochastic parallelgradient descent (SPGD) algorithm. The SPGD algorithm iteratively adjusts the phasedistributions of the dual phase only LC-SLMs to reduce the variance between the targetand the actual beam shape. One phase only LC-SLM adaptively redistributes the intensityand the other adaptively compensates the wavefront of the output beam. The shapingeffect and influencing factors have been studied in detail. The theoretical and experimentalresults show that the technique is capable of adaptive creation, on demand, of anear-diffraction-limited flattop beam that closely matches the desired target parameters.

Influence and simulated correction of tip/tilt phase error on fiber laser coherent beam combination

Near-field models of coherent beam combination (CBC) with different beam channels and fill factors are employed, and the influences of tip/tilt phase errors on CBC are studied. The key device for tilt-error correction, named adaptive fiber optics collimator(AFOC), is introduced. A MOPA-configuration fiber laser CBC system compensating both piston and tip/tilt phase errors is designed. Then, the dynamic courses of tilt-error correction using stochastic parallel gradient descent (SPGD) algorithm in a seven-channel system are simulated, and the effects of CBC at different tilt-error amplitudes and frequencies are investigated. Experimental results show that the tilt-error should be corrected to improve CBC effects, and algorithm's control ability drops off when tilt-error amplitude and frequency increase. The results in this paper present a reference for multi-channel high power fiber laser CBC systems in real atmospheric environments.

基于随机并行梯度下降法的两路板条激光器相干合成

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.

Adaptive conversion of multimode beam to near-diffraction-limited flattop beam based on dual-phase-only liquid-crystal spatial light modulators

We propose and demonstrate the adaptive conversion of a multimode beam into a near-diffraction-limited flattop beam in the near field based on a combination of dual-phase-only liquid-crystal spatial light modulators (LC-SLMs) and the stochastic parallel gradient descent (SPGD) algorithm. One phase-only LC-SLM redistributes the intensity of the multimode beam, and the other compensates the wavefront of the output beam. The SPGD algorithm adaptively optimizes the phase distributions of dual-phase-only LC-SLMs to reduce the variance between the actual beam shape and the target beam shape. The experimental results on a fiber multimode beam show that the system is capable of adaptively creating square and rectangle flattop beams with desired parameters. Beam quality can be greatly improved by this system. The power in the main lobe of the far-field spot is about 4 times larger than that of the input multimode beam.

Coherent beam combining of high-order-mode fiber lasers with active phase control

Coherent beam combining of high-order-mode fiber lasers is an attractive choice forhigh-power lasers as high-order-mode fiber lasers have a higher power handling capabilitythan fundamental mode lasers. As active phasing provides a robust way for in-phase modecoherent beam combining, coherent beam combining of high-order-mode fibers with activephase control is proposed and a proof-of-concept experiment is performed. In the experiment,LP11 mode lasers are generated by off-center launching of single-mode fiber laser beams intofew-mode fibers and active phasing is realized using a stochastic parallel gradient descentalgorithm. The results show that the long-exposure fringe contrast is increased from zero to40% when the system evolves from open-loop to closed-loop. A scalable architecture forcoherent beam combining of high-order-mode amplifiers with active phase controlin a master oscillator power amplifier configuration (MOPA) is also proposed.

Coherent Beam Combining of Two Fiber Amplifiers Seeded by Multi-Wavelength Fiber Laser

Multi-wavelength seed laser can mitigate stimulated Brillouin scattering (SBS) and improve the output power of the narrow-linewidth fiber amplifier. In this present study, coherent combining of two fiber amplifiers seeded by a multi-wavelength laser is proposed and demonstrated using stochastic parallel gradient descent (SPGD) algorithm. The long-exposure visibility of the far field interference pattern is increased from 0.15 to 0.97 when the system evolves from open-loop to closed-loop. The feasibility of coherent combining of fiber amplifiers seeded by multi-wavelength seed laser is validated.

