Recent advances in laser self-injection locking to high-Q microresonators

Abstract

The stabilization and manipulation of laser frequency by means of an external cavity are nearly ubiquitously used in fundamental research and laser applications. While most of the laser light transmits through the cavity, in the presence of some back-scattered light from the cavity to the laser, the self-injection locking effect can take place, which locks the laser emission frequency to the cavity mode of similar frequency. The self-injection locking leads to dramatic reduction of laser linewidth and noise. Using this approach, a common semiconductor laser locked to an ultrahigh-Q microresonator can obtain sub-Hertz linewidth, on par with state-of-the-art fiber lasers. Therefore it paves the way to manufacture high-performance semiconductor lasers with reduced footprint and cost. Moreover, with high laser power, the optical nonlinearity of the microresonator drastically changes the laser dynamics, offering routes for simultaneous pulse and frequency comb generation in the same microresonator. Particularly, integrated photonics technology, enabling components fabricated via semiconductor CMOS process, has brought increasing and extending interest to laser manufacturing using this method. In this article, we present a comprehensive tutorial on analytical and numerical methods of laser self-injection locking, as well a review of most recent theoretical and experimental achievements.

Graphical abstract

Keywords

self-injection locking / laser stabilization / microresonator / nonlinearity / single-frequency lasing / multi-frequency lasing

References

[1] G. Hadley . Injection locking of diode lasers. IEEE J. Quantum Electron., 1986, 22(3): 419

[2] R. W. P. Drever , J. L. Hall , F. V. Kowalski , J. Hough , G. M. Ford , A. J. Munley , H. Ward . Laser phase and frequency stabilization using an optical resonator. Appl. Phys. B, 1983, 31(2): 97

[3] H. R. Telle . Narrow linewidth laser diodes with broad continuous tuning range. Appl. Phys. B, 1989, 49(3): 217

[4] M. Zhu , J. L. Hall . Stabilization of optical phase/frequency of a laser system: Application to a commercial dye laser with an external stabilizer. J. Opt. Soc. Am. B, 1993, 10(5): 802

[5] M. Kourogi , M. Ohtsu . Novel optical frequency discriminator for FM noise reduction of semiconductor lasers. Opt. Commun., 1991, 81(3−4): 204

[6] T. Ohta , K. Murakami . Reducing negative resistance oscillator noise by self-injection. Electron. Commun. Jpn., 1968, 51-B: 80

[7] T.OhtaS.MakinoH.NakanoS.EndoS.Ono, New self-injection oscillator using directional filter. 1973 3rd European Microwave Conference (1973), Vol. 1, pp 1–4

[8] T. Ota , M. Nata . Noise reduction of oscillator by injection locking. Trans. IECEJ, 1970, 53-B: 487

[9] H. C. Chang . Phase noise in self-injection-locked oscillators - theory and experiment. IEEE Trans. Microw. Theory Tech., 2003, 51(9): 1994

[10] H. C. Chang . Stability analysis of self-injection-locked oscillators. IEEE Trans. Microw. Theory Tech., 2003, 51(9): 1989

[11] J. J. Choi , G. W. Choi . Experimental observation of frequency locking and noise reduction in a self-injection-locked magnetron. IEEE Trans. Electron. Devices, 2007, 54: 3430

[12] Y. P. Bliokh , Y. E. Krasik , J. Felsteiner . Self-injection-locked magnetron as an active ring resonator side coupled to a waveguide with a delayed feedback loop. IEEE Trans. Plasma Sci., 2012, 40(1): 78

[13] M. Y. Glyavin , G. G. Denisov , M. L. Kulygin , Y. V. Novozhilova . Stabilization of gyrotron frequency by reflection from nonresonant and resonant loads. Tech. Phys. Lett., 2015, 41(7): 628

[14] M. M. Melnikova , A. G. Rozhnev , N. M. Ryskin , A. V. Tyshkun , M. Y. Glyavin , Y. V. Novozhilova . Frequency stabilization of a 0.67-THz gyrotron by self-injection locking. IEEE Trans. Electron Dev., 2016, 63(3): 1288

[15] L. Zhang , A. K. Poddar , U. L. Rohde , A. S. Daryoush . Self-ilpll using optical feedback for phase noise reduction in microwave oscillators. IEEE Photonics Technol. Lett., 2015, 27(6): 624

[16] L.ZhangA.K. PoddarU.L. RohdeA.S. Daryoush, Phase noise reduction in RF oscillators utilizing self-injection locked and phase locked loop, 2015 IEEE 15th Topical Meeting on Silicon Monolithic Integrated Circuits in RF Systems (2015), pp 86–88

[17] B. Dahmani , L. Hollberg , R. Drullinger . Frequency stabilization of semiconductor lasers by resonant optical feedback. Opt. Lett., 1987, 12(11): 876

[18] H. Li , N. B. Abraham . Power spectrum of frequency noise of semiconductor lasers with optical feedback from a high-finesse resonator. Appl. Phys. Lett., 1988, 53(23): 2257

[19] P. Laurent , A. Clairon , C. Breant . Frequency noise analysis of optically self-locked diode lasers. IEEE J. Quantum Electron., 1989, 25(6): 1131

[20] W. Liang , V. Ilchenko , A. Savchenkov , A. Matsko , D. Seidel , L. Maleki . Whispering-gallery-mode-resonator-based ultranarrow linewidth external-cavity semiconductor laser. Opt. Lett., 2010, 35(16): 2822

[21] W. Liang , V. Ilchenko , A. D. Eliyahu , A. A. Savchenkov , A. B. Matsko , D. Seidel , L. Maleki . Ultralow noise miniature external cavity semiconductor laser. Nat. Commun., 2015, 6(1): 7371

[22] V. Velichanskii , A. Zibrov , V. Kargopol’tsev , V. Molochev , V. Nikitin , V. Sautenkov . . Minimum line width of an injection laser. Sov. Tech. Phys. Lett., 1978, 4

[23] R. Lang , K. Kobayashi . External optical feedback effects on semiconductor injection laser properties. IEEE J. Quantum Electron., 1980, 16(3): 347

[24] É. Belenov , V. Velichanskiĭ , A. Zibrov , V. Nikitin , V. Sautenkov , A. Uskov . Methods for narrowing the emission line of an injection laser. Sov. J. Quantum Electron., 1983, 13(6): 792

[25] E. Patzak , H. Olesen , A. Sugimura , S. Saito , T. Mukai . Spectral linewidth reduction in semiconductor lasers by an external cavity with weak optical feedback. Electron. Lett., 1983, 19: 938

[26] E. Patzak , A. Sugimura , S. Saito , T. Mukai , H. Olesen . Semiconductor laser linewidth in optical feedback configurations. Electron. Lett., 1983, 19: 1026

[27] C. Henry . Theory of the linewidth of semiconductor lasers. IEEE J. Quantum Electron., 1982, 18(2): 259

[28] G. Agrawal . Line narrowing in a single-mode injection laser due to external optical feedback. IEEE J. Quantum Electron., 1984, 20(5): 468

[29] R. Tkach , A. Chraplyvy . Regimes of feedback effects in 1.5-µm distributed feedback lasers. J. Lightwave Technol., 1986, 4(11): 1655

[30] H. Olesen , S. Saito , T. Mukai , T. Saitoh , O. Mikami . Solitary spectral linewidth and its reduction with external grating feedback for a 1.55 µm InGaAsP BH laser. Jpn. J. Appl. Phys., 1983, 22(10A): L664

[31] S. Saito , O. Nilsson , Y. Yamamoto . Oscillation center frequency tuning, quantum FM noise, and direct frequency characteristics in external grating loaded semiconductor lasers. IEEE J. Quantum Electron., 1982, 18(6): 961

[32] G. Acket , D. Lenstra , A. Den Boef , B. Verbeek . The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers. IEEE J. Quantum Electron., 1984, 20(10): 1163

[33] K. Petermann . External optical feedback phenomena in semiconductor lasers. IEEE J. Sel. Top. Quantum Electron., 1995, 1(2): 480

[34] S. Donati . Developing self-mixing interferometry for instrumentation and measurements. Laser Photonics Rev., 2012, 6(3): 393

[35] L. Hollberg , M. Ohtsu . Modulatable narrow-linewidth semiconductor lasers. Appl. Phys. Lett., 1988, 53(11): 944

[36] H. Li , N. B. Abraham . Analysis of the noise spectra of a laser diode with optical feedback from a high-finesse resonator. IEEE J. Quantum Electron., 1989, 25(8): 1782

[37] A. Hemmerich , D. McIntyre , D. Jr Schropp , D. Meschede , T. Hansch . Optically stabilized narrow linewidth semiconductor laser for high resolution spectroscopy. Opt. Commun., 1990, 75(2): 118

[38] A. Hemmerich , C. Zimmermann , T. W. Hansch . Compact source of coherent blue light. Appl. Opt., 1994, 33(6): 988

[39] A. Hemmerich , D. H. McIntyre , C. Zimmermann , T. W. Hansen . Second-harmonic generation and optical stabilization of a diode laser in an external ring resonator. Opt. Lett., 1990, 15(7): 372

[40] D. R. Hjelme , A. R. Mickelson , R. G. Beausoleil . Semiconductor laser stabilization by external optical feedback. IEEE J. Quantum Electron., 1991, 27(3): 352

