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Nd:YVO4晶体是单轴晶体,属于四方晶系结构。Nd:YVO4晶体普遍采用a轴切割方式,这样的优势在于晶体的π偏振方向(//c轴)的受激发射截面较大,便于实现较高的斜率效率和良好的放大效果;同时,其荧光寿命较短且在受热工作情况下,几乎不会产生退偏现象,具有良好的保偏特性,因此特别适合用于连续激光或高重频准连续激光的放大过程。Nd:YVO4晶体特性如表 1所示[18]。
Table 1. Specifications of Nd:YVO4 (atomic fraction of 0.01)
absorption coefficient/cm-1 emission cross-section/cm2 thermo-optic coefficient/K-1 wavelength/nm fluorescence lifetime/μs π polarization 37 15.6×1019 3×10-6 1064.3 100 σ polarization 10 7×1019 8.5×10-6 在双程放大环节,需要利用激光的偏振特性以实现放大激光的提取与输出,通常情况下,双程放大的光路示意图如图 1所示。
利用偏振片与λ/4波片实现双程放大,是将p方向的线偏振种子光透过偏振片,经过增益介质实现放大后,通过λ/4波片后经过全反镜反射再次通过λ/4波片,使得激光的偏振方向旋转90°,变为s方向的线偏光;此时,激光再次经过增益介质实现双程放大,并在偏振片处反射输出。若图 1中的增益介质为a切型Nd:YVO4晶体,那么种子激光在进入Nd:YVO4晶体时为π偏振方向,由于π偏振方向的受激发射截面较大,将获得较好的放大效果;两次经过λ/4波片后,反射激光在晶体内部为σ偏振方向,由于其受激发射截面较小,因此反射激光无法获得较高的增益系数,导致双程放大的效果减弱。
因此,对于Nd:YVO4这类单轴晶体,设计了一种双程放大方式使得入射及反射的线偏振激光在晶体内部均处于π偏振方向以获得更佳的放大效果,如图 2所示。
图 2中的双程放大结构由法拉第隔离器、倾斜45°放置的Nd:YVO4晶体和全反镜组成。法拉第隔离器由两块夹角为45°的偏振分光棱镜(polarized beam splitter, PBS)与一块磁光晶体组成。其中,一块偏振分光棱镜的透光方向为p偏振方向,另一块偏振分光棱镜的透光方向旋转了45°,旋光晶体的作用是将经过的线偏振激光的偏振方向旋转45°。从图 2中可以看出,偏振态为p光的种子激光可以完全通过法拉第隔离器的第1块PBS,经过磁光晶体后种子激光偏振方向逆时针旋转45°,并无损通过第2块PBS;此时,种子激光的偏振方向与45°倾斜放置的Nd:YVO4晶体的c轴方向平行,获得了一次增益放大,经过全反镜反射再次进入Nd:YVO4晶体实现双程放大;由于Nd:YVO4晶体不存在明显的热退偏现象,获得双程增益的激光经过磁光晶体后,其偏振方向再次旋转45°变为s方向,在第1块PBS处被反射输出。
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种子激光的放大过程可以通过Franz-Nodvik方程描述,如下式中的3个联立方程所示:
$ \left\{ \begin{array}{l} {\rm{ }}{E_{{\rm{out}}}} = \frac{{{E_{\rm{s}}}}}{M}{\rm{ln}}\left\{ {1 + \left[ {{\rm{exp}}\left( {\frac{{M{E_{{\rm{in}}}}}}{{{E_{\rm{s}}}}}} \right) - 1} \right]{\rm{exp}}(M{\sigma _{\rm{e}}}{N_0})} \right\}\\ {N_{{\rm{TE}}}} = \left( {\frac{1}{{M{\sigma _{\rm{e}}}}}} \right){\rm{ln}}\left\{ {1 - \left[ {1 - {\rm{ exp}}(M{\sigma _{\rm{e}}}{N_0})} \right] \times } \right.\\ \;\;\;\;\;\;\;\;\;\;\;\;\;\left. {{\rm{exp}}\left( { - \frac{{M{E_{{\rm{in}}}}}}{{{E_{\rm{s}}}}}} \right)} \right\}\\ {N_{{\rm{TS}}}} = {N_0}\left[ {1 - {\rm{exp}}\left( {\frac{{ - 1}}{{f\tau }}} \right)} \right] + {N_{{\rm{TE}}}}{\rm{exp}}\left( {\frac{{ - 1}}{{f\tau \;}}} \right) \end{array} \right. $
(1) 式中,M为放大次数;f为重复频率;τ为荧光寿命;Es=hν/σe为饱和能流密度,其中h为普朗克常数,ν为激光频率,σe为受激发射截面;Ein为种子激光能流密度,Eout为放大激光能流密度;N0为最大反转粒子数在增益介质长度方向上的积分;NTE为激光放大后剩余反转粒子数在增益介质长度方向上的积分;NTS为储能阶段反转粒子数在增益介质长度方向上的积分。
N0可以通过速率方程计算反转粒子数n求出,速率方程由一组联立微分方程给出,如下式所示:
$ \left\{ \begin{array}{l} \frac{{{\rm{d}}n}}{{{\rm{d}}t}}\; = - c\phi n{\sigma _{\rm{e}}} - \frac{n}{\tau } + {w_{\rm{p}}}({n_0} - n)\\ \frac{{{\rm{d}}\phi }}{{{\rm{d}}t}} = \frac{{2{\sigma _{\rm{e}}}\phi nl}}{{{t_{\rm{r}}}}} - \frac{\phi }{{{t_{\rm{c}}}}} \end{array} \right. $
(2) 式中,wp为抽运速率;l为增益介质长度;Φ为腔内光子数;tr为光在谐振腔内传输的往返时间;c为光速;tc=tr/[L+ln(1/R)]为腔内光子寿命,L为腔内损耗,R为输出镜反射率;n0为总粒子数密度。