Theoretical analysis of adaptive optics system based on stochastic parallel gradient descent algorithm

The adaptive optics (AO) technology without a wave-front sensor is simple and has more application fields than conventional AO technologies. The theory basis of the AO system based on stochastic parallel gradient descent (SPGD) from the convergence, the stability, and the averaged convergence rate is analyzed, where SPGD is used to control the AO system. The results show that the AO system based on SPGD can obtain good convergence and stability, and the fast convergence rate, which is in inverse proportion to \( \sqrt n \) (n is the number of control parameters).

Multimode fiber laser beam cleanup based on stochastic parallel gradient descent algorithm

We present experimental research on multimode fiber laser beam cleanup based on a stochastic parallel gradient descent (SPGD) algorithm. The multimode laser is obtained by injecting a 1064 nm central wavelength single mode fiber laser into a multimode fiber and the system is setup by using phase only liquid crystal spatial light modulators (LC-SLM). The quality evaluation function is increased by a factor of 10.5 and 65% of the laser energy is encircled in the central lobe when the system evolves from open-loop into close-loop state. Experimental results indicate the feasibility of the multimode fiber laser beam cleanup by adaptive optics (AO).

Coherent beam combining of hybrid phase control in master oscillator-power amplifier configuration

A novel scalable architecture for coherent beam combining with hybrid phase control involving passive phasing and active phasing in master oscillator-power amplifier configuration is presented. Wide-linewidth mutually injected passive phasing fibre laser arrays serve as master oscillators for the power amplifiers, and the active phasing using stochastic parallel gradient descent algorithm is induced. Wide-linewidth seed laser can suppress the stimulated Brillouin scattering effectively and improve the output power of the fibre laser amplifier, while hybrid phase control provides a robust way for in-phase mode coherent beam combining simultaneously. Experiment is performed by active phasing fibre laser amplifiers with passive phasing fibre ring laser array seed lasers. Power encircled in the main-lobe increases 1.57 times and long-exposure fringe contrast is obtained to be 78% when the system evolves from passive phasing to hybrid phasing.

Near-diffraction-limited flattop laser beam adaptively generated by stochastic parallel gradient descent algorithm

We demonstrate the adaptive generation of a near-diffraction-limited flattop laser beam in the near field based on the stochastic parallel gradient descent algorithm and dual-phase-only liquid crystal spatial light modulators (LC-SLMs). One LC-SLM redistributes the intensity, and the other compensates the wavefront of the output beam. The experimental results show that approximately 69% of the power is enclosed in a region with less than 6% rms intensity variation. The 5mm diameter near-diffraction-limited output beam retains a flattop intensity distribution without significant diffraction peaks for a working distance of more than 30 cm.

Coherent combining of multi-wavelength fiber amplifiers using a stochastic parallel gradientdescent algorithm

Multi-wavelength and non-single-frequency seed lasers can be used to suppress stimulatedBrillouin scattering and improve the ultimate output power of a fiber laser amplifier.Coherent combining of non-single-frequency and/or multi-wavelength lasers/amplifiers is apromising way to obtain much higher total output power than from coherent combining ofsingle-frequency lasers/amplifiers. Using a stochastic parallel gradient descent algorithm,we demonstrate coherent combining of four-channel multi-wavelength lasers in a masteroscillator power amplifier (MOPA) configuration. Four lasers with different wavelengths,namely two non-single-frequency and two single-frequency lasers, are used. Themean power of the main lobe in the closed-loop case is three times that for theopen-loop case, approaching 75% of its ideal value. The coherent combining ofmulti-wavelength and non-single-frequency lasers in a MOPA configuration isvalidated, and a feasible approach for scaling to high power coherent combining isprovided.

