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三镜腔激光器外腔中的回馈镜会将光反射回谐振腔内,改变了激光器输出镜的有效反射率,进而对谐振腔内的光场产生调制作用。将输出腔镜M2和外腔回馈镜M3合并为一个等效反射镜M2′,三镜腔模型[17]就可等效为两镜腔模型,如图 7所示。
微片激光器输出角频率为ω的激光束击打在回馈镜上,当用不同调制频率fPZT驱动PZT会带动回馈镜进行往复移动,即回馈镜在初始外腔长的基础上发生小范围的周期性振动变化,此时激光角频率则变为ω+ωPZT,ωPZT=2πfPZT是回馈镜谐振时的角频率。
此时,会有部分回馈光沿原路返回谐振腔内,并与腔内光场发生作用,引起自混合干涉信号的强度呈周期性变化。外腔中由于存在PZT调制回馈镜的作用,光束在经过外腔以及M2′反射后回到M2处的电场[17]为:
$ \begin{array}{c} E_2\left(t-\tau_{\mathrm{e}}\right)=E_1\left(t-\tau_{\mathrm{e}}\right) \kappa \sqrt{1-r_2^2} \times \\ \quad \exp \left(\mathrm{i} \;\omega_{\mathrm{PZT}} t\right) \exp \left[-\mathrm{i}\left(\omega+\omega_{\mathrm{PZT}}\right) \tau_{\mathrm{e}}\right] \end{array} $
(1) 式中:E1是激光器的腔内电场;τe=2n0Le/c是激光在外腔的行进时间;n0为外腔介质折射率;c是真空中的光速;Le为激光器外腔腔长;κ为外腔回馈镜的电场反射系数;r2是激光腔镜M2的反射系数。
根据速率方程理论,激光形成振荡是腔内的激光与粒子数反转状态下的激光增益介质的相互作用的动态过程,外腔存在PZT调制的单纵模线偏振微片激光器的速率方程[18]为:
$ \frac{\mathrm{d} N}{\mathrm{d} t}=\gamma\left(N_0-N\right)-B N|E(t)|^2 $
(2) $ \begin{array}{r} \frac{\mathrm{d} E(t)}{\mathrm{d} t}=\left[\mathrm{i}\left(\omega_{\mathrm{c}}-\omega\right)+\frac{1}{2}\left(B N-\gamma_{\mathrm{c}}\right)\right] E(t)+ \\ \kappa \gamma_{\mathrm{c}} \exp \left(-\mathrm{i} \omega_{\mathrm{PZT}}\right) \exp \left[-\mathrm{i}\left(\omega+\omega_{\mathrm{PZT}}\right) \tau_{\mathrm{e}}\right] E(t) \end{array} $
(3) 式中:N0是小信号反转粒子数;N是上能级反转粒子数;B是爱因斯坦受激辐射系数;E(t)是腔内光场;ωc为激光谐振腔的共振频率。
结合式(1)~式(3),可得到在PZT调频回馈下的激光器输出光强的相对调制[19]:
$ \frac{\Delta I\left(\omega_{\mathrm{PZT}}\right)}{I}=\kappa G\left(\omega_{\mathrm{PZT}}\right) \cos \left(\omega_{\mathrm{PZT}} t-\varphi+\varphi_0\right) $
(4) 式中:ΔI(ωPZT)为表示激光器输出光强的调制信号;I为稳态输出光强;φ是可反映回馈外腔长信息的外腔回馈相位;φ0为固定的附加相位。可知PZT调制回馈外腔对微片激光器光回馈条纹的影响,实质上是对激光器的类余弦回馈光条纹进行一定程度的放大。G(ωPZT)是一个对回馈光有放大作用的增益项[19]:
$ \begin{array}{c} G\left(\omega_{\mathrm{PZT}}\right)= \\ 2 r_{\mathrm{c}} \frac{\left(\eta^2 \gamma^2+\omega_{\mathrm{PZT}}{ }^2\right)^{1 / 2}}{\left[\eta^2 \gamma^2 \omega_{\mathrm{PZT}}{ }^2+\left(\omega_{\mathrm{r}}{ }^2-\omega_{\mathrm{PZT}}{ }^2\right)^2\right]^{1 / 2}} \end{array} $
(5) 取Nd∶YVO4激光器的上能级粒子数衰减速率γ=1.11×104/s,腔内光场衰减速率γc=2.75×1010/s,不同抽运电流值可转算为抽运水平因子η,对式(5)进行数值仿真,增益项随PZT调制频率的变化曲线如图 8所示。
从图 8可知,选择不同抽运电流值,微片激光器的回馈光受弛豫振荡峰影响,所获得的增益各不相同。在同样的PZT低频调制范围内,抽运电流值越小,增益项整体放大作用越强。若PZT调制频率靠近弛豫振荡峰,增益项变大,对回馈光的放大作用增强。当ωPZT=ωr时,增益项最大可达106量级,表明微片激光器经PZT调频回馈后能具有极高的光回馈灵敏度,能用于微弱信号检测。
再对式(4)进行数值仿真,在相同PZT调频量(50 kHz)时,得到不同抽运电流的输出光强的相对调制,如图 9所示。图 9的仿真结果表明,回馈光在相同PZT调制电压作用下,减小抽运电流值,输出幅值会整体增大。
