Propagation of coherently combined flattened laser beam array in turbulent atmosphere

The analytical expression for the propagation of a flattened laser beam array in a turbulent atmosphere is derived based on extended Huygens–Fresnel principle. The influence of beam order and turbulent atmosphere on beam quality is studied. It is revealed that the beam quality of a coherently combined laser beam array with higher order is better than its lower order counterpart when propagating in free-space, weak and medium turbulence (i.e. C_n²<10^?13 m^?2/3). The beam quality of higher order beam arrays degrades faster as the intensity of turbulence gets stronger. In the case of propagating in strong turbulence, the beam order has no influence on coherently combined beam quality.     

不同波形脉冲激光的时域误差对相干合成的影响

相干合成技术是实现高功率、高亮度光纤激光系统的重要技术途径.然而, 脉冲激光阵列中常常存在时域误差,这将影响脉冲激光的相干合成效果. 建立了脉冲激光存在时域误差时的相干合成理论模型,并在不同波形(方波、三角波、正弦波) 的脉冲激光存在时域误差时,对相干合成光束在远场的脉冲波形、峰值功率、 光强分布和桶中功率(PIB)等特性进行了数值计算和对比分析.计算结果表明: 方波脉冲激光相干合成光束的脉冲波形受时域误差影响严重,光强分布和PIB随着时域误差 的增大发生线性变化;三角波脉冲激光相干合成光束的脉冲波形和峰值功率受时域误差 影响严重,光强分布和PIB在时域误差较大时随着时域误差的增大发生较为剧烈的变化; 正弦波脉冲激光相干合成光束具有较好的输出特性,在两路正弦波脉冲激光相干合成中, 将两脉冲之间的时延控制在脉冲持续时间的10%以内,就能取得良好的合成效果.     

单口径相干合成系统激光光束的M2因子研究

单口径相干合成系统激光光束的光束质量是一个亟待解决的重要问题.基于二阶矩定义, 文中给出了单口径TEM₀₀, TEM₀₁及TEM₁₀两两相干光束M²因子的解析表达式, 并比较分析了束腰宽度、传输距离、振幅之比,以及源场位置矢量对相干光束M²因子的影响, 得到了诸如源场位置参量d₁<100λ时,各相干光束M²因子恒定,反之, 其随位置参量d₁的增大而增大等一些结论.最后,文章对两TEM₀₀模相干光束M²因子的 部分理论进行了实验验证.     

Numerical analysis of coherent combination for fiber lasers and application to beam steering

A coherent combination model of fiber lasers has been established. The relative beam quality factor has been introduced and studied as a proper beam quality factor for the combined coherent beam. The disturbance of the phase shift, polarization degradation, distribution characteristic, the wave-front aberration and the tilt error has been numerically studied to investigate their effects on the beam quality. This model has been also used to analyze the control of beam steering. The results have shown that the impact of the phase shift on the combination is more serious than that caused by polarization degradation, and the coherence degradation caused by the phase grating is more severe than that caused by the phase shifter.     

Coherent beam combination of two thulium-doped fiber laser beams with the multi-ditheringtechnique

Coherent beam combination of two thulium-doped fiber laser beams using a multi-dithering technique is presented for the first time. In the experiment, two fiber lasers centered at 1948.6 nm are coherently combined, and a phase modulator based on piezoelectric ceramics transducer is connected in one beam path to compensate for the phase errors between the two beams. When the phase control system is closed loop, the fringe contrast of the far-field intensity pattern is improved to be more than 75%, from 15% in open-loop, and the residual phase error is less than λ/20. The experimental results show that the performance of the phase control system is robust and the control bandwidth is more than 1 kHz, which indicates that the above approach can be scaled to facilitate the coherent beam combination of kilo-watt level thulium-doped fiberlaser.     

Threshold analysis of fiber-coupler-combined fiber lasers

Threshold conditions of coherently combined fiber lasers, joint by fiber couplers (FCs), have been studied. After considering the phase change of a light wave crossing the fiber inside the FC, it has been shown that, at the two input ports of the coupler connecting with the amplifying fibers, the phase difference between the two incoming fields should be equal to −π/2 if the threshold gain of the compound system is to be minimized. Starting from these input ports, following the circulations of waves, threshold conditions can be established. Expressions for the output and leakage powers, and optimum coupler splitting ratio nullifying the leakage when constituent fiber lasers giving different free-running powers have been derived. And, the threshold gain reductions of individual lasers after being coherently combined have been predicted.     

