-
电光梳产生的基本原理是材料中的电光效应。电光效应是指材料的折射率随材料两端外加电场的变化而线性变化的光学非线性现象,同时又被称为Pockels效应[54]。接下来,探讨如何利用电光效应使得载波两端产生新的边带。考虑一个折射率为n1的无损耗理想晶体,其材料折射率随外加电场的变化而线性变化。假设一束频率为fc,振幅为E1的连续激光在该晶体直波导中传播,直波导长度为L1,上下两端嵌有长度为L2的金属电极以施加电场,电场具有振幅V1与频率fm,如图3(a)所示。当电场V1为零,激光经过该波导时,输出电场为
${E_0}(t) = {E_1}{{\rm e}^{j2\pi {f_c}t}}$ 。当振幅V1不为零时,此时波导折射率发生变化为:$n = {n_1} + \alpha {V_1}\sin ({f_m}t)$ ,$\alpha $ 为折射率随电场变化的线性系数,此时输出光场可表示为:图 3 电光调制器件示意图。(a) 单相位调制器;(b) 双驱动马赫-曾德尔调制器
Figure 3. Schematic of electro-optic modulators.(a) Single-phase modulator;(b) Dual-drive Mach-Zehnder modulator
$$ {E_0}(t) = {E_1}{{\rm e}^{j2\pi {f_c}t}}{{\rm e}^{j\phi (t)}} $$ (1) 其中:
$$ \phi (t) = \frac{{\pi V(t)}}{{{V_\pi }}} = \frac{{\pi {V_1}}}{{{V_\pi }}}\sin (2\pi {f_m}t) $$ (2) Vπ为使得输出激光刚好发生π相移时对应的电压,也被称为半波电压。利用Jacob-Anger展开公式[55]对输出光场进行快速傅里叶变换,可得到光场在频域对应的函数:
$$ {E_1}(f) = {E_i}\sum\limits_{n = - \infty }^\infty {{J_n}\left(\frac{\pi }{{{V_\pi }}}{V_1}\right)} \delta (f - n{f_m} - {f_c}) _{ } $$ (3) 式中:Jn为第一类贝塞尔函数;δ(f-nfm-fc)为狄拉克函数,代表频谱中的频率分量。可以看到,经过电光调制后的光载波在fc两端产生了新的频率分量,图4(a)展示了单相位调制器产生的频谱。
图 4 (a) 单相位调制器频谱;(b) DD-MZM调制器频谱
Figure 4. (a) Frequency spectrum of a single-phase modulator;(b) Frequency spectrum of a DD-MZM
此外,当合理设置输入光偏振方向与晶体折射率轴的相对位置,再配合偏振控制器便可以对输入光的强度、偏振方向进行调制。波导两端通常会被施加偏置电压,用来选择调制器的工作位置与调制范围,并补偿调制器的漂移以保持性能稳定。
考虑单个双驱动马赫-曾德尔调制器(Dual drive Mach-Zehnder modulator, DD-MZM)产生电光梳的情况,如图3(b)所示。此时调制器末端的输出光场可以表示为:
$$ \begin{gathered} {E_0}(t) = \frac{{{E_1}}}{2}{{\rm e}^{j2\pi {f_c}t}}[{{\rm e}^{j{\phi _1}(t)}} + {{\rm e}^{j{\phi _2}(t)}}] = \hfill \\ \frac{{{E_1}}}{2}{{\rm e}^{j2\pi {f_c}t}}\left[{{\rm e}^{j\frac{{\pi ({V_1}\sin (2\pi {f_m}t) + {V_{b,1}})}}{{{V_\pi }}}}} + {{\rm e}^{j\frac{{\pi ({V_2}\sin (2\pi {f_m}t) + {V_{b,2}})}}{{{V_\pi }}}}}\right] \hfill \\ \end{gathered} $$ (4) 式中:
${\phi _1}(t)$ 与${\phi _2}(t)$ 分别为两臂上的光场所经历的相位改变,与公式(2)具有同样的表达形式,但对应调制信号的电压发生了改变,且考虑了偏置电压。公式(4)同样可以通过傅里叶变换得到频域表达式[55]:$$ \begin{split} \\ {E_0}(f) =& \pi {E_i}\sum\limits_{n = - \infty }^\infty {\left[{J_n}(\frac{\pi }{{{V_\pi }}}{V_1}){{\rm e}^{j\frac{{\pi {V_{b,1}}}}{{{V_\pi }}}}} +{J_n}(\frac{\pi }{{{V_\pi }}}{V_2}){{\rm e}^{j\frac{{\pi {V_{b,2}}}}{{{V_\pi }}}}}\right] }\cdot\\ & \delta (f - n{f_m} - {f_c}) \hfill \\ \end{split} $$ (5) 上式对应的频谱如图4(b)所示。可以看到,此时产生的边带数目由于DD-MZM的调制方式并未改变,但是产生的光梳形状变得更加平坦,这主要是由于引入了偏置电压,使得能够对光梳的形状进行再次调控。独立的电光调制器产生的边带相对来说较少,所以一般采用级联相位调制器及强度调制器以拓宽所产生边带的范围。输出端通常级联强度调制器以使光谱更为平坦,经过级联后产生的频率分量数目有所增加,拓宽了光谱范围。当MZM与相位调制器级联时,此时的输出光场可以表示为[56]:
$$ \begin{split} {E_0}(t) = &{E_i}{{\rm e}^{j2\pi {f_c}t}}\cos \left[\frac{\pi }{4}\alpha \sin (2\pi {f_m}t) \hfill - \frac{\pi }{2}\gamma \right]\cdot\\ & {{\rm e}^{j(\theta \frac{\pi }{4}\alpha + \frac{\pi }{2}\beta )\sin (2\pi {f_m}t) - j\theta \frac{\pi }{2}\gamma }} \hfill \\ \end{split} $$ (6) 式中:
