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双频微片激光器的结构及对输出双频激光的测量方法如图 1所示。激光器谐振腔由掺杂原子数分数为0.01的Nd3+:YAG增益介质与电光晶体钽酸锂(li-thium tantalite,LTO)光胶而成,Nd3+:YAG和LTO晶体厚度分别为0.4mm和1.0mm,横截面积为5mm×5mm。在Nd:YAG端面镀有对1064nm的高反膜(R>99.7%)和对808nm的增透膜(T>97%),作为谐振腔的输入镜。LTO的端面镀有对1064nm的高反膜(R=99%),作为谐振腔的输出镜。半导体抽运固体激光器(diode pumped solid-state laser,DPSSL)尾纤输出中心波长为793nm的激光作为抽运源,与Nd3+离子的吸收峰相匹配。抽运光束通过一对耦合透镜聚焦到Nd:YAG晶体中,聚焦光斑直径约为100μm。利用LTO的双折射特性,可以分裂单纵模,产生具有垂直偏振特性的双频激光。半导体热电制冷器(thermoelectric cooler,TEC)用来控制微片激光器的温度,LTO的两个相对的侧表面镀有一层金膜,金膜与电极相连,通过外加电压,可以对LTO施加横向电场。双频微片激光器产生的双频光通过偏振片后可以产生拍频信号,经过对于1064nm波段的高反镜,分离输出激光和抽运光。后端利用光电探测器(photoelectric detector, PD)、频谱分析仪(optical spectrum analyzer, OSA)和波
长计探测输出激光。
在谐振腔中,满足驻波条件能够稳定振荡的频率为:
$ {{v}_{q}}=q\frac{c}{2L} $
(1) 式中,c是真空中的光速,L是谐振腔光程,q是自然数,每一个q值对应一个纵模。相邻纵模间隔为c/(2L)。对于本次实验中研究的激光器谐振腔,其光程为:
$ L={{n}_{\text{YAG}}}\times {{l}_{\text{YAG}}}+{{n}_{\text{LTO}}}\times {{l}_{\text{LTO}}} $
(2) 式中,lYAG与lLTO分别表示Nd:YAG和LTO晶体的厚度;nYAG表示Nd:YAG的折射率为1.82,nLTO表示LTO的平均折射率为2.14,计算得到纵模间隔为52.3GHz。Nd:YAG的总增益带宽约为120GHz,这意味着谐振腔中最多可以产生两个纵模模式。在实验中通过使用相对较低的抽运功率(在阈值功率范围1.6倍以内),可以很容易地得到单纵模。
LTO晶体采用a轴切割,其自然双折射效应将单纵模分裂为垂直偏振的两个频率,分别为沿y轴方向偏振的寻常光和沿x轴方向偏振的非寻常光。二者的频差可由下式计算得到:
$ \Delta v=\frac{2{{l}_{\text{LTO}}}}{\lambda }\left( {{n}_{\text{e}}}-{{n}_{\text{o}}} \right)\frac{c}{2L} $
(3) 式中,ne和no是寻常光和非寻常光的折射率,其值分别为ne=2.1403,no=2.1363[17]。λ取近似值等于1064nm。LTO晶体的双折射率的变化与温度有关,双频频差受LTO的温度影响。(3)式等号两端分别对温度求导,并考虑热膨胀效应:
$ \frac{\text{d}\Delta v}{\text{d}T}=\frac{2{{l}_{\text{LTO}}}}{\lambda }\left[ \frac{\partial {{n}_{\text{e}}}}{\partial T}-\frac{\partial {{n}_{\text{o}}}}{\partial T}+\alpha \left( {{n}_{\text{e}}}-{{n}_{\text{o}}} \right) \right]\frac{c}{2L} $
(4) 式中,α为LTO沿z轴方向的热膨胀系数,α=16×10-6/℃。本文中取∂no/∂T=25×10-6/℃,∂ne/∂T=2.4×10-6/℃[17]。(4)式决定了频差与温度的变化关系。
LTO作为一种电光晶体,其双折射率也可以通过电场进行调谐。在实验中,沿x轴方向对LTO晶体施加横向电场。电光效应使LTO晶体沿x轴和y轴的折射率发生了变化,变化值与电场强度和LTO晶体的电光系数有关:
$ \left\{ \begin{align} & \Delta {{n}_{\text{o}}}=-\frac{{{\gamma }_{13}}n_{\text{o}}^{3}V}{2d} \\ & \Delta {{n}_{\text{e}}}=-\frac{{{\gamma }_{33}}n_{\text{e}}^{3}V}{2d} \\ \end{align} \right. $
(5) 式中,V为电压,电光系数γ13=8pm/V, γ33=33pm/V, d表示电极间距,即LTO沿x轴方向的宽度。将(5)式代入(3)式,双频频差与电压的关系为:
$ \frac{{{\rm{d}}\Delta v}}{{{\rm{d}}\mathit{V}}} = \frac{{{l_{{\rm{LTO}}}}}}{\lambda }\left[ {\frac{{{\gamma _{13}}n_{\rm{o}}^3 - {\gamma _{33}}n_{\rm{e}}^3}}{d}} \right]\frac{c}{{2L}} $