[41] Y. Zhao , Y. Peng , T. Yang , Y. Li , Q. Wang , F. Meng , J. Cao , Z. Fang , T. Li , E. Zang . External cavity diode laser with kilohertz linewidth by a monolithic folded Fabry–Pérot cavity optical feedback. Opt. Lett., 2011, 36(1): 34

[42] Liu Y . Liang W. Compact narrow linewidth external cavity semiconductor laser realized by self-injection locking to Fabry−Pérot cavity. Chin. J. Lasers, 2021, 48: 1715001

[43] V. Braginsky , M. Gorodetsky , V. Ilchenko . Quality-factor and nonlinear properties of optical whispering-gallery modes. Phys. Lett. A, 1989, 137(7−8): 393

[44] A. A. Savchenkov , V. S. Ilchenko , A. B. Matsko , L. Maleki . Kilohertz optical resonances in dielectric crystal cavities. Phys. Rev. A, 2004, 70(5): 051804

[45] A. B. Matsko , V. S. Ilchenko . Optical resonators with whispering-gallery modes (part I): basics. IEEE J. Sel. Top. Quantum Electron., 2006, 12(1): 3

[46] A. A. Savchenkov , A. B. Matsko , V. S. Ilchenko , L. Maleki . Optical resonators with ten million finesse. Opt. Express, 2007, 15(11): 6768

[47] J.WardO.Benson, WGM microresonators: Sensing, lasing and fundamental optics with microspheres, Laser Photonics Rev. 5(4), 553 (2011)

[48] G. Lin , S. Diallo , R. Henriet , M. Jacquot , Y. K. Chembo . Barium fluoride whispering-gallery-mode disk-resonator with one billion quality-factor. Opt. Lett., 2014, 39: 6009

[49] R. Henriet , G. Lin , A. Coillet , M. Jacquot , L. Furfaro , L. Larger , Y. K. Chembo . Kerr optical frequency comb generation in strontium fluoride whispering-gallery mode resonators with billion quality factor. Opt. Lett., 2015, 40(7): 1567

[50] D. V. Strekalov , C. Marquardt , A. B. Matsko , H. G. L. Schwefel , G. Leuchs . Nonlinear and quantum optics with whispering gallery resonators. J. Opt., 2016, 18(12): 123002

[51] I. S. Grudinin , A. B. Matsko , A. A. Savchenkov , D. Strekalov , V. S. Ilchenko , L. Maleki . Ultra high Q crystalline microcavities. Opt. Commun., 2006, 265(1): 33

[52] C. Lecaplain , C. Javerzac-Galy , M. L. Gorodetsky , T. J. Kippenberg . Mid-infrared ultra-high-Q resonators based on fluoride crystalline materials. Nat. Commun., 2016, 7(1): 13383

[53] A. E. Shitikov , I. A. Bilenko , N. M. Kondratiev , V. E. Lobanov , A. Markosyan , M. L. Gorodetsky . Billion Q-factor in silicon WGM resonators. Optica, 2018, 5(12): 1525

[54] V. Vassiliev , V. Velichansky , V. Ilchenko , M. Gorodetsky , L. Hollberg , A. Yarovitsky . Narrow-line-width diode laser with a high-Q microsphere resonator. Opt. Commun., 1998, 158(1-6): 305

[55] M. L. Gorodetsky , A. D. Pryamikov , V. S. Ilchenko . Rayleigh scattering in high-Q microspheres. J. Opt. Soc. Am. B, 2000, 17(6): 1051

[56] V. S. Ilchenko , X. S. Yao , L. Maleki . High-Q microsphere cavity for laser stabilization and optoelectronic microwave oscillator. Laser Resonators II, 1999, 3611: 190

[57] A. N. Oraevsky , A. V. Yarovitsky , V. L. Velichansky . Frequency stabilisation of a diode laser by a whispering-gallery mode. Quantum Electron., 2001, 31(10): 897

[58] J.P. RezacA.T. Rosenberger, Locking and laser-frequency tracking of a microsphere whispering-gallery mode, Laser Resonators IV 4270, 112 (2001) (SPIE)

[59] I.BilenkoA.SamoilenkoV.S. Ilchenko, Measurement of small stress fluctuations in fused silica fibers using an optical microcavity sensor, Laser Resonators and Beam Control V 4629, 222 (2002) (SPIE)

[60] A. B. Matsko , A. A. Savchenkov , N. Yu , L. Maleki . Whispering-gallery-mode resonators as frequency references (I): Fundamental limitations. J. Opt. Soc. Am. B, 2007, 24: 1324

[61] N. Kondratiev , M. Gorodetsky . Thermorefractive noise in whispering gallery mode microresonators: Analytical results and numerical simulation. Phys. Lett. A, 2018, 382: 2265

[62] D. Huang , M. A. Tran , J. Guo , J. Peters , T. Komljenovic , A. Malik , P. A. Morton , J. E. Bowers . High-power sub-khz linewidth lasers fully integrated on silicon. Optica, 2019, 6(6): 745

[63] V. Vassiliev , S. Il’ina , V. Velichansky . Diode laser coupled to a high-Q microcavity via a GRIN lens. Appl. Phys. B, 2003, 76(5): 521

[64] E. Dale , M. Bagheri , A. Matsko , C. Frez , W. Liang , S. Forouhar . . Microresonator stabilized 2µm distributed-feedback GaSb-based diode laser. Opt. Lett., 2016, 41: 5559

[65] Z. Xie , W. Liang , A. A. Savchenkov , J. Lim , J. Burkhart , M. McDonald , T. Zelevinsky , V. S. Ilchenko , A. B. Matsko , L. Maleki , C. W. Wong . Extended ultrahigh-Q-cavity diode laser. Opt. Lett., 2015, 40(11): 2596

[66] A. Savchenkov , D. Eliyahu , B. Heist , A. Matsko , M. Bagheri , C. Frez , S. Forouhar . On acceleration sensitivity of 2 µm whispering gallery mode-based semiconductor self-injection locked laser. Appl. Opt., 2019, 58(9): 2138

[67] A. Savchenkov , E. Lopez , I. Solomatine , D. Eliyahu , A. Matsko , L. Maleki . Spectral purity improvement in flickering self-injection locked lasers. IEEE J. Quantum Electron., 2022, 58(5): 1

[68] N. G. Pavlov , S. Koptyaev , G. V. Lihachev , A. S. Voloshin , A. S. Gorodnitskiy , M. V. Ryabko , S. V. Polonsky , M. L. Gorodetsky . Narrow-linewidth lasing and soliton Kerr microcombs with ordinary laser diodes. Nat. Photonics, 2018, 12(11): 694

[69] P. Donvalkar , A. Savchenkov , A. Matsko . Self-injection locked blue laser. J. Opt., 2018, 20(4): 045801

[70] R. R. Galiev , N. G. Pavlov , N. M. Kondratiev , S. Koptyaev , V. E. Lobanov , A. S. Voloshin , A. S. Gorodnitskiy , M. L. Gorodetsky . Spectrum collapse, narrow linewidth, and Bogatov effect in diode lasers locked to high-Q optical microresonators. Opt. Express, 2018, 26(23): 30509

[71] N. G. Pavlov , G. V. Lihachev , A. S. Voloshin , S. Koptyaev , N. M. Kondratiev , V. E. Lobanov . . Narrow linewidth diode laser self-injection locked to a high-Q microresonator. AIP Conf. Proc., 2018, 1936: 020005

[72] A. A. Savchenkov , S. W. Chiow , M. Ghasemkhani , S. Williams , N. Yu , R. C. Stirbl , A. B. Matsko . Self-injection locking efficiency of a UV Fabry−Pérot laser diode. Opt. Lett., 2019, 44(17): 4175

[73] A. A. Savchenkov , J. E. Christensen , D. Hucul , W. C. Campbell , E. R. Hudson , S. Williams , A. B. Matsko . Application of a self-injection locked cyan laser for barium ion cooling and spectroscopy. Sci. Rep., 2020, 10(1): 16494

[74] E. Yacoby , C. Goren , S. Goldring , G. Guendelman , S. Pearl . Discretely tunable, single mode lasing from a multimode diode laser, locked to silica microsphere resonator. Opt. Laser Technol., 2021, 143: 107343

[75] J. Ji , H. Wang , J. Ma , J. Guo , J. Zhang , D. Tang , D. Shen . Narrow linewidth self-injection locked fiber laser based on a crystalline resonator in add-drop configuration. Opt. Lett., 2022, 47(6): 1525

[76] L.Maleki, Novel lasers: Whispering-gallery-mode resonators create ultranarrow-linewidth semiconductor lasers, Laser Focus World (2014)

[77] H. Lee , T. Chen , J. Li , K. Y. Yang , S. Jeon , O. Painter , K. J. Vahala . Chemically etched ultrahigh-Q wedge-resonator on a silicon chip. Nat. Photonics, 2012, 6(6): 369

[78] K. Y. Yang , K. Beha , D. C. Cole , X. Yi , P. Del’Haye , H. Lee , J. Li , D. Y. Oh , S. A. Diddams , S. B. Papp , K. J. Vahala . Broadband dispersion-engineered microresonator on a chip. Nat. Photonics, 2016, 10(5): 316

