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首先确定高功率光纤激光器的基本结构模型。表1给出了典型的万瓦级光纤激光系统相关文献报道参数,激光器的基本结构均为一级振荡器+一级放大器的MOPA结构,振荡器谐振腔由光纤光栅构成,输出功率170 W~1 kW不等,经放大器放大后达到10 kW, 振荡器和放大器均采用双包层有源光纤,包层泵浦。泵浦波长方面,IPG公司曾使用掺Yb光纤激光器的1018 nm输出对放大器进行级联泵浦实现单纤10 kW输出,与常用的976 nm半导体激光器(LD)泵浦方式相比,1018 nm级联泵浦具有更低的量子亏损,热效应相对较轻,被认为是实现单纤高功率输出的关键,但随着高功率光纤激光器研究的不断深入,研究人员发现1018 nm泵浦主要解决的是泵浦源亮度问题,即光束质量较高的1018 nm激光提高了能够耦合进入有源光纤的最大泵浦功率,随着LD以及合束器等无源器件工艺的进步,直接使用976 nm LD作为泵浦源也能够为系统提供足够的泵浦功率,其相对1018 nm级联泵浦方式略高的热负载对系统运行的稳定性也不会产生影响,后续的高功率光纤激光器相关报道中多采用976 nm LD直接对激光器进行泵浦,因此文中仿真计算中也采用976 nm LD半导体激光器作为泵浦源,端面耦合,正向包层泵浦,图1给出了掺镱光纤放大器的示意图。
表 1 典型万瓦光纤激光器系统参数
Table 1. Parameters of typical 10-kW-level fiber laser systems
Parameters IPG Photonics[3] CAEP report [7] SIOM report[7] Output power/kW 10 10.6 10.14 Structure Oscillator and one-stage amplifier Laser wavelength/nm 1 070 1 080 1 070 Seed power 1 kW 1 kW 170 W Fiber core size and lengths 30 μm,15 m 30/900 μm,25 m 30/900 μm,18 m Pump scheme 1018 nm,12690 W,
backward pumping976 nm,11500 W,
forward pumping976 nm,11359 W,
bidirectional pumping图1所示的掺镱光纤放大器中,其上能级反转粒子数密度、泵浦光、信号光随时间t和增益光纤位置z的变化规律可以用如下速率方程进行描述[8-11],此处z以有源光纤的正向起点为原点:
$$\begin{split} \dfrac{{\partial {N_2}(z,t)}}{{\partial t}} =& \dfrac{{{\lambda _{\rm{p}}}{\varGamma _{\rm{p}}}}}{{hcA}}\left[ {{\sigma _{{\rm{pa}}}}{N_1}(z,t) - {\sigma _{{\rm{pe}}}}{N_2}(z,t)} \right] \cdot \left[ {P_{\rm{p}}^ + (z,t) + P_{\rm{p}}^ - (z,t)} \right] - \dfrac{{{N_2}(z,t)}}{\tau } +\\ & \dfrac{{{\varGamma _{\rm{s}}}{\lambda _{\rm{s}}}}}{{hcA}}\left[ {{\sigma _{{\rm{sa}}}}({\lambda _{\rm{s}}}){N_1}(z,t) - {\sigma _{{\rm{se}}}}({\lambda _{\rm{s}}}){N_2}(z,t)} \right] \cdot \left[ {P_{\rm{s}}^ + (z,t,{\lambda _{\rm{s}}}) + P_{\rm{s}}^ - (z,t,{\lambda _{\rm{s}}})} \right] \\ \end{split} $$ (1) $$N = {N_1}(z,t) + {N_2}(z,t)$$ (2) $$\begin{split} \pm \dfrac{{\partial {P_{\rm{s}}}^ \pm (z,t,{\lambda _{\rm{s}}})}}{{\partial z}} + \dfrac{1}{v}\dfrac{{\partial {P_{\rm{s}}}^ \pm (z,t,{\lambda _{\rm{s}}})}}{{\partial t}} =& {\varGamma _{\rm{s}}}\left[ {{\sigma _{{\rm{se}}}}({\lambda _{\rm{s}}}){N_2}(z,t) - {\sigma _{{\rm{sa}}}}({\lambda _{\rm{s}}}){N_1}(z,t)} \right] \cdot {P_{\rm{s}}}^ \pm (z,t,{\lambda _{\rm{s}}}) - {\alpha _{\rm{s}}}{P_{\rm{s}}}^ \pm (z,t,{\lambda _{\rm{s}}}) \\ \end{split} $$ (3) $$ \pm \dfrac{{\partial {P_{\rm{p}}}^ \pm (z,t)}}{{\partial z}} + \dfrac{1}{{{v_{\rm{p}}}}}\frac{{\partial {P_{\rm{p}}}^ \pm (z,t)}}{{\partial t}} = - {\varGamma _{\rm{p}}}\left[ {{\sigma _{{\rm{pa}}}}{N_1}(z,t) - {\sigma _{{\rm{pe}}}}{N_2}(z,t)} \right] \cdot {P_{\rm{p}}}^ \pm (z,t) - {\alpha _{\rm{p}}}{P_{\rm{p}}}^ \pm (z,t)$$ (4) 式中:N为YDFA所用增益光纤的掺杂浓度;N1(z,t)为基能态粒子密度随时间t和增益光纤位置z的变化函数;N2(z,t)为上能级反转的粒子数密度随时间t、增益光纤位置z的变化函数;Γs和Γp为ASE光和泵浦光的重叠因子;A为增益光纤的模场面积;σpa和σpe分别为泵浦光的吸收和发射截面;σsa