图 9 不同抽运电流的激光器输出光强的相对调制
Figure 9. Relative modulation of laser output intensity with different pump currents
在同一抽运电流(110 mA),得到不同PZT调频量的输出光强的相对调制,如图 10所示。图 10的仿真结果说明,输出幅值会随PZT调频量的增大而增大。仿真结果很好地印证了图 2中的实验现象。
压电陶瓷调制激光回馈外腔的实验和分析
Experiment and analysis of piezoelectric transducer modulated laser feedback external cavity
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摘要: 为了研究微片激光器的光回馈效应的调制方式对激光器光灵敏度的影响,采用不同调制电压、频率驱动压电陶瓷(PZT)来调谐微片激光器外腔的方法,观察光回馈条纹幅值和灵敏度的变化情况,并结合复合腔等效模型进行了数值仿真和分析。结果表明,增大PZT调制频率,使其越靠近激光器的弛豫振荡频率,光放大效果越明显,输出幅值和PZT调制频率具有相同变化趋势;PZT调制频率不变,将140 mA抽运电流调小至出光阈值电流约100 mA,弛豫振荡峰值会逐渐靠近PZT移频调制量,能主动放大回馈光,增益可高达105;光灵敏度与PZT移频量相对弛豫振荡峰值的距离有关,两者越接近,光灵敏度则越强;经PZT调制的激光回馈系统相对声光调制,有降低成本、易于调节的优势。该研究为联动调节抽运电流和PZT调制量获得幅值合适、噪声小的光回馈条纹提供了参考。Abstract: In order to study the influence of the modulation method of the optical feedback effect of the microchip laser on the optical sensitivity of the laser, a method of driving piezoelectric transducer (PZT) with different modulation voltages and frequencies was used to tune the external cavity of the microchip laser, and the changes of the amplitude and sensitivity of the optical feedback fringe were observed. Numerical simulation and analysis based on the composite cavity equivalent model were conducted. The results show that by increasing the PZT modulation frequency so that it is closer to the relaxation oscillation frequency of the laser, the optical amplification effect becomes more obvious, and the output amplitude and PZT modulation frequency have the same trend. The PZT modulation frequency remains unchanged, and the 140 mA pump current is reduced to the light emission threshold current of about 100 mA, the relaxation oscillation peak will gradually approach the PZT frequency shift modulation amount, which can actively amplify the feedback light, and the gain can be as high as 105. The optical sensitivity is related to the distance between the PZT frequency shift amount and the relaxation oscillation peak. The closer the two are, the stronger the optical sensitivity is. The laser feedback system modulated by PZT has the advantages of lower cost and easy adjustment compared with acousto-optic modulation. This study provides a reference for jointly adjusting the pump current and PZT modulation amount to obtain optical feedback stripes with appropriate amplitude and low noise.
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