Influence of optical nonlinearity on combining efficiency in ultrashort pulse fiber laser coherent combining system

The influence of optical nonlinearity on combining efficiency in ultrashort pulse fiber laser coherent combining system is investigated theoretically and experimentally.In the theoretical work,a new theoretical algorithm is presented for the coherent combining efficiency,which can be used to quantify the spectral coherence decay induced by optical nonlinearity imbalance between the sub-beams.The spectral information of the sub-beam is obtained by numerically solving the nonlinear Schrödinger equation(NLSE)in this algorithm to ensure an accurate prediction.In the experimental work,the coherent combining of two all-fiber picosecond lasers is achieved,and the influence of imbalanced optical nonlinearity on the combining efficiency is studied,which agrees with the theoretical prediction.This paper reveals the physical mechanism for the influence of optical nonlinearity on the combining efficiency,which is valuable for the coherent combining of ultrashort pulse fiber laser beams.

Evaluation of the Coherent Combining Lasers Array by the Power in the Bucket of the Main Lobe Method

Coherent combination of laser beam is an important and challenging area of high power laser science. And how to evaluate the high power laser by coherent beam combination is a new research spot. Formulas for the radiated intensity distributions of coherent combined Gaussian beam array are derived via Fraunhofer scalar diffraction model by utilizing representations of the cross-spectral density of the far field. Effects of beam array numbers and separate distances etc. on far field radiated profiles are shown and analyzed. A new conception named power in the bucket of the main lobe (PIMm) is advanced to measure the beam quality of combined beams. This evaluation method is useful for efficiently determining the peak irradiance and power in the bucket for single emitting apertures of general shape.

Coherent combining of a fiber laser array via cascaded internal phase control technique

We experimentally demonstrated a cascaded internal phase control technique.A laser array with 12 channels was divided into three sub-arrays and a stage array,and phases of the sub-arrays and the stage array were locked by four phase controllers based on the stochastic parallel gradient descent(SPGD)algorithm,respectively.In this way,the phases of the whole array were locked,and the visibility of the interference pattern of the whole emitted laser array in the far field was∼93%.In addition,the technique has the advantage of element expanding and can be further used in the high-power coherent beam combination(CBC)system due to its compact spatial structure.

Terahertz shaping technology based on coherent beam combining

The generation of terahertz(THz) waves by focusing a femtosecond pulsed laser beam at a distance is able to overcome the strong absorption properties of air and has rapidly attracted the attention of industry. However, the poor directionality of the THz wave radiation generated by this method is not conducive to THz wave applications. By controlling the morphology of the ultrafast laser-excited plasma filament and its electron density distribution through coherent beam combining technology, we achieve direct THz beam shaping and are able to obtain THz wave radiation of Gaussian or arbitrary transverse distribution. The novel experimental approach proposed in this paper opens up the research field of direct THz wave shaping using plasma. Moreover, it innovates multi-parameter convergence algorithms and, by doing so, has the potential to find beam patterns with higher energy conversion efficiency and break the energy limit of THz waves emitted by lasers at high power.

Spatial channel pairing based coherent combining for relay networks

In this paper, spatial channel pairing(SCP) is introduced to coherent combining at the relay in relay networks. Closed-form solution to optimal coherent combining is derived. Given coherent combining, the approximate SCP solution is presented. Finally, an alternating iterative structure is developed. Simulation results and analysis show that, given the symbol error rate and data rate, the proposed alternating iterative structure achieves signal-to-noise ratio gains over existing schemes in maximum ratio combining(MRC) plus matched filter,MRC plus antenna selection, and distributed space-time block coding due to the use of SCP and iterative structure.

The 260-W coherent beam combining of two compact fibre amplifier chains

Coherent beam combining of two fibre amplifier chains with a total power of 260 W in a compact system using the stochastic parallel gradient descent （SPGD） algorithm is demonstrated. A 150 MHz linewidth fibre laser is built and introduced for high-power amplification to mitigate stimulated Brillouin scattering （SBS）. Compact high-power amplifier chains are built with low power all-fibre system and high-power bulk free-optics fibre amplifiers. When the total power is about 260 W, active phase-locking of two high-power amplifiers is demonstrated using the SPGD algorithm. In closed-loop, the power in the main lobe increases 1.68 times, the visibility is increased from 0 to 0.62, and the phase residual error is less than λ/10.