[79] L. Wu , H. Wang , Q. Yang , Q. Ji , B. Shen , C. Bao , M. Gao , K. Vahala . Greater than one billion Q factor for on-chip microresonators. Opt. Lett., 2020, 45(18): 5129

[80] D. T. Spencer , J. F. Bauters , M. J. R. Heck , J. E. Bowers . Integrated waveguide coupled Si₃N₄ resonators in the ultrahigh-Q regime. Optica, 2014, 1(3): 153

[81] Y. Xuan , Y. Liu , L. T. Varghese , A. J. Metcalf , X. Xue , P. H. Wang , K. Han , J. A. Jaramillo-Villegas , A. Al Noman , C. Wang , S. Kim , M. Teng , Y. J. Lee , B. Niu , L. Fan , J. Wang , D. E. Leaird , A. M. Weiner , M. Qi . High-Q silicon nitride microresonators exhibiting low-power frequency comb initiation. Optica, 2016, 3(11): 1171

[82] M. H. P. Pfeiffer , A. Kordts , V. Brasch , M. Zervas , M. Geiselmann , J. D. Jost , T. J. Kippenberg . Photonic Damascene process for integrated high-Q microresonator based nonlinear photonics. Optica, 2016, 3(1): 20

[83] Z. Ye , K. Twayana , P. A. Andrekson , V. Torres-Company . High-Q Si₃N₄ microresonators based on a subtractive processing for Kerr nonlinear optics. Opt. Express, 2019, 27(24): 35719

[84] X. Ji , S. Roberts , M. Corato-Zanarella , M. Lipson . Methods to achieve ultra-high quality factor silicon nitride resonators. APL Photonics, 2021, 6(7): 071101

[85] B. Stern , X. Ji , Y. Okawachi , A. Gaeta , M. Lipson . Battery-operated integrated frequency comb generator. Nature, 2018, 562(7727): 401

[86] Y. Li , Y. Zhang , H. Chen , S. Yang , M. Chen . Tunable self-injected Fabry–Pérot laser diode coupled to an external high-Q Si3N4/SiO2 microring resonator. J. Lightwave Technol., 2018, 36(16): 3269

[87] A. Gaeta , M. Lipson , T. Kippenberg . Photonic-chip-based frequency combs. Nat. Photonics, 2019, 13(3): 158

[88] A. S. Raja , A. S. Voloshin , H. Guo , S. E. Agafonova , J. Liu , A. S. Gorodnitskiy , M. Karpov , N. G. Pavlov , E. Lucas , R. R. Galiev , A. E. Shitikov , J. D. Jost , M. L. Gorodetsky , T. J. Kippenberg . Electrically pumped photonic integrated soliton microcomb. Nat. Commun., 2019, 10(1): 680

[89] B. Shen , L. Chang , J. Liu , H. Wang , Q. F. Yang , C. Xiang , R. N. Wang , J. He , T. Liu , W. Xie , J. Guo , D. Kinghorn , L. Wu , Q. X. Ji , T. J. Kippenberg , K. Vahala , J. E. Bowers . Integrated turnkey soliton microcombs. Nature, 2020, 582(7812): 365

[90] A. S. Raja , J. Liu , N. Volet , R. N. Wang , J. He , E. Lucas , R. Bouchandand , P. Morton , J. Bowers , T. J. Kippenberg . Chip-based soliton microcomb module using a hybrid semiconductor laser. Opt. Express, 2020, 28(3): 2714

[91] A. Kovach , D. Chen , J. He , H. Choi , A. H. Dogan , M. Ghasemkhani . . Emerging material systems for integrated optical Kerr frequency combs. Adv. Opt. Photon., 2020, 12: 135

[92] W. Jin , Q. F. Yang , L. Chang , B. Shen , H. Wang , M. A. Leal , L. Wu , M. Gao , A. Feshali , M. Paniccia , K. J. Vahala , J. E. Bowers . Hertz-linewidth semiconductor lasers using CMOS-ready ultra-high-Q microresonators. Nat. Photonics, 2021, 15(5): 346

[93] E. Shim , A. Gil-Molina , O. Westreich , Y. Dikmelik , K. Lascola , A. L. Gaeta , M. Lipson . Tunable single-mode chip-scale mid-infrared laser. Commun. Phys., 2021, 4(1): 268

[94] G. Lihachev , J. Riemensberger , W. Weng , J. Liu , H. Tian , A. Siddharth , V. Snigirev , V. Shadymov , A. Voloshin , R. N. Wang , J. He , S. A. Bhave , T. J. Kippenberg . Low-noise frequency-agile photonic integrated lasers for coherent ranging. Nat. Commun., 2022, 13(1): 3522

[95] A. Siddharth , T. Wunderer , G. Lihachev , A. S. Voloshin , C. Haller , R. N. Wang . . Near ultraviolet photonic integrated lasers based on silicon nitride. APL Photon., 2022, 7: 046108

[96] J. Guo , C. A. McLemore , C. Xiang , D. Lee , L. Wu , W. Jin , M. Kelleher , N. Jin , D. Mason , L. Chang , A. Feshali , M. Paniccia , P. T. Rakich , K. J. Vahala , S. A. Diddams , F. Quinlan , J. E. Bowers . Chip-based laser with 1-Hertz integrated linewidth. Sci. Adv., 2022, 8(43): eabp9006

[97] D. A. Korobko , I. O. Zolotovskii , K. Panajotov , V. V. Spirin , A. A. Fotiadi . Self-injection-locking linewidth narrowing in a semiconductor laser coupled to an external fiber-optic ring resonator. Opt. Commun., 2017, 405: 253

[98] V. V. Spirin , J. L. Bueno Escobedo , D. A. Korobko , P. Mégret , A. A. Fotiadi . Stabilizing DFB laser injection-locked to an external fiber-optic ring resonator. Opt. Express, 2020, 28(1): 478

[99] S. Shao , J. Li , Y. Wu , S. Yang , H. Chen , M. Chen . Modulation bandwidth enhanced self-injection locking laser with an external high-Q microring reflector. Opt. Lett., 2021, 46: 3251

[100] L. Jiang , L. Shi , J. Luo , Q. Gao , T. Lan , L. Huang , T. Zhu . Narrow linewidth VCSEL based on resonant optical feedback from an on-chip microring add-drop filter. Opt. Lett., 2021, 46(10): 2320

[101] L. Jiang , L. Shi , J. Luo , Q. Gao , M. Bai , T. Lan , P. I. Iroegbu , L. Dang , L. Huang , T. Zhu . Simultaneous self-injection locking of two VCSELs to a single whispering-gallery-mode microcavity. Opt. Express, 2021, 29(23): 37845

[102] V. V. Vasil’ev , V. L. Velichansky , M. L. Gorodetskii , V. S. Il’chenko , L. Holberg , A. V. Yarovitsky . High-coherence diode laser with optical feedback via a microcavity with “whispering gallery” modes. Quantum Electron., 1996, 26(8): 657

[103] W. Liang , V. S. Ilchenko , D. Eliyahu , E. Dale , A. A. Savchenkov , D. Seidel . . Compact stabilized semiconductor laser for frequency metrology. Appl. Opt., 2015, 54: 3353

[104] B. Sprenger , H. G. L. Schwefel , L. J. Wang . Whispering-gallery-mode-resonator-stabilized narrow-linewidth fiber loop laser. Opt. Lett., 2009, 34(21): 3370

[105] R. R. Galiev , N. M. Kondratiev , V. E. Lobanov , A. B. Matsko , I. A. Bilenko . Optimization of laser stabilization via self-injection locking to a whispering-gallery-mode microresonator. Phys. Rev. Appl., 2020, 14(1): 014036

[106] N. M. Kondratiev , V. E. Lobanov , A. V. Cherenkov , A. S. Voloshin , N. G. Pavlov , S. Koptyaev , M. L. Gorodetsky . Self-injection locking of a laser diode to a high-Q WGM microresonator. Opt. Express, 2017, 25(23): 28167

[107] R. Kazarinov , C. Henry . The relation of line narrowing and chirp reduction resulting from the coupling of a semiconductor laser to passive resonator. IEEE J. Quantum Electron., 1987, 23(9): 1401

[108] M. Osinski , J. Buus . Linewidth broadening factor in semiconductor lasers–an overview. IEEE J. Quantum Electron., 1987, 23(1): 9

[109] N.M. KondratievR.GalievI.GorelovA.ShitikovV.Lobanov, Strong-feedback regime of self-injection locking and external cavity laser, Eds. : M. Sciamanna, K. Panajotov, and S. Hofling, Semiconductor Lasers and Laser Dynamics X. International Society for Optics and Photonics (SPIE) (2022), Vol. 12141, 121410K

[110] N. M. Kondratiev , V. E. Lobanov , E. A. Lonshakov , N. Y. Dmitriev , A. S. Voloshin , I. A. Bilenko . Numerical study of solitonic pulse generation in the self-injection locking regime at normal and anomalous group velocity dispersion. Opt. Express, 2020, 28(26): 38892

[111] A. E. Shitikov , I. I. Lykov , O. V. Benderov , D. A. Chermoshentsev , I. K. Gorelov , A. N. Danilin , R. R. Galiev , N. M. Kondratiev , S. J. Cordette , A. V. Rodin , A. V. Masalov , V. E. Lobanov , I. A. Bilenko . Optimization of laser stabilization via self-injection locking to a whispering-gallery-mode microresonator: Experimental study. Opt. Express, 2023, 31(1): 313

