Abstract

Dissipative Kerr solitons offer broadband coherent and low-noise frequency combs and stable temporal pulse trains, having shown great potential applications in spectroscopy, communications, and metrology. Breathing solitons are a particular kind of dissipative Kerr soliton in which the pulse duration and peak intensity show periodic oscillation. Here we have investigated the breathing dissipative Kerr solitons in silicon nitride (Si3N4) microrings, while the breathing period shows uncertainties of around megahertz (MHz) order in both simulation and experiments. This instability is the main obstacle for future applications. By applying a modulated signal to the pump laser, the breathing frequency can be injection locked to the modulation frequency and tuned over tens of MHz with frequency noise significantly suppressed. Our demonstration offers an alternative knob for the control of soliton dynamics in microresonators and paves a new avenue towards practical applications of breathing solitons.

© 2020 Chinese Laser Press

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  43. K. Luke, Y. Okawachi, M. R. Lamont, A. L. Gaeta, and M. Lipson, “Broadband mid-infrared frequency comb generation in a Si3N4 microresonator,” Opt. Lett. 40, 4823–4826 (2015).
    [Crossref]
  44. M. H. Pfeiffer, C. Herkommer, L. Jumqiu, T. Morais, M. Zervas, M. Geiselmann, and T. Kippenberg, “Photonic damascene process for low-loss, high-confinement silicon nitride waveguides,” IEEE J. Sel. Top. Quantum Electron. 24, 6101411 (2018).
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    [Crossref]

2020 (2)

H.-J. Chen, Q.-X. Ji, H. Wang, Q.-F. Yang, Q.-T. Cao, Q. Gong, X. Yi, and Y.-F. Xiao, “Chaos-assisted two-octave-spanning microcombs,” Nat. Commun. 11, 2336 (2020).
[Crossref]

F.-X. Wang, W. Wang, R. Niu, X. Wang, C.-L. Zou, C.-H. Dong, B. E. Little, S. T. Chu, H. Liu, P. Hao, S. Liu, S. Wang, Z.-Q. Yin, D.-Y. He, W. Zhang, W. Zhao, Z.-F. Han, G.-C. Guo, and W. Chen, “Quantum key distribution with on-chip dissipative Kerr soliton,” Laser Photon. Rev. 14, 1900190 (2020).
[Crossref]

2019 (9)

J. Ma, L. Xiao, J. Gu, H. Li, X. Cheng, G. He, X. Jiang, and M. Xiao, “Visible Kerr comb generation in a high-Q silica microdisk resonator with a large wedge angle,” Photon. Res. 7, 573–578 (2019).
[Crossref]

X. Xue, X. Zheng, and B. Zhou, “Super-efficient temporal solitons in mutually coupled optical cavities,” Nat. Photonics 13, 616–622 (2019).
[Crossref]

J. Peng, S. Boscolo, Z. Zhao, and H. Zeng, “Breathing dissipative solitons in mode-locked fiber lasers,” Sci. Adv. 5, eaax1110 (2019).
[Crossref]

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

W. Weng, E. Lucas, G. Lihachev, V. E. Lobanov, H. Guo, M. L. Gorodetsky, and T. J. Kippenberg, “Spectral purification of microwave signals with disciplined dissipative Kerr solitons,” Phys. Rev. Lett. 122, 013902 (2019).
[Crossref]

Z. L. Newman, V. Maurice, T. Drake, J. R. Stone, T. C. Briles, D. T. 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, and M. T. Hummon, “Architecture for the photonic integration of an optical atomic clock,” Optica 6, 680–685 (2019).
[Crossref]

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, and K. Vahala, “Searching for exoplanets using a microresonator astrocomb,” Nat. Photonics 13, 25–30 (2019).
[Crossref]

E. Obrzud, M. Rainer, A. Harutyunyan, M. H. Anderson, J. Liu, M. Geiselmann, B. Chazelas, S. Kundermann, S. Lecomte, M. Cecconi, A. Ghedina, E. Molinari, F. Pepe, F. Wildi, F. Bouchy, T. J. Kippenberg, and T. Herr, “A microphotonic astrocomb,” Nat. Photonics 13, 31–35 (2019).
[Crossref]

D. C. Cole and S. B. Papp, “Subharmonic entrainment of Kerr breather solitons,” Phys. Rev. Lett. 123, 173904 (2019).
[Crossref]

2018 (11)

