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对于光纤激光器,输出光束截面为圆形,假设多路光纤激光在近场按图 1所示的圆环状分布排列,单元光束束腰半径为w0,相邻单元光束中心间距为d。若中心路单元光束外有N圈阵列光束,则激光阵列总单元数M=3N(N+1)+1。在该模型中,单元光束中心间距d越小,表明单元光束之间的距离越小,激光阵列排布越紧凑。特别地,当单元光束中心间距d=0时,光束合成由分孔径合成变为共孔径合成。
假定单元光束服从高斯分布,光束束腰位于z=0的平面上,传输距离z处的光场分布为[12]:
$ \begin{array}{l} {U_q}(x, y, z) = {\rm{exp}}\left[ { - \frac{{{r_q}^2}}{{{w^2}(z)}}} \right] \times \\ {\rm{exp}}\left\{ { - {\rm{i}}\left[ {kz + k\frac{{{r_q}^2}}{{2R\left( z \right)}} - {\rm{arctan}}\left( {\frac{{\lambda z}}{{{\rm{ \mathit{ π} }}{w_0}^2}}} \right) + {\mathit{\Phi }_q}} \right]} \right\} \end{array} $
(1) $ \left\{ \begin{array}{l} {w^2}\left( z \right) = {w_0}^2\left[ {1 + {{\left( {\frac{{\lambda z}}{{{\rm{ \mathit{ π} }}{w_0}^2}}} \right)}^2}} \right]\\ R\left( z \right) = z\left[ {1 + {{\left( {\frac{{{\rm{ \mathit{ π} }}{w_0}^2}}{{\lambda z}}} \right)}^2}} \right]\\ {r_q}^2 = {(x - {x_q})^2} + {(y - {y_q})^2} \end{array} \right. $
(2) 式中,k为波数,且k=2π/λ,λ为激光波长;Φq为附加相位因子, (xq, yq)为第q路单元光束的中心坐标,q为整数。圈数N=1,总单元数M=7的激光阵列:对于中心路单元光束,x0=y0=0;对于圆周单元光束,xq>=dcos(π/3×q),yq=dsin(π/3×q),其中,q=1,2,…,6。图 2即为一典型光纤激光阵列光束的近场光强分布,本文中主要对这种情形进行模拟分析。
高功率光纤激光器受热透镜效应等因素的影响,输出光束或多或少存在一定程度的波前畸变,波前畸变相位可以采用随机相位屏的方法进行构建[13-14]:
$ \begin{array}{l} \;\;\;\;\;\;\;\mathit{\Phi }\left( {x, y} \right) = AR\left( { - 1, 1} \right) \otimes {\rm{ }}\\ {\rm{exp}} - \left[ {{{\left( {\frac{x}{{{g_x}}}} \right)}^2} + {{\left( {\frac{y}{{{g_y}}}} \right)}^2}} \right] + \mathit{\sigma R}( - 1, 1) \end{array} $
(3) 式中,A为低频相位幅度,R(-1, 1)为-1~1均匀分布的2维随机数序列,⊗为卷积运算符,gx和gy为x、y方向上的相位畸变起伏参量,σ为高频扰动幅度。
根据广义惠更斯-菲涅耳衍射积分公式,单元光束远场分布可以表示为:
$ $$\eqalign{ & {U_q}\prime \left( {x\prime ,y\prime } \right) = \left( { - {{\rm{i}} \over {\lambda f}}} \right){\rm{exp}}\left[ {{{{\rm{i2 }}\pi {\rm{ }}} \over \lambda }({d_1} + f)} \right] \times \cr & \int\!\!\!\int {{U_q}(x,y,0)} {\rm{exp}}\left\{ {{{{\rm{i }}\pi {\rm{ }}} \over {\lambda f}}\left[ {\left( {1 - {{{d_1}} \over f}} \right)(x{\prime ^2} + y{\prime ^2}) - } \right.} \right. \cr & \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\left. {\left. {2\left( {xx\prime + yy\prime } \right)} \right]} \right\}{\rm{d}}x{\rm{d}}y{\rm{ }} \cr} $$ $
(4) 式中,f为聚焦系统的焦距,d1为激光器输出到聚焦系统的距离。
对于非相干合成,合成光束的远场光强分布为:
$ {I_{{\rm{NR}}}}(x\prime , y\prime ) = \sum\limits_q {\{ {U_q}\prime \left( {x\prime , y\prime } \right)} {\left[ {{U_q}\prime \left( {x\prime , y\prime } \right)} \right]^*}\} $
(5) 相干合成光束的远场光强分布为:
$ {I_\rm{r}}\left( {x\prime , y\prime } \right) = {\rm{ }}\left[ {\sum\limits_q {{U_q}\prime \left( {x\prime , y\prime } \right)} } \right]{\rm{ }}{\left[ {\sum\limits_q {{U_q}\prime \left( {x\prime , y\prime } \right)} } \right]^*} $
(6) -
光束合成效果可以以远场光束质量β因子作为评价标准。光束质量β因子定义为被测实际光束远场发散角θr与同样尺度的理想光束远场发散角θi之比。对于高斯光束,其理想远场发散角θi为[15]:
$ {\theta _{\rm{i}}} = \frac{{2\lambda }}{{{\rm{ \mathit{ π} }}D}} $
(7) 式中,D为聚焦系统有效通光孔径直径。
实际光束远场发散角θr由光束发射系统聚焦后远场光斑环围功率半径r与焦距f的比值计算得到。环围功率半径r是根据规范功率份额定义的,即以远场光斑的质心为中心,包含规范功率份额P0的桶半径[16]。对于高斯光束,规范功率份额P0=86.5%。
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为了得到较好的光束合成效果,光束合成装置需要将多路激光光轴相互调平行。定义各路光束光轴与中心路光束光轴的不平行度为θq,q=1, 2, …, 6。这里为了便于计算讨论,假设每路激光光轴与中心路光轴的不平行度均为θ。当各路激光光轴与中心路光轴不平行度θ分别为0μrad, 5μrad, 10μrad, 15μrad, 20μrad, 25μrad时,激光阵列非相干合成远场光斑分布如图 5所示,并将计算得到的非相干合成远场发散角及光束质量β因子填入表 1。当单元光束波前畸变参量gx=gy=0.05,A=0.23,σ=1.0时,单路远场发散角为0.106mrad,光束质量β因子为2.782;当gx=gy=0.05,A=0.20,σ=0.9时,单路远场发散角为0.083mrad,光束质量β值为2.168。
Figure 5. Far-field intensity distribution of incoherent beam combination at different parallel errors (A=0.23, σ=1)
Table 1. Far-field divergence angle and beam quality of incoherent beam combination at different parallel errors
parallel error θ /μrad wave-front distortion(A=0.23, σ=1.0) wave-front distortion(A=0.20, σ=0.9) divergence angle/mrad β divergence angle/mrad β 0 0.114 8.295 0.086 6.250 5 0.114 8.295 0.091 6.590 10 0.122 8.863 0.098 7.159 15 0.125 9.090 0.102 7.386 20 0.130 9.431 0.109 7.954 25 0.138 9.999 0.117 8.522 从图 5和表 1可以看出,随着各路激光光轴与中心路光轴不平行度θ的增大,非相干合成远场能量集中度逐渐降低,远场发散角及光束质量β因子存在不断增大的趋势,非相干合成效果越来越差。这是因为对于非相干合成来说,多路激光之间的不平行主要体现在各路单元光束在远场的偏移。并且可以发现,为了获得较好的非相干合成效果,所期望各路激光的光束质量越好,那么对多路激光之间的平行性要求就越高。
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7路激光经光束合成装置调平行后,从同一光学口径输出,经石英光楔分光衰减后,再经透镜聚焦在均匀漫反射屏上,光楔透射和反射的无用光束用激光吸收体吸收,实验系统原理图如图 6所示。实验中,7路激光经光束合成装置后最大不平行度分别小于5μrad和10μrad时,CCD采集到的光斑图像如图 7所示。同时,表 2中给出了根据采集到的远场光强分布计算得到的远场发散角及光束质量β因子,以及采用同种排布方式的7路阵列光束模拟计算结果。计算所用参量:单元光束束腰半径w0=13mm,光束中心间距d=32mm,单元光束远场发散角在0.11mrad~0.13mrad。
Table 2. Far-field divergence angle and beam quality of incoherent beam combination
parallel error θ /μrad experimental results simulated results divergence angle/mrad β divergence angle/mrad β 5 0.120 8.727 0.118 8.636 10 0.128 9.308 0.126 9.147 从图 7和表 2可以看到,随着多路激光最大不平行度从5μrad增大到10μrad,非相干合成远场能量集中度明显降低,非相干合成远场发散角及光束质量β因子值均有所增大,并且,实验结果与模拟计算结果较为一致。
光纤激光非相干合成效果分析
Analysis of incoherent beam combination effect of fiber lasers