Tiled-aperture coherent beam combining of two high-power fibre amplifiers

We demonstrate coherent beam combining of two tiled-aperture single-frequency fibre amplifiers with a total output power of 29.65 W by using the multi-dithering technique. The two laser beams are packaged closely by using free-space mirrors side by side into a tiled-aperture with a near-field fill factor of 62%. Active phase control of the amplifier is performed on commercially available digital lock-in amplifiers. Experimental results show that the power contained in the main-lobe in closed-loop is 1.72 times greater than that in open-loop, which is 86% for the ideal case. The fringe contrast of the far-field fringe pattern is as high as 80% when the system is in closed-loop. The beam quality of the combined beam is computed to he BQ = 1.48. The whole system in closed-loop performs well in a long-time observation.

Numerical and experimental study on coherent beam combining of fibre amplifiers using simulated annealing algorithm

We present the numerical and experimental study on the coherent beam combining of fibre amplifiers by means of simulated annealing （SA） algorithm. The feasibility is validated by the Monte Carlo simulation of correcting static phase distortion using SA algorithm. The performance of SA algorithm under time-varying phase noise is numerically studied by dynamic simulation. It is revealed that the influence of phase noise on the performance of SA algorithm gets stronger with an increase in amplitude or frequency of phase noise; and the laser array that contains more lasers will be more affected from phase noise. The performance of SA algorithm for coherent beam combining is also compared with a widely used stochastic optimization algorithm, i.e., the stochastic parallel gradient descent （SPGD） algorithm. In a proof-of-concept experiment we demonstrate the coherent beam combining of two 1083~nm fibre amplifiers with a total output power of 12~W and 93% combining efficiency. The contrast of the far-field coherently combined beam profiles is calculated to be as high as 95%.

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 increases1.57 times and long-exposure fringe contrast is obtained to be 78% when the system evolves from passive phasing to hybrid phasing.

Integrated coherent combining of angled-grating broad-area lasers

In this paper, we investigated coherent beam combining of angled-grating broad-area lasers in a completely integrated approach. We obtained the simultaneous coherent beam combining and single transverse mode operation on a single chip through the integrated coupling regions and the transverse Bragg resonance （TBR） gratings, respectively. The proposed combining method can be easily extended to a zigzag-like laser array. We analyzed the scalability of the zigzag-like combining structure and compared it with other coherent combining methods. Two and six angled-grating broad-area lasers are fabricated and coherently combined by use of the proposed method. The high contrast interference fringes within an overall single lobe envelope in the measured far field prove that the emitters in the array are indeed coherently combined. By p-side-down bonding, we obtained over l W output power with over 90% combining efficiency in the two coherently combined lasers.

Realization of an efficient coherent combination via Michelson cavity

An intracavity coherent coupling Michelson erbium-doped fibre （EDF） laser （MCEDFL） is proposed and demonstrated. By using this laser system, we find a means to obtain a maximum power output at the same pumping power level. From the experiment based on fibre Bragg gratings （FBGs） with different refiectivities from 6% to 100%, we find that the reflectivity of the FBG plays a vital role in improving the performance of the MCEDFL. At the same time, the MCEDFL with a polarizer can be coherently combined effectively. This type of system, in principle, is compatible with other more powerful pumping methods, such as cladding pumping, and brings some novel perspectives to the realization of high power lasers.

Internal phase control of fiber laser array based on photodetector array

Coherent beam combining(CBC) of fiber laser array is a promising technique to realize high output power while maintaining near diffraction-limited beam quality. To implement CBC, an appropriate phase control feedback structure should be established to realize phase-locking. In this paper, an innovative internal active phase control CBC fiber laser array based on photodetector array is proposed. The dynamic phase noises of the laser amplifiers are compensated before being emitted into free space. And the static phase difference compensation of emitting laser array is realized by interference measurement based on photodetector array. The principle of the technique is illustrated and corresponding simulations are carried out, and a CBC system with four laser channels is built to verify the technique. When the phase controllers are turned on, the phase deviation of the laser array is less than λ/20, and ~ 95% fringe contrast of the irradiation distribution is obtained. The technique proposed in this paper could provide a reference for the system design of a massive high-power CBC system.

Coherent beam combining of two all‑PM thulium‑doped fiber chirped pulse amplifiers

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.

Coherent beam combination of adaptive fiber laser array with tilt-tip and phase-locking control

We present an experimental study on tilt-tip（TT） and phase-locking（PL） control in a coherent beam combination（CBC） system of adaptive fiber laser array.The TT control is performed using the adaptive fiber-optics collimator（AFOC）,and the PL control is realized by the phase modulator（PM）.Cascaded and simultaneous controls of TT and PL using stochastic parallel gradient descent（SPGD） algorithm are investigated in this paper.Two-fiber-laser-,four-fiber-laser-,and six-fiber-laser-arrays are employed to study the TT and PL control.In the cascaded control system,only one high-speed CMOS camera is used to collect beam data and a computer is used as the controller.In a simultaneous control system one high-speed CMOS camera and one photonic detector（PD） are employed,and a computer and a control circuit based on field programmable gate array（FPGA） are used as the controllers.Experimental results reveal that both cascaded and simultaneous controls of TT using AFOC and PL using PM in fiber laser array are feasible and effective.Cascaded control is more effective in static control situation and simultaneous control can be applied to the dynamic control system directly.The control signals of simultaneous PL and TT disturb each other obviously and TT and PL control may compete with each other,so the control effect is limited.

