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光学频率梳的本质是一种超短脉冲锁模激光器[15],如图1所示,其输出的超短脉冲在频域上表现为一系列具有严格等间距的脉冲序列,像一根根的“梳齿”一样。相邻两个脉冲之间的频率间隔就称为输出脉冲的重复频率
$ {f_r} $ ,而激光器的输出脉冲由于受到腔内外部各种噪声的影响,会使得脉冲序列会有一个整体的偏移,称为脉冲的载波包络偏移频率$ {f_0} $ ,因此在光学频率梳中,其重复频率为:$$ {f_r} = \frac{c}{{2nL}} $$ (1) 式中:
$c$ 为光速(真空);$n$ 为激光器谐振腔内的折射率;$L$ 为激光器谐振腔的长度。 每一根频率梳齿就可以表示为:$$ {f_k} = k{f_r} + {f_0} $$ (2) 式中:
${f_k}$ 为第k根梳齿的频率;$k$ 为正整数;$ {f_r} $ 为重复频率;$ {f_0} $ 为载波包络偏移频率。在时域上,如图2所示,光学频率梳表现为一系列周期
$ T $ 为$ {1 \mathord{\left/ {\vphantom {1 {{f_r}}}} \right. } {{f_r}}} $ 的脉冲序列。从时域上可以更加直观和形象的理解光梳,其中$ \vartriangle\varphi $ 为载波包络相位差,与频域中的载波包络偏移频率$ {f_0} $ 相对应,表示由于腔内色散等因素的影响,包络与载波的相对相位关系会出现细微改变。在双光梳测距系统中,可以利用飞行时间法[16]求得待测绝对距离
$D$ 为:$$ D = \frac{1}{2} \cdot c \cdot \frac{{\Delta T \cdot \Delta {f_r}}}{{{f_r}}} $$ (3) 式中:
$\Delta T$ 为参考与测量脉冲之间的时间延迟;$\Delta {f_r}$ 为双光梳重复频率差。从公式(3)可知,若重复频率差的稳定性很差,则测距的精度会大大降低,为了得到精确的测距结果,必须要对双光梳系统中的重复频率差进行锁定。锁定重复频率差与锁定重复频率的原理是相同的,由公式(1)可知,激光器的重复频率与谐振腔的等效腔长以及腔内介质的折射率有关,故可以通过控制腔长或者折射率来达到锁定重复频率的目的。在文中的双光梳系统中,重复频率差的锁定部分主要是通过控制谐振腔的腔长来实现的。实验中,将PZT固定在反射腔镜上,通过改变作用在PZT上的加载电压而改变自由空间光传输距离(即谐振腔等效腔长),从而达到控制重复频率的目的。
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文中设计的双光梳重复频率差异步锁定装置如图3所示,包括光学系统和电学系统两部分。光学部分包括重复频率
${f_{r1}}$ 为155.711 MHz的信号光梳、重复频率${f_{r2}}$ (${f_{r2}} = {f_{r1}} + \Delta {f_r}$ )为155.714 MHz的本振光梳(即重复频率差$\Delta {f_r}$ 为3 kHz)以及谐振腔内的PZT;电学系统部分主要是基于商用器件搭建而成,包括了光电探测器(PD)、功分器(Spliter, mini circuits FSC211等)、混频器(Mixer, mnicircuits ZFM150等)、带通/低通滤波器(BPF/LPF, Minicircuits BPF1090及BLP-5等)、放大器(Amp)、高精度信号发生器(Signal generator, R&S SMB100A)、数字信号发生器(DDS, Analog devices AD9912)、伺服控制器(PI Controller, New focus LB1005)、压电驱动器(PZT driver, 芯明天E00.C3)和频率计数器(Counter, Keysight 5323A)等。图 3 双光梳系统重复频率差异步锁定装置
Figure 3. Dual-comb system repetition rate difference asynchronous locking device
如图3所示,光电探测器PD1将探测到的信号光梳的重复频率及其高次谐波转换为电信号输出到带通滤波器BPF1中,利用带通滤波器提取出其七次谐波信号
$7{f_{r1}}$ ,即1.09 GHz,这受限于所使用的信号发生器(R&S SMB100 A)的上限频率(1.1 GHz)。因为重复频率的高次谐波相比于基频信号具有更多的相位噪声信息[17],但锁相回路在基频(150 MHz附近)和七次谐波(1 GHz附近)的工作性能接近,从而锁定重频的高次谐波可以获得更好的精度。将提取出的重复频率七次谐波信号$7{f_{r1}}$ 经过放大器Amp1放大后与高精度信号发生器输出的信号$ {f_s} $ 通过混频器Mixer1进行混频,用低通滤波器LPF1提取出混频器中的差频信号并输入到PI伺服控制器中生成相应的误差控制信号${f_s} - 7{f_{r1}}$ ,利用这个误差信号经过压电控制器来驱动信号光梳谐振腔内的PZT产生微小形变就可以改变谐振腔的腔长,形成一个闭环的反馈回路,从而实现信号光梳重复频率的锁定。锁定后重复频率与高精度信号发生器输出的频率相等,即${f_{r1}} = {f_s}$ ,并且具有与高精度信号发生器输出频率类似的频率稳定度。