和σse分别表示信号光的吸收和发射截面;c为真空中的光速;τ为荧光寿命;αs和αp分别为泵浦光的损耗系数;h为普朗克常数;“+”和 “−”分别为正向和反向传输;各物理量数值见表2。对连续波反向回光进行分析时,系统处于稳态,公式(1)~(4)中各物理量对时间的导数项均为零,结合放大器边界条件(5)~(6)对方程进行求解,即可获得光纤激光器中上能级粒子数密度、泵浦光功率以及正向和反向信号光功率随增益光纤位置的变化规律。边界条件(5)~(6)中,P1和P2分别表示正向和反向注入的泵浦光功率;P3和P4分别表示正向和反向注入的、中心波长为λs的信号光功率,其余波长对应功率为零。 表 2 模拟仿真所用参数
Table 2. Parameters adopted in the calculation
Parameters Value Parameters Value λp/nm Pump wavelength 976 λs/nm Signal wavelength 1080 Γp Signal overlap efficiency 0.85 Γs Signal overlap efficiency 0.85 Rcore/μm Core diameter 30 Rcladding/μm Clad diameter 900 σa (λp)/m2 Pump absorption cross section 8.5×10−25 σa(λs)/m2 Pump absorption cross section 8.5×10−26 σe(λp)/m2 Pump emission cross section 8.2×10−25 σe(λs)/m2 Pump emission cross section 9.9×10−26 h/J·s−1 Planck constant 6.626×10−34 c/m·s−1 Light speed 3×108 N/m−3 Yb3+doping concentration 1.3×1026 τ/ms Upper laser level lifetime 0.84 $$P_{\rm{p}}^ + (0) = {P_1},P_{\rm{p}}^ - (L) = {P_2}$$ (5) $${P^{\rm{ + }}}(0,{\lambda _{\rm{s}}}) = {P_3},{P^ - }(L,{\lambda _{\rm{s}}}) = {P_4}$$ (6) 参考表1中相关报道,有源光纤芯径取30 μm,另外高功率系统中为避免高泵浦吸收使热负载过于集中,应采用较小的芯包比,取包层直径900 μm。考虑高功率光纤激光系统多工作于1070~1080 nm波长,进行反向光模拟时取正向和反向信号光波长均为1080 nm,计算中代入相应的受激发射截面和受激吸收截面。计算中所用的相关参数数值如表2所示。
Numerical analysis on backward light amplification and damage in high-power fiber laser
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摘要: 利用速率方程模型对主振荡−功率放大器结构的1 μm波段掺镱(Yb)高功率光纤激光器中存在连续波反向信号光时的功率特性进行了理论分析,结果显示反向信号光功率会被高功率激光放大器所明显放大,10 kW级的光纤激光器中,100 W的反向信号经过放大器后功率会被放大至kW量级;与此同时,反向信号放大过程对反转粒子数的消耗会导致激光器的正向输出功率的严重下降。另外,反向信号放大也会导致放大器输出端的激光功率过强,加剧泵浦吸收和受激发射过程,增加该处的热负载、导致温度大幅上升100 ℃以上,对稳定性产生潜在影响。反向信号导致振荡器提供的正向种子光功率波动和下降时,正向信号不能充分饱和有源光纤中的增益,会进一步加强反向信号在主放大级中的放大作用,进而对系统造成更严重的影响。提高正向种子光功率、增强正向信号对激光增益的饱和作用,有助于抑制反向信号的放大过程,但需综合考虑种子源稳定性、热负载、热致模式不稳定和受激拉曼散射等因素合理选择种子光功率。Abstract: The amplification of continuous-wave backward signal in 1 μm high-power master-oscillator-power-amplifier based Yb-doped fiber laser was investigated using rate equation model. The results show that the backward light power would be amplified significantly by the high-power amplifier. The 100 W backward signal from the output end of the fiber amplifier can be amplified to up to kW level. Meanwhile, the amplification of backward signal can consume the population inversion, saturate laser gain and thus decrease the laser output power seriously. Furthermore, the backward signal amplification would result in a much higher laser intensity at the incident end of the amplifier gain fiber, where the highest pump power existed. The temperature at the incident