Propagation characteristics of the Yb-doped fiber lasers after spectral beam combining by the VBGs

The propagation model for the spectral beam combining system of five Yb-doped fiber laser beams by the volume Bragg gratings (VBGs) has been built up. Considering the surface distortion by thermal effect, the intensity of an individual beam passing through the spectral beam combining system by the VBGs with deformation has been analyzed numerically and iteratively by using finite-different and sparse matrix methods, and the intensity of combined beam has been studied by the principle of incoherent superposition. Consequently, according to the intensity second-order moments method, the M²-factor of the combined beam has been calculated. The effects of deformation of the VBGs on the intensity, the combining efficiency, the M²-factor and the power in the bucket of the combined beam have been analyzed quantitatively. It can be shown that the effects of the deformation of the VBGs on the intensity distribution of combined beam become more and more obvious with the increasing of the deformation of the VBGs. The results show that the surface distortion of the VBGs due to high-power lasers dramatically degrades both the beam quality of the combined beam and the combining efficiency of the spectral beam combining system.     

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%.     

半导体激光器的M2因子可以小于1

根据Porras的非傍轴矢量矩理论,对双异质结半导体激光器的光束质量进行了研究.结果表明,在有源层厚度d_a远小于波长λ的条件下,半导体激光器的M²因子可以小于1,并且没有下限.     

Analysis of beam quality for the laser beams after spectral beam combining

The beam quality of the laser beams after spectral beam combining (SBC) has been analyzed in this paper. Based on the propagation model of the spectral beam combining system, the expression for the output field of an individual beam passing through the spectral beam combining system with lens aberration has been given and the intensity distribution of the combined beam has been studied by the principle of incoherent superposition. Consequently, according to the intensity second-order moments method, the M²-factor of the combined beam has been calculated and the effect of lens aberration on the characteristics of the combined beam has been analyzed quantitatively. It can be shown that the SBC system can improve the beam quality of laser array significantly, and the M²-factor of the combined beam passing through the ideal spectral beam combining system is almost the same as that of an individual beam. For the spectral beam combining system with lens aberration, the spherical aberration has greater effect on the off-axis beam than on the on-axis beam, and the beam quality of combined beam degrades with increase in lens aberration.     

两路120 W固体激光高光束质量相干合成

通过主动相位控制实现了两路固体激光器的高光束质量相干合成输出,总输出功率达到240W。建立了两路120W板条激光放大器,通过光束整形获得了高光束质量方形光斑,并实现了高占空比光束拼接,填充因子高于92.4%。研制了光轴一致性探测与控制系统,采用基于压电陶瓷的快反镜实现了光轴的高精度闭环控制,两束激光光轴一致性优于2μrad(RMS)。设计了基于现场可编程门阵列(FPGA)的相位探测与控制系统,用随机并行梯度下降算法(SPGD)锁定了两束激光的活塞相位。相位闭环后,远场光斑峰值提高到开环状态的1.7倍,为理想值的84%。合成光束主瓣包含67%的激光总能量,光束质量(BQ)为1.1。     

Beam quality changes of radially and azimuthally polarized fields propagating through quartic phase plates

In terms of the so-called irradiance moments of a light field, the beam quality change, ΔQ, of radially and azimuthally polarized beams caused by propagation through a quartic phase plate (as occurs, for example, in strongly pumped laser rods used in high-power solid-state lasers) is studied. Analytical expressions for ΔQ are given, and a comparison between the scalar and vectorial regimes is also shown. The results are applied to several cases of interest.     

Comparative study on the propagation performance of coherently combined and incoherently combined beams

Taking phase error, turbulent atmosphere, jitter, vacancy factor and tilt error into consideration, we propose a general propagation formula for both coherent and incoherent combined beams with different kinds of aberrations. Comparative study on the propagation performance of coherent and incoherent combined beams is presented. Beam propagation factor (BPF) defined as laser output power in a specified far-field bucket divided by the total output power radiating from the effective near-field exit aperture of the laser beam is introduced as the beam quality factor to give a quantitative study. It is revealed that the coherent combined beam has great advantage when propagating in free-space compared with the incoherent combined beams. However, the coherent combined beam is more sensitive to the environmental aberrations, and the beam quality degrades faster with an increase in the aberrations’ intensity. Scintillation index as the high moments of the combined intensity field is also studied. It is revealed that both coherent and incoherent combined beams exhibit less scintillations compared with a single-aperture beam, and the incoherent combined beam demonstrates better scintillations reducing the performance. Our methodology offers an all-round performance evaluation on the two kinds of laser systems.     

