-
图 1为用于光谱合成的二向色镜,图 2为二向色镜光谱合束原理图。如图 2所示,掺Yb光纤激光器的中心波长分别为1070nm和1090nm,当多模激光束入射至二向色镜表面时,由于二向色镜对1070nm激光具有高反特性,同时对1090nm激光具有高透特性,两路激光经二向色镜后实现光谱合成。
相比于小角度二向色镜,适当增大二向色镜使用角度可以对系统进行结构优化,但这会使二向色镜镀膜难度显著增大,0°的镀制技术相对简单, 但在合束结构上无法实现,45°入射虽然是理论最优的结构,但经过尝试,其镀制结果并不理想。相比之下,小角度二向色镜在使用角度和镀膜光控角度上具有较好的一致性,镀制效果相对理想,是目前合束系统较优的选择。
图 3为多层膜系结构图。假设其有m层膜系,其中第i层膜的折射率为ni,厚度为di,入射介质折射率为n0,基底折射率为ns[10-12]。单个粗糙界面表面面形函数f(x, y)的平均值为0,其几率密度函数呈高斯分布[13-14]。此多层膜系粗糙表面反射模型建立在以下基本假设的基础上:(1)表面粗糙度远小于入射波长;(2)不考虑多层膜系内部及基底的吸收;(3)入射介质和基底假设为半无限大,且基底中不存在反射[15-19]。
假设波长为λ的入射光以小角度θ0入射到多层膜系结构,则入射波电场E0+、反射波电场E0-和透射波电场Es+满足如下关系:
$ \left[ \begin{array}{c}{E_{0}^{+}} \\ {E_{0}^{-}}\end{array}\right]=\boldsymbol{P} \left[ \begin{array}{c}{E_{\mathrm{s}}^{+}} \\ {0}\end{array}\right] $
(1) $ \boldsymbol{P}=\boldsymbol{S}_{01} \boldsymbol{I}_{01} \boldsymbol{T}_{1} \boldsymbol{S}_{12} \boldsymbol{I}_{12} \boldsymbol{T}_{2} \cdots \boldsymbol{T}_{m} \boldsymbol{S}_{m \boldsymbol{S}} \boldsymbol{I}_{m \boldsymbol{S}}=\left[ \begin{array}{ll}{p_{1}} & {p_{3}} \\ {p_{2}} & {p_{4}}\end{array}\right] $
(2) 式中,Sij为第i层和第j层粗糙表面的散射矩阵,Iij为第i层和第j层之间的复振幅传播矩阵,Tj为第j层内部的相位传播矩阵,p1, p2, p3, p4为矩阵元。
$ \boldsymbol{S}_{i j}=\frac{1}{1-r_{i j}^{2}}=\left[ \begin{array}{cc}{a-r_{i j}^{2} b} & {r_{i j}(b-a)} \\ {r_{i j}\left(b^{-1}-a^{-1}\right)} & {a^{-1}-r_{i j}^{2} b^{-1}}\end{array}\right] $
(3) 式中,a和b为与每层厚度、折射率、面形函数相关的光学因子, rij为菲涅耳振幅反射系数。
$ \boldsymbol{I}_{i j}=\frac{1}{t_{i j}} \left[ \begin{array}{cc}{1} & {r_{i j}} \\ {r_{i j}} & {1}\end{array}\right] $
(4) 式中,tij为透射系数。
$ \boldsymbol{T}_{j}=\left[ \begin{array}{cc}{\mathrm{e}^{\mathrm{i} \phi_{j}}} & {0} \\ {0} & {\mathrm{e}^{-\mathrm{i} \phi_{j}}}\end{array}\right] $
(5) 式中,ϕj为第j层的相位厚度。则多层膜系的振幅反射系数为:
$ r=p_{2} / p_{1} $
(6) 反射率为:
$ R=r \cdot r^{*} $
(7) 式中,*表示共轭。合束效率是激光合束效果评价的重要指标之一,高效率的合束装置可以获得更高的输出功率。在合束系统中,入射光通道的光谱展宽是建立光纤激光器与二向色镜耦合效率关系的重要因素[23],因此可在激光光谱的基础上建立以下耦合效率模型:
$ \eta=\frac{\sum\limits_{\lambda_{1}}^{\lambda_{2}}[F(\lambda) R(\lambda)]}{\sum\limits_{\lambda_{1}}^{\lambda_{2}} F(\lambda)} $
(8) 式中,F(λ)为入射光光谱,R(λ)为二向色镜的反射曲线,计算间隔为λ1~λ2。
对于二向色镜合束系统,合束效率则可以表示为:
$\begin{array} [c]{c} \eta=\\ \frac{\sum\limits_{\lambda_{1}}^{\lambda_{2}}\left[F_{1}(\lambda) R(\lambda)\right]+\sum\limits_{\lambda_{1}}^{\lambda_{2}}\left\{F_{2}(\lambda)[1-R(\lambda)]\right\}}{\sum\limits_{\lambda_{1}}^{\lambda_{2}} F_{1}(\lambda)+\sum\limits_{\lambda_{1}}^{\lambda_{2}} F_{2}(\lambda)} \end{array} $
(9) 式中,F1(λ)和F2(λ)分别表示不同中心波长光纤激光器的光谱曲线[5]。可见在光谱曲线已知的情况下,二向色镜的反射率对合束效率具有重要影响。
光谱合束二向色镜反射率及合束效率仿真研究
Simulation of reflectivity and combining efficiency of dichroic mirrors for spectral beam combining
-
摘要: 为了研究合束效率与二向色镜的反射性质之间的关系,通过建立多层膜系粗糙表面反射模型,采用模拟仿真的方法对用于光谱合束的大陡度二向色镜反射率曲线进行了计算分析,结合光纤激光器光谱曲线得到了合束效率的仿真结果。对不同角度二向色镜表面面形与反射率、合束效率的关系进行了分析,对二向色镜合束系统的稳定性进行了模拟讨论,并对二向色镜的部分参量提出了要求。结果表明,使用小角度二向色镜可以获得10kW以上的输出功率,合束效率达97%。这一结果对二向色镜参量的提高是有帮助的。Abstract: In order to study the important relationship between combining efficiency and reflectivity of dichroic mirrors, rough surface reflection model of multilayer coatings was established. Reflective curves of high-steepness dichroic mirrors for spectral beam combining were calculated and analyzed. Simulation results of combining efficiency were obtained by combining the spectral curves of fiber lasers. The relationship between the surface shape of dichroic mirrors with different angles and reflectivity and combining efficiency were analyzed. The stability of the beam combining system based on dichroic mirrors was simulated and discussed. The results show that, output power of more than 10kW can be obtained by using a small angle dichroic mirror, and combining efficiency can reach 97%. This result is helpful for the improvement of the parameters of dichroic mirrors.