end of the fiber can be 100 ℃ higher than that without backward signal. The higher laser intensity at the incident end could break the pump absorption saturation, and enhance the rates of pump absorption and stimulated emission a lot, hence increased the thermal load and the temperature significantly. Since the backward signal gain was determined by the saturation of population inversion by the forward seed, the power fluctuation of oscillator caused by the amplified backward signal may aggravate the backward signal amplification, and further increase the risk of damage. Higher forward seed power resulted in stronger saturation of the laser gain in the active fiber, which could suppress the backward signal amplification effectively. However, higher seed power put forwards much complex requirements to laser oscillator, and the thermal load in the active fiber of the laser amplifier would be more concentrated, which made the thermal management more difficult. Furthermore, with higher seed power, the stimulated Raman scattering and thermal induced transverse mode instability are more likely to occur. Therefore, it is important to optimize the seed laser power based on a comprehensive consideration of the above issues, and to prevent the backward light from coupling into the fiber amplifier.
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Key words:
- fiber laser /
- fiber amplifier /
- rate equation /
- backward signal amplification /
- damage threshold
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表 1 典型万瓦光纤激光器系统参数
Table 1. Parameters of typical 10-kW-level fiber laser systems
Parameters IPG Photonics[3] CAEP report [7] SIOM report[7] Output power/kW 10 10.6 10.14 Structure Oscillator and one-stage amplifier Laser wavelength/nm 1 070 1 080 1 070 Seed power 1 kW 1 kW 170 W Fiber core size and lengths 30 μm,15 m 30/900 μm,25 m 30/900 μm,18 m Pump scheme 1018 nm,12690 W,
backward pumping976 nm,11500 W,
forward pumping976 nm,11359 W,
bidirectional pumping表 2 模拟仿真所用参数
Table 2. Parameters adopted in the calculation
Parameters Value Parameters Value λp/nm Pump wavelength 976 λs/nm Signal wavelength 1080 Γp Signal overlap efficiency 0.85 Γs Signal overlap efficiency 0.85 Rcore/μm Core diameter 30 Rcladding/μm Clad diameter 900 σa (λp)/m2 Pump absorption cross section 8.5×10−25 σa(λs)/m2 Pump absorption cross section 8.5×10−26 σe(λp)/m2 Pump emission cross section 8.2×10−25 σe(λs)/m2 Pump emission cross section 9.9×10−26 h/J·s−1 Planck constant 6.626×10−34 c/m·s−1 Light speed 3×108 N/m−3 Yb3+doping concentration 1.3×1026 τ/ms Upper laser level lifetime 0.84 -
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