(6) (4) 式和(6)式给出了频差Δν与温度和电压的理论关系。计算出频差随温度和电压的变化率分别为:$\frac{\text{d}\Delta v}{\text{d}T}=2.36$GHz/℃, $\frac{\text{d}\Delta v}{\text{d}\mathit{V}}=2.56$MHz/V。
温度和电压可以调谐频差的原因在于温度和外加电场改变了钽酸锂晶体的折射率,这种折射率的变化与光波前相位特征没有关系。所以以上分析适用于所有相同条件下正交偏振光之间的频差调谐特性,包括x偏振方向(xp)TEM00和y偏振方向(yp)TEM00,以及y偏振方向(yp)TEM00和x偏振方向(xp)LG01。这有助于更好地预测实验结果。
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抽运光从谐振腔的中心入射,保证晶体温度分布接近轴对称,用以产生拉盖尔-高斯模。在输出端放置布儒斯特棱镜,分离垂直偏振的两个光束。由于3个横模的竞争,双偏振态光束可以很容易产生。它们分别是x偏振方向(xp)的TEM00,y偏振方向(yp)的TEM00和x偏振方向的LG01。x方向和y方向偏振光的波长不同,而且x方向的偏振光的阈值比y方向低,所以观察到的LG01经常是沿x方向偏振。在抽运功率增加的过程中,抽运功率达到0.4W时,达到激光输出阈值,此时输出(xp)TEM00。当抽运功率达到1.1W,x方向偏振光中的LG01模开始起振。当抽运功率达到1.4W时,LG01模处于主导地位,LG01对TEM00的增益有抑制作用,由于模式竞争,(xp)TEM00变弱。随着抽运功率增加,(yp)TEM00逐渐到达输出阈值,它和(xp)TEM00也有竞争。因为(yp)TEM00的光频与(xp)LG01不同,所以二者的驻波在谐振腔中有相移。考虑到空间烧孔效应,(yp)TEM00和(xp)LG01之间的竞争强度弱于(xp)TEM00和LG01。所以2个TEM00的竞争中,(yp)TEM00能够抑制(xp)TEM00。最终抽运光功率在1.4W~1.7W之间时,激光器输出的双频分别为(xp)LG01和(yp)TEM00。
为了检验x偏振方向涡旋光的相前,在输出光路上放置布儒斯特棱镜,分离(xp)LG01和(yp)TEM00,其后搭建了Mach-Zehnder干涉系统。利用球面波和平面波分别与涡旋光产生干涉。产生干涉时主要考虑涡旋光的相位因子项,涡旋光的电场表达式为:
$ {E_1}{\rm{ = }}{A_1}\exp \left( {{\rm{i}}l\theta } \right) $
(7) 式中,l为拓扑荷数,θ为方位角。
简单起见,假设其振幅A1为固定值, 考虑其与平面波和球面波干涉。平面波和球面波的电场表达式为:
$ {E_2} = {A_2}\exp \left( {{\rm{i}}\frac{{2{\rm{ \mathsf{ π} }}\mathit{x}}}{\lambda }} \right) $
(8) $ {E_3} = {A_3}\exp \left[ {{\rm{ - i}}kz\left( {1 + \frac{1}{2}\frac{{{x^2}}}{{{z^2}}} + \frac{1}{2}\frac{{{y^2}}}{{{z^2}}}} \right)} \right] $
(9) 式中,波数k=2π/λ。
令A2=A1=A3=E0,E0表示简谐波的振幅。(7)式分别和(8)式、(9)式叠加后,干涉光的光强表达式如下:
$ I = E{E^*} - E_0^2\left[ {2 + 2\cos \left( {{\rm{i}}l\theta + {\rm{i}}2{\rm{ \mathsf{ π} }}\mathit{x/}\lambda } \right)} \right] $
(10) $ \begin{array}{l} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;I = E{E^*} = \\ 2E_0^2\left\{ {1 + \cos \left[ {{\rm{i}}l\theta - {\rm{i}}kz\left( {1 + \frac{1}{2}\frac{{{x^2}}}{{{z^2}}} + \frac{1}{2}\frac{{{y^2}}}{{{z^2}}}} \right)} \right]} \right\} \end{array} $
(11) 式中,E表示光电场,E*为其共轭复数。
由(10)式和(11)式可以仿真出涡旋光和平面波的干涉图形,当拓扑荷数l=1时,其干涉图形如图 2所示。在实验中用CCD对干涉条纹进行观测,如图 2a和图 2c所示,并与对应的理论仿真结果作对比(见图 2b和图 2d),表明产生的涡旋光的拓扑荷数l的绝对值等于1。