$\alpha $ 和$\;\beta $ 分别是MZM和相位调制器上所施加的电压;$\gamma $ 对应MZM上所施加的偏置电压。传统的电光梳一般采用体块状电光晶体来实现电光调制,而在片上集成电光梳中一般使用微环谐振腔结构来产生。通过对微环腔本身进行电光调制来产生电光梳,典型装置如图5(a)所示。当光场在微环内进行传输时,微环折射率的变化导致了光波相位的变化,从而可对载波实现相位调制,使得载波两端产生新的边带,该过程在微环内循环往复,最终产生光频梳。由于微环腔所具备的高Q值使得微腔中的电光效应得到显著增强,产生的光频梳具有优异性能。此外,对微环与总线波导之间的耦合强度进行调制[57-58],同样可以在微环内产生光梳,不过该法相对复杂,实际应用时使用较少,典型装置如图5(b)所示。
Progress in integrated electro-optic frequency combs (Invited)
-
摘要: 光学频率梳是由一系列离散且等间隔分布的频率成分所组成的光谱结构,作为光谱分析的天然刻度尺,其已广泛应用于光谱学、精密测量、光通信、传感等多个领域。光学频率梳根据其产生技术可分为基于锁模激光器的光学频率梳、克尔微腔光学频率梳、电光频率梳。电光频率梳由于其频率间隔可调、梳齿功率较高、可实现微波到光波的转换等优势,得到了充分发展。但传统电光频率梳的产生器件存在体积大、功耗高的缺点,限制了其进一步应用。随着微纳加工技术的不断发展,越来越多的材料应用于片上集成光学器件,包括硅、氮化硅、氮化铝、磷化铟、铌酸锂、砷化铝镓等。集成电光频率梳器件具有体积小、功耗低等优势,是构建光电集成芯片的重要器件。文中旨在对集成电光频率梳的研究现状进行综述,首先介绍光学频率梳的类型,并详细论述电光频率梳的产生机制;其次介绍产生集成电光频率梳的材料平台、相应的光梳性能指标及其应用;最后基于目前集成电光频率梳领域存在的问题,对未来的研究趋势做出展望。Abstract: Optical frequency comb (OFC) is the spectrum structure composed of a set of discrete and equally spaced frequency components, which has been widely used in many areas such as spectroscopy, precision measurement, optical communication and sensing as the natural scale for spectral analysis. According to its generation methods, OFC can be generated in three ways, including mode-locked laser based OFC, Kerr microresonator OFC and electro-optic frequency comb (EOFC). EOFC has been greatly developed because of its advantages including remarkable tunability of frequency spacing, high comb line power, as well as the accessible conversion from microwave to optical wave. However, there are some drawbacks in conventional EOFC generator, for instance, the bulk size and required high power, which limit its further development. As the micro/nanofabrication technology gradually grows, more and more materials are applied into integrated chip-scale optical devices, including Si, Silicon Nitride, Aluminum Nitride, Indium Phosphide, Lithium Niobate and Aluminium Gallium Arsenide. Integrated EOFC possesses the excellent characteristics, such as small volume and low power consumption, which is an important device for optoelectronic integrated chip. The research status of the integrated EOFC is reviewed in this paper. First, the classification of optical frequency comb, as well as detailed content about generation mechanism of EOFC are introduced. Next, the information comprising various material platforms, corresponding devices performance metrics and applications about EOFC is presented. Finally, the future research directions are prospected in view of the existing problems of integrated EOFC.