[112] A. E. Shitikov , O. V. Benderov , N. M. Kondratiev , V. E. Lobanov , A. V. Rodin , I. A. Bilenko . Microresonator and laser parameter definition via self-injection locking. Phys. Rev. Appl., 2020, 14(6): 064047

[113] A. P. Bogatov , P. G. Eliseev , B. N. Sverdlov . Anomalous interaction of spectral modes in a semiconductor laser. Sov. J. Quantum Electron., 1975, 4(10): 1275

[114] A. Bogatov , P. Eliseev , B. Sverdlov . Anomalous interaction of spectral modes in a semiconductor laser. IEEE J. Quantum Electron., 1975, 11(7): 510

[115] M. Yamada . Theoretical analysis of nonlinear optical phenomena taking into account the beating vibration of the electron density in semiconductor lasers. J. Appl. Phys., 1989, 66(1): 81

[116] M. Yamada , Y. Suematsu . Analysis of gain suppression in undoped injection lasers. J. Appl. Phys., 1981, 52(4): 2653

[117] H. Ishikawa , M. Yano , M. Takusagawa . Mechanism of asymmetric longitudinal mode competition in InGaAsP/InP lasers. Appl. Phys. Lett., 1982, 40(7): 553

[118] N.M. KondratievR.R. GalievV.E. LobanovI.A. Bilenko, Multimode laser diode self-injection locking to a whispering gallery mode microresonator modeling, Frontiers in Optics + Laser Science 2021 (Optica Publishing Group) (2021), JTu1A. 119

[119] Y. A. Demchenko , M. L. Gorodetsky . Analytical estimates of eigenfrequencies, dispersion, and field distribution in whispering gallery resonators. J. Opt. Soc. Am. B, 2013, 30(11): 3056

[120] E. Lucas , G. Lihachev , R. Bouchand , N. G. Pavlov , A. S. Raja , M. Karpov , M. L. Gorodetsky , T. J. Kippenberg . Spatial multiplexing of soliton microcombs. Nat. Photonics, 2018, 12(11): 699

[121] P. Spano , S. Piazzolla , M. Tamburrini . Theory of noise in semiconductor lasers in the presence of optical feedback. IEEE J. Quantum Electron., 1984, 20(4): 350

[122] A. Savchenkov , S. Williams , A. Matsko . On stiffness of optical self-injection locking. Photonics, 2018, 5(4): 43

[123] R. R. Galiev , N. M. Kondratiev , V. E. Lobanov , A. B. Matsko , I. A. Bilenko . Mirror-assisted self-injection locking of a laser to a whispering-gallery-mode microresonator. Phys. Rev. Appl., 2021, 16(6): 064043

[124] M.Corato-ZanarellaA.Gil-MolinaX.JiM.C. ShinA.MohantyM.Lipson, Widely tunable and narrow-linewidth chip-scale lasers from near-ultraviolet to near-infrared wavelengths, Nat. Photonics (2022)

[125] de Cumis M. Siciliani , S. Borri , G. Insero , I. Galli , A. Savchenkov , D. Eliyahu . . Microcavity-stabilized quantum cascade laser. Laser Photon. Rev., 2016, 10: 153

[126] J. Lim , A. A. Savchenkov , E. Dale , W. Liang , D. Eliyahu , V. Ilchenko , A. B. Matsko , L. Maleki , C. W. Wong . Chasing the thermodynamical noise limit in whispering-gallery-mode resonators for ultrastable laser frequency stabilization. Nat. Commun., 2017, 8(1): 8

[127] A. Savchenkov , A. Matsko . Calcium fluoride whispering gallery mode optical resonator with reduced thermal sensitivity. J. Opt., 2018, 20(3): 035801

[128] Q. Zhao , R. O. Behunin , P. T. Rakich , N. Chauhan , A. Isichenko , J. Wang , C. Hoyt , C. Fertig , M. Lin , D. J. Blumenthal . Low-loss low thermo-optic coefficient Ta₂O₅ on crystal quartz planar optical waveguides. APL Photonics, 2020, 5(11): 116103

[129] M. Fu , Y. Zheng , G. Li , H. Hu , M. Pu , L. K. Oxenløwe , L. H. Frandsen , X. Li , X. Guan . High-Q titanium dioxide micro-ring resonators for integrated nonlinear photonics. Opt. Express, 2020, 28(26): 39084

[130] I. Hegeman , M. Dijkstra , F. B. Segerink , W. Lee , S. M. Garcia-Blanco . Development of low-loss TiO₂ waveguides. Opt. Express, 2020, 28(5): 5982

[131] L. He , Y. F. Xiao , C. Dong , J. Zhu , V. Gaddam , L. Yang . Compensation of thermal refraction effect in high-Q toroidal microresonator by polydimethylsiloxane coating. Appl. Phys. Lett., 2008, 93(20): 201102

[132] B. Guha , J. Cardenas , M. Lipson . Athermal silicon microring resonators with titanium oxide cladding. Opt. Express, 2013, 21(22): 26557

[133] S.S. DjordjevicK.ShangB.GuanS.T. S. CheungL.LiaoJ.BasakH.F. LiuS.J. B. Yoo, CMOS-compatible, athermal silicon ring modulators clad with titanium dioxide, Opt. Express 21(12), 13958 (2013)

[134] F. Qiu , A. M. Spring , S. Yokoyama . Athermal and high-Q hybrid TiO₂–Si₃N₄ ring resonator via an etching-free fabrication technique. ACS Photonics, 2015, 2(3): 405

[135] J. Ling , Y. He , R. Luo , M. Li , H. Liang , Q. Lin . Athermal lithium niobate microresonator. Opt. Express, 2020, 28(15): 21682

[136] Z. Yang , Z. Wang , R. Zhang , P. Xu , W. Zhang , Z. Kang , R. Wang . Athermal chalcogenide microresonator cladded with polymer. IEEE Photonics J., 2022, 14(5): 1

[137] T. J. Wang , P. K. Chen , Y. T. Li , A. N. Sung . Athermal high-Q tantalum-pentoxide-based microresonators on silicon substrates. Opt. Laser Technol., 2021, 138: 106925

[138] M. Wang , D. J. Perez-Morelo , V. Aksyuk . Overcoming thermo-optical dynamics in broadband nanophotonic sensing. Microsyst. Nanoeng., 2021, 7(1): 52

[139] Y. Levin . Fluctuation–dissipation theorem for thermo-refractive noise. Phys. Lett. A, 2008, 372(12): 1941

[140] M. L. Gorodetsky , I. S. Grudinin . Fundamental thermal fluctuations in microspheres. J. Opt. Soc. Am. B, 2004, 21(4): 697

[141] L. Duan . General treatment of the thermal noises in optical fibers. Phys. Rev. A, 2012, 86(2): 023817

[142] G. Huang , E. Lucas , J. Liu , A. S. Raja , G. Lihachev , M. L. Gorodetsky , N. J. Engelsen , T. J. Kippenberg . Thermorefractive noise in silicon−nitride microresonators. Phys. Rev. A, 2019, 99(6): 061801

[143] V.I. PavlovI.Y. BlinovN.P. KhatyrevN.M. KondratievI.A. Bilenko, Numerical simulation of influence of the thermal and mechanical fluctuations in the coupling elements of microresonators, 2021 Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS) (2021), pp 1–4

[144] C. Panuski , D. Englund , R. Hamerly . Fundamental thermal noise limits for optical microcavities. Phys. Rev. X, 2020, 10(4): 041046

[145] B. Li , W. Jin , L. Wu , L. Chang , H. Wang , B. Shen , Z. Yuan , A. Feshali , M. Paniccia , K. J. Vahala , J. E. Bowers . Reaching fiber-laser coherence in integrated photonics. Opt. Lett., 2021, 46(20): 5201

[146] B. Merkel , D. Repp , A. Reiserer . Laser stabilization to a cryogenic fiber ring resonator. Opt. Lett., 2021, 46(2): 444

[147] G. Moille , X. Lu , A. Rao , Q. Li , D. A. Westly , L. Ranzani . . Kerr-microresonator soliton frequency combs at cryogenic temperatures. Phys. Rev. Appl., 2019, 12: 034057

[148] A. B. Matsko , A. A. Savchenkov , V. S. Ilchenko , D. Seidel , L. Maleki . Self-referenced stabilization of temperature of an optomechanical microresonator. Phys. Rev. A, 2011, 83(2): 021801

[149] A. A. Savchenkov , A. B. Matsko , V. S. Ilchenko , N. Yu , L. Maleki . Whispering-gallery-mode resonators as frequency references (ii): Stabilization. J. Opt. Soc. Am. B, 2007, 24: 2988

[150] J. Lim , W. Liang , A. A. Savchenkov , A. B. Matsko , L. Maleki , C. W. Wong . Probing 10 µk stability and residual drifts in the cross-polarized dual-mode stabilization of single-crystal ultrahigh-Q optical resonators. Light Sci. Appl., 2019, 8(1): 1