Figure 2. Experiment and simulation results of vortex beam interference fringes a—experimental interference fringe of LG01 and spherical wave b—simulation interference fringe of LG01 and spherical wave c—experimental interference fringe of LG01and plane wave d—simulation interference fringe of LG01 and plane wave
双横模输出微片谐振腔双频频差调谐特性研究
Study on dual-frequency difference tuning characteristics of microchip cavity with two transverse mode output
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摘要: 双偏振激光谐振腔能够产生两个垂直偏振的横模模式, 分别为基横模(TEM00)和具有轨道角动量的涡旋光束(LG01), 二者在光频率上具有频差。为了研究两个横模的频率差调谐特性, 采用温度与电压相结合的调谐技术方法, 实现拍频信号在不同频率范围的连续调谐。理论计算分析了两模式频差分别与温度和电压的对应关系, 实验实现了频差的大范围可调谐性, 并对频差的调谐精度进行了测量分析。结果表明, 频差与温度和电压之间都呈现出良好的线性关系, 并得到对温度和电压的调谐斜率分别为3.14GHz/K和1.76MHz/V。该研究能够更好地分析双偏振谐振腔直接产生涡旋光束现象, 并在激光通信和激光雷达探测等技术领域具有应用价值。Abstract: Two perpendicularly polarized transverse mode modes can be generated by a bipolarized laser resonator, namely fundamental transverse mode (TEM00) and vortex beam with orbital angular momentum (LG01). There is frequency difference in optical frequency. In order to study frequency difference tuning characteristics of two transverse modes, tuning technique combining temperature and voltage was adopted. Continuous tuning of beat signal in different frequency ranges was realized. The relationship between frequency difference of two modes vs. temperature and voltage was analyzed theoretically. Experiments showed that frequency difference can be tuned in wide range. Tuning accuracy of frequency difference was measured and analyzed. The results show that, there is good linear relationship between frequency difference vs. temperature and voltage. The tuning slopes of temperature and voltage are 3.14GHz/K and 1.76MHz/V, respectively. This study can better analyze the phenomenon of vortex beam generated directly by dual polarization resonator. It has application value in the fields of laser communication and lidar detection.
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Figure 2. Experiment and simulation results of vortex beam interference fringes a—experimental interference fringe of LG01 and spherical wave b—simulation interference fringe of LG01 and spherical wave c—experimental interference fringe of LG01and plane wave d—simulation interference fringe of LG01 and plane wave
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