-
Key words:
- optical frequency comb /
- electro-optic modulation /
- integrated optics
-
图 7 基于LNOI的集成电光梳产生器件及其输出光谱[67]。(a) 铌酸锂跑道型微环谐振腔的光学显微照片;(b) 微环谐振腔电光梳的测量输出光谱,带宽超过80 nm且包含超过900根斜率为1 dB·nm−1的梳齿
Figure 7. Integrated EO comb generator and its output spectrum based on LNOI[67]. (a) Optical micrograph of a fabricated lithium niobate microring resonator; (b) Measured output spectrum of the EO comb generated from the microring resonator, demonstrating a bandwidth exceeding 80 nm and more than 900 comb lines with a slope of 1 dB·nm−1
图 8 基于LNOI的中红外频率梳产生器件及其输出光谱[69]。(a) 方案一,差频过程在微环谐振腔外进行;(b) 方案一中调制系数β为1.2π时输出中红外频率梳的功率谱;(c) 方案二,差频过程在微环谐振腔内进行;(d) 方案二中调制系数β为0.4π时的输出中红外频率梳的功率谱
Figure 8. Schematic of mid-infrared frequency combs generator based on LNOI and their corresponding spectrums[69]. (a) Design 1, the DFG process occurs outside the microring resonator; (b) Power spectrum of the output mid-infrared frequency comb for modulation coefficient β=1.2π in design 1; (c) Design 2, the DFG process occurs in the microring resonator; (d) Power spectrum of the output mid-infrared frequency comb for modulation coefficient β=0.4π in design 2
图 9 InP集成电光梳产生器件[48]。(a) 器件结构示意图;(b) 所制作的光梳产生器的光学显微照片 (面积:4.5 mm×2.5 mm);(c) 集成光子芯片-印刷电路板的封装
Figure 9. Schematic of an InP integrated EO comb generator[48]. (a) Integrated comb generator PIC schematic; (b) Optical micrograph of the fabricated PIC (Photonic integrated chip, PIC) (Footprint: 4.5 mm× 2.5 mm); (c) PIC-PCB assembly
图 10 MRM集成电光梳产生器件[99]。(a) MRM的光学显微照片 (MRM及电极面积:0.062 mm2);(b) 波导横截面示意图;(c) 0.22 V前向偏置电压驱动下产生的10 GHz间隔电光梳
Figure 10. Schematic of MRM integrated EO comb[99]. (a) Optical micrograph of a microring resonator modulator (Footprint of the MRM and electrical pads: 0.062 mm2); (b) Schematic of waveguide cross section; (c) Generated EO frequency comb at 10 GHz line spacing for a 0.22 V forward bias voltage applied
图 11 级联MRM集成电光梳产生器件示意图[100]。(a) 提出的MRM的结构示意图;(b) 微环PN结的横截面示意图;(c) 测试装置;(d) MRM1与MRM2的驱动频率分别为20 GHz与10 GHz时的光梳光谱,包含5根梳齿
Figure 11. Schematic of cascaded MRM integrated EO comb[100]. (a) Schematic of the proposed MRM; (b) Cross-section schematic of the PN junction of the microring; (c) Experimental setup; (d) Comb spectrum demonstrating 5 lines when driving MRM 1 at 20 GHz and MRM 2 at 10 GHz
图 12 基于级联MZM的集成电光梳产生器件示意图[53]。(a) 级联MZM光梳产生方案示意图,插图为MZM主动臂的横截面示意图;(b) 包含9根梳齿的输出光谱;(c) 实验所得时域Nyquist脉冲;(d) 所测单Nyquist脉冲(红色实线)与理论计算脉冲(黑色虚线)的对比结果
Figure 12. Schematic of cascaded MZM integrated EO comb generator[53]. (a) Schematic of the cascaded MZMs optical frequency comb generation, the inset shows the cross-sectional view of active arms in the MZM; (b) Measured optical spectrum of the 9-line OFC; (c) Measured Nyquist pulses in the time domain; (d) Comparison of the measured single Nyquist pulse (red solid line) with the calculated theoretical pulse (black dashed line)
图 13 用于WDM的电光频率梳示意图[111]。(a) 双驱MZM设计示意图;(b) MZM相位调制器的横截面示意图;(c) 包含5条间隔为20 GHz梳齿的输出光谱;(d) 5 × 16 Gbaud 16/32 QAM and 5 × 20 Gbaud 16 QAM Nyquist-WDM信号对应的误码率
Figure 13. Schematic of EOFC for WDM[111]. (a) Illustration of the dual-drive MZM design; (b) Cross section schematic of MZM phase shifter; (c) Output spectrum of generated 5-line comb with 20 GHz spacing; (d) BER of Nyquist-WDM signals of 5×16 Gbaud 16/32 QAM and 5 × 20 Gbaud 16 QAM
图 14 用于WDM的MRM [96]。(a) 基于级联MRM的硅基灵活栅格WDM光电发射模块;(b) 用于光梳产生、数据传输及表征的实验装置图;(c) 频率间隔为20 GHz的光梳经数据传输后的光谱,其分别对应信道1 (1554 nm),信道2 (1554.16 nm)与信道3 (1553.84 nm)
Figure 14. Schematic of MRM for WDM[96]. (a) Schematic of a flexible-grid WDM silicon photonic transmitter based on cascaded MRMs; (b) Experimental setup for optical comb generation, data transmission, and characterization; (c) Spectrum after data transmission when MRM1 is aligned at 20 GHz comb line with channel 1 (1554 nm), channel 2 (1554.16 nm), and channel 3 (1553.84 nm)
图 15 用于DCS的LNOI电光频率梳[116]。(a) 用于DCS的集成电光MRM (AOFS:声光移频器,BS:分束器,BD:平衡探测器,DAU:数据获取单元);(b) 195 s内测量所得双光梳光谱;(c) 测量所得乙炔吸收光谱
Figure 15. Schematic of EOFC based on LNOI for DCS[116]. (a) Scheme of DCS with integrated EO microrings (AOFS: acousto-optic frequency shifter, BS: beam splitter, BD: balanced detector, DAU: data acquisition Unit); (b) Measured dual comb spectrum with a measurement time of 195 s; (c) Measured absorption spectra of the acetylene
图 16 用于DCS的LNOI电光频率梳示意图[98]。(a) 4 mm长的硅基单驱推挽MZM俯视图;(b) 射频信号与射频频率间隔为1 GHz与4 MHz时的拍频信号;(c) 实验所得光带通滤波器转换函数
