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基于AOM的光学锁相环偏频锁定系统同时具有AOM的高频率响应特性和光学锁相环的高灵敏度特性,能够快速对误差信号做出反应,实现快速、准确的相位锁定。
实验选用基于碘分子腔内饱和吸收稳频的高稳定He-Ne激光作为波长参考光源,用于偏频锁定热稳频全内腔He-Ne激光器。碘稳频He-Ne激光器频率稳定度高、复现性好,是国际主流的633 nm波长参考光源,以它作为频率标准,可以实现基于光学锁相环的高稳定度锁定。该激光器采用半内腔结构的腔内饱和吸收方式,利用碘分子反兰姆凹陷光谱实现激光频率的精准锁定,波长的相对标准不确定度达到E-12量级,频率稳定度达到1 E-11(1 s)[9],为热稳频He-Ne激光光学锁相环锁定提供了理想的参考频率。
热稳频He-Ne激光器的光学锁相环偏频锁定系统原理如图1所示。图1(a)为拍频信号模块,从激光器发出的光束首先通过半波片改变自身的偏振状态,使光束尽可能多的向后传递。之后光束通过偏振分光棱镜(PBS)被分为反射光和透射光,透射光经过凸透镜会聚入射到AOM中。当光束第一次经过AOM衍射后,使一级衍射光通过四分之一波片和反射镜,经反射镜反射后再次通过四分之一波片(此时光束两次经过四分之一波片,偏振方向旋转$ \pi /2 $),再经过凸透镜会聚入射到AOM中。此时两束光的偏振态互相垂直,无法产生拍频,因此需要再通过一个半波片改变合束光的偏振状态,再通过PBS产生拍频信号。图1(a)中模块产生的拍频信号通过功分器分为三路,一路传入频谱仪用于观察拍频信号,一路传入频率计数器用于计数,最后一路传入图1(c)中模块。图1(c)中模块首先将拍频信号和参考信号转换成方波,然后将两路方波信号输入到鉴频鉴相器得到误差信号,最后,PID控制电路将误差信号转换成控制信号,反馈输入到AOM进行偏频锁定。该系统依据AOM双次通过光路和光学锁相环原理设计,主要包括光源及拍频信号模块、光学锁相环电路模块和拍频监测模块三部分。搭建的光学锁相环系统实物如图2所示。
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为了实现全内腔热稳频He-Ne激光器的频率调谐,实验选取AOM作为频率调谐和反馈单元。AOM由声光介质和压电换能器构成[10]。当驱动源的某种特定载波频率驱动换能器时,换能器能够产生同一频率的超声波并传入声光介质,在介质内形成折射率变化,光束通过介质时会发生相互作用而改变光的传播方向,即发生衍射。但是采用AOM的光路会存在一个问题:经过AOM移频后,衍射光的衍射角会随着入射光频率的改变而改变,导致系统的光路失去唯一性,无法产生稳定的拍频信号。
为了解决AOM的衍射角依赖问题,文中采用双次通过光路[11−14]来防止激光束方向随着驱动频率的改变而发生变化:当激光束入射到AOM中,AOM使激光束发生衍射,其一阶衍射光以一个小角度出射,并且产生移频,角度可以作为AOM的输入功率和驱动频率的函数。为了避免光束路径对$ \theta $的依赖,在AOM后方放置一个凸透镜,AOM到凸透镜的距离等于透镜的焦距,这样保证了AOM的所有出射光经过透镜后以平行光出射。在透镜的后方有一面反射镜,所有的出射光经过反射镜后会原路返回,再次进入AOM。为了防止零级光也经过反射镜后再次进入拍频光路,需要在反射镜的前面用光阑将零级光挡住,只允许一阶衍射光被反射镜反射并再次通过AOM返回,以确保即使角度发生了变化,返回光束的一阶衍射光与入射光束相比不会改变其光束路径(见图3)。基于双次通过光路搭建的系统有效避免了光束路径对$ \theta $的依赖,克服了因为$ \theta $角度变化而导致的拍频信号无法重合的问题。
AOM的驱动频率和输入电压的关系如图4所示,可以看出,在调制频率为150~250 MHz的区间内与驱动控制电压呈线性关系。因为文中采用Double-pass的光路设计,所以热稳频激光器经过AOM以后的频率为:
$$ {f}_{a}=f\pm 2{f}_{\mathrm{A}\mathrm{O}\mathrm{M}} $$ (1) 式中:${f、f}_{{a}}$分别为经过AOM移频前后激光器频率;${f}_{{\rm{AOM}}}$为AOM的驱动频率。因此,该系统的可调谐频率范围为$ 2{\Delta f}_{\mathrm{A}\mathrm{O}\mathrm{M}} $,约为200 MHz。
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光学锁相环[15−19]主要由参考激光器、待锁定激光器、光电接收器、鉴频鉴相器、环路滤波器以及PI控制电路组成,其与传统的锁相环工作原理相类似。光电接收器先将接收到的光信号转换为电信号;鉴频鉴相器探测出拍频信号与参考信号相位之差,并输出与之对应的误差信号;环路滤波器根据环路的需求对这一误差信号进行滤波、去噪;经过滤波得到的误差信号最后经过PI控制电路处理,产生一个控制信号,控制信号反馈输出到待锁定激光器上,对激光器的频率进行控制,从而实现闭环控制。
光学锁相环的环路模型如图5所示,这是一个相位负反馈的误差控制系统,图中,${U}_{{\rm{d}}}\mathrm{sin}\left[\cdot\right]$为鉴频鉴相器的传递函数,$ F\left(p\right) $为环路滤波器的传递函数,${K}_{{\rm{p}}}+{K}_{{\rm{i}}}{\int }_{0}^{t}\left[\cdot\right]{\mathrm{d}}\tau$为PI控制器的传递函数,其中${K}_{{\rm{p}}}$和${K}_{{\rm{i}}}$分别为比例系数和积分系数,$ {{K}_{0}}/{p} $为待锁定激光器的传递函数。待锁定激光器和参考激光器的拍频信号与参考频率信号进行比较,得到误差信号$ {\theta }_{\mathrm{e}}\left(t\right) $,由误差信号产生误差电压$ {u}_{\mathrm{d}}\left(t\right) $,误差电压经过环路滤波器和PI控制电路得到控制电压$ {u}_{\mathrm{c}}\left(t\right) $,控制电压加到待锁定激光器上使拍频信号向参考信号产生频率偏移。一旦达到两者频率相等时,在特定条件下,控制环路就能稳定工作,实现相位锁定。
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实验中,碘稳频He-Ne激光器作为该系统的主激光器,热稳频He-Ne激光器和AOM共同作为从激光器。热稳频He-Ne激光器发出的激光束首先通过AOM进行第一次移频,经过反射镜反射后,再次通过AOM进行二次移频,经过二次移频后的光路路径不再依赖于出射角$ \theta $,即当AOM的驱动频率发生改变时,拍频光路依然能够保持不变,产生稳定的拍频信号。在通过AOM移频激光束的过程中,由于AOM的特性,入射光经过AOM会变成零级衍射光和一级衍射光,为了防止零级衍射光对实验系统产生影响,需要加入光阑隔离零级衍射光。
