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为了测试微腔的谐振峰特性,搭建了微腔耦合的测试系统,如图3(a)所示。系统使用可调谐连续波激光器(CTL1550_Toptica)作为光源,经过锥腰直径约为3 μm的锥形光纤波导实现SiO2微腔的耦合。通过扫描激光频率,可以在示波器(OSC)中观察微腔的透射信号,并研判谐振峰的特性。当激光频率调谐速度为2.5 GHz/s,测得的微腔透射谱如图3(b)所示,由测得的结果可知,其FSR为17.8 GHz。采用洛伦兹线形对各个谐振峰进行拟合,结果显示微腔中最佳的Q值约为3.87×108,如图3(c)所示;当激光调谐速度为350 GHz/s,实验中观察到谐振峰出现了振荡衰退(Ring down)现象,如图3(d)所示。理论上[37],一个谐振模式内腔场的时间演化可以描述为一个简单的谐振模型,即:
图 3 SiO2微腔谐振峰测试。(a) 微腔耦合测试示意图;(b) 微腔功率透射谱;(c) 洛伦兹拟合谱线;(d) Ringdown拟合
Figure 3. Measurement of resonant peak of SiO2 microcavity. (a) Schematic diagram of microcavity coupling test; (b) Power transmission spectrum of microcavity; (c) Lorentz fitting spectral line; (d) Ringdown fitting
$$ \frac{\partial A}{\partial t}=\mathrm{i}{\omega }_{0}A-\frac{k}{2}A+\sqrt{{k}_{ex}}\cdot {s}_{in} $$ (1) 式中:
$ {\omega }_{0} $ 为谐振角频率;$ k $ 为系统总损耗率,包括固有损耗率$ {k}_{0} $ 和耦合损耗率$ {k}_{ex} $ ,即$ k={k}_{0}+{k}_{ex} $ ;$ {s}_{in} $ 为外部源,在频率可调的连续波模式下,其变化${s}_{in}={s}_{0}{\rm exp}\left(i\phi \left(t\right)\right)$ 。在稳态形式下,即相对于其初始值$ {\omega }_{i} $ 的激光频率调谐与腔内光子寿命相比缓慢变化,笔者得到$ \phi \left(t\right)={\omega }_{i}t $ ,公式(1)的解给出了作为激光失谐$ {\delta }_{\omega }={\omega }_{i}-{\omega }_{0} $ 函数的标准洛伦兹分布。相反,在激光频率调谐与光子寿命相当的条件下,得到$ \phi \left(t\right)=\left({\omega }_{i}+\dfrac{{V}_{s}t}{2}\right)t $ ,其中,$ {V}_{s} $ 为激光频率的调谐速度。因此,设$A=a\cdot {\rm exp}\left(i\phi \left(t\right)\right)$ ,公式(1)可以变换为:$$ \frac{\partial a}{\partial t}=i\left({\delta }_{\omega }-{V}_{s}t\right)a-\frac{k}{2}a+\sqrt{{k}_{ex}}\cdot {s}_{0} $$ (2) 对上式积分可得:
$$ a=\sqrt{{k}_{ex}}\cdot {s}_{0}\cdot \mathrm{exp}\left(\mathrm{i}{\delta }_{\omega }t-\dfrac{k}{2}t\right) \times \left[f\left(t\right)-\dfrac{1}{i{\delta }_{\omega }-\dfrac{k}{2}}\right] $$ (3) 其中,
$$ \begin{split} {f\left(t\right)}=&{-\sqrt{\dfrac{i\pi }{2{V}_{s}}}\mathrm{e}\mathrm{x}\mathrm{p}\left(i\dfrac{{\left(i{\delta }_{\omega }-\raisebox{1ex}{$k$} \left/ \raisebox{-1ex}{$2$}\right.\right)}^{2}}{2{V}_{s}}\right) \times \left[{\rm erf}\left(-i\dfrac{i({\delta }_{\omega }-{V}_{s}t)-\raisebox{1ex}{$k$} \left/ \raisebox{-1ex}{$2$}\right.}{\sqrt{2i{V}_{s}}}\right)-\right.}\\ &{ \left. {\rm erf}\left(-i\dfrac{i({\delta }_{\omega }-\raisebox{1ex}{$k$} \left/ \raisebox{-1ex}{$2$}\right.}{\sqrt{2i{V}_{s}}}\right)\right]} \end{split} $$ 式中:erf(z)为复误差函数。腔透射率可以计算为:
$$ T={\left|\frac{{s}_{0}-\sqrt{{k}_{ex}}\cdot a}{{s}_{0}}\right|}^{2} $$ (4) 注意,使用公式(4)进行拟合将确定地返回耦合率kex作为整体损耗率k的一部分,从而可以区分腔体的耦合状态(过度耦合或欠耦合)。
通过对实验观察到的Ringdown曲线进行拟合,结果显示谐振峰对应的固有品质因子为:
${Q}_{0}= {{\omega }_{0}}/{k}_{0}=7.32\times {10}^{8}$ ,耦合品质因子为$ {Q}_{e}=9.86\times {10}^{8} $ 。以及总体的品质因子Q值为:$ {1}/{{Q}_{0}}+{1}/{{Q}_{e}}=4.2\times {10}^{8} $ ,该结果与低速频率调谐下洛伦兹拟合的谐振峰Q值相似。因此,笔者验证了Q值超过108的SiO2回音壁模式微腔。 -
为了研究微腔的耦合特性,笔者通过实验测得微腔的耦合理想曲线(Ideality)。首先,通过调整光纤锥和微腔的耦合状态,找到一个耦合效率较高的位置,此时,再将光纤锥移至远离微腔的位置处;然后,将光纤锥从远处慢慢靠近微腔,在这个过程中采集同一模式下的谐振峰的数据,利用洛伦兹曲线对采集的谐振峰数据进行拟合,得到了不同耦合状态下的谐振峰数据。最后,通过拟合得到微腔谐振峰深度和线宽Ideality曲线,如图4所示。
需要说明的是,本征损耗主要由材料吸收损耗、辐射损耗和散射损耗所决定,而耦合损耗主 要与微腔和光纤锥的耦合距离有关。由结果可知,当光纤锥从远处慢慢靠近微腔直到刚出现谐振峰时,此时,耦合损耗小于本征损耗,系统处于欠耦合状态;当光纤锥逐步靠近微腔直到谐振峰深度达到最深时,此时,耦合损耗等于本征损耗,系统处于临界耦合;当光纤锥再贴近微腔直到谐振峰深度变浅时,此时,耦合损耗大于本征损耗,系统处于过耦合。 实验中测的谐振峰深度与线宽的变化,基本符合标准的Ideality曲线,证明在微腔耦合过程中,没有额外的能量损耗。
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由于制备SiO2微腔材料的水羟基的存在,使其具有较强的亲水性,这也导致了SiO2微腔放置一段时间后其Q值会有所下降。为了测试其Q值随时间的变化关系,每隔一段时间对微腔的Q值进行测试,其结果如图5所示。由结果可知,微腔Q值随着时间不断降低,经过一段时间后,其Q值的变化趋于平稳,主要原因可能是由于SiO2微腔表面的水羟基饱和,导致其Q值最终变化不大。
为了能实现对制备的SiO2微腔重复使用,一是要对制备的SiO2微腔进行隔绝空气保存,二是对Q值退化的微腔进行退火处理来使微腔表面的水汽蒸发,来实现Q值的回升。处理方案主要有两种,一是利用CO2激光器对微腔进行重新熔融处理,但基于目前的微腔制备系统,无法重新找到微腔的精确位置,因此,笔者选择了另外一种方式,即利用马弗炉对已经放置一段时间的SiO2微腔进行退火处理,来验证此方法的可行性。为了比较退火前后的Q值的变化,以及Q值的恢复程度,先对刚制备的微腔的部分谐振峰Q值进行了测试,其中,Depth为0时表示此时系统处于临界耦合。一段时间后,再次对退火前后同级深度的谐振峰Q值进行了测试,其中,退火温度设置为950 ℃,退火时间设置为6 h,其结果如表1所示。由表可知,其Q值较未退火前有所提升,但未能恢复到刚制备好时的水平。由于笔者对微腔退火的研究还处于探索阶段,并没有找到最佳的退火温度和退火时间。并且在退火过程中,马弗炉内的微尘可能吸附到微腔表面,也会导致Q值恢复不明显。因此,可以通过探索最佳的退火温度和退火时间以及优化微腔退火的夹具来实现Q值的高效恢复。
表 1 退火前后微腔Q值变化
Table 1. Change of Q value of microcavity before and after annealing
Depth 0.6 0.5 0.4 0.3 0.2 0.1 0 Initial Q value - 3.23×108 - 2.14×108 1.43×108 - - Before annealing 1.78×108 1.66×108 8.57×107 6.9×107 6.1×107 5.7×107 5.96×107 After annealing 3.11×108 2.12×108 1.59×108 1.3×108 7.9×107 7.1×107 7.57×107
Fabrication and optical frequency comb generation in high-quality factor silicon oxide microcavity (Invited)
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摘要: 基于超高品质因子(Q值)和非线性光学微腔产生的光学频率梳(微腔光频梳)在大容量光通信、光学数据中心、光子神经形态运算以及大规模并行激光雷达等方面有着重要的应用。回音壁模式(WGM)微腔是研究微腔光频梳技术的一个重要平台,具有创纪录的超高Q值和超高精细度(Finesse),能够实现超窄线宽激光、窄线宽光学频率梳,合成超低噪声的光子微波;同时也是研究腔内孤子动力学的重要平台,对掌握孤子态的光学频率梳特性起到了重要的支撑作用。利用二氧化碳(CO2)激光器熔融氧化硅(SiO2)石英棒制备了高Q值的WGM微腔。其自由光谱范围(FSR)在10 GHz以上,Q值达到了108。对腔的谐振和耦合理想特性进行了表征,并在开放环境下观察到微腔受潮引起的Q值退化现象,通过二次退火实现了Q值的回升。在SiO2微腔中验证了基于非线性克尔(Kerr)效应的光学频率梳产生,其主要状态为调整不稳定性主导的低相干频率梳。同时,实验中也观察到了对应于全相干耗散孤子态频率梳的“阶跃”信号,表明目前制备的SiO2微腔具备实现低噪声孤子光频梳的能力,并具有微腔光频梳的应用潜力。
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关键词:
- 光学频率梳 /
- 回音壁模式微腔 /
- 激光熔融二氧化硅微腔