Figure 16. Schematic of EOFC based on MZM for DCS[98]. (a) Top-view schematic of the 4-mm long Si single-drive push-pull MZM; (b) Beat notes for fRF= 1 GHz and ΔfRF = 4 MHz; (c) Experimentally measured transfer function of optical bandpass filter
-
[1] Kippenberg T J, Gaeta A L, Lipson M, et al. Dissipative Kerr solitons in optical microresonators [J]. Science, 2018, 361(6402): eaan8083. doi: 10.1126/science.aan8083 [2] Gaeta A L, Lipson M, Kippenberg T J. Photonic-chip-based frequency combs [J]. Nature Photonics, 2019, 13(3): 158-169. doi: 10.1038/s41566-019-0358-x [3] Guo H, Karpov M, Lucas E, et al. Universal dynamics and deterministic switching of dissipative Kerr solitons in optical microresonators [J]. Nature Physics, 2017, 13(1): 94-102. doi: 10.1038/nphys3893 [4] Kippenberg T J, Holzwarth R, Diddams S A. Microresonator-based optical frequency combs [J]. Science, 2011, 332(6029): 555-559. doi: 10.1126/science.1193968 [5] Hargrove L E, Fork R L, Pollack M A. Locking of He-Ne laser modes induced by synchronous intracavity modulation [J]. Applied Physics Letters, 1964, 5: 4. doi: 10.1063/1.1754025 [6] Hall J L. Nobel lecture: Defining and measuring optical frequencies [J]. Reviews of Modern Physics, 2006, 78(4): 1279-1295. doi: 10.1103/RevModPhys.78.1279 [7] Hänsch T W. Nobel lecture: Passion for precision [J]. Reviews of Modern Physics, 2006, 78(4): 1297-1309. doi: 10.1103/RevModPhys.78.1297 [8] Diddams S A. The evolving optical frequency comb [invited] [J]. Journal of the Optical Society of America B, 2010, 27(11): B51-B62. doi: 10.1364/JOSAB.27.000B51 [9] Diddams S A, Vahala K, Udem T. Optical frequency combs: Coherently uniting the electromagnetic spectrum [J]. Science, 2020, 369(6501): eaay3676. doi: 10.1126/science.aay3676 [10] Del’Haye P, Schliesser A, Arcizet O, et al. Optical frequency comb generation from a monolithic microresonator [J]. Nature, 2007, 450(7173): 1214-1217. doi: 10.1038/nature06401 [11] Picqué N, Hänsch T W. Frequency comb spectroscopy [J]. Nature Photonics, 2019, 13(3): 146-157. doi: 10.1038/s41566-018-0347-5 [12] Ycas G, Giorgetta F R, Baumann E, et al. High-coherence mid-infrared dual-comb spectroscopy spanning 2.6 to 5.2 μm [J]. Nature Photonics, 2018, 12(4): 202-208. doi: 10.1038/s41566-018-0114-7 [13] Coddington I, Newbury N, Swann W. Dual-comb spectroscopy [J]. Optica, 2016, 3(4): 414-426. doi: 10.1364/OPTICA.3.000414 [14] Millot G, Pitois S, Yan M, et al. Frequency-agile dual-comb spectroscopy [J]. Nature Photonics, 2016, 10(1): 27-30. doi: 10.1038/nphoton.2015.250 [15] Suh M G, Yang Q F, Yang K Y, et al. Microresonator soliton dual-comb spectroscopy [J]. Science, 2016, 354(6312): 600-603. doi: 10.1126/science.aah6516 [16] Yasui T, Yokoyama S, Inaba H, et al. Terahertz frequency metrology based on frequency comb [J]. IEEE Journal of Selected Topics in Quantum Electronics, 2011, 17(1): 191-201. doi: 10.1109/JSTQE.2010.2047099 [17] Ye J, Schnatz H, Hollberg L W. Optical frequency combs: From frequency metrology to optical phase control [J]. IEEE Journal of Selected Topics in Quantum Electronics, 2003, 9(4): 1041-1058. doi: 10.1109/JSTQE.2003.819109 [18] Yoshii K, Nomura J, Taguchi K, et al. Optical frequency metrology study on nonlinear processes in a waveguide device for ultrabroadband comb generation [J]. Physical Review Applied, 2019, 11(5): 054031. doi: 10.1103/PhysRevApplied.11.054031 [19] Suh M G, Vahala K J. Soliton microcomb range measurement [J]. Science, 2018, 359(6378): 884-887. doi: 10.1126/science.aao1968 [20] Trocha P, Karpov M, Ganin D, et al. Ultrafast optical ranging using microresonator soliton frequency combs [J]. Science, 2018, 359(6378): 887-891. doi: 10.1126/science.aao3924 [21] Marin-Palomo P, Kemal J N, Karpov M, et al. Microresonator-based solitons for massively parallel coherent optical communications [J]. Nature, 2017, 546(7657): 274-279. doi: 10.1038/nature22387 [22] Corcoran B, Tan M X, Xu X Y, et al. Ultra-dense optical data transmission over standard fibre with a single chip source [J]. Nature Communications, 2020, 11(1): 7. doi: 10.1038/s41467-019-13787-x [23] Hu H, Oxenlowe L K. Chip-based optical frequency combs for high-capacity optical communications [J]. Nanophotonics, 2021, 10(5): 1367-1385. doi: 10.1515/nanoph-2020-0561 [24] Liu J Q, Lucas E, Raja A S, et al. Photonic microwave generation in the X- and K-band using integrated soliton microcombs [J]. Nature Photonics, 2020, 14(8): 486-491. doi: 10.1038/s41566-020-0617-x [25] Rieker G B, Giorgetta F R, Swann W C, et al. Frequency-comb-based remote sensing of greenhouse gases over kilometer air paths [J]. Optica, 2014, 1(5): 290-298. doi: 10.1364/OPTICA.1.000290 [26] Zhao S X, Liu Q W, He Z Y. Multi-tone Pound-Drever-Hall technique for high-resolution multiplexed Fabry-Perot resonator sensors [J]. Journal of Lightwave Technology, 2020, 38(22): 6379-6384. doi: 10.1109/JLT.2020.3011575 [27] Muraviev A V, Smolski V O, Loparo Z E, et al. Massively parallel sensing of trace molecules and their isotopologues with broadband subharmonic mid-infrared frequency combs [J]. Nature Photonics, 2018, 12(4): 209-214. doi: 10.1038/s41566-018-0135-2 [28] Fortier T, Baumann E. 20 years of developments in optical frequency comb technology and applications [J]. Communications Physics, 2019, 2(1): 153. doi: 10.1038/s42005-019-0249-y [29] Kues M, Reimer C, Lukens J M, et al. Quantum optical microcombs [J]. Nature Photonics, 2019, 13(3): 170-179. doi: 10.1038/s41566-019-0363-0 [30] Kim J, Song Y J. Ultralow-noise mode-locked fiber lasers and frequency combs: Principles, status, and applications [J]. Advances in Optics and Photonics, 2016, 8(3): 465-540. doi: 10.1364/AOP.8.000465 [31] Herr T, Brasch V, Jost J D, et al. Temporal solitons in optical microresonators [J]. Nature Photonics, 2013, 8(2): 145-152. [32] Brasch V, Geiselmann M, Herr T, et al. Photonic chip-based optical frequency comb using soliton Cherenkov radiation [J]. Science, 2016, 351(6271): 357-360. doi: 10.1126/science.aad4811 [33] Stern B, Ji X C, Okawachi Y, et al. Battery-operated integrated frequency comb generator [J]. Nature, 2018, 562(7727): 401-405. doi: 10.1038/s41586-018-0598-9 [34] Cole D C, Lamb E S, Del'Haye P, et al. Soliton crystals in Kerr resonators [J]. Nature Photonics, 2017, 11(10): 671-676. doi: 10.1038/s41566-017-0009-z [35] Sich M, Krizhanovskii D N, Skolnick M S, et al. Observation of bright polariton solitons in a semiconductor microcavity [J]. Nature Photonics, 2012, 6(1): 50-55. doi: 10.1038/nphoton.2011.267 [36] Xue X X, Xuan Y, Liu Y, et al. Mode-locked dark pulse Kerr combs in normal-dispersion microresonators [J]. Nature Photonics, 2015, 9(9): 594-600. doi: 10.1038/nphoton.2015.137 [37] Herr T, Hartinger K, Riemensberger J, et al. Universal formation dynamics and noise of Kerr-frequency combs in microresonators [J]. Nature Photonics, 2012, 6(7): 480-487. doi: 10.1038/nphoton.2012.127 [38] Godey C, Balakireva I V, Coillet A, et al. Stability analysis of the spatiotemporal lugiato-lefever model for Kerr optical frequency combs in the anomalous and normal dispersion regimes [J]. Physical Review A, 2014, 89(6): 063814. doi: 10.1103/PhysRevA.89.063814 [39] Wang W, Wang L, Zhang W. Advances in soliton microcomb generation [J]. Advanced Photonics, 2020, 2(3): 034001. [40] Herr T, Brasch V, Jost J D, et al. Temporal solitons in optical microresonators [J]. Nature Photonics, 2014, 8(2): 145-152. doi: 10.1038/nphoton.2013.343 [41] Lundberg L, Karlsson M, Lorences-Riesgo A, et al. Frequency comb-based WDM transmission systems enabling joint signal processing [J]. Applied Sciences, 2018, 8(5): 718. doi: 10.3390/app8050718 [42] Rueda A, Sedlmeir F, Kumari M, et al. Resonant electro-optic frequency comb [J]. Nature, 2019, 568(7752): 378-381. doi: 10.1038/s41586-019-1110-x [43] Chang L, Liu S, Bowers J E. Integrated optical frequency comb technologies [J]. Nature Photonics, 2022, 16(2): 95-108. doi: 10.1038/s41566-021-00945-1 [44] Buscaino B, Zhang M, Loncar M, et al. Design of efficient resonator-enhanced electro-optic frequency comb generators [J]. Journal of Lightwave Technology, 2020, 38(6): 1400-1413. doi: 10.1109/JLT.2020.2973884 [45] Wang C, Zhang M, Chen X, et al. Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages [J]. Nature, 2018, 562(7725): 101-104. doi: 10.1038/s41586-018-0551-y [46] Xu M Y, He M B, Zhu Y T, et al. Flat optical frequency comb generator based on integrated lithium niobate modulators [J]. Journal of Lightwave Technology, 2022, 40(2): 339-345. doi: 10.1109/JLT.2021.3100254 [47] Ren T H, Zhang M, Wang C, et al. An integrated low-voltage broadband lithium niobate phase modulator [J]. IEEE Photonics Technology Letters, 2019, 31(11): 889-892. doi: 10.1109/LPT.2019.2911876 [48] Andriolli N, Cassese T, Chiesa M, et al. Photonic integrated fully tunable comb generator cascading optical modulators [J]. Journal of Lightwave Technology, 2018, 36(23): 5685-5689. doi: 10.1109/JLT.2018.2877020 [49] Slavik R, Farwell S G, Wale M J, et al. Compact optical comb generator using InP tunable laser and push-pull modulator [J]. IEEE Photonics Technology Letters, 2015, 27(2): 217-220. doi: 10.1109/LPT.2014.2365259 [50] Yokota N, Yasaka H. Operation strategy of InP Mach-Zehnder modulators for flat optical frequency comb generation [J]. IEEE Journal of Quantum Electronics, 2016, 52(8): 1-7. [51] Nagarjun K P, Jeyaselvan V, Selvaraja S K, et al. Generation of tunable, high repetition rate optical frequency combs using on-chip silicon modulators [J]. Opt Express, 2018, 26(8): 10744-10753. doi: 10.1364/OE.26.010744 [52] Nagarjun K P, Raj P, Jeyaselvan V, et al. Microwave power induced resonance shifting of silicon ring modulators for continuously tunable, bandwidth scaled frequency combs [J]. Opt Express, 2020, 28(9): 13032-13042. doi: 10.1364/OE.386810 [53] Liu S, Wu K, Zhou L, et al. Repetition-frequency-doubled transform-limited optical pulse generation based on silicon modulators [J]. Journal of Lightwave Technology, 2020, 38(22): 6299-6311. doi: 10.1109/JLT.2020.3010993 [54] Pockels F. Ueber den einfluss elastischer deformationen, speciell einseitigen druckes, auf das optische verhalten krystallinischer körper [J]. Annalen der Physik, 1889, 273(5): 144-172. doi: 10.1002/andp.18892730509 [55] Parriaux A, Hammani K, Millot G. Electro-optic frequency combs [J]. Advances in Optics and Photonics, 2020, 12(1): 223-287. doi: 10.1364/AOP.382052 [56] Imran M, Anandarajah P M, Kaszubowska-Anandarajah A, et al. A survey of optical carrier generation techniques for terabit capacity elastic optical networks [J]. IEEE Communications Surveys & Tutorials, 2018, 20(1): 211-263. [57] Pile B, Taylor G. Small-signal analysis of microring resonator modulators [J]. Optics Express, 2014, 22(12): 14913-14928. doi: 10.1364/OE.22.014913 [58] Sacher W D, Green W M J, Gill D M, et al. Binary phase-shift keying by coupling modulation of microrings [J]. Optics Express, 2014, 22(17): 20252-20259. doi: 10.1364/OE.22.020252 [59] Qi Y F, Li Y. Integrated lithium niobate photonics [J]. Nanophotonics, 2020, 9(6): 1287-1320. doi: 10.1515/nanoph-2020-0013 [60] Kourogi M, Nakagawa K, Ohtsu M. Wide-span optical frequency comb generator for accurate optical frequency difference measurement [J]. IEEE Journal of Quantum Electronics, 1993, 29(10): 2693-2701. doi: 10.1109/3.250392 [61] Brothers L R, Wong N C. Dispersion compensation for terahertz optical frequency comb generation [J]. Optics Letters, 1997, 22(13): 1015-1017. doi: 10.1364/OL.22.001015 [62] Bruel M. Silicon on insulator material technology [J]. Electronics Letters, 1995, 31(14): 1201-1202. doi: 10.1049/el:19950805 [63] Levy M, Osgood R M, Liu R, et al. Fabrication of single-crystal lithium niobate films by crystal ion slicing [J]. Applied Physics Letters, 1998, 73(16): 2293-2295. doi: 10.1063/1.121801 [64] Poberaj G, Hu H, Sohler W, et al. Lithium niobate on insulator (LNOI) for micro-photonic devices [J]. Laser & Photonics Reviews, 2012, 6(4): 488-503. [65] Lin J, Bo F, Cheng Y, et al. Advances in on-chip photonic devices based on lithium niobate on insulator [J]. Photonics Research, 2020, 8(12): 1910-1936. doi: 10.1364/PRJ.395305 [66] Zhu D, Shao L B, Yu M J, et al. Integrated photonics on thin-film lithium niobate [J]. Advances in Optics and Photonics, 2021, 13(2): 242-352. doi: 10.1364/AOP.411024 [67] Zhang M, Buscaino B, Wang C, et al. Broadband electro-optic frequency comb generation in a lithium niobate microring resonator [J]. Nature, 2019, 568(7752): 373-377. doi: 10.1038/s41586-019-1008-7 [68] Xu M, He M, Zhu Y, et al. Integrated thin film lithium niobate Fabry–Perot modulator [invited] [J]. Chinese Optics Letters, 2021, 19(6): 060003. doi: 10.3788/COL202119.060003 [69] He J, Li Y. Design of on-chip mid-IR frequency comb with ultra-low power pump in near-IR [J]. Opt Express, 2020, 28(21): 30771-30783. doi: 10.1364/OE.401881 [70] Zafar F, Iqbal A. Indium phosphide nanowires and their applications in optoelectronic devices [J]. Proceedings of the Royal Society a-Mathematical Physical and Engineering Sciences, 2016, 472(2187): 18. [71] Tol van der J J G M, Jiao Y, Shen L, et al. Indium phosphide integrated