锁定了信号光梳的重复频率后,将其重复频率的七次谐波信号作为信号源去触发数字信号发生器DDS1和DDS2,产生两个频率略有差异的信号${f_{DDS1}}$ 和${f_{DDS2}}$ ,其中${f_{DDS1}}$ =137.021 MHz,${f_{DDS2}}$ =137 MHz,而两个信号之间的差值就是预设的双光梳重复频率差的七倍,即$ {f_{DDS1}} - {f_{DDS2}} = 7\Delta {f_{set}} $ =21 kHz(此差值的大小可根据需求通过调整两台DDS信号发生器的输出值来决定);然后再将信号光梳重复频率的七次谐波信号$7{f_{r1}}$ 与经过光电探测器PD2探测并用带通滤波器BPF4提取到的本振光梳重复频率的七次谐波信号$7{f_{r2}}$ 分别与DDS数字信号发生器输出的信号${f_{DDS1}}$ 和${f_{DDS2}}$ 通过混频器Mixer2与Mixer3进行混频,并用带通滤波器BPF2和BPF3滤除Mixer2与Mixer3中的差频信号,保留和频信号,两个和频信号再通过Mixer4进行一次混频,最终利用低通滤波器LPF2提取混频得到的差频信号输入到PI控制器中生成相应的误差控制信号$7\Delta {f_{set}} - 7\Delta {f_r}$ ,利用这个误差信号经过压电控制器来驱动本振光梳谐振腔内的PZT就可以反馈控制谐振腔的腔长,形成一个闭环的反馈回路,使本振光梳重复频率锁定,锁定后重复频率为$ {f_{r2}} = {f_{r1}} + \Delta {f_r} $ 。此时,两台光梳之间的实际重复频率差值与预设的重复频率差相等,即$\Delta {f_r} = \Delta {f_{set}}$ ,实现了双光梳重复频率差的异步锁定。在整个实验装置中,PZT是控制重复频率最重要的一个器件,其影响了整个锁定系统的响应特性以及最大调谐频率。在文中的锁定系统中,选用的PZT是Thorlabs的PK44LA2P2,其驱动电压量程为0~150 V,行程为9 μm。为了测试PZT的重复频率调谐能力,在调节PZT驱动电压的同时,在0~120 V范围内(实验装置中使用的压电驱动器驱动电压范围)测量了重复频率的变化量,如图4所示,实验装置中所选用的PZT可以调谐重复频率的最大范围是1.58 kHz,完全满足自由运转状态下激光器重复频率的变化量。
Research on repetition rate difference asynchronous locking technique of dual-comb
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摘要: 双光梳系统在高精度绝对距离测量、三维成像以及光谱测量等领域有着其独特的优势和广阔的发展前景。文中提出一种基于锁相环原理的异步锁定技术,可以对双光梳系统中的重复频率差进行精密锁定。实验中,采用了重复频率约为155.711 MHz和155.714 MHz的双光梳系统,通过反馈控制压电陶瓷(PZT)驱动电压从而控制激光器谐振腔腔长来实现重复频率差的锁定,并利用频率计数器采集锁定后双光梳重复频率差的数据,使用Allan方差和标准差作为频率稳定度的评价指标。最终在1 s的平均时间内,得到重复频率差的Allan偏差为1.8×10−13,抖动标准差为40.689 μHz。结果表明,该技术可以对双光梳系统的重复频率差进行灵活调整,并具有锁定精度高、抗扰能力强等优点。Abstract: The dual-comb system has its unique advantages and broad development prospects in the fields of high precision absolute distance measurement, 3-D imaging and spectral measurement. In this paper, an asynchronous locking technique based on phase-locked loop principle was proposed, which can precisely lock the repetition rate difference in dual-comb system. In the experiment, a dual-comb system with a repetition rate of about 155.711 MHz and 155.714 MHz was adopted. By controlling the driving voltage of PZTs through feedback, the length of the laser resonator was controlled to achieve the locking of the repetition rate difference, and the frequency counter was used to collect the data of the repetition rate difference after locking. Allan deviation and standard deviation were used as evaluation indexes of frequency stability. Finally, within the average time of 1 s, the Allan deviation of repetition rate difference was 1.8×10−13, and the jittering standard deviation was 40.689 μHz. The results show that this technology can adjust the repetition rate difference flexibly, and has the advantages of high locking accuracy and strong disturbance rejection.
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