在确保两束零级光被光阑遮挡后,通过偏振分光棱镜使碘稳频He-Ne激光器的激光束与二次移频后的热稳频He-Ne激光器的激光束进行拍频,产生的拍频信号由光电探测器接收并转换成电信号,然后通过功分器分为三路,其中两路分别连接到频谱仪和频率计数器上,对拍频信号进行监视和计数,剩下的一路则进入锁相环系统进行闭环控制。
在构建拍频光路时,AOM的位置选择至关重要。实验中要求AOM的衍射效率尽可能高,以达到增强拍频信噪比的目的。双通道光路虽然克服了光路对$ \theta $角的依赖,但是同时两次经过AOM也会大幅度降低激光的功率。为了保证拍频信号的信噪比达到锁相环的要求,对AOM的安装位置进行了仔细优化,使其衍射效率最大。衍射效率和驱动电压的关系如图6所示。光电接收器接受到的拍频信号的信噪比与AOM驱动电压的关系如图7所示。图中数据表明,该系统中的双通道光路满足实验要求,在0~9 V区间内能够产生大于40 dB的高信噪比拍频信号,系统的可调谐波长范围为300~480 MHz。
图 7 拍频信号信噪比和驱动电压关系图
Figure 7. The relationship between signal to noise ratio of beat frequency signal and driving voltage
由图5可知,锁相环的系统增益函数由鉴频鉴相器、环路滤波器、PI控制电路和激光器自身的传递函数决定。由于鉴相器、环路滤波器和激光器自身的传递函数在系统设计时就已经确定,通过改变系统中PI控制电路的参数来改变系统的增益函数。PI控制电路的积分常数与系统闭环锁定后拍频信号的标准差的关系如图8所示。可以看出,当积分常数${K}_{{\rm{i}}}$在$ {1\times 10}^{6} $附近时,系统锁定后的标准差最小,低于0.05;当积分常数小于$ 1\times {10}^{4} $时,锁相环系统将无法实现环路锁定。
Frequency stabilization method of optical phase-locked loop He-Ne laser based on acousto-optic modulator
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摘要: 报道了一种基于声光调制器与光学锁相环相结合的高稳定度激光稳频方法,用于提高热稳频He-Ne激光器的频率稳定度和准确度。为了克服全内腔热稳频He-Ne激光精密调谐困难的缺点,发展了基于声光调制器两次移频的频率调谐光路,有效地消除声光调制器移频光束路径对衍射角$ \theta $的依赖。自行研制了具有高灵敏度与捕获带宽的光学锁相环系统,利用声光调制器的高频率响应特性实现热稳频He-Ne激光高速、准确的锁定。成功实现了热稳频He-Ne激光器偏频锁定至碘稳频He-Ne激光器。实验结果表明,环路锁定后拍频频率波动在±0.2 Hz范围内,频率抖动的标准差为0.04。偏置频率为30 MHz时,系统在1 s和1000 s积分时间的相对阿伦方差分别为$ 3.3\times {10}^{-9} $和$ 1.4\times {10}^{-12} $。系统锁定后,压缩后的拍频线宽小于2 kHz。该研究表明,采用基于声光调制器与光学锁相环相结合的激光稳频方法可以实现亚赫兹级的激光频差控制,通过将热稳频He-Ne激光器偏频锁定至高稳定度的参考激光源可以显著提升其频率稳定度和准确度。Abstract:
Objective With the rapid development of the aerospace and microelectronics industries, the demand for ultra precision measurement is also increasing. He-Ne lasers are widely used in mechanical and ultra precision measurement fields due to their excellent coherence and other characteristics. Among them, the thermally stabilized He-Ne laser is suitable as a wavelength scale laser for laser interferometry due to its high frequency stability, good beam quality, and low cost. However, traditional thermally stabilized lasers have poor frequency stability and reproducibility, which cannot further meet the requirements of high-precision laser interferometry for frequency stability and accuracy. This article reports a frequency biased locking system for thermally stable He-Ne laser based on a combination of an acousto-optic modulator and an optical phase-locked loop. This system combines the high-frequency response characteristics of an acousto-optic modulator with the high sensitivity characteristics of an optical phase-locked loop, enabling fast and accurate frequency locking of a thermally stable He-Ne laser. Methods This article reports an optical phase-locked loop bias locking system based on an acousto-optic modulator. An iodine stabilized frequency laser is chosen as master laser, and a thermally stabilized He-Ne laser as the slave laser. The beam of the slave laser is modulated by an acousto-optic modulator and locked onto the master laser. The reference signal for frequency offset locking is a 30 MHz signal generated by a signal generator. Data are collected using a