[151] Q. Zhao , M. W. Harrington , A. Isichenko , K. Liu , R. O. Behunin , S. B. Papp , P. T. Rakich , C. W. Hoyt , C. Fertig , D. J. Blumenthal . Integrated reference cavity with dual-mode optical thermometry for frequency correction. Optica, 2021, 8(11): 1481

[152] W. Loh , S. Yegnanarayanan , F. O’Donnell , P. W. Juodawlkis . Ultra-narrow linewidth brillouin laser with nanokelvin temperature self-referencing. Optica, 2019, 6(2): 152

[153] X. Sun , R. Luo , X. C. Zhang , Q. Lin . Squeezing the fundamental temperature fluctuations of a high-Q microresonator. Phys. Rev. A, 2017, 95(2): 023822

[154] T. E. Drake , J. R. Stone , T. C. Briles , S. B. Papp . Thermal decoherence and laser cooling of Kerr microresonator solitons. Nat. Photonics, 2020, 14(8): 480

[155] F. Lei , Z. Ye , V. Torres-Company . Thermal noise reduction in soliton microcombs via laser self-cooling. Opt. Lett., 2022, 47(3): 513

[156] V. Ilchenko , M. L. Gorodetskii . Thermal nonlinear effects in optical whispering gallery microresonators. Laser Phys., 1992, 2: 1004

[157] W. Liang , D. Eliyahu , V. S. Ilchenko , A. A. Savchenkov , A. B. Matsko , D. Seidel , L. Maleki . High spectral purity Kerr frequency comb radio frequency photonic oscillator. Nat. Commun., 2015, 6(1): 7957

[158] A. D. Ludlow , X. Huang , M. Notcutt , T. Zanon-Willette , S. M. Foreman , M. M. Boyd , S. Blatt , J. Ye . Compact, thermal-noise-limited optical cavity for diode laser stabilization at 1×10⁻¹⁵. Opt. Lett., 2007, 32(6): 641

[159] Y.ZhaoY.LiQ.WangF.MengY.LinS.Wang, ., 100-Hz linewidth diode laser with external optical feedback, IEEE Photon. Technol. Lett. 24, 1795 (2012)

[160] Y. Zhao , Q. Wang , F. Meng , Y. Lin , S. Wang , Y. Li , B. Lin , S. Cao , J. Cao , Z. Fang , T. Li , E. Zang . High-finesse cavity external optical feedback DFB laser with hertz relative linewidth. Opt. Lett., 2012, 37(22): 4729

[161] Z. Newman , V. Maurice , T. Drake , J. Stone , T. Briles , D. Spencer , C. Fredrick , Q. Li , D. Westly , B. R. Ilic , B. Shen , M. G. Suh , K. Y. Yang , C. Johnson , D. M. S. Johnson , L. Hollberg , K. J. Vahala , K. Srinivasan , S. A. Diddams , J. Kitching , S. B. Papp , M. T. Hummon . Architecture for the photonic integration of an optical atomic clock. Optica, 2019, 6(5): 680

[162] W. Lewoczko-Adamczyk , C. Pyrlik , J. Hager , S. Schwertfeger , A. Wicht , A. Peters , G. Erbert , G. Tränkle . Ultra-narrow linewidth DFB-laser with optical feedback from a monolithic confocal Fabry-Pérot cavity. Opt. Express, 2015, 23(8): 9705

[163] H.ChristopherB.ArarA.BawamiaC.KurbisW.Lewoczko-AdamczykM.Schiemangk, ., Narrow linewidth micro-integrated high power diode laser module for deployment in space, 2017 IEEE International Conference on Space Optical Systems and Applications (ICSOS) (IEEE) (2017), pp 150–153

[164] W.LiangY.Liu, Compact sub-Hz linewidth laser enabled by self injection lock to a sub-mL FP cavity, arXiv: 2212.00426 (2022)

[165] F. Favre , D. Guen . Spectral properties of a semiconductor laser coupled to a single mode fiber resonator. IEEE J. Quantum Electron., 1985, 21(12): 1937

[166] L. Hao , X. Wang , D. Guo , K. Jia , P. Fan , J. Guo , X. Ni , G. Zhao , Z. Xie , S. Zhu . Narrow-linewidth self-injection locked diode laser with a high-Q fiber Fabry–Pérot resonator. Opt. Lett., 2021, 46(6): 1397

[167] K. Jia , X. Wang , D. Kwon , J. Wang , E. Tsao , H. Liu , X. Ni , J. Guo , M. Yang , X. Jiang , J. Kim , S. Zhu , Z. Xie , S. W. Huang . Photonic flywheel in a monolithic fiber resonator. Phys. Rev. Lett., 2020, 125(14): 143902

[168] K.JiaX.YiX.WangY.LiuS.W. HuangX.Jiang, ., Automated turnkey microcomb for low-noise microwave synthesis, arXiv: 2211.10031 (2022)

[169] A. S. Voloshin , N. M. Kondratiev , G. V. Lihachev , J. Liu , V. E. Lobanov , N. Y. Dmitriev , W. Weng , T. J. Kippenberg , I. A. Bilenko . Dynamics of soliton self-injection locking in optical microresonators. Nat. Commun., 2021, 12(1): 235

[170] N. Y. Dmitriev , S. N. Koptyaev , A. S. Voloshin , N. M. Kondratiev , K. N. Min’kov , V. E. Lobanov . . Hybrid integrated dual-microcomb source. Phys. Rev. Appl., 2022, 18: 034068

[171] N.KondratievV.LobanovN.DmitrievS.CordetteI.Bilenko, Detailed analysis of ultimate soliton microcomb generation efficiency, arXiv: 2209.03707 (2022)

[172] G. Lihachev , W. Weng , J. Liu , L. Chang , J. Guo , J. He , R. N. Wang , M. H. Anderson , Y. Liu , J. E. Bowers , T. J. Kippenberg . Platicon microcomb generation using laser self-injection locking. Nat. Commun., 2022, 13(1): 1771

[173] V. Lobanov , G. Lihachev , T. J. Kippenberg , M. Gorodetsky . Frequency combs and platicons in optical microresonators with normal GVD. Opt. Express, 2015, 23(6): 7713

[174] V. E. Lobanov , N. M. Kondratiev , A. E. Shitikov , R. R. Galiev , I. A. Bilenko . Generation and dynamics of solitonic pulses due to pump amplitude modulation at normal group-velocity dispersion. Phys. Rev. A, 2019, 100(1): 013807

[175] X. Xue , Y. Xuan , P. H. Wang , Y. Liu , D. E. Leaird , M. Qi . . Normal-dispersion microcombs enabled by controllable mode interactions. Laser Photon. Rev., 2015, 9: L23

[176] A. E. Fomin , M. L. Gorodetsky , I. S. Grudinin , V. S. Ilchenko . Nonstationary nonlinear effects in optical microspheres. J. Opt. Soc. Am. B, 2005, 22(2): 459

[177] T. Carmon , L. Yang , K. J. Vahala . Dynamical thermal behavior and thermal self-stability of microcavities. Opt. Express, 2004, 12(20): 4742

[178] S. Diallo , G. Lin , Y. K. Chembo . Giant thermo-optical relaxation oscillations in millimeter-size whispering gallery mode disk resonators. Opt. Lett., 2015, 40: 3834

[179] A. Leshem , Z. Qi , T. F. Carruthers , C. R. Menyuk , O. Gat . Thermal instabilities, frequency-comb formation, and temporal oscillations in Kerr microresonators. Phys. Rev. A, 2021, 103(1): 013512

[180] T. Herr , V. Brasch , J. D. Jost , C. Y. Wang , N. M. Kondratiev , M. L. Gorodetsky , T. J. Kippenberg . Temporal solitons in optical microresonators. Nat. Photonics, 2014, 8(2): 145

[181] C. Bao , Y. Xuan , J. A. Jaramillo-Villegas , D. E. Leaird , M. Qi , A. M. Weiner . Direct soliton generation in microresonators. Opt. Lett., 2017, 42(13): 2519

[182] V. E. Lobanov , N. M. Kondratiev , I. A. Bilenko . Thermally induced generation of platicons in optical microresonators. Opt. Lett., 2021, 46(10): 2380

[183] N. M. Kondratiev , V. E. Lobanov . Modulational instability and frequency combs in whispering-gallery-mode microresonators with backscattering. Phys. Rev. A, 2020, 101: 013816

[184] N. M. Kondratiev , S. E. Agafonova , A. S. Gorodnitskiy , A. S. Voloshin , V. E. Lobanov . Modification of the self-injection locking effect due to the microresonator nonlinearity. AIP Conf. Proc., 2020, 2241: 020021

[185] N.M. KondratievR.R. GalievV.E. Lobanov, Thermal influence on laser self-injection locking to nonlinear microresonator, Eds. : M. Bertolotti, A. V. Zayats, and A. M. Zheltikov, Nonlinear Optics and Applications XII, International Society for Optics and Photonics (SPIE) (2021), Vol. 11770, 117700Q

[186] V. E. Lobanov , G. V. Lihachev , N. G. Pavlov , A. V. Cherenkov , T. J. Kippenberg , M. L. Gorodetsky . Harmonization of chaos into a soliton in Kerr frequency combs. Opt. Express, 2016, 24(24): 27382

