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提出一种利用锁相双频激光泵浦正常色散碳化硅微环谐振腔产生光频率梳的方案. 对绝缘体上碳化硅微环谐振腔光波导进行色散调控, 实现1550 nm波段平坦正常色散优化设计. 利用Lugiato-Lefever方程对锁相双频激光泵浦正常色散碳化硅微环谐振腔的光频率梳产生进行仿真, 研究了泵浦失谐量改变时光频率梳产生的时域和频域演化过程. 同时探究了泵浦功率、微腔波导损耗、微腔色散、双频激光功率占比、双频激光频率间隔等各项参数对光频率梳产生的影响, 仿真产生的光频率梳带宽可覆盖1500—1600 nm. 仿真结果有助于推动基于正常色散碳化硅微环谐振腔的1550 nm波段高重复频率宽带光频率梳的研究和应用.
The scheme of generating optical frequency comb (OFC) mainly includes mode-locked laser, electro-optic modulation comb, and nonlinear Kerr micro-resonator comb. The OFC with frequency spacing on the order of 10–200 GHz can be employed in optical communication, microwave photonics, and other fields. Silicon carbide (SiC) has aroused the considerable research interest in integrated nonlinear photonics owing to its high second nonlinear coefficient and third order nonlinear coefficient, low optical loss, without multiphoton absorption loss owing to the wide bandgap. Single soliton microcomb in anomalous group velocity dispersion regime based on a 4H-SiC-on-insulator thin film has been demonstrated with the relative lower pump to comb efficiency, while the OFC in normal dispersion regime based on the SiC microresonator has not been reported. The pump conversion efficiency of OFC in the normal dispersion regime is high, and the pump frequency detuning range for the OFC generation is large, which is conducive to the OFC generation and long-term stable operation. Since there is no modulation instability effect in normal dispersion regime, the key to generating the OFC in normal dispersion regime is that the initial state needs the assistance of a multi-frequency laser (or four-wave mixing sideband). The phase-locked dual-frequency laser can be regarded as a pulse pump laser source with wide pulse duration, which can be realized by integrated distributed feedback laser. In this paper, a scheme of generating OFC by pumping the normal dispersion SiC microresonator with phase locked dual-frequency laser is proposed. The flat normal dispersion in 1550 nm band is realized through dispersion engineering of the SiC microresonator. The effective mode field area of the TE0 fundamental mode at 1550 nm in the optimized SiC ridge waveguide is about 0.94 μm2, and the nonlinear coefficient is about 3.69 $ {{\mathrm{W}}}^{-1}{\cdot} {{\mathrm{m}}}^{-1} $ . Meanwhile, dispersion parameters of the microresonator with 100 GHz FSR are also obtained. The OFC generation pumped by a phase-locked dual-frequency laser based on normal dispersion SiC microresonator is simulated through using the Lugiato-Lefever equation. The evolution process of the OFC in time and frequency domain related to the pump detuning is studied. The effects of several parameters such as the pump power, microresonator waveguide loss, microresonator dispersion, proportion of the dual-frequency laser, and the frequency interval of dual-frequency laser on the performance of the OFC are also investigated. The conclusions can be obtained through the OFC generation simulation as follows, 1) When the microresonator waveguide loss is larger, the pump detuning range for the OFC generation becomes smaller, and the pulse peak power under the same pulse intensity filling rate decreases. 2) When the input pump power is larger, the pump detuning range for the OFC generation becomes larger, the pulse peak power under the same pulse intensity filling rate increases, and the corresponding spectrum becomes wider. 3) With the increase of absolute dispersion value, the spectrum bandwidth of the generated OFC decreases obviously. 4) The power proportion of dual-frequency laser has little influence on the OFC generation. 5) The frequency spacing of the generated OFC can be tuned through changing the frequency spacing of the two phase-locked lasers with integral multiple of free spectral range.The OFC with spectrum bandwidth of about 70 nm can be generated in a range of 1500—1600 nm through the simulation. The simulation results are beneficial to promoting the research and practical application of high repetition rate broadband optical frequency comb in a 1550 nm band based on the normal dispersion silicon carbide microresonator. -
Keywords:
- nonlinear optics /
- optical frequency comb /
- normal dispersion /
- microresonator
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图 1 碳化硅波导结构与TE0基模色散调控 (a) 碳化硅波导结构; (b) 固定脊形高度D = 350 nm, 色散β2随宽度变化曲线; (c) 固定宽度W = 3000 nm, 色散β2随高度变化曲线; (d) 最终优化的高350 nm、宽3000 nm脊型波导中TE0 基模的有效模场面积Aeff和非线性系数γ曲线
Fig. 1. Silicon carbide waveguide structure and dispersion engineering of TE0 fundamental mode: (a) Silicon carbide waveguide structure; (b) simulation on GVD versus W with the fixed ridge height D = 350 nm; (c) simulation on GVD versus D with the fixed width W = 3000 nm; (d) Aeff and γ of TE0 mode with a height D = 350 nm and width W = 3000 nm.