frequency counter. The locking result is shown (Fig.9). Results and Discussions In the experiment, a highly stable He-Ne laser based on intracavity saturation absorption stabilization was used as the wavelength reference source for thermal stabilization laser locking. Through beat frequency measurement with iodine stabilized laser wavelength reference, the results show that the 1 s wavelength stability of the iodine stabilized laser is $ 1.3\times {10}^{-11} $, reaching $ 4.1\times {10}^{-13} $ in 1 000 s, reproducibility better than $ 1.0\times {10}^{-11} $. The frequency jitter of the laser beat frequency after the system is locked is shown (Fig.10). As a comparison, the figure shows the drift of the beat frequency under free operation. In the experiment, a frequency counter was used to count the beat frequency signal for 30 min in the open-loop state of the optical phase-locked loop. Then, the reference frequency was set to 30 MHz to lock the thermal stabilized frequency laser to the iodine stabilized frequency laser, and the beat frequency after the loop locking was continued to be counted for 180 min. The beat frequency was locked at a bias frequency of 30 MHz, with a fluctuation range below 0.2 Hz. We have achieved high stability frequency locking of thermally stabilized lasers compared to iodine stabilized lasers. The relative Allen variance of the frequency offset of the optical phase-locked loop is shown (Fig.11). Among them, the relative Allen variance of the integration time of 1 s and 1000 s is $ 3.3\times {10}^{-9} $ and$ 1.4\times {10}^{-12} $ respectively. Conclusions This article introduces a high stability laser frequency stabilization method based on the combination of an acousto-optic modulator and an optical phase-locked loop. An experiment was conducted using a self-developed optical phase-locked loop system to lock the bias of a thermally stable all cavity He-Ne laser to an iodine stable frequency laser. The signal-to-noise ratio of the beat frequency signal was increased to over 40 dB (Fig.9) through a beat frequency signal detection unit based on an acousto-optic modulator. A digital frequency discriminator and PI control circuit were used to feedback control the acousto-optic modulator, achieving closed-loop control of the optical phase-locked loop. The frequency stability of the thermally stable He-Ne laser is significantly improved, enabling it to meet the requirements for laser frequency stability and accuracy in the fields such as ultra precision interferometry and ultra sensitive spectral detection. -
图 9 (a) 环路锁定前拍频频谱图;(b) 环路锁定后拍频频谱图;(c) 拍频信号展开图;(d) 环路未锁定时AOM驱动频率图; (e) 环路锁定时AOM驱动频率图;(f)环路未锁定时AOM驱动频率展开图
Figure 9. (a) Beat frequency spectrum before loop locking; (b) Beat frequency spectrum after loop locking; (c) Beat frequency signal expansion diagram; (d) AOM drive frequency map when the loop is not locked; (e) AOM drive frequency map during loop locking; (f) AOM drive frequency expansion diagram when the loop is not locked
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