[187] H. Guo , M. Karpov , E. Lucas , A. Kordts , M. H. P. Pfeiffer , V. Brasch , G. Lihachev , V. E. Lobanov , M. L. Gorodetsky , T. J. Kippenberg . Universal dynamics and deterministic switching of dissipative Kerr solitons in optical microresonators. Nat. Phys., 2017, 13(1): 94

[188] C. Xiang , J. Liu , J. Guo , L. Chang , R. N. Wang , W. Weng , J. Peters , W. Xie , Z. Zhang , J. Riemensberger , J. Selvidge , T. J. Kippenberg , J. E. Bowers . Laser soliton microcombs heterogeneously integrated on silicon. Science, 2021, 373(6550): 99

[189] D. A. Chermoshentsev , A. E. Shitikov , E. A. Lonshakov , G. V. Grechko , E. A. Sazhina , N. M. Kondratiev , A. V. Masalov , I. A. Bilenko , A. I. Lvovsky , A. E. Ulanov . Dual-laser self-injection locking to an integrated microresonator. Opt. Express, 2022, 30(10): 17094

[190] J. Liu , E. Lucas , A. S. Raja , J. He , J. Riemensberger , R. N. Wang , M. Karpov , H. Guo , R. Bouchand , T. J. Kippenberg . Photonic microwave generation in the X- and K-band using integrated soliton microcombs. Nat. Photonics, 2020, 14(8): 486

[191] M. H. Khan , H. Shen , Y. Xuan , L. Zhao , S. Xiao , D. E. Leaird , A. M. Weiner , M. Qi . Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper. Nat. Photonics, 2010, 4(2): 117

[192] X. Hu , W. Wang , L. Wang , W. Zhang , Y. Wang , W. Zhao . Numerical simulation and temporal characterization of dual-pumped microring-resonator-based optical frequency combs. Photon. Res., 2017, 5(3): 207

[193] W. Wang , S. T. Chu , B. E. Little , A. Pasquazi , Y. Wang , L. Wang , W. Zhang , L. Wang , X. Hu , G. Wang , H. Hu , Y. Su , F. Li , Y. Liu , W. Zhao . Dual-pump Kerr micro-cavity optical frequency comb with varying FSR spacing. Sci. Rep., 2016, 6(1): 28501

[194] J. Wen , L. Duan , W. Fan . Influences of pump power and high-order dispersion on dual-pumped silicon-on-insulator micro-ring resonator-based optical frequency combs. Mod. Phys. Lett. B, 2019, 33(10): 1950117

[195] J. Wen , L. Duan , C. Ma , W. Fan . Numerical investigation of dual-pumped optical frequency combs based on silicon-on-insulator microring resonator. Microw. Opt. Technol. Lett., 2019, 61(11): 2640

[196] Y. Okawachi , M. Yu , K. Luke , D. O. Carvalho , S. Ramelow , A. Farsi . . Dual-pumped degenerate Kerr oscillator in a silicon nitride microresonator. Opt. Lett., 2015, 40: 5267

[197] Y. Okawachi , M. Yu , K. Luke , D. O. Carvalho , M. Lipson , A. L. Gaeta . Quantum random number generator using a microresonator-based Kerr oscillator. Opt. Lett., 2016, 41: 4194

[198] V. D. Vaidya , B. Morrison , L. G. Helt , R. Shahrokshahi , D. H. Mahler , M. J. Collins , K. Tan , J. Lavoie , A. Repingon , M. Menotti , N. Quesada , R. C. Pooser , A. E. Lita , T. Gerrits , S. W. Nam , Z. Vernon . Broadband quadrature-squeezed vacuum and nonclassical photon number correlations from a nanophotonic device. Sci. Adv., 2020, 6(39): eaba9186

[199] J. M. Arrazola , V. Bergholm , K. Bradler , T. R. Bromley , M. J. Collins , I. Dhand , A. Fumagalli , T. Gerrits , A. Goussev , L. G. Helt , J. Hundal , T. Isacsson , R. B. Israel , J. Izaac , S. Jahangiri , R. Janik , N. Killoran , S. P. Kumar , J. Lavoie , A. E. Lita , D. H. Mahler , M. Menotti , B. Morrison , S. W. Nam , L. Neuhaus , H. Y. Qi , N. Quesada , A. Repingon , K. K. Sabapathy , M. Schuld , D. Su , J. Swinarton , A. Száva , K. Tan , P. Tan , V. D. Vaidya , Z. Vernon , Z. Zabaneh , Y. Zhang . Quantum circuits with many photons on a programmable nanophotonic chip. Nature, 2021, 591(7848): 54

[200] Y. Zhao , Y. Okawachi , J. K. Jang , X. Ji , M. Lipson , A. L. Gaeta . Near-degenerate quadrature-squeezed vacuum generation on a silicon-nitride chip. Phys. Rev. Lett., 2020, 124(19): 193601

[201] Y. Okawachi , M. Yu , J. K. Jang , X. Ji , Y. Zhao , B. Y. Kim , M. Lipson , A. L. Gaeta . Demonstration of chip-based coupled degenerate optical parametric oscillators for realizing a nanophotonic spin-glass. Nat. Commun., 2020, 11(1): 4119

[202] H. Taheri , A. B. Matsko , L. Maleki , K. Sacha . All-optical dissipative discrete time crystals. Nat. Commun., 2022, 13(1): 848

[203] A. E. Shitikov , V. E. Lobanov , N. M. Kondratiev , A. S. Voloshin , E. A. Lonshakov , I. A. Bilenko . Self-injection locking of a gain-switched laser diode. Phys. Rev. Appl., 2021, 15(6): 064066

[204] S. Shao , J. Li , H Chen , S. Yang , M. Chen . Gain-switched optical frequency comb source using a hybrid integrated self-injection locking DFB laser. IEEE Photon. J., 2022, 14: 1

[205] T. J. Kippenberg , A. L. Gaeta , M. Lipson , M. L. Gorodetsky . Dissipative Kerr solitons in optical microresonators. Science, 2018, 361(6402): eaan8083

[206] Q. Li , M. Davanço , K. Srinivasan . Efficient and low-noise single-photon-level frequency conversion interfaces using silicon nanophotonics. Nat. Photonics, 2016, 10: 406

[207] S. Gundavarapu , G. M. Brodnik , M. Puckett , T. Huffman , D. Bose , R. Behunin , J. Wu , T. Qiu , C. Pinho , N. Chauhan , J. Nohava , P. T. Rakich , K. D. Nelson , M. Salit , D. J. Blumenthal . Sub-Hertz fundamental linewidth photonic integrated Brillouin laser. Nat. Photonics, 2019, 13(1): 60

[208] X. Ji , J. Liu , J. He , R. N. Wang , Z. Qiu , J. Riemensberger , T. J. Kippenberg . Compact, spatial-mode-interaction-free, ultralow-loss, nonlinear photonic integrated circuits. Commun. Phys., 2022, 5(1): 1

[209] Z. Ye , F. Lei , K. Twayana , M. Girardi , P. A. Andrekson , V. Torres-Company . Integrated, ultra-compact high-Q silicon nitride microresonators for low-repetition-rate soliton microcombs. Laser Photon. Rev., 2021, 16(3): 2100147

[210] V.SnigirevA.RiedhauserG.LihachevJ.RiemensbergerR.N. WangC.Moehl, ., Ultrafast tunable lasers using lithium niobate integrated photonics, arXiv: 2112.02036 (2021)

[211] A. Gondarenko , J. S. Levy , M. Lipson . High confinement micron-scale silicon nitride high Q ring resonator. Opt. Express, 2009, 17(14): 11366

[212] J.S. LevyA.GondarenkoM.A. FosterA.C. Turner-FosterA.L. GaetaM.Lipson, CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects, Nat. Photonics 4(1), 37 (2010)

[213] X. Ji , F. A. S. Barbosa , S. P. Roberts , A. Dutt , J. Cardenas , Y. Okawachi , A. Bryant , A. L. Gaeta , M. Lipson . Ultra-low-loss on-chip resonators with sub-milliwatt parametric oscillation threshold. Optica, 2017, 4(6): 619

[214] K. Wu , A. W. Poon . Stress-released si3n4 fabrication process for dispersion-engineered integrated silicon photonics. Opt. Express, 2020, 28(12): 17708

[215] J. Liu , G. Huang , R. N. Wang , J. He , A. S. Raja , T. Liu , N. J. Engelsen , T. J. Kippenberg . High-yield, wafer-scale fabrication of ultralow-loss, dispersion-engineered silicon nitride photonic circuits. Nat. Commun., 2021, 12(1): 2236

[216] D. J. Moss , R. Morandotti , A. L. Gaeta , M. Lipson . New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics. Nat. Photonics, 2013, 7(8): 597

[217] C. Xiang , W. Jin , J. E. Bowers . Silicon nitride passive and active photonic integrated circuits: Trends and prospects. Photon. Res., 2022, 10(6): A82

[218] C. H. Henry , R. F. Kazarinov , H. J. Lee , K. J. Orlowsky , L. E. Katz . Low loss Si₃N₄–SiO₂ optical waveguides on Si. Appl. Opt., 1987, 26(13): 2621

