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根据高斯光束的特点,高阶高斯光束的光斑大小和发散角均与阶数的平方根成正比,当增益介质截面不变,腔内存在的高阶模式阶数将受截面限制。为了获得更好的光束质量,应使基模在晶体内尺寸尽可能大,这样可以抑制高阶模振荡,当晶体尺寸一定而腔体不对称时,高阶模主要由基模在晶体端面尺寸较大的一侧限制。
由于激光器固有的量子亏损及量子效率不可能达到100%,因此其运行过程中不可避免产生废热,由此将产生热应力双折射、折射率变化、热应力形变[12]等等,综合为晶体热透镜效应。所以对于腔内的稳定性和模尺寸相关参量进行理论分析时,必须考虑热透镜效应[13]。即在一级近似下,圆棒晶体的热透镜效应等效为一个热焦距为f的厚透镜,屈光度为D=1/f,则:
$ D = \left( {\sigma /F} \right){P_{\rm{p}}} $
(1) 式中,σ为热透镜系数,与晶体材料、掺杂浓度、光学均匀性等有关;F为晶体横截面积;Pp为抽运功率。所以理论上热透镜屈光度与抽运功率成线性关系,抽运功率越高,热透镜屈光度越高,热透镜焦距越短[6]。
又因为本文中板条两个方向尺寸不同,所以热效应产生的等效热焦距也会不同,故应分别研究。根据初步的实验研究结果,当板条激光器抽运功率在1000W~1500W左右时,晶体宽度方向热焦距在50mm~200mm,高度方向热焦距在200mm~350mm之间,以下的理论分析设定热焦距在上述范围变化。
将晶体的水平方向热效应等效为一个厚透镜[14],板条激光器谐振腔的等效腔模型如图 1所示,竖直方向同理。
图 1为腔内有一根Nd:YAG晶体的光学谐振腔,M1和M2为谐振腔反射镜面,R1和R2为其曲率半径,L1和L2分别为两反射镜面到棒两端面的距离。f为晶体的等效热焦距[15],h为主面到透镜表面距离,l为晶体总长度,n=1.83为晶体折射率,h=l/(2n),d1=L1+h,d2=L2+h。对于热焦距的测量,将He-Ne激光器扩束之后,覆盖端面射入晶体,在晶体后端放置光屏。可以测得在不同抽运下,水平和竖直方向光斑压缩至最小时离主面距离,分别记为水平和竖直方向热焦距。测量结构如图 2所示。
拟选用的He-Ne激光器2m内光斑直径在1.2mm左右,晶体高度为5.8mm,故需扩束6倍以保证晶体全部覆盖,选用f1=50mm,f2=300mm的透镜,相距350mm组合成6倍扩束系统,使扩束后光斑正入射晶体端面,在出射端分别测量水平和竖直方向光斑压缩最小点离晶体的距离,即为该抽运功率下水平和竖直方向热焦距。
利用传输矩阵和q参量法可计算不同热焦距f时谐振腔的稳定性以及腔内不同位置基模光斑尺寸[16-17]。对板条激光器谐振腔结构进行计算时,有如下几点需要考虑:保证腔为稳定腔,使基模体积在晶体内部尺寸尽可能大,最后考虑腔体积尽量紧凑。受热效应影响晶体内折射率比较复杂,故晶体内的基模尺寸不容易仿真,作者选择q参量法计算基模在晶体端面的较大尺寸的一侧为参考标准。根据谐振腔稳定性条件,引入谐振腔的G参量,当G1G2满足0 < G1G2 < 1时,谐振腔为稳腔。对于平-平腔的稳定性,画出不同热焦距情况下基模尺寸在腔内的连续变化,再比较计算结果后得出热效应等效腔在L1=L2=120mm时可以获得较大的基模尺寸,并且腔体也较为紧凑。对比水平方向上不同腔内不同位置基模光斑半径,如图 3b所示,竖直方向则如图 4b所示。在对多个腔型仿真分析后,发现只有平-凹腔能获得较大的稳区范围且腔型紧凑,并可同时扩大晶体单侧端面基模尺寸。同样腔长的腔内水平和竖直方向基模尺寸如图 3a和图 4a所示。
仿真结果显示:水平方向上平-平腔晶体两侧端面基模半径为0.293mm,而平-凹腔一侧端面基模半径减小,另一端基模半径增大到0.310mm;竖直方向上,晶体一侧端面处平-平腔基模半径只有0.330mm,平-凹腔增大到0.399mm,即平-凹腔在水平和竖直方向上,均有一侧基模尺寸大于平-平腔基模尺寸。因此,理论上平-凹腔输出高阶模式的阶数将小于平-平腔,也即平-凹腔输出的光束质量将优于同腔长和输出镜透过率的平-平腔。
根据激光谐振腔的稳定条件[18-19],计算热焦距等效腔L1=L2=120mm时,平-凹腔不同热焦距下的稳定条件,计算结果如图 5所示。
结果显示, 当热焦距在78mm~125mm以及156mm~400mm范围时,满足0<G1G2<1,谐振腔稳定。因为随着抽运功率增大,热效应严重,热焦距有变短趋势,所以可能在抽运功率很高并使水平方向热焦距f<78mm,或者抽运功率较低而水平方向热焦距在125mm~156mm之间时,水平方向才进入非稳腔,而竖直方向将保持稳定腔。
半导体侧面抽运板条激光器光束质量优化
Beam quality optimization of semiconductor side-pumped slab lasers
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摘要: 为了优化高功率板条激光器的光束质量, 采用提高单侧基模光束的尺寸来限制腔内部分高阶模式振荡的方法, 针对半导体侧面抽运板条激光器, 测量了激光器在抽运状态下水平和竖直方向热焦距, 建立了热透镜等效模型, 并以平-平腔为参考, 设计了水平和竖直方向单侧基模尺寸均会扩大的平-凹腔。验证了对于激光介质截面尺寸固定的板条激光器, 扩大单侧基模尺寸可以限制高阶模式从而优化光束质量, 并提出了进一步优化板条激光器性能的研究方法。结果表明, 当平-凹腔的腔长为370mm时, 输出功率为59.9W, 水平方向M2因子由平-平腔的115.6显著优化至32.9, 竖直方向M2因子由116.4显著优化为60.9。该研究对于板条激光器获得高质量输出及相关应用有实际意义。Abstract: In order to optimize beam quality of high power slab lasers, the oscillation of some high-order modes in the cavity was limited by increasing the size of unilateral fundamental mode beam. For semiconductor side-pumped slab lasers, horizontal and vertical thermal focal lengths of the laser under pumping were measured. The equivalent model of thermal lens was established. By using flat-flat cavity as reference, a flat-concave cavity with enlarged dimension of unilateral fundamental modes in both horizontal and vertical directions was designed. It was verified that, for slab lasers with fixed cross-section size of laser medium, expanding the size of one-sided fundamental mode can limit the higher-order mode and optimize the beam quality. A method for further optimizing the performance of slab lasers was proposed. The results show that, when the length of flat-concave cavity is 370mm and the output power is 59.9W, horizontal M2 factor is significantly optimized from 115.6 for flat-flat cavity to 32.9 and vertical M2 factor is significantly optimized from 116.4 to 60.9. This research has practical significance for obtaining high quality output of slab lasers and the related application.
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Key words:
- lasers /
- semiconductor side-pumped /
- resonant cavity /
- thermal focal length /
- fundamental mode /
- beam quality
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