Beam shaping for uplink transmission of a relay mirror system

We establish the model of a two-Cassegrain-telescope system that is commonly used in a relay mirror system. With this model, uplink transmission of the relay mirror system is theoretically analyzed. We determined that uplink transmission with turbulence completely corrected is not an optimal mode. We improve power coupling efficiency of the two-Cassegrain-telescope system by optimizing the optical phase at the launching telescope by use of the stochastic parallel gradient descent algorithm. For a 10 km vertical uplink transmission, power coupling efficiencies of the system are 63.10%, 87.82%, and 97.80% corresponding to an open-loop mode, a closed-loop mode, and a closed-loop with optimization mode, respectively. For a 30 km vertical uplink transmission, power coupling efficiencies of the system are 22.35%, 82.66%, and 91.91%, corresponding to an open-loop mode, a closed-loop mode, and a closed-loop with optimization mode, respectively. The results show that power coupling efficiency of the two-Cassegrain-telescope system is significantly improved.

Coherent beam combining of pulsed fiber lasers with hybrid phase control

We demonstrate a scalable architecture for coherent combining of all-fiber pulsed lasers with hybrid phase control involving passive phasing and active phasing for the first time. Synchronized and passive phased pulsed laser array is built by intra-activity phase modulation. Active phase control on the passive phased pulsed laser array using stochastic parallel gradient descent algorithm provides stable in-phase coherent beam combining pattern in a turbulent atmosphere. The fringe visibility is increased from 0 two 0.43 and the power encircled in the main-lobe is 1.616 times increased when the system evolves from passive phasing to hybrid phasing. The architecture can be easily scaled up to high power by increasing power of each individual laser, number of laser elements and introduction of power amplifiers, which will lead a promising way for scaleable high power coherent beam combining of pulsed lasers.

Enhancement of the beam quality of non-uniform output slab laser amplifier with a 39-actuator rectangular piezoelectric deformable mirror

We present a slab laser amplifier beam cleanup experimental system based on a 39-actuator rectangular piezoelectric deformable mirror. Rather than use a wave-front sensor to measure distortions in the wave-front and then apply a conjugation wave-front for compensating them, the system uses a Stochastic Parallel Gradient Descent algorithm to maximize the power contained within a far-field designated bucket. Experimental results demonstrate that at the output power of 335W, more than 30% energy concentrates in the 1x diffraction-limited area while the beam quality is enhanced greatly.

Efficient Phase Locking of Fiber Amplifiers Using a Low-Cost and High-Damage-Threshold Phase Control System

We propose a low-cost and high-damage-threshold phase control system that employs a piezoelectric ceramic transducer modulator controlled by a stochastic parallel gradient descent algorithm. Efficient phase locking of two fiber amplifiers is demonstrated. Experimental results show that energy encircled in the target pinhole is increased by a factor of 1.76 and the visibility of the fringe pattern is as high as 90% when the system is in close-loop. The phase control system has potential in phase locking of large-number and high-power fiber laser endeavors.

Coherent Beam Combination of Eight Watt-Level Polarization-Maintained Fiber Amplifiers

We demonstrate the coherent beam combination of eight Watt-level polarization-maintained fiber amplifiers. The phase control signal of each amplifier is generated by running a stochastic parallel gradient descent algorithm on a digital signal processor (DSP). The experimental result shows that the whole system in close-loop performs well for long-time observation. Energy encircled in the target pinhole is 6.68 times more than that in open-loop. The combination efficiency is as high as 84.5%.

Bandwidth analysis and improvement of the beam phasing of fiber amplifiers using the stochastic parallel gradient descent algorithm

We present the numerical analysis and improvement of the bandwidth of the beam phasing of fiber amplifiers using the stochastic parallel gradient descent (SPGD) algorithm. Time-varying phase distortions are incorporated into the dynamic simulation. It is shown by numerical calculation that the bandwidth of the standard SPGD algorithm is dependent on the phase distortions and on the number of lasers. The time-averaged cost function will decrease with an increase in the amplitude and frequency of phase distortions, and in the number of lasers. A cross-grouped SPGD algorithm is proposed, which offers attractive performance due to its robustness to various time-varying phase distortions and faster convergence rate for beam phasing of larger number of lasers. Dynamic simulation shows that the control bandwidth can be improved using the cross-grouped SPGD algorithm.