M. H. Pfeiffer, C. Herkommer, L. Jumqiu, T. Morais, M. Zervas, M. Geiselmann, and T. Kippenberg, “Photonic damascene process for low-loss, high-confinement silicon nitride waveguides,” IEEE J. Sel. Top. Quantum Electron. 24, 6101411 (2018).
[Crossref]

X. Guo, C.-L. Zou, H. Jung, Z. Gong, A. Bruch, L. Jiang, and H. X. Tang, “Efficient generation of a near-visible frequency comb via Cherenkov-like radiation from a Kerr microcomb,” Phys. Rev. Appl. 10, 014012 (2018).
[Crossref]

A. Dutt, C. Joshi, X. Ji, J. Cardenas, Y. Okawachi, K. Luke, A. L. Gaeta, and M. Lipson, “On-chip dual-comb source for spectroscopy,” Sci. Adv. 4, e1701858 (2018).
[Crossref]

X. Yi, Q.-F. Yang, K. Y. Yang, and K. Vahala, “Imaging soliton dynamics in optical microcavities,” Nat. Commun. 9, 3565 (2018).
[Crossref]

E. Lucas, G. Lihachev, R. Bouchand, N. G. Pavlov, A. S. Raja, M. Karpov, M. L. Gorodetsky, and T. J. Kippenberg, “Spatial multiplexing of soliton microcombs,” Nat. Photonics 12, 699–705 (2018).
[Crossref]

C. Bao, Y. Xuan, C. Wang, A. Fülöp, D. E. Leaird, M. Qi, and A. M. Weiner, “Observation of breathing dark pulses in normal dispersion optical microresonators,” Phys. Rev. Lett. 121, 257401 (2018).
[Crossref]

T. J. Kippenberg, A. L. Gaeta, M. Lipson, and M. L. Gorodetsky, “Dissipative Kerr solitons in optical microresonators,” Science 361, eaan8083 (2018).
[Crossref]

W. Wang, W. Zhang, Z. Lu, S. T. Chu, B. E. Little, Q. Yang, L. Wang, and W. Zhao, “Self-locked orthogonal polarized dual comb in a microresonator,” Photon. Res. 6, 363–367 (2018).
[Crossref]

X. Xu, J. Wu, T. G. Nguyen, T. Moein, S. T. Chu, B. E. Little, R. Morandotti, A. Mitchell, and D. J. Moss, “Photonic microwave true time delays for phased array antennas using a 49 GHz FSR integrated optical micro-comb source invited,” Photon. Res. 6, B30–B36 (2018).
[Crossref]

M.-G. Suh and K. J. Vahala, “Soliton microcomb range measurement,” Science 359, 884–887 (2018).
[Crossref]

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, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359, 887–891 (2018).
[Crossref]

2017 (4)

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017).
[Crossref]

H. Guo, E. Lucas, M. H. Pfeiffer, M. Karpov, M. Anderson, J. Liu, M. Geiselmann, J. D. Jost, and T. J. Kippenberg, “Intermode breather solitons in optical microresonators,” Phys. Rev. X 7, 041055 (2017).
[Crossref]

M. Yu, J. K. Jang, Y. Okawachi, A. G. Griffith, K. Luke, S. A. Miller, X. Ji, M. Lipson, and A. L. Gaeta, “Breather soliton dynamics in microresonators,” Nat. Commun. 8, 145969 (2017).
[Crossref]

E. Lucas, M. Karpov, H. Guo, M. Gorodetsky, and T. J. Kippenberg, “Breathing dissipative solitons in optical microresonators,” Nat. Commun. 8, 736 (2017).
[Crossref]

2016 (6)

M. Karpov, H. Guo, A. Kordts, V. Brasch, M. H. P. Pfeiffer, M. Zervas, M. Geiselmann, and T. J. Kippenberg, “Raman self-frequency shift of dissipative Kerr solitons in an optical microresonator,” Phys. Rev. Lett. 116, 103902 (2016).
[Crossref]

C. Bao, J. A. Jaramillo-Villegas, Y. Xuan, D. E. Leaird, M. Qi, and A. M. Weiner, “Observation of Fermi-Pasta-Ulam recurrence induced by breather solitons in an optical microresonator,” Phys. Rev. Lett. 117, 163901 (2016).
[Crossref]

M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354, 600–603 (2016).
[Crossref]

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip-based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).
[Crossref]

M. H. Pfeiffer, A. Kordts, V. Brasch, M. Zervas, M. Geiselmann, J. D. Jost, and T. J. Kippenberg, “Photonic damascene process for integrated high-Q microresonator based nonlinear photonics,” Optica 3, 20–25 (2016).
[Crossref]

