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取出回馈腔中的WP,此时回馈腔是各向同性的,给PZT施加三角波电压,回馈镜M将在PZT驱动下沿z轴往复移动,调谐回馈腔长。通过示波器观察PD1输出电压的变化,得到光强调制曲线,如图 2所示。调制波形类似于正弦波,波形每变化一个周期对应回馈外腔长变化λ/2[16]。
将λ/8波片置入回馈腔中,绕z轴旋转波片,使波片快轴和慢轴分别与x轴和y轴平行,观察PD1输出电压变化,得到图 3所示光强调制曲线。此时在PZT三角波电压上升沿和下降沿分别对应的光强调制曲线上均出现一个凹陷点B,说明双折射元件对激光输出强度有影响。观察PD2输出电压变化,由于偏振片的通光方向与激光初始偏振方向垂直,即y轴方向,只有偏振态与偏振片通光方向平行的激光才能到达PD2,探测器有电压输出。在PZT电压上升沿,激光初始偏振方向为x方向,无法通过偏振片,为低电平,在光强调制曲线凹陷位置B点,出现高低电平转换,激光从x偏振方向跳变到y偏振方向。注意到在压电陶瓷伸长和缩短的过程中,跳变方向是相反的,若伸长过程中由x方向跳变至y方向,则缩短过程中由y方向跳变至x方向,图中每一次高低电平的转换就意味着激光偏振态发生一次跳变。
图 3 λ/8波片回馈波形和偏振态变化
Figure 3. Modulation waveform and polarization state variation with λ/8 wave-plate feedback
为了观察回馈腔中不同相位延迟下的偏振跳变现象,在回馈腔里置入两个可绕z轴旋转的λ/4波片[17-18],改变其中一个波片的快轴相对于另一波片的慢轴的夹角θ来改变回馈腔内的相位延迟。在调节夹角的过程中,光强调制曲线的凹陷深度会发生明显变化,凹陷深度为:
$ d=\frac{I_1}{I} $
(1) 式中,d为两光强信号电压差的比,无量纲。I1表示光强调制曲线一个周期内最高点与凹陷点的光强差,如图 3所示。对于PZT电压上升沿对应的光强调制曲线来说,I1为D1点与B1点的光强差;下降沿为E2点与B2点的光强差。I表示光强调制曲线一个周期内最高点与最低点的光强差,分别为D1点与C1点的光强差以及E2点与C2点的光强差。
随着夹角θ从0°增加至45°,回馈腔内的相位延迟从0°逐渐逼近90°,所对应的光强调制曲线凹陷深度d的变化如图 4所示。无论是在PZT电压上升沿或是下降沿,B点凹陷均逐渐加深,且夹角θ越接近45°,即回馈腔相位延迟越接近90°,凹陷深度变化趋势越快。
随着回馈腔相位延迟改变,在光强调制曲线一个周期内,单个偏振态的持续时间T也有所差异。如图 3所示,在PZT电压上升沿对应的光强调制曲线中,一个周期内平行于x轴的激光偏振态(x偏振态)持续时间为:
$ T_x=\frac{t_x}{t} $
(2) 式中,tx为A1点与B1点间的横坐标差值,t为A1点与C1点横坐标差值。同理,在PZT电压下降沿对应的光强调制曲线中,一个周期内平行于y轴的激光偏振态(y偏振态)持续时间为:
$ T_y=\frac{t_y}{t} $
(3) 此时,ty为A2点与B2点间的横坐标差值,t为A2点与C2点横坐标差值。单个偏振态持续时间T是一个比例值,其随夹角θ的变化关系如图 5所示。在PZT电压上升沿,x偏振态持续时间在一个周期内逐渐增大,同周期内所对应的y偏振态持续时间就会逐渐减小;在PZT电压下降沿,y偏振态持续时间逐渐减小,同周期内所对应的x偏振态持续时间就会逐渐增大。但无论是上升沿还是下降沿,同一周期内两偏振态持续时间都会随回馈腔内相位延迟接近90°而趋于一致,即图中纵坐标为0.50的直线。
图 5 单个偏振态持续时间与夹角的变化关系
Figure 5. Relationship between the duration of one specific polarization and the included angle
为了进一步研究回馈腔内相位延迟等于90°时,激光输出强度与偏振态变化的特性,将一片λ/4波片置入回馈腔中,绕z轴旋转波片,使波片快轴和慢轴分别与x轴和y轴平行,当回馈腔长被调谐时,实验结果如图 6所示。光强调制曲线类似于各向同性激光回馈波形的全波整流,曲线上B点凹陷最深,两正交偏振态在光强调制曲线的同一周期内持续时间基本相同,即光强调制波形宽度趋于相同。各向同性回馈时激光强度每变化一个周期对应回馈腔长改变λ/2,而当回馈腔相位延迟等于90°时,每一次偏振跳变对应回馈腔长改变λ/4。
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对存在光回馈的激光系统,可以用三镜腔等效模型[19]将反射镜M和输出腔镜复合成一个复数反射率的等效腔镜,这一等效的复合腔激光系统也满足两腔镜激光器激发条件。双折射外腔回馈中,反射镜M将一部分光反射回激光器,由于双折射元件的存在,使得o光和e光分别沿x轴和y轴两个方向上的等效反射率是不同的。若激光初始偏振方向和波片快轴均平行于x轴,此时回馈腔中o光偏振方向沿x轴,x和y方向上的等效反射率为:
$ \left\{\begin{array}{l} R_{\mathrm{o}, x}=R_2+\zeta \cos \left(\varphi_{\mathrm{f}}-2 \delta\right) \\ R_{\mathrm{o}, y}=R_2 \end{array}\right. $
(4) $ \varphi_{\mathrm{f}}=\frac{4 \pi l}{\lambda} $
(5) 式中,R2为微片激光器输出端反射率,φf为回馈腔调谐过程中引起的相位变化,δ为双折射元件的相位延迟,l为回馈腔长度,λ为波长,ζ为等效反射率系数。
对应x和y方向上的光强为:
$ \left\{\begin{array}{l} I_{0, x}=I_0+\eta \cos \left(\varphi_{\mathrm{f}}-2 \delta\right) \\ I_{\mathrm{o}, y}=I_0 \end{array}\right. $
(6) 式中,I0为无光回馈时激光初始强度,η为等效光强系数。当激光初始线偏振方向和双折射元件慢轴均平行于y轴时,此时回馈腔中e光偏振方向沿y轴,x和y方向上的等效反射率为:
$ \left\{\begin{array}{l} R_{\mathrm{e}, x}=R_2 \\ R_{\mathrm{e}, y}=R_2+\zeta \cos \varphi_{\mathrm{f}} \end{array}\right. $
(7) 对应x和y方向上的光强为:
$ \left\{\begin{array}{l} I_{\mathrm{e}, x}=I_0 \\ I_{\mathrm{e}, y}=I_0+\eta \cos \varphi_{\mathrm{f}} \end{array}\right. $