图 2 弯曲半径173.1 μm的微环谐振腔的色散参量 (a) D1/2π; (b) D2/2π; (c) D3/2π; (d) Dint/2π
Fig. 2. Dispersion parameters of a micro-ring resonator with a bending radius of 173.1 μm: (a) D1/2π; (b) D2/2π; (c) D3/2π; (d) Dint/2π.
图 3 锁相双频激光泵浦碳化硅微环谐振腔的光频率梳产生系统示意图
Fig. 3. Structural diagram of the optical frequency comb generation system with phase-locked dual-frequency laser pumped silicon carbide micro-ring resonator.
图 4 锁相双频激光泵浦正常色散SiC微环产生光频率梳的时频演化 (a) 腔内平均功率随泵浦失谐的变化; (b) 腔内时域脉冲与频谱随泵浦失谐的演化; (c) 泵浦失谐分别为3, 6, 11时的腔内时域脉冲和对应频谱
Fig. 4. Time-frequency evolution of optical frequency comb generated in normal dispersion SiC micro-ring pumped by phase-locked dual-frequency laser: (a) Evolution of the average intracavity power with the pump detuning; (b) evolution of time-domain pulse and frequency spectrum in the cavity with the pump detuning; (c) the time-domain pulse and corresponding optical frequency spectrum when the pump detuning is 3, 6 and 11, respectively.
图 5 微环波导损耗对光频率梳产生的影响 (a) 不同损耗下随泵浦失谐的腔内平均功率演化; (b) 不同损耗下时域脉冲强度填充率相同时的光频率梳频谱; (c) 不同损耗下时域脉冲强度填充率相同时的时域脉冲
Fig. 5. Influence of micro-ring waveguide loss on optical frequency comb: (a) Evolution of the average intracavity power with the pump detuning under different waveguide loss; (b) optical frequency comb spectra with the same pulse intensity filling rate under different waveguide loss; (c) time-domain pulses with the same pulse intensity filling rate under different waveguide loss.
图 6 输入泵浦功率对光频率梳产生的影响 (a) 不同输入功率下随泵浦失谐的腔内平均功率演化; (b) 不同输入功率下时域脉冲强度填充率相同时的光频率梳频谱; (c) 不同输入功率下时域脉冲强度填充率相同时的时域脉冲
Fig. 6. Influence of pump power on optical frequency comb: (a) Evolution of the average intracavity power with the pump detuning under different pump power; (b) optical frequency comb spectra with the same pulse intensity filling rate under different pump power; (c) time-domain pulses with the same pulse intensity filling rate under different pump power.
图 7 微环色散对光频率梳产生的影响 (a) 不同色散下腔内平均功率随泵浦失谐的演化; (b) 不同色散下在时域脉冲强度填充率相同时的光频率梳频谱; (c) 不同色散下在时域脉冲强度填充率相同时的时域脉冲
Fig. 7. Influence of micro-ring dispersion on optical frequency comb: (a) Evolution of the average intracavity power with the pump detuning under different micro-ring dispersion; (b) optical frequency comb spectra with the same pulse intensity filling rate under different micro-ring dispersion; (c) time-domain pulses with the same filling rate under different micro-ring dispersion.
图 8 双频激光功率占比对光频率梳产生的影响 (a) 不同功率占比下随腔内平均功率泵浦失谐的演化; (b) 不同功率占比下时域脉冲强度填充率相同时的光频率梳频谱; (c) 不同功率占比下时域脉冲强度填充率相同时的时域脉冲
Fig. 8. Influence of dual-frequency laser power ratio on optical frequency comb: (a) Evolution of the average intracavity power with the pump detuning under different power ratio; (b) optical frequency comb spectra with the same pulse intensity filling rate under different power ratio; (c) time-domain pulses with the same pulse intensity filling rate under different power ratio.
图 9 双频激光频率间隔对光频率梳产生的影响 (a) 不同频率间隔下腔内平均功率随泵浦失谐的演化; (b) 不同频率间隔下时域脉冲强度填充率相同时的时域脉冲; (c), (d), (e) 双频激光频率间隔为1倍FSR、2倍FSR、3倍FSR产生的光频率梳在时域脉冲强度填充率相同时的频谱
Fig. 9. Influence of frequency interval of dual-frequency laser on optical frequency comb: (a) Evolution of the average intracavity power with the pump detuning under different frequency interval; (b) time-domain pulses with the same pulse intensity filling rate under different frequency interval; (c), (d), (e) optical frequency comb spectra with one, two and three FSR frequency intervals under the same pulse intensity filling rate.
表 1 产生光频率梳所采用的各项参数
Table 1. Parameters used to generate optical frequency comb.