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摘要: 为了研究光纤激光的非相干合成特性, 建立了圆环状排布的光纤激光阵列光束合成模型, 模拟分析了单元光束束腰半径w0、波前畸变和光束间距对非相干及相干合成远场光束质量的影响。讨论了多路激光平行性对非相干合成效果的影响, 并进行了相关实验验证。结果表明, 单元光束无波前畸变时, 当光束间距为d0=2.8w0时, 非相干与相干合成光束质量相等; 单元光束存在波前畸变时, 光束间距有所减小, 这是因为波前畸变对非相干合成影响更小; 对于非相干合成, 随着多路激光之间不平行度的增大, 非相干合成光束质量逐渐变差, 并且单元光束质量越好, 对多路激光平行性要求越高。该研究可为实际光纤激光合成系统设计分析提供参考。Abstract: To study the incoherent beam combination characteristics of fiber lasers, a beam combination model of a circular array of multiple fiber lasers was established, and effect of waist radius w0, wave-front distortion of unit beam and beam separation distance on the far field beam quality of incoherent and coherent combination was simulated and analyzed. In addition, the influence of axis parallelism of multiple laser beams on the incoherent beam combination effect was studied, and experimental verification was carried out. The results show that, when the beam separation distance is d0=2.8w0, the beam quality β factor of incoherent combination of multiple laser beams without wave-front distortion is equal to that of coherent combination. The beam separation distance d0 decreases when the wave-front phase of laser beam is distorted, and the influence of wave-front distortion on the incoherent combination is less than that on the coherent combination. With the increasing of the parallel error among multiple laser beams, the beam quality of incoherent combination becomes worse. And the better the beam quality of unit beam is, the higher the demand for the axis parallelism of multiple laser beams. This research can provide references for the design and analysis of beam combination system of fiber lasers.
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Table 1. Far-field divergence angle and beam quality of incoherent beam combination at different parallel errors
parallel error θ /μrad wave-front distortion(A=0.23, σ=1.0) wave-front distortion(A=0.20, σ=0.9) divergence angle/mrad β divergence angle/mrad β 0 0.114 8.295 0.086 6.250 5 0.114 8.295 0.091 6.590 10 0.122 8.863 0.098 7.159 15 0.125 9.090 0.102 7.386 20 0.130 9.431 0.109 7.954 25 0.138 9.999 0.117 8.522 Table 2. Far-field divergence angle and beam quality of incoherent beam combination
parallel error θ /μrad experimental results simulated results divergence angle/mrad β divergence angle/mrad β 5 0.120 8.727 0.118 8.636 10 0.128 9.308 0.126 9.147 -
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