photonics in membranes [J]. IEEE Journal of Selected Topics in Quantum Electronics, 2018, 24(1): 1-9. [72] Wang Z, Tian B, Pantouvaki M, et al. Room-temperature InP distributed feedback laser array directly grown on silicon [J]. Nature Photonics, 2015, 9(12): 837-842. doi: 10.1038/nphoton.2015.199 [73] Shen L, Jiao Y, Yao W, et al. High-Bandwidth uni-traveling carrier waveguide photodetector on an InP-membrane-on-silicon platform [J]. Optics Express, 2016, 24(8): 8290-8301. doi: 10.1364/OE.24.008290 [74] Xue Y, Han Y, Tong Y, et al. High-performance III-V photodetectors on a monolithic InP/SOI platform [J]. Optica, 2021, 8(9): 1204-1209. doi: 10.1364/OPTICA.431357 [75] Nguyen N L K, Nguyen D P, Stameroff A N, et al. A 1-160-GHz InP distributed amplifier using 3-D interdigital capacitors [J]. IEEE Microwave and Wireless Components Letters, 2020, 30(5): 492-495. doi: 10.1109/LMWC.2020.2980280 [76] Liu T, Pagliano F, van Veldhoven R, et al. Low-voltage MEMS optical phase modulators and switches on a indium phosphide membrane on silicon [J]. Applied Physics Letters, 2019, 115(25): 251104. doi: 10.1063/1.5128212 [77] Kashi A A, Tol van der J J G M, Williams K A, et al. Electro-optic slot waveguide phase modulator on the InP membrane on silicon platform [J]. IEEE Journal of Quantum Electronics, 2021, 57(1): 1-10. [78] Betancur-Perez A, Martin-Mateos P, Dios C, et al. Design of a multipurpose photonic chip architecture for THz Dual-Comb spectrometers [J]. Sensors, 2020, 20(21): 6089. doi: 10.3390/s20216089 [79] Liu D P, Tang J, Meng Y, et al. Ultra-low Vpp and high-modulation-depth InP-based electro-optic microring modulator [J]. Journal of Semiconductors, 2021, 42(8): 082301. doi: 10.1088/1674-4926/42/8/082301 [80] Bontempi F, Andriolli N, Scotti F, et al. Comb line multiplication in an InP integrated photonic circuit based on cascaded modulators [J]. IEEE Journal of Selected Topics in Quantum Electronics, 2019, 25(6): 1-7. [81] Jalali B, Fathpour S. Silicon photonics [J]. Journal of Lightwave Technology, 2006, 24(12): 4600-4615. doi: 10.1109/JLT.2006.885782 [82] Bruel M, Aspar B, Auberton-Herve A J. Smart-cut: A new silicon on insulator material technology based on hydrogen implantation and wafer bonding [J]. Japanese Journal of Applied Physics Part 1-Regular Papers Short Notes & Review Papers, 1997, 36(3B): 1636-1641. [83] Aspar B, Moriceau H, Jalaguier E, et al. The generic nature of the smart-cut® process for thin film transfer [J]. Journal of Electronic Materials, 2001, 30(7): 834-840. doi: 10.1007/s11664-001-0067-2 [84] Thomson D, Zilkie A, Bowers J E, et al. Roadmap on silicon photonics [J]. Journal of Optics, 2016, 18(7): 073003. doi: 10.1088/2040-8978/18/7/073003 [85] Bogaerts W, Chrostowski L. Silicon photonics circuit design: Methods, tools and challenges [J]. Laser & Photonics Reviews, 2018, 12(4): 1700237. [86] Arakawa Y, Nakamura T, Urino Y, et al. Silicon photonics for next generation system integration platform [J]. IEEE Communications Magazine, 2013, 51(3): 72-77. doi: 10.1109/MCOM.2013.6476868 [87] Marchetti R, Lacava C, Carroll L, et al. Coupling strategies for silicon photonics integrated chips [invited] [J]. Photonics Research, 2019, 7(2): 201-239. doi: 10.1364/PRJ.7.000201 [88] Lin H, Luo Z, Gu T, et al. Mid-infrared integrated photonics on silicon: A perspective [J]. Nanophotonics, 2018, 7(2): 393-420. [89] Siew S Y, Li B, Gao F, et al. Review of silicon photonics technology and platform development [J]. Journal of Lightwave Technology, 2021, 39(13): 4374-4389. doi: 10.1109/JLT.2021.3066203 [90] Lee C H, Chang R K, Bloembergen N. Nonlinear electroreflectance in silicon and silver [J]. Physical Review Letters, 1967, 18(5): 167-170. doi: 10.1103/PhysRevLett.18.167 [91] Chen Z, Zhao J, Zhang Y, et al. Pockel’s effect and optical rectification in (111)-cut near-intrinsic silicon crystals [J]. Applied Physics Letters, 2008, 92(25): 251111. doi: 10.1063/1.2952462 [92] Wu X, Xu K, Zhou W, et al. Scalable ultra-wideband pulse generation based on silicon photonic integrated circuits [J]. IEEE Photonics Technology Letters, 2017, 29(21): 1896-1899. doi: 10.1109/LPT.2017.2755589 [93] Deniel L, Weckenmann E, Pérez Galacho D, et al. Silicon photonics phase and intensity modulators for flat frequency comb generation [J]. Photonics Research, 2021, 9(10): 2068-2076. doi: 10.1364/PRJ.431282 [94] Wang Z, Ma