[219] F. Gyger , J. Liu , F. Yang , J. He , A. S. Raja , R. N. Wang , S. A. Bhave , T. J. Kippenberg , L. Thévenaz . Observation of stimulated Brillouin scattering in silicon nitride integrated waveguides. Phys. Rev. Lett., 2020, 124(1): 013902

[220] B. Stern , X. Ji , A. Dutt , M. Lipson . Compact narrow-linewidth integrated laser based on a low-loss silicon nitride ring resonator. Opt. Lett., 2017, 42(21): 4541

[221] Y. Fan , A. van Rees , P. J. M. van der Slot , J. Mak , R. M. Oldenbeuving , M. Hoekman , D. Geskus , C. G. H. Roeloffzen , K. J. Boller . Hybrid integrated InP-Si3N4 diode laser with a 40-Hz intrinsic linewidth. Opt. Express, 2020, 28(15): 21713

[222] J. Liu , A. S. Raja , M. Karpov , B. Ghadiani , M. H. P. Pfeiffer , B. Du , N. J. Engelsen , H. Guo , M. Zervas , T. J. Kippenberg . Ultralow-power chip-based soliton microcombs for photonic integration. Optica, 2018, 5(10): 1347

[223] V. Brasch , M. Geiselmann , M. H. P. Pfeiffer , T. J. Kippenberg . Bringing short-lived dissipative Kerr soliton states in microresonators into a steady state. Opt. Express, 2016, 24: 29312

[224] Q. Li , T. C. Briles , D. A. Westly , T. E. Drake , J. R. Stone , B. R. Ilic , S. A. Diddams , S. B. Papp , K. Srinivasan . Stably accessing octave-spanning microresonator frequency combs in the soliton regime. Optica, 2017, 4(2): 193

[225] J. R. Stone , T. C. Briles , T. E. Drake , D. T. Spencer , D. R. Carlson , S. A. Diddams , S. B. Papp . Thermal and nonlinear dissipative-soliton dynamics in Kerr-microresonator frequency combs. Phys. Rev. Lett., 2018, 121(6): 063902

[226] H. Zhou , Y. Geng , W. Cui , S. W. Huang , Q. Zhou , K. Qiu , C. Wei Wong . Soliton bursts and deterministic dissipative Kerr soliton generation in auxiliary-assisted microcavities. Light Sci. Appl., 2019, 8(1): 50

[227] S.P. YuE.LucasJ.ZangS.B. Papp, A continuum of bright and dark-pulse states in a photonic-crystal resonator, Nat. Commun. 13(1), 3134 (2022)

[228] H. Wang , B. Shen , Y. Yu , Z. Yuan , C. Bao , W. Jin , L. Chang , M. A. Leal , A. Feshali , M. Paniccia , J. E. Bowers , K. Vahala . Self-regulating soliton switching waves in microresonators. Phys. Rev. A, 2022, 106(5): 053508

[229] J. Liu , H. Tian , E. Lucas , A. S. Raja , G. Lihachev , R. N. Wang , J. He , T. Liu , M. H. Anderson , W. Weng , S. A. Bhave , T. J. Kippenberg . Monolithic piezoelectric control of soliton microcombs. Nature, 2020, 583(7816): 385

[230] C. Xiang , J. Guo , W. Jin , L. Wu , J. Peters , W. Xie , L. Chang , B. Shen , H. Wang , Q. F. Yang , D. Kinghorn , M. Paniccia , K. J. Vahala , P. A. Morton , J. E. Bowers . High-performance lasers for fully integrated silicon nitride photonics. Nat. Commun., 2021, 12(1): 6650

[231] T. Komljenovic , M. Davenport , J. Hulme , A. Y. Liu , C. T. Santis , A. Spott , S. Srinivasan , E. J. Stanton , C. Zhang , J. E. Bowers . Heterogeneous silicon photonic integrated circuits. J. Lightwave Technol., 2016, 34(1): 20

[232] H. Park , C. Zhang , M. A. Tran , T. Komljenovic . Heterogeneous silicon nitride photonics. Optica, 2020, 7(4): 336

[233] C. Xiang , W. Jin , J. Guo , J. D. Peters , M. J. Kennedy , J. Selvidge . . Narrow-linewidth III-V/Si/Si₃N₄ laser using multilayer heterogeneous integration. Optica, 2020, 7: 20

[234] C. Joshi , J. K. Jang , K. Luke , X. Ji , S. A. Miller , A. Klenner . . Thermally controlled comb generation and soliton modelocking in microresonators. Opt. Lett., 2016, 41: 2565

[235] X. Xue , Y. Xuan , C. Wang , P. H. Wang , Y. Liu , B. Niu , D. E. Leaird , M. Qi , A. M. Weiner . Thermal tuning of Kerr frequency combs in silicon nitride microring resonators. Opt. Express, 2016, 24(1): 687

[236] G. Liang , H. Huang , A. Mohanty , M. C. Shin , X. Ji , M. J. Carter , S. Shrestha , M. Lipson , N. Yu . Robust, efficient, micrometre-scale phase modulators at visible wavelengths. Nat. Photonics, 2021, 15(12): 908

[237] A. Arbabi , L. L. Goddard . Measurements of the refractive indices and thermo-optic coefficients of Si₃N₄ and SiO_x using microring resonances. Opt. Lett., 2013, 38(19): 3878

[238] J. Komma , C. Schwarz , G. Hofmann , D. Heinert , R. Nawrodt . Thermo-optic coefficient of silicon at 1550 nm and cryogenic temperatures. Appl. Phys. Lett., 2012, 101(4): 041905

[239] H. Tian , J. Liu , B. Dong , J. C. Skehan , M. Zervas , T. J. Kippenberg , S. A. Bhave . Hybrid integrated photonics using bulk acoustic resonators. Nat. Commun., 2020, 11(1): 3073

[240] M. Huang . Stress effects on the performance of optical waveguides. Int. J. Solids Struct., 2003, 40(7): 1615

[241] P. J. M. van der Slot , M. A. G. Porcel , K. J. Boller . Surface acoustic waves for acousto-optic modulation in buried silicon nitride waveguides. Opt. Express, 2019, 27(2): 1433

[242] N. Hosseini , R. Dekker , M. Hoekman , M. Dekkers , J. Bos , A. Leinse , R. Heideman . Stress-optic modulator in TriPlex platform using a piezoelectric lead zirconate titanate (PZT) thin film. Opt. Express, 2015, 23(11): 14018

[243] K. Alexander , J. P. George , J. Verbist , K. Neyts , B. Kuyken , D. Van Thourhout , J. Beeckman . Nanophotonic Pockels modulators on a silicon nitride platform. Nat. Commun., 2018, 9(1): 3444

[244] W. Jin , R. G. Polcawich , P. A. Morton , J. E. Bowers . Piezoelectrically tuned silicon nitride ring resonator. Opt. Express, 2018, 26: 3174

[245] Y.H. LaiA.E. AmiliD.EliyahuR.MossS.GanjiS.Singer, ., Ultra-narrow-linewidth lasers for quantum applications. Conference on Lasers and Electro-Optics (Optica Publishing Group) (2022), STu5O.2

[246] T.WundererA.SiddharthN.M. JohnsonC.L. ChuaM.TeepeZ.Yang, ., Low-noise hybrid photonic integrated violet and blue lasers for quantum applications, 2022 IEEE Research and Applications of Photonics in Defense Conference (RAPID) (2022), pp 1–2

[247] J. Geng , L. Yang , S. Zhao , Y. Zhang . Resonant micro-optical gyro based on self-injection locking. Opt. Express, 2020, 28(22): 32907

[248] J. Geng , L. Yang , J. Liang , S. Liu , Y. Zhang . Stability in self-injection locking of the DFB laser through a fiber optic resonator. Opt. Commun., 2022, 505: 127531

[249] Y. Zhang , J. Geng , L. Li , Y. Wang , L. Yang . Exceptional-point-enhanced Brillouin micro-optical gyroscope based on self-injection locking. Opt. Commun., 2023, 528: 129008

[250] E.DaleW.LiangD.EliyahuA.SavchenkovV.IlchenkoA.B. Matsko, ., Ultra-narrow line tunable semiconductor lasers for coherent lidar applications, Imaging and Applied Optics 2014 (Optical Society of America) (2014), JTu2C.3

[251] C. A. Lopez-Mercado , D. A. Korobko , I. O. Zolotovskii , A. A. Fotiadi . Application of dual-frequency self-injection locked DFB laser for Brillouin optical time domain analysis. Sensors (Basel), 2021, 21(20): 6859

[252] F. Karim , A. F. Mitul , B. Zhou , M. Han . High-sensitivity demodulation of fiber-optic acoustic emission sensor using self-injection locked diode laser. IEEE Photonics J., 2022, 14(4): 1

[253] D.J. Blumenthal, Integrated ultra-narrow linewidth stabilized SBS lasers. Optical Fiber Communication Conference (OFC) 2022 (Optica Publishing Group) (2022), Tu3D. 1

[254] Y.H. LaiS.LoveA.SavchenkovD.EliyahuR.MossL.Maleki, 871 nm ultra-narrow-linewidth laser for Yb⁺ clock, Conference on Lasers and Electro-Optics (Optica Publishing Group) (2021), SF2P. 3

[255] R.AminJ.GreenbergB.HeffernanT.NagatsumaA.Rolland, Exceeding octave tunable terahertz waves with zepto-second level timing noise, arXiv: 2207.07750 (2022)