-
Key words:
- laser technique /
- spectral beam combining /
- simulation /
- dichroic mirror /
- surface roughness /
- combining efficiency
-
[1] MA Y, YAN H, TIAN F, et al. Common aperture spectral beam combination of fiber lasers with 5kW power high-efficiency and high quality output[J]. High Power Laser and Particle Beams, 2015, 27(4):7-9(in Chinese). [2] MA Y, YAN H, PENG W J, et al. 9.6kW common aperture spectral beam combination system based on multi-channel narrow-linewidth fiber lasers[J]. Chinese Journal of Lasers, 2016, 43(9):0901009(in Chinese). [3] HOU H H, FAN Zh X, SHAO J D, et al. Scalar scattering theory of optical surfaces[J]. Laser & Optoelectronics Progress, 2005, 42(11):35-38(in Chinese). [4] CARNIGLIA C K. Scalar scattering theory for multilayer optical coatings[J]. Optical Engineering, 1979, 18(18):104-115. [5] CHEN F, MA J, ZHU R, et al. Coupling efficiency model for spectral beam combining of high-power fiber lasers calculated from spectrum[J]. Applied Optics, 2017, 56(10):2574. doi: 10.1364/AO.56.002574 [6] CHENG X, WANG J L, LIU Ch H. Beam combining of high energy fiber lasers[J]. Infrared and Laser Engineering, 2018, 47(1):106-116(in Chinese). [7] MA Y, YAN H, SUN Y H, et al. Recent progress of key technologies for spectral beam combining of fiber laser with dual-gratings configuration[J]. Infrared and Laser Engineering, 2018, 47(1):32-45(in Chinese). [8] WANG F, TANG X H, ZHONG L J, et al. Research of beam combination and focusing system of laser diode applied in ceramic welding[J]. Laser Technology, 2018, 42(2):282-288(in Chinese). [9] ZHANG H, SANG Sh B, DUAN Q Q, et al. Research progress of surface roughness of silicon-on-insulator nano-optical waveguide[J]. Laser Technology, 2017, 41(3):367-375(in Chinese). [10] ZHENG Y, YANG Y F, ZHAO X, et al. Research progress on spectral beam combining technology of high-power fiber lasers[J]. Chinese Journal of Lasers, 2017, 44(2):0201002(in Chinese). [11] ZHANG D Y, HAO J P, ZHU Ch, et al. Review on spectral beam combining of fiber lasers[J]. Laser & Infrared, 2016, 46(5):517-521(in Chinese). [12] HAN D F, HU J, NIE Z P. The calculation of scattering for Gaussian rough surface based on stochastic integral equation method[J]. Chinese Journal of Radio Science, 2016, 31(3):457-461(in Chinese). [13] SHEN B Y, ZENG L J, LI L F, et al. Fabrication of polarization independent gratings made on multilayer dielectric thin film substrates[J]. High Power Laser and Particle Beams, 2015, 27(11):79-80(in Chinese). [14] GUO C, KONG M, GAO W, et al. Simultaneous determination of optical constants, thickness, and surface roughness of thin film from spectrophotometric measurements[J]. Optics Letters, 2013, 38(1):40-42. [15] MILOUA R, KEBBAB Z, CHIKER F, et al. Determination of layer thickness and optical constants of thin films by using a modified pattern search method[J]. Optics Letters, 2012, 37(4):449-451. [16] YU Y, WANG W M, LU Y H, et al. Experimental research of spectrally beam combined diode laser based on grating-cavity[J]. Laser Technology, 2010, 34(1):138-140(in Chinese). [17] SCHMIDT O, WIRTH C, NODOP D, et al. Spectral beam combination of fiber amplified ns-pulses by means of interference filters[J]. Optics Express, 2009, 17(25):22974-22982. doi: 10.1364/OE.17.022974 [18] HOU H H, SHEN J, SHEN Z C, et al. Stratified-interface scattering model for multilayer optical coatings[J]. Acta Optica Sinica, 2006, 26(7):1102-1106(in Chinese). [19] HOU H H, SUN X L, SHEN Y M, et al. Roughness and light scattering properties of ZrO2 thin films deposited by electron beam evaporation[J]. Acta Physica Sinica, 2006, 55(6):3124-3127(in Chinese). [20] YU H. Mathematics model analysis of scattering method on measuring surface roughness[J]. Journal of Changchun University of Science and Technology, 2006, 29(1):109-112(in Chinese). [21] TIKHONRAVOV A V, TRUBETSKOV M K, TIKHONRAVOV A A, et al. Effects of interface roughness on the spectral properties of thin films and multilayers[J]. Applied Optics, 2003, 42(25):5140-5148. doi: 10.1364/AO.42.005140 [22] CARNIGLIA C K, JENSEN D G. Single-layer model for surface roughness[J]. Applied Optics, 2002, 41(16):3167-3171. doi: 10.1364/AO.41.003167 [23] BENNETT H E, PORTEUS J O. Relation between surface roughness and specular reflectance at normal incidence[J]. Journal of the Optical Society of America, 1961, 51(2):123-129. doi: 10.1364/JOSA.51.000123