Multi-wavelength laser active coherent combination

A seed laser oscillating at different frequencies is proved to have the potential to mitigate the stimulated Brillouin scattering（SBS） effect in a fiber amplifier,which may increase the emission power of a coherent beam combination（CBC） system greatly.In this study,a basic mathematical model describing the multi-wavelength CBC is proposed on the fundamentals of CBC.A useful method for estimating the combination effect and analysing the feasibility and the validity of the multi-wavelength coherent combination is provided.In the numerical analysis,accordant results with four-wavelength four-channel CBC experiments are obtained.Through calculations of some examples with certain spectra,the unanticipated excellent combination effect with a few frequencies involved is explained,and the dependence of the combination effect on the variance of the amplifier chain length and the channel number is clarified.

Comparative study on the power scaling performance of three different coherent polarization beam combination system structures

Coherent polarization beam combination （CPBC） is a new kind of coherent beam combination configuration with high combining efficiency and excellent beam quality. In order to extend the CPBC system to a large scale, we provide a comparative study on the power scaling performance of three different coherent polarization beam combination system structures. It is found that the pairwise structure has high tolerance to aberrations and has the potential to extend to a large scale with high combining efficiency. In consideration of all the aberrations, the combining efficiency of the pairwise structure can be attained as high as 90% when the combined beams are more than 200. Some instructive suggestions are given to extend the CPBC system to a large scale.

Incoherent and coherent beam combination for master oscillator/power amplifier system with stimulated Brillouin scattering mirror

In this paper, we studied incoherent and coherent beam combining for the master oscillator/power amplifier （MOPA） system with stimulated Brillouin scattering （SBS） mirror. Optic field intensity distributions in the near and far field are numerically calculated for the two kinds of system. The results show that good beam quality in the far field could be obtained. It provides a theoretical basis for experimental research in the future.

260 fs,403 W coherently combined fiber laser with precise high‑order dispersion management

An ultrafast fiber laser system comprising two coherently combined amplifier channels is reported.Within this system,each channel incorporates a rod-type fiber power amplifier,with individual operations reaching approximately 233 W.The active-locking of these coherently combined channels,followed by compression using gratings,yields an output with a pulse energy of 504μJ and an average power of 403 W.Exceptional stability is maintained,with a 0.3%root mean square(RMS)deviation and a beam quality factor M^(2)<1.2.Notably,precise dispersion management of the front-end seed light effectively compensates for the accumulated high-order dispersion in subsequent amplification stages.This strategic approach results in a significant reduction in the final output pulse duration for the coherently combined laser beam,reducing it from 488 to 260 fs after the gratings compressor,while concurrently enhancing the energy of the primary peak from 65%to 92%.

Mismatch analysis of all-fiber coherent beam combiners based on the self-imaging effect

All-fiber coherent beam combiners based on the self-imaging effect can achieve a near-perfect single laser beam,which can provide a promising way to overcome the power limitation of a single-fiber laser.One of the key points is combining efficiency,which is determined by various mismatches during fabrication.A theoretical model has been built,and the mismatch error is analyzed numerically for the first time.The mismatch errors have been numerically studied with the beam quality and combining efficiency being chosen as the evaluation criteria.The tolerance of each mismatch error for causing 1%loss is calculated to guide the design of the beam combiners.The simulation results are consistent with the experimental results,which show that the mismatch error of the square-core fiber is the main cause of the efficiency loss.The results can provide useful guidance for the fabrication of all-fiber coherent beam combiners.

Deep-learning-based phase control method for tiled aperture coherent beam combining systems

We incorporate deep learning(DL)into tiled aperture coherent beam combining(CBC)systems for the first time,to the best of our knowledge.By using a well-trained convolutional neural network DL model,which has been constructed at a non-focal-plane to avoid the data collision problem,the relative phase of each beamlet could be accurately estimated,and then the phase error in the CBC system could be compensated directly by a servo phase control system.The feasibility and extensibility of the phase control method have been demonstrated by simulating the coherent combining of different hexagonal arrays.This DL-based phase control method offers a new way of eliminating dynamic phase noise in tiled aperture CBC systems,and it could provide a valuable reference on alleviating the long-standing problem that the phase control bandwidth decreases as the number of array elements increases.