[256] R.AminJ.GreenbergB.M. HeffernanA.Rolland, 0.5 THz wave based on two wavelength difference beat with self-injected diode lasers, 2022 47th International Conference on Infrared, Millimeter and Terahertz Waves (IRMMW-THz) (2022), pp 1–2

[257] T. J. Kippenberg , R. Holzwarth , S. A. Diddams . Microresonator-based optical frequency combs. Science, 2011, 332(6029): 555

[258] A. Pasquazi , M. Peccianti , L. Razzari , D. J. Moss , S. Coen , M. Erkintalo , Y. K. Chembo , T. Hansson , S. Wabnitz , P. Del’Haye , X. Xue , A. M. Weiner , R. Morandotti . Micro-combs: A novel generation of optical sources. Phys. Rep., 2018, 729: 1

[259] S. Papp , K. Beha , P. Del’Haye , F. Quinlan , H. Lee , K. Vahala , S. A. Diddams . Microresonator frequency comb optical clock. Optica, 2014, 1(1): 10

[260] M. G. Suh , Q. F. Yang , K. Yang , X. Yi , K. Vahala . Microresonator soliton dual-comb spectroscopy. Science, 2016, 354(6312): 600

[261] Q. F. Yang , B. Shen , H. Wang , M. Tran , Z. Zhang , K. Y. Yang , L. Wu , C. Bao , J. Bowers , A. Yariv , K. Vahala . Vernier spectrometer using counterpropagating soliton microcombs. Science, 2019, 363(6430): 965

[262] M. G. Suh , K. J. Vahala . Soliton microcomb range measurement. Science, 2018, 359(6378): 884

[263] P. Trocha , M. Karpov , D. Ganin , M. H. P. Pfeiffer , A. Kordts , S. Wolf , J. Krockenberger , P. Marin-Palomo , C. Weimann , S. Randel , W. Freude , T. J. Kippenberg , C. Koos . Ultrafast optical ranging using microresonator soliton frequency combs. Science, 2018, 359(6378): 887

[264] M. G. Suh , X. Yi , Y. H. Lai , S. Leifer , I. S. Grudinin , G. Vasisht , E. C. Martin , M. P. Fitzgerald , G. Doppmann , J. Wang , D. Mawet , S. B. Papp , S. A. Diddams , C. Beichman , K. Vahala . Searching for exoplanets using a microresonator astrocomb. Nat. Photonics, 2019, 13(1): 25

[265] E.ObrzudM.RainerA.HarutyunyanM.H. AndersonJ.LiuM.GeiselmannB.ChazelasS.KundermannS.LecomteM.CecconiA.GhedinaE.MolinariF.PepeF.WildiF.BouchyT.J. KippenbergT.Herr, A microphotonic astrocomb, Nat. Photonics 13(1), 31 (2019)

[266] P. Marin-Palomo , J. N. Kemal , M. Karpov , A. Kordts , J. Pfeifle , M. H. P. Pfeiffer , P. Trocha , S. Wolf , V. Brasch , M. H. Anderson , R. Rosenberger , K. Vijayan , W. Freude , T. J. Kippenberg , C. Koos . Microresonator-based solitons for massively parallel coherent optical communications. Nature, 2017, 546(7657): 274

[267] A. Fölöp , M. Mazur , A. Lorences-Riesgo , Ó. Helgason , P. H. Wang , Y. Xuan . . High-order coherent communications using mode-locked dark-pulse Kerr combs from microresonators. Nat. Commun., 2018, 9(1): 1598

[268] Ó. B. Helgason , A. Fülöp , J. Schröder , P. A. Andrekson , A. M. Weiner , V. Torres-Company . Superchannel engineering of microcombs for optical communications. J. Opt. Soc. Am. B, 2019, 36(8): 2013

[269] B. Y. Kim , Y. Okawachi , J. K. Jang , M. Yu , X. Ji , Y. Zhao , C. Joshi , M. Lipson , A. L. Gaeta . Turnkey, high-efficiency Kerr comb source. Opt. Lett., 2019, 44(18): 4475

[270] H. Liu , S. W. Huang , W. Wang , J. Yang , M. Yu , D. L. Kwong , P. Colman , C. W. Wong . Stimulated generation of deterministic platicon frequency microcombs. Photon. Res., 2022, 10(8): 1877

[271] J.LingJ.StaffaH.WangB.ShenL.ChangU.A. Javid, ., Self-injection-locked second-harmonic integrated source, arXiv: 2207.03071 (2022)

[272] A. W. Bruch , X. Liu , Z. Gong , J. B. Surya , M. Li , C. L. Zou , H. X. Tang . Pockels soliton microcomb. Nat. Photonics, 2021, 15(1): 21

[273] X. Liu , Z. Gong , A. W. Bruch , J. B. Surya , J. Lu , H. X. Tang . Aluminum nitride nanophotonics for beyond-octave soliton microcomb generation and self-referencing. Nat. Commun., 2021, 12(1): 5428

[274] H. Jung , S. P. Yu , D. R. Carlson , T. E. Drake , T. C. Briles , S. B. Papp . Tantala Kerr nonlinear integrated photonics. Optica, 2021, 8(6): 811

[275] D. J. Wilson , K. Schneider , S. Honl , M. Anderson , Y. Baumgartner , L. Czornomaz , T. J. Kippenberg , P. Seidler . Integrated gallium phosphide nonlinear photonics. Nat. Photonics, 2020, 14(1): 57

[276] M. Pu , L. Ottaviano , E. Semenova , K. Yvind . Efficient frequency comb generation in AlGaAs-on-insulator. Optica, 2016, 3(8): 823

[277] L. Chang , W. Xie , H. Shu , Q. F. Yang , B. Shen , A. Boes , J. D. Peters , W. Jin , C. Xiang , S. Liu , G. Moille , S. P. Yu , X. Wang , K. Srinivasan , S. B. Papp , K. Vahala , J. E. Bowers . Ultra-efficient frequency comb generation in AlGaAs-on-insulator microresonators. Nat. Commun., 2020, 11(1): 1331

[278] M. A. Guidry , D. M. Lukin , K. Y. Yang , R. Trivedi , J. Vučković . Quantum optics of soliton microcombs. Nat. Photonics, 2022, 16(1): 52

[279] C. Wang , J. Li , A. Yi , Z. Fang , L. Zhou , Z. Wang , R. Niu , Y. Chen , J. Zhang , Y. Cheng , J. Liu , C. H. Dong , X. Ou . Soliton formation and spectral translation into visible on CMOS-compatible 4H-silicon-carbide-on-insulator platform. Light Sci. Appl., 2022, 11(1): 341

[280] D. Xia , Z. Yang , P. Zeng , B. Zhang , J. Wu , Z. Wang , J. Zhao , J. Huang , L. Luo , D. Liu , S. Yang , H. Guo , Z. Li . Integrated chalcogenide photonics for microresonator soliton combs. Laser Photon. Rev., 2022, 2200219

[281] X. Xue , X. Zheng , B. Zhou . Super-efficient temporal solitons in mutually coupled optical cavities. Nat. Photonics, 2019, 13(9): 616

[282] J. M. C. Boggio , D. Bodenmuller , S. Ahmed , S. Wabnitz , D. Modotto , T. Hansson . Efficient Kerr soliton comb generation in micro-resonator with interferometric back-coupling. Nat. Commun., 2022, 13(1): 1292

[283] O.B. HelgasonM.GirardiZ.YeF.LeiJ.SchröderV.T. Company, Power-efficient soliton microcombs, arXiv: 2202.09410 (2022)

Conflict of interest statement

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Author contributions

N.M.K., V.E.L., I.A.B., and J.L. contributed to conception and organization of the manuscript. N.M.K., V.E.L., W.L., J.L. and I.A.B. wrote the introduction. N.M.K., R.R.G., V.E.L., and D.A.C. organized and wrote the theoretical review part. A.E.S., D.A.C., N.Y.D., A.N.D., E.A.L., Y.-H.L., W.L., and J.L. organized and wrote the experimental review part. All authors contributed to manuscript revision, read, and approved the submitted version.

Funding information

The results presented in Sections 2.5 and 3.2 were obtained with the support of the Russian Science Foundation (project 22-22-00872). The results presented in Sections 2.3, 3.4 and 4 were obtained with the support of the Russian Science Foundation (Project 20-12-00344). Y.-H. L. acknowledges support from the China Postdoctoral Science Foundation (Grant No. 2022M721482). W. L. acknowledges support from the National Natural Science Foundation of China (Grant No. 62075233) and the CAS Project for Young Scientists in Basic Research (Grant No. YSBR-69). J. L. acknowledges support from the National Natural Science Foundation of China (Grant No.12261131503), Shenzhen−Hong Kong Cooperation Zone for Technology and Innovation (HZQB-KCZYB2020050), and from the Guangdong Provincial Key Laboratory (2019B121203002).

Data availability statement

All original data used in this review are available from the corresponding authors upon reasonable request.

Acknowledgements

The authors are grateful for the fruitful discussion and collaboration with colleagues at EPFL, UCSB, Caltech, Purdue, and OEWaves, during and especially prior to the preparation of this review.

RIGHTS & PERMISSIONS

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