Abstract: Based on ultra-high quality factor(Q) and nonlinear optical microcavities, optical microcombs(microcavity optical frequency comb) have enabled a variety of important applications including high volume optical communications, optical data center, photonic neuromorphic computation and massive parallel LIDAR. Whispering gallery mode (WGM) microcavities stand for an important platform for studying the microcavity optical frequency comb technology, particularly having record ultra-high Q factors as well as the ultra-high finesse. It can realize ultra-narrow linewidth lasers and optical frequency combs, and photonic microwaves for synthesizing ultra-low noise. Here we developed high Q WGM microcavities from a silica (SiO2) rod fused and shaped with the CO2 laser. The quality factor is above 108 with a free spectrum range at the level of 10 GHz. The cavity resonances as well as the coupling ideality have been characterized, where a degradation of Q factors in a humid environment was observed and recovered with a second annealing process. Moreover, Kerr comb generation was demonstrated in such SiO2 microcavities, which at the moment is mostly in a noisy state governed by the modulation instability regime. Yet the footprint of the cavity soliton state was experimentally observed as a “soliton step” signal. The results indicate that a low-noise and fully coherent soliton microcomb is potentially accessible in home developed SiO2 microcavities, and is readily for comb-related applications. -
图 6 光频梳产生。(a) 高泵浦功率下微腔的透射谱线;(b) 图(a)的部分放大的透射谱线;(c)~(e) 光频梳的演化过程,分别对应于图(a)中微腔透射谱线的三个不同的位置
Figure 6. Optical frequency comb generation. (a) Transmission lines of microcavity at high pump power;(b) Partially amplified transmission line of Fig.(a); (c)-(e) Evolution process of optical frequency comb corresponds to three different positions of microcavity transmission line in Fig.(a)
图 7 LLE仿真得到的光频梳演化过程。(a) I、II、III、IV图为光频梳的演化过程;(b) 分别对应图(a)中不同梳齿状态下的时域谱
Figure 7. Simulated optical frequency comb evolution based on LLE. (a) Figures I, II,III and IV show the evolution process of optical frequency comb; (b) Corresponding to the time-domain spectra in different comb states in Fig.(a)
表 1 退火前后微腔Q值变化
Table 1. Change of Q value of microcavity before and after annealing
Depth 0.6 0.5 0.4 0.3 0.2 0.1 0 Initial Q value - 3.23×108 - 2.14×108 1.43×108 - - Before annealing 1.78×108 1.66×108 8.57×107 6.9×107 6.1×107 5.7×107 5.96×107 After annealing 3.11×108 2.12×108 1.59×108 1.3×108 7.9×107 7.1×107 7.57×107 -
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