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, and M. Qi, “High-Q silicon nitride microresonators exhibiting low-power frequency comb initiation,” Optica 3, 1171–1180 (2016).
[Crossref]

2015 (4)

K. Luke, Y. Okawachi, M. R. Lamont, A. L. Gaeta, and M. Lipson, “Broadband mid-infrared frequency comb generation in a Si3N4 microresonator,” Opt. Lett. 40, 4823–4826 (2015).
[Crossref]

X. Yi, Q.-F. Yang, K. Y. Yang, M.-G. Suh, and K. Vahala, “Soliton frequency comb at microwave rates in a high-Q silica microresonator,” Optica 2, 1078–1085 (2015).
[Crossref]

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

X. Xue, Y. Xuan, Y. Liu, P. H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photonics 9, 594–600 (2015).
[Crossref]

2014 (2)

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014).
[Crossref]

T. Hansson, D. Modotto, and S. Wabnitz, “On the numerical simulation of Kerr frequency combs using coupled mode equations,” Opt. Commun. 312, 134–136 (2014).
[Crossref]

2013 (1)

2012 (1)

P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6, 84–92 (2012).
[Crossref]

2010 (2)

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, P. Emplit, and M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4, 471–476 (2010).
[Crossref]

Y. K. Chembo and N. Yu, “Modal expansion approach to optical-frequency-comb generation with monolithic whispering-gallery-mode resonators,” Phys. Rev. A 82, 033801 (2010).
[Crossref]

2007 (1)

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

2003 (1)

K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
[Crossref]

1993 (1)

Akhmediev, N.

P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6, 84–92 (2012).
[Crossref]

N. Akhmediev and A. Ankiewicz, Dissipative Solitons: From Optics to Biology and Medicine (Springer, 2008).

Al Noman, A.

Alishashi, F.

P. Liao, K. Zou, C. Bao, A. Kordts, M. Karpov, M. H. P. Pfeiffer, L. Zhang, Y. Cao, A. Almaiman, F. Alishashi, A. Mohajerin-Ariaei, A. Fallahpour, M. Tur, T. J. Kippenberg, and A. E. Willner, “Chip-scale dual-comb source using a breathing soliton with an increased resolution,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2018), paper JTh5A.4.

Almaiman, A.

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M. Karpov, H. Guo, A. Kordts, V. Brasch, M. H. P. Pfeiffer, M. Zervas, M. Geiselmann, and T. J. Kippenberg, “Raman self-frequency shift of dissipative Kerr solitons in an optical microresonator,” Phys. Rev. Lett. 116, 103902 (2016).
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F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, P. Emplit, and M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4, 471–476 (2010).
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W. Weng, E. Lucas, G. Lihachev, V. E. Lobanov, H. Guo, M. L. Gorodetsky, and T. J. Kippenberg, “Spectral purification of microwave signals with disciplined dissipative Kerr solitons,” Phys. Rev. Lett. 122, 013902 (2019).
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P. Liao, K. Zou, C. Bao, A. Kordts, M. Karpov, M. H. P. Pfeiffer, L. Zhang, Y. Cao, A. Almaiman, F. Alishashi, A. Mohajerin-Ariaei, A. Fallahpour, M. Tur, T. J. Kippenberg, and A. E. Willner, “Chip-scale dual-comb source using a breathing soliton with an increased resolution,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2018), paper JTh5A.4.

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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, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359, 887–891 (2018).
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P. Liao, K. Zou, C. Bao, A. Kordts, M. Karpov, M. H. P. Pfeiffer, L. Zhang, Y. Cao, A. Almaiman, F. Alishashi, A. Mohajerin-Ariaei, A. Fallahpour, M. Tur, T. J. Kippenberg, and A. E. Willner, “Chip-scale dual-comb source using a breathing soliton with an increased resolution,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2018), paper JTh5A.4.

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M. H. Pfeiffer, C. Herkommer, L. Jumqiu, T. Morais, M. Zervas, M. Geiselmann, and T. Kippenberg, “Photonic damascene process for low-loss, high-confinement silicon nitride waveguides,” IEEE J. Sel. Top. Quantum Electron. 24, 6101411 (2018).
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M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354, 600–603 (2016).
[Crossref]

Other (2)

N. Akhmediev and A. Ankiewicz, Dissipative Solitons: From Optics to Biology and Medicine (Springer, 2008).

P. Liao, K. Zou, C. Bao, A. Kordts, M. Karpov, M. H. P. Pfeiffer, L. Zhang, Y. Cao, A. Almaiman, F. Alishashi, A. Mohajerin-Ariaei, A. Fallahpour, M. Tur, T. J. Kippenberg, and A. E. Willner, “Chip-scale dual-comb source using a breathing soliton with an increased resolution,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2018), paper JTh5A.4.