(8) 现假设回馈腔中相位延迟δ=45°,激光初始偏振方向和波片慢轴均平行于y轴,此时只有y轴方向有回馈光进入激光器,输出光强为(8)式中的Ie, y,如图 7a所示。图 7中纵坐标光强每小格刻度代表对应的示波器电压200 mV。从A点开始,当0 < φf < π时,ζcosφf>0,相当于输出腔镜在y方向上的反射率增大,激光在y偏振方向上获得较大增益,稳定振荡,并抑制x偏振使其无法振荡,输出光强为AB段;当φf=π,即图中B点处,cosφf=0,此时Ie, y=Ie, x,若φf继续增大,将导致Ie, y < Ie, x,激光偏振态将在此处发生跳变,从y偏振方向跳变为x偏振方向,这时Ro, x>Ro, y,x偏振将稳定振荡,光强由Ie, y转化为Io, x,为图中虚线CD段;当φf增大至cos(φf-2δ)=0时,若再继续增大,Io, x < Io, y,偏振方向将从x方向变为y方向,但由于此时Ro, x> Re, y,使得x方向获得增益大于y方向,偏振方向维持在x方向;当cos(φf-2δ)变化至D点,Ie, y=Io, x,继续增大φf,Ie, y < Io, x,同时满足Re, y>Ro, x,y方向获得增益大于x方向,偏振方向跳变至y方向,光强曲线为Ie, y,直至图中E点,完成偏振跳变的一个周期,再按此规律重复下去。
图 7 回馈腔中不同相位延迟对应的偏振跳变和强度转移示意图
Figure 7. Illustrations of laser polarization flipping and intensity transfer corresponding to different phase retardation in feedback cavity
当δ=90°时,即λ/4波片回馈,输出光强理论曲线图 7b所示。根据上述分析可得,从A点开始,激光输出为Ie, y,到达B点时发生偏振跳变,激光输出为Io, x,D点时偏振态再次跳变,并以此循环,类似于正弦波全波整流。由图 7可知,在一个周期内,单个偏振态持续时间与相位延迟δ有关,随着相位延迟增大,单个偏振态持续时间逐渐接近0.50,与图 5的曲线趋势一致,当相位延迟为90°时,x或y偏振态持续时间占整个跳变周期的一半,与图 6的实验结果吻合。
固体微片Nd∶YAG激光器的偏振跳变效应研究
Research on polarization flipping effect of microchip Nd∶YAG laser
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摘要: 为了研究基于激光回馈的偏振跳变效应与相位延迟间的内在联系, 采用微片Nd∶YAG激光器(中心波长1064 nm)为光源, 回馈腔内置两个相对旋转的λ/4波片改变相位延迟, 在调谐回馈腔长的过程中研究了激光器的光强输出和偏振态变化。结果表明, 随着回馈腔内相位延迟增大, 偏振跳变点的凹陷逐渐加深, 两个偏振态的光强调制波形宽度趋于相同; 当回馈腔中相位延迟为90°时, 两正交偏振态在一个强度调制周期内持续时间相同, 每一次偏振跳变对应回馈腔长改变λ/4。此不同相位延迟下偏振跳变点的变化规律, 为1064 nm波长下的波片相位延迟测量提供了潜在方法, 同时相位延迟对激光器输出光强曲线的整形、为激光回馈条纹(自混合干涉条纹)的光学细分提供了依据。Abstract: In order to study the intrinsic relationship between the polarization flipping effect and the phase retardation based on laser feedback, the output intensity and polarization state of the laser were observed during the tuning of the feedback cavity length by using a microchip Nd∶YAG laser (central wavelength of 1064 nm) as the light source and two relative rotating λ/4 wave-plates in the feedback cavity to change the phase retardation. The results indicate that, with the increase of phase retardation in the feedback cavity, the indentation depth of the polarization flipping position gradually deepens, and the width of the light intensity modulation waveform of the two polarization states tends to be the same. When the phase retardation in the feedback cavity is 90°, the duration of two orthogonal polarization states to be the same in an intensity modulation period, and each polarization flipping corresponds to a change of λ/4 feedback cavity length. The variation of the characteristic point of polarization flipping caused by different phase retardation provides a potential measuring method for phase retardation of waveplate at 1064 nm wavelength. Meanwhile, the change of phase retardation shapes the output light intensity waveform of laser, which provides a basis for optical subdivision of laser feedback fringe (self-mixing interference fringe).
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