Numerical investigation of beam quality in unstable optical resonators and the effects of practical imperfections

Field characteristics and beam quality of confocal positive branch unstable resonator under some practical imperfections has been investigated. Based on Fresnel-Kirchhoff integral, the near and far field intensity of the resonator was calculated numerically. Using the second order moment method, the beam quality factor, M² of the resonator was also calculated. Variety of practical distorting affects, mainly misalignment, off-axis, and thermal deflection of the mirrors, as well as gain non-uniformity were considered in these calculations. The results show that the beam quality factor is more sensitive to the off-axis and misalignment distortions while the non-uniform gain has significant effect only for unusual conditions. The effects of geometrical parameters, i.e. Fresnel number as well as magnification factor on the beam quality were also investigated.     

分数自成像平面波导的光束组束

研究了激光束在分数自成像平面波导中的传输特性,提出了利用分数自成像平面波导进行光束组束的技术方案,讨论了激光束之间相位失配对光束组束的影响,并对两个输出平均功率为300W的板条激光器的光束组束进行了数值实验模拟.结果表明,分数自成像平面波导的光束组束可以有效地改善多个激光器组束后的光束质量因子M²,从而提高激光输出的亮度;而且这种组束方法对激光束之间相位失配的敏感度明显降低. 关键词： 分数自成像 平面波导 组束 光束质量     

Tolerance on tilt error for coherent combining of fiber lasers

Limited by the precision of optical machining and assembling, the optical axes of lasers in an array cannot be strictly parallel to each other, which will result in the beam quality degradation of the combined beam. The tolerance on tilt error for coherent combining of fiber lasers is studied in detail. The complex amplitude distribution in the far field for the Gaussian beam with tilt angle is obtained by a novel coordinate transform method. Effect of tilt error on coherent combining is modelled analytically. Beam propagation factor is used to evaluate the effect of coherent combining. Numerical results show that for ring-distributed fiber laser array with central wavelength A and geometry size D, if the root-mean-square （RMS） value of the tilt error is smaller than 0.72A/D, the energy encircled in the diffraction-limited bucket can be ensured to be more than 50% of the value when there is no tilt error. The results are helpful to the designing and manufacturing of fiber array for coherent combining.     

Propagation of partially coherent partially phase-locked laser array in turbulent atmosphere

The mechanism for beam quality degradation in recently developed phase locking of high power solid state lasers, which is caused mainly by partially coherent property of element beam and partially phase locking of the laser array, is analyzed in detail. Analytical expression for propagation of partially coherent partially phase-locked laser array in turbulent atmosphere is obtained based on extended Huygens-Fresnel principle. The effect of coherence width, phase error and intensity of turbulence on the beam quality in the target-plane is studied in detail. The tolerance on phase error for laser array with different coherence property is analyzed. It is concluded that the laser array with better coherence is more sensitive to turbulence, and phase control can improve beam quality in the receiving plane only in the case when the element beam has good beam quality and propagates in weak turbulence.     

Beam quality of truncated laser beams with amplitude modulations and phase fluctuations in turbulence

The closed-form expressions for the Rayleigh range z_R and the M²-factor of truncated laser beams with amplitude modulations (AMs) and phase fluctuations (PFs) in turbulence are derived, and the beam quality is studied by taking the z_R and the M²-factor as the characteristic parameters of beam quality. The M²-factor of truncated laser beams with AMs and PFs is always larger than that of truncated Gaussian beams both in free space and in turbulence. However, in turbulence the beam quality of truncated laser beams with AMs and PFs may be better than that of truncated Gaussian beams if the z_R is taken as the characteristic parameter of beam quality. For laser beams with AMs and PFs in turbulence, the beam quality expressed in terms of z_R is consistent with that in terms of the M²-factor versus the phase fluctuation parameter α, but not versus the intensity modulation parameter σ_A. The beam quality of truncated laser beams with AMs and PFs is less sensitive to turbulence than that of truncated Gaussian beams. The beam quality of laser beams with smaller α and larger σ_A is less affected by turbulence than those with larger α and smaller σ_A.     

Watt-class green-emitting laser modules using direct second harmonic generation of diode laser radiation

Large-area high-resolution displays, using a flying-spot to create the picture, require light sources in the red, green and blue wavelength range with a high optical output power and nearly diffraction limited beam. In this paper we present experimental results of high-brightness distributed Bragg reflector tapered diode lasers at 106x nm that can be used for single-pass second harmonic generation into the green. Based on these lasers we developed compact (2.5 cm³) green laser modules with an output power of 1W at 53x nm and an electro-optical conversion efficiency of about 5%. The output power stability is better than 2% and the wavelength stability is ±10 pm. The excellent beam quality M _?? ² < 2 of the green light allows operation in flying spot application systems. Furthermore, we estimate that our concept allows power scaling up to 2W by using nonlinear planar waveguide crystals and into the multi-watt level by spectral beam combining.