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Figures (6)

Fig. 1.
Fig. 1. (a) Scanning electron micrographs of a Si3N4 microring with diameter of 200 μm. Insets show the microring cross section of 1.8  μm×0.8  μm and the corresponding fundamental transverse-magnetic mode profile. (b) Experimental setup for Kerr frequency comb generation. EDFA, FPC, EOM, WDM, DWDM, FP, OSC, and ESA are erbium-doped fiber amplifier, fiber polarization controller, electro-optical modulator, wavelength-division multiplexer, dense wavelength-division multiplexer, Fabry–Perot cavity, oscilloscope, and electronic spectrum analyzer, respectively. (c) Detailed comb line spectrum of a breathing soliton measured by the FP spectrum analyzer, with two sidebands indicating the breathing frequency around 0.4 GHz. The inset shows a typical resonance of the microring, with a loaded Q of 1.5×106 according to the Lorentzian fitting (red line).
Fig. 2.
Fig. 2. Evolution of the soliton generation processes during the scanning of the pump laser detuning. (a)–(d) Typical optical spectra. Four evolution stages are (a) primary comb, (b) modulation instability comb, (c) breathing soliton, and (d) stable soliton, respectively. (e)–(h) The corresponding evolution of RF spectra. Inset: the transmission spectrum of the microring when the laser frequency is scanned across the resonance mode.
Fig. 3.
Fig. 3. Features of a breathing soliton. (a) The detailed RF spectrum of a breathing soliton state. Inset: the corresponding optical spectrum. (b) The recorded fast power evolution of a single comb line around the center (1562 nm, blue curve) and in the wings (1531 nm, green curve) of the optical spectrum of a breathing soliton. Inset: the corresponding Fourier transform spectrum.
Fig. 4.
Fig. 4. (a) Simulated evolution of the intracavity power when the laser frequency is scanned across the resonance mode. The inset shows the oscillations of the power for a fixed laser frequency in the breathing soliton state. (b) Periodic spectrum evolution of a breathing soliton state. (c) RF spectra of the initial breathing soliton state (blue line) and modulated breathing soliton state (red line). The initial breathing frequency fbr is 287 MHz, and the modulated frequency fmod is 270 MHz. The inset shows the concept of injection locking of a breathing soliton. A modulation signal with fmod is applied to the pump laser after the appearance of breathing soliton, and fbr is injection locked if fmod is within the locking range.
Fig. 5.
Fig. 5. (a) Evolution of the RF spectrum when gradually increasing the modulation power from 50 to 5  dBm. The initial breathing frequency fbr is 276 MHz (I) and the modulation frequency fmod is 281 MHz. With the increase of the modulation power, there is a competition between fbr and fmod, and other harmonics components appear (II and III). Eventually, fbr is synchronized to fmod as the modulation power is strong enough (IV). fbr returns back to the initial frequency after turning off the modulation signal (V). (b) Snapshots with different evolution stages in (a).
Fig. 6.
Fig. 6. (a) Evolution of the RF spectrum centered at 262 MHz with varied fmod. The modulation power is 0.1 mW, and fbr is synchronized to fmod when the frequency difference Δf is less than 15  MHz. (b) Locking ranges with varied modulation power.

Equations (12)

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Aμt=κ2Aμ+igk,l,nAkAl*Anei(ωkωl+ωnωμ)t+δμ0ηκsinei(ωpω0)t.
aμτ=(1+iΩμ)aμ+ik,l,nδμ+lknakal*an+δμ0f.
xν=F[aμ]=1Nμaμei2πμν/N,
aμ=F1[xν]=1Nνxνei2πμν/N,
aμτ=(1+iΩμ)aμ+iF1[|F[a]|2F[a]]μ+δμ0f.
f=fi1{ei[π2+πϵsin(2πνt)]1},
=fi1[ieiπϵsin(2πνt)i+i1],
=f+ifi1[eiπϵsin(2πνt)1].
|f|2=|f|2|1i12[eiπϵsin(2πνt)1]|2,
=|f|2{sin[πϵsin(2πνt)]+cos[πϵsin(2πνt)]},
=|f|22cos[πϵsin(2πνt)π4].
f=Ein×[1+noise(t)].