反转粒子数密度随抽运过程的增长是以wp表示的,它与抽运功率之间的关系可以由下式表示:
$ {w_{\rm{p}}} = \frac{{{\sigma _{13}}P}}{{Ah{\nu _p}}} $
(3) 式中,σ13=α/n0为受激吸收截面,α为吸收系数;P为抽运光功率;A为增益介质的有效截面积;νp为抽运光频率。将(3)式代入(2)式,求得抽运光抽运状态下的最大反转粒子数,再代入(1)式中即可求出放大激光的能流密度和平均功率。
仿真了Nd:YVO4晶体作为放大级时,不同参量的种子激光的放大效果。在计算过程中,最大抽运功率限定在100W,抽运光斑直径为1mm,晶体长度为20mm,掺杂原子数分数为0.003。
仿真了不同重复频率的种子激光的放大效果,如图 3所示。
由图 3可以看出,工作在不同重复频率的种子激光的放大效果相差不大。特别是在抽运功率较低的情况下,放大效果基本相同;而在高功率抽运时,高重频种子激光的放大效果要略好于较低重频种子激光的放大效果。分析其原因,认为这是由于高重频工作下Nd:YVO4晶体储能时间较短,其反转粒子数相对较少,因此自发辐射所造成的上能级粒子数的浪费较少。
同时,对比了不同平均功率种子激光的双程放大与单程放大效果,如图 4所示。
Figure 4. Ratio of the double-pass amplification to the single-pass one with di-fferent powers of a seed laser
由图 4可以看出,1W平均功率的种子激光经过双程放大后,其输出激光功率较单程放大情况得到了较大的提高,特别在抽运注入功率50W的情况下,双程放大输出功率是单程放大时的2.4倍;而对于5W平均功率的种子激光经过双程放大后,其输出激光功率较之单程放大情况提高程度有限,说明提高种子激光注入功率后,在单程放大过程中多数反转粒子数已被种子激光消耗转化为激光输出,反射进行双程放大时没有多余反转粒子数来提升放大功率,双程放大功率最高仅为单程放大的1.4倍。
那么,对于低功率种子激光的双程放大,对比了图 1中利用偏振片与λ/4波片实现双程放大与图 2中利用法拉第隔离器实现双程放大的效果,如图 5所示。
由图 5可以看出,低功率种子激光采用不同的双程放大方式,放大效果差异较大。采用法拉第隔离器实现双程放大的效果更好,在100W抽运功率下,其放大输出功率为36.2W,较之偏振片与λ/4波片组成的双程放大结构提高了41.5%。
高重频掺钕钒酸钇激光器双程放大理论研究
Study on double-pass amplification of Nd:YVO4 laser system with high repetition
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摘要: 为了提高高重频掺钕钒酸钇激光器的放大效率,提出了一种针对Nd:YVO4单轴晶体的新型双程放大方式,采用法拉第隔离器与Nd:YVO4晶体旋转45°放置的方式,使得种子激光在往返通过晶体时的线偏方向均为π偏振方向。结果表明,在100W抽运功率下,1W种子激光采用该双程放大方式的输出功率能够达到36.2W,放大效果较之偏振片与λ/4波片组成的双程放大结构提高了41.5%。本研究对以Nd:YVO4单轴晶体为放大级的弱种子激光放大有重要意义。Abstract: In order to improve the amplification efficiency of high repetition frequency Nd:YVO4 laser, a new method of double-pass amplification for the uniaxial crystal like Nd:YVO4 was introduced. The Faraday isolator and Nd:YVO4 was placed with a rotation angle of 45°, and this method could be applied to keep the polarization direction of the seed laser in parallel with the Nd:YVO4 c-axis. The simulation results show that the seed laser with 1W average power could be amplified to 36.2W in this double-pass amplification, and the amplification factor was improved 41.5% corresponding to a amplification method consisted with a polarizer and a quarter wave plate. This study is very important for laser amplify of weak seeds with Nd:YVO4 as laser amplification.
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Key words:
- lasers /
- double-pass amplification /
- Nd:YVO4 /
- narrow pulse /
- π polarization
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Table 1. Specifications of Nd:YVO4 (atomic fraction of 0.01)
absorption coefficient/cm-1 emission cross-section/cm2 thermo-optic coefficient/K-1 wavelength/nm fluorescence lifetime/μs π polarization 37 15.6×1019 3×10-6 1064.3 100 σ polarization 10 7×1019 8.5×10-6 -
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