Waveguide Parameter β2/(ps2·km–1) β3/(ps3·km–1) β4/(ps4·km–1) P0/W α/(dB·m–1) $ {D}_{1}/2{\mathrm{\pi }} $/GHz $ {D}_{2}/2{\mathrm{\pi }} $/MHz $ {D}_{3}/2{\mathrm{\pi }} $/kHz SiC waveguide 145.283 –0.18298 0.00209637 0.2 20 100 –0.993974 0.844218 
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[1] Diddams S A, Vahala K, Udem T 2020 Science 369 eaay3676
Google Scholar
[2] Ma Y, Li W J, Xu Y F, Liu J Q, Zhuo N, Yang K, Zhang J C, Zhai S Q, Liu S M, Wang L J 2023 Chin. Phys. Lett. 40 014201
Google Scholar
[3] Bartels A, Heinecke D, Diddams S A 2008 Opt. Lett. 33 1905
Google Scholar
[4] Duan G H, Shen A, Akrout A, Dijk F V, Lelarge F, Pommereau F, Le G O, Provost J G, Gariah H, Blache F, Mallecot F, Merghem K, Martinez A, Ramdane A 2009 Bell Labs Tech. J. 14 63
Google Scholar
[5] Lo M C, Guzmán R, Ali M, Santos R, Augustin L, Carpintero G 2017 Opt. Lett. 42 3872
Google Scholar
[6] Parriaux A, Hammani K, Millot G 2020 Adv. Opt. Photonics 12 223
Google Scholar
[7] Kippenberg T J, Gaeta A L, Lipson M, Gorodetsky M L 2018 Science 361 aan8083
Google Scholar
[8] Yu S, Bao F, Hu H, Hu H 2018 IEEE Photonics J. 10 7202107
Google Scholar
[9] Deng Y, Wu C J, Liu Y, Feng S C 2021 Opt. Commun. 502 127415
Google Scholar
[10] Ji X, Barbosa F A S, Roberts S P, Dutt A, Cardenas J, Okawachi Y, Bryant A, Gaeta A L, Lipson M 2017 Optica 4 619
Google Scholar
[11] Hu H, Da Ros F, Pu M, Ye F, Ingerslev K, Porto Da Silva E, Nooruzzaman M, Amma Y, Sasaki Y, Mizuno T, Miyamoto Y, Ottaviano L, Semenova E, Guan P, Zibar D, Galili M, Yvind K, Morioka T, Oxenløwe L K 2018 Nat. Photonics 12 469
Google Scholar
[12] Zheng Y, Pu M, Yi A, Ou X, Ou H 2019 Opt. Lett. 44 5784
Google Scholar
[13] Yu S P, Lucas E, Zang J, Papp S B 2022 Nat. Commun. 13 3134
Google Scholar
[14] Tan D T H, Ooi K J A, Ng D K T 2018 Photonics Res. 6 B50
Google Scholar
[15] Boes A, Corcoran B, Chang L, Bowers J, Mitchell A 2018 Laser Photonics Rev. 12 1700256
Google Scholar
[16] Li H, Wang G B, Yang J Y, Zhang Z S, Deng J, Du S X 2023 Chin. Phys. Lett. 40 128101
Google Scholar
[17] Cai L T, Li J W, Wang R X, Li Q 2022 Photon. Res. 10 870
Google Scholar
[18] Wang C, Li J, Yi A, Fang Z, Zhou L, Wang Z, Niu R, Chen Y, Zhang J, Cheng Y, Liu J, Dong C H, Ou X 2022 Light-Sci. Appl. 11 341
Google Scholar
[19] Xue X, Xuan Y, Liu Y, Wang P H, Chen S, Wang J, Leaird D E, Qi M, Weiner A M 2015 Nat. Photonics 9 594
Google Scholar
[20] Jin W, Yang Q F, Chang L, Shen B, Wang H, Leal M A, Wu L, Gao M, Feshali A, Paniccia M, Vahala K J, Bowers J E 2021 Nat. Photonics 15 346
Google Scholar
[21] Helgason Ó B, Arteaga-Sierra F R, Ye Z, Twayana K, Andrekson P A, Karlsson M, Schröder J, Company V T 2021 Nat. Photonics 15 305
Google Scholar
[22] Anderson M H, Weng W, Lihachev G, Tikan A, Liu J, Kippenberg T J 2022 Nat. Commun. 13 4764
Google Scholar
[23] Rahim M, Zeb K, Lu Z, Pakulski G, Liu J, Poole P, Song C, Barrios P, Jiang W, Zhang X 2019 Opt. Express 27 35368
Google Scholar
[24] 王佳强, 吴志芳, 冯素春 2022 71 234209
Google Scholar
Wang J Q, Wu Z F, Feng S C 2022 Acta Phys. Sin. 71 234209
Google Scholar
[25] Wang S C, Zhan M J, Wang G, Xuan H W, Zhang W, Liu C J, Xu C H, Liu Y, Wei Z Y, Chen X L 2013 Laser Photonics Rev. 7 831
Google Scholar
[26] Malitson I H 1965 J. Opt. Soc. Am. 55 1205
Google Scholar
[27] Herr T, Brasch V, Jost J D, Wang C Y, Kondratiev N M, Gorodetsky M L, Kippenberg T J 2014 Nat. Photonics 8 145
Google Scholar
[28] Chembo Y K, Menyuk C R 2013 Phys. Rev. A 87 053852
Google Scholar
[29] Tong Z, Wiberg A O, Myslivets E, Kuo B P, Alic N, Radic S 2012 Opt. Express 20 17610
Google Scholar
[30] Antikainen A, Agrawal G P 2015 J. Opt. Soc. Am. B 32 1705
Google Scholar
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