M, Sun H, et al. Optical frequency comb generation using CMOS compatible cascaded Mach–Zehnder modulators [J]. IEEE Journal of Quantum Electronics, 2019, 55(6): 1-6. doi: 10.1109/JQE.2019.2948152 [95] Lipson M. Compact electro-optic modulators on a silicon chip [J]. IEEE Journal of Selected Topics in Quantum Electronics, 2006, 12(6): 1520-1526. doi: 10.1109/JSTQE.2006.885341 [96] Xu Y, Lin J, Dube-Demers R, et al. Integrated flexible-grid WDM transmitter using an optical frequency comb in microring modulators [J]. Opt Lett, 2018, 43(7): 1554-1557. doi: 10.1364/OL.43.001554 [97] Liu S, Wu K, Zhou L, et al. Microwave pulse generation with a silicon Dual-Parallel modulator [J]. Journal of Lightwave Technology, 2020, 38(8): 2134-2143. doi: 10.1109/JLT.2020.2964102 [98] Deniel L, Weckenmann E, Pérez Galacho D, et al. Frequency-tuning dual-comb spectroscopy using silicon mach-zehnder modulators [J]. Optics Express, 2020, 28(8): 10888-10898. doi: 10.1364/OE.390041 [99] Demirtzioglou I, Lacava C, Bottrill K R H, et al. Frequency comb generation in a silicon ring resonator modulator [J]. Opt Express, 2018, 26(2): 790-796. doi: 10.1364/OE.26.000790 [100] Khalil M, Maram R, Naghdi B, et al. Electro-optic frequency comb generation using cascaded silicon microring modulators [C]// Proceedings of the OSA Advanced Photonics Congress (AP), 2020. [101] Kowligy A S, Carlson D R, Hickstein D D, et al. Mid-infrared frequency combs at 10 GHz [J]. Opt Lett, 2020, 45(13): 3677-3680. doi: 10.1364/OL.391651 [102] Weimann C, Schindler P C, Palmer R, et al. Silicon-organic hybrid (SOH) frequency comb sources for terabit/s data transmission [J]. Opt Express, 2014, 22(3): 3629-3637. doi: 10.1364/OE.22.003629 [103] Jiang P, Balram K C. Suspended gallium arsenide platform for building large scale photonic integrated circuits: Passive devices [J]. Opt Express, 2020, 28(8): 12262-12271. doi: 10.1364/OE.385618 [104] Pasquazi A, Peccianti M, Razzari L, et al. Micro-combs: A novel generation of optical sources [J]. Physics Reports, 2018, 729: 1-81. doi: 10.1016/j.physrep.2017.08.004 [105] Roslund J, de Araújo R M, Jiang S, et al. Wavelength-multiplexed quantum networks with ultrafast frequency combs [J]. Nature Photonics, 2014, 8(2): 109-112. doi: 10.1038/nphoton.2013.340 [106] Pfeifle J, Brasch V, Lauermann M, et al. Coherent terabit communications with microresonator Kerr frequency combs [J]. Nature Photonics, 2014, 8(5): 375-380. doi: 10.1038/nphoton.2014.57 [107] Pfeifle J, Vujicic V, Watts R T, et al. Flexible terabit/s nyquist-wdm super-channels using a gain-switched comb source [J]. Optics Express, 2015, 23(2): 724-738. doi: 10.1364/OE.23.000724 [108] Doi M, Sugiyama M, Tanaka K, et al. Advanced LiNbO3 optical modulators for broadband optical communications [J]. IEEE Journal of Selected Topics in Quantum Electronics, 2006, 12(4): 745-750. doi: 10.1109/JSTQE.2006.876192 [109] Li X, Wang M, Li J, et al. Monolithic 1×4 reconfigurable electro-optic tunable interleaver in lithium niobate thin film [J]. IEEE Photonics Technology Letters, 2019, 31(20): 1611-1614. doi: 10.1109/LPT.2019.2938325 [110] Dupuis N, Doerr C R, Zhang L M, et al. InP-based comb generator for optical OFDM [J]. Journal of Lightwave Technology, 2012, 30(4): 466-472. doi: 10.1109/JLT.2011.2173463 [111] Lin J C, Sepehrian H, Xu Y L, et al. Frequency comb generation using a CMOS compatible SiP DD-MZM for flexible networks [J]. IEEE Photonics Technology Letters, 2018, 30(17): 1495-1498. doi: 10.1109/LPT.2018.2856767 [112] Cingöz A, Yost D C, Allison T K, et al. Direct frequency comb spectroscopy in the extreme ultraviolet [J]. Nature, 2012, 482(7383): 68-71. doi: 10.1038/nature10711 [113] Ideguchi T, Poisson A, Guelachvili G, et al. Adaptive real-time dual-comb spectroscopy [J]. Nature Communications, 2014, 5(1): 3375. doi: 10.1038/ncomms4375 [114] Dutt A, Joshi C, Ji X, et al. On-chip dual-comb source for spectroscopy [J]. Science Advances, 2018, 4(3): e1701858. doi: 10.1126/sciadv.1701858 [115] Yu M, Okawachi Y, Griffith A G, et al. Silicon-chip-based mid-infrared dual-comb spectroscopy [J]. Nature Commu-nications, 2018, 9(1): 1869. doi: 10.1038/s41467-018-04350-1 [116] Shams-Ansari A, Yu M, Chen Z, et al. Thin-film lithium-niobate electro-optic platform for spectrally tailored dual-comb spectroscopy [J]. Communications Physics, 2022, 5(1): 